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DOI: 10.1002/lpor.202200544 (2022). + + + +Ultra-Low-Loss Silicon Nitride Photonics Based on +Deposited Films Compatible with Foundries + +Xingchen Ji,1,3,* Yoshitomo Okawachi,2 Andres Gil-Molina,1 Mateus Corato-Zanarella,1 +Samantha Roberts,1 Alexander L. Gaeta,2 and Michal Lipson1,* + +1Department of Electrical Engineering, Columbia University, New York, NY, 10027, USA +2Department of Applied Physics and Applied Mathematics, Columbia University, New York, +NY, 10027, USA +3Currently at John Hopcroft Center for Computer Science, School of Electronic Information and +Electrical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China +*Corresponding Author: E-mail: xingchenji@sjtu.edu.cn and ml3745@columbia.edu + +Abstract: + +The fabrication processes of silicon nitride (Si3N4) photonic devices used in foundries require low +temperature deposition, which typically leads to high propagation losses. Here, we show that +propagation loss as low as 0.42 dB/cm can be achieved using foundry compatible processes by +solely reducing waveguide surface roughness. By post-processing the fabricated devices using +rapid thermal anneal (RTA) and furnace anneal, we achieve propagation losses down to 0.28 +dB/cm and 0.06 dB/cm, respectively. These low losses are comparable to the conventional devices +using high temperature, high-stress LPCVD films. We also tune the dispersion of the devices, and +proved that these devices can be used for linear and nonlinear applications. Low threshold +parametric oscillation, broadband frequency combs and narrow-linewidth laser are demonstrated. +Our work demonstrates the feasibility of scalable photonic systems based on foundries. + + +Published in Laser & Photonics Reviews. DOI: 10.1002/lpor.202200544 (2022). + + + +1. Introduction +To date, ultra-low-loss silicon nitride (Si3N4) waveguides and resonators have been demonstrated +almost exclusively using films deposited at high temperature, while foundries mostly rely on Si3N4 +films deposited at low temperature. The high temperature deposition uses low-pressure chemical +vapor deposition (LPCVD), while low temperature deposition uses plasma-enhanced chemical +vapor deposition (PECVD). PECVD Si3N4 is the most commonly used thin film in foundries as an +insulator or a chemical barrier layer, however, the high propagation losses in these films limit their +applications in photonics. LPCVD Si3N4 is not used in foundries due to the high temperature +required and high film stress. Therefore, reducing losses in PECVD Si3N4 photonic devices is +critical for integrating photonics devices with electronics, which could be used to realize high +performance, scalable systems and realize system-level innovation[1]. +Previously, there have been efforts to reduce losses in PECVD Si3N4 films by chemically +changing the film composition[2–5]. By lowering the ammonium concentration during the +deposition, losses down to 1.5 dB/cm have been shown[2]. However, these losses remain too high +for most photonic applications. Researchers have also substituted conventional precursors with +deuterated ones to reduce the losses of the film, losses down to 0.3 dB/cm have been shown[6]. +However, these methods require special precursors and deposition tools, which are not commonly +available in foundries. + +2. Film deposition and waveguide fabrication +Here we show that low-loss can be achieved in a standard PECVD process by physically reducing +waveguide surface roughness. The fabrication process is schematically shown in Figure 1. We +deposit Si3N4 using PECVD at 350 °C in a single step onto a thermally oxidized 4-inch silicon + +Published in Laser & Photonics Reviews. DOI: 10.1002/lpor.202200544 (2022). + + + +wafer. The gases used for deposition are a mixture of silane (SiH4: 20 sccm) diluted by nitrogen +(N2: 1425 sccm) and pure ammonia (NH3: 30 sccm), with a process pressure of 1900 mTorr. The +plasma frequencies alternate between a high frequency (13.56 MHz) with a power of 200 W and +a low frequency (100 kHz) with a power of 160 W. The time duration for the two frequencies is 8 +seconds and 12 seconds, respectively. The above parameters ensure that the deposition of Si3N4 +film has very low film stress and high uniformity. The measured stress for the Si3N4 film on a test +wafer is 93.4 MPa and tensile, which is more than an order of magnitude lower than LPCVD Si3N4 +films deposited at high temperature. The low stress allows us to deposit thicker films without any +cracking. + +Figure 1. Schematic of our low-temperature PECVD Si3N4 fabrication processes. +The process steps here are fully compatible with CMOS electronics. + +We design high confinement waveguides based on the deposited PECVD films allows for +strong dispersion engineering. One can see in Figure 2, the strong mode overlaps with the top +surface that can exhibit a roughness of several nanometers for PECVD films[7,8]. + +Si,N4 +SiO2 +Si,N4 +SiO2 +SisN4 +SiO2 +SiO2 +SiO2 +Resist +Resist +SiO2 +SiO, +Sio, +SigN4 +SisN4 +SisN4 + SiO2 +SiO2 +SiO2 +SiO2 +SisN4 +SiO2Published in Laser & Photonics Reviews. DOI: 10.1002/lpor.202200544 (2022). + + + + +Figure 2. Mode simulation and microscope images of fabricated devices. (a) Mode +simulation of 730 nm tall and 1500 nm wide waveguide showing that the mode is +highly confined in the geometry we have chosen. (b) Top view optical microscope +image of a 115 µm radius ring resonator. +To reduce scattering from the top surface of PECVD Si3N4, we use chemical mechanical +planarization (CMP) to smooth the surface, as roughness traditionally leads to a high loss. We +show the atomic-force microscopy (AFM) scans before and after the polishing step in Figure 3. +The root-mean-squared (RMS) roughness is decreased from 1.36 nm before polishing to 0.20 nm +after polishing. In order to reduce the roughness from the sidewalls and protect the polished top +surface, we use a SiO2 hard mask deposited using PECVD after CMP and use a dry etching process +with a much higher oxygen flow. This etching process has been proved to substantially reduce the +polymerization process during etching and decreases the roughness[9]. We pattern our devices with +electron beam lithography using ma-N 2403 resist and use multipass writing algorithms to further +reduce sidewall roughness caused by the lithography itself[9,10]. Finally, we clad the devices with +2 μm of SiO2 deposited using PECVD for waveguide protection. The fabricated devices consist of +resonators with a radius of 115 μm, a height of 730 nm and a width of 1500 nm, which are coupled +to a waveguide of the same width and height. These dimensions ensure high confinement. + +730nm +1500 nm +100μmPublished in Laser & Photonics Reviews. DOI: 10.1002/lpor.202200544 (2022). + + + + + +Figure 3. AFM measurement of the top surface of PECVD Si3N4. (a) 3D AFM scan +of the top surface before CMP with RMS roughness of 1.36 nm and a correlation +length of 27.6 nm. (b) 2D image of Si3N4 top surface before CMP and scaled to - +5.0 – 5.0 nm with RMS roughness of 1.36 nm. (c) 3D image of Si3N4 top surface +after CMP with RMS roughness of 0.20 nm and a correlation length of 2.96 nm. (d) +2D image of Si3N4 top surface after CMP and scaled to -1.0 – 1.0 nm with RMS +roughness of 0.20 nm. Note the different scale bars on (a) and (c). + +3. Fundamental loss extraction and discussion +The quality factor is a measure of the sharpness of the resonance relative to its central frequency. +It represents how well the resonator can store energy and can be written as[11,12]: + + (1) +The quality factor defined in Equation 1 is the loaded quality factor. The intrinsic quality factor +of the cavity which is directly related to the propagation losses can be written as[13,14]: + + (2) +0 +L +Q +w +w += D +min +2 +1 +L +i +Q +Q +T += +± + +5.0 +5.0 nm +300 nm +300 nm +100 nm +100 nm +100 nm +-5.0 +5 +.0 nm +300 nm +300 nm +100 nm +100 nm +-1.0 +100 nmPublished in Laser & Photonics Reviews. DOI: 10.1002/lpor.202200544 (2022). + + + +Tmin is the on-resonance normalized transmission minimum, +sign is corresponding to +undercoupled and overcoupled condition. The schematic of the experimental setup for quality +factor measurement and frequency comb generation is shown in Figure 4. The resonators we +fabricated and measured here have a height of 730 nm, a width of 1500 nm and a bending radius +of 115 µm. We measure an intrinsic quality factor of 724,000, corresponding to a propagation loss +of 0.42 dB/cm. In Figure 5(a), we show the measured resonance and normalized transmission +spectrum over a broad wavelength range. To the best of our knowledge, this is the lowest +propagation loss reported to date in a standard PECVD film compatible with foundries. + +Figure 4. Schematic of the experimental setup for measuring transmission spectra +and resonator linewidth to characterize the quality factor and generate frequency +combs. FPC: fiber polarization controller; PD: photodetector; and OSA: optical +spectrum analyzer. Note that amplifier is not needed for transmission measurement. + +To minimize both surface scattering losses, as well as bulk loss, we post-process the films with +a rapid thermal anneal (RTA). With RTA, we achieve an even higher intrinsic quality factor of +more than 1 million, corresponding to a propagation loss of 0.28 dB/cm. RTA has been +successfully applied in the microelectronics industry and it has particular relevance for CMOS +technology, specifically in steps such as implant annealing, oxidation, and source and drain contact +junctions[15,16]. The process reduces loss by driving out the non-bonded atomic and molecular +hydrogen trapped in microvoids of the structure and further densifies the films[17,18]. We apply +RTA at 800 °C for 5 mins to the cladded devices. In Figure 5(b), we show the measured resonance +± + +000 +Laser +Amplifier +ChipPublished in Laser & Photonics Reviews. DOI: 10.1002/lpor.202200544 (2022). + + + +and normalized transmission spectrum over a broad wavelength range. The thermal budget is +below the tolerance of most CMOS electronics and can be used to further reduce losses for devices +with microheaters or dopants. +We show that by post-processing foundry-compatible devices with furnace anneal (appropriate +for devices with high thermal budget), the propagation loss can be comparable to those fabricated +using high temperature, high-stress LPCVD films. Furnace anneal differs from RTA, with higher +temperatures (above 1000 °C [19–24]) and longer anneal times (several hours). We anneal cladded +devices at 1150 °C in a nitrogen atmosphere for 3 hours and no defects or cracks were observed. +We achieve a quality factor of 4.7 million, which corresponds to a propagation loss of 0.06 dB/cm. +In Figure 5(c), we show the measured resonance and normalized transmission spectrum over a +broad wavelength range. + +Published in Laser & Photonics Reviews. DOI: 10.1002/lpor.202200544 (2022). + + + + +Figure 5. (a) Device without annealing shows a measured full width half maximum +(FWHM) of 595 MHz around 1600 nm and measured normalized transmission +spectrum over a broad wavelength range. (b) Device after rapid thermal anneal +shows a measured full width half maximum (FWHM) of 423 MHz around 1600 nm +and measured normalized transmission spectrum over a broad wavelength range. +(c) Device after furnace anneal shows a measured full width half maximum +(FWHM) of 52 MHz around 1600 nm and measured normalized transmission +spectrum over a broad wavelength range. + +We show that for as-fabricated devices, the bulk losses dominate over the surface scattering +loss, and can be as low as 0.33 dB/cm, while for post-fabrication annealed devices, the bulk losses + +No anneal +(a) +1.0 +0.8 +0.8 +0.6 +ed +Normalized +0.4 +595 MHz +0.2 +Qi = 0.72 million +0.2 +ION +0.0 +1320 1530 1540 1550 1560 1570 1580 1590 1600 1610 1620 +-2000 +-1000 +0 +1000 +2000 +Wavelength (nm) + Frequency (MHz) +(b) +Rapidthermalanneal +1.0 +0.8 +0.6 +Normalized +0.4 +423 MHz +0.2 +Qi = 1.1 million +0.2 +0.0 +-2000 +-1000 +0 +1000 +2000 +Wavelength (nm) +△Frequency (MHz) +(c) +Furnace anneal +1.0 +0.8 +0.8 +0.6 +52 MHz +ed +0.4 +Qi= 4.7million +0.2 +Nor +0.0 +1320 1530 1540 1550 1560 1570 1580 1590 1600 1610 1620 +-400 +-200 +0 +200 +400 +Wavelength (nm) +△Frequency(MHz)Published in Laser & Photonics Reviews. DOI: 10.1002/lpor.202200544 (2022). + + + +are comparable to the surface scattering loss, and can be as low as 0.04 dB/cm. We extract the loss +contributions by comparing the losses between two different structures with different mode +overlap with the interfaces. +, +, + are the overlap of the optical field with the waveguide core, +the top and bottom surfaces, and sidewalls respectively for the two different waveguide widths[25]. +These parameters are calculated using FEM simulations (performed with COMSOL). We also use +the Payne-Lacey model[26] to relate scattering loss to the surface’s RMS roughness (σ) and the +correlation length (Lc), both extracted from the AFM measurements. The method used here to +extract the loss contributions is similar to the one used in ref[9]. We find that for complete overlap +of the mode with the interfaces, the scattering losses are +~ 0.0002 dB/cm and +~ 0.0024 dB/cm at the SiO2/Si3N4 top interface and Si3N4/SiO2 bottom interface, respectively. The +estimated surface scattering and bulk loss contributions for different thermal treatments (shown in +Table 1) are extracted from Equation 3 and Equation 4 below: + + (3) + (4) +We find that both bulk loss and surface scattering losses are reduced after RTA and furnace +anneal, which indicates that the chemical and physical properties of the films are improved by +thermal treatment. From Table 1 and Equation 3, if the surface scattering loss were eliminated, +one could reduce the propagation loss down to 0.33 dB/cm. By post-processing with RTA at 800 +°C, one could reduce the propagation loss to 0.23 dB/cm. The propagation loss can be further +reduced if RTA were performed at a higher temperature to break down bonded hydrogen. By post- +processing with furnace anneal, one could reduce the propagation loss in these devices to 0.04 +dB/cm if the surface scattering loss were eliminated. +1 +h +2 +h +3 +h +_ +top scatter +a +_ +bottom scatter +a +1 +_ +_ +_ +_ +ring +bulk +loss +top +scatter +bottom +scatter +sidewalls +scatter +a +a +a +a +a += ++ ++ ++ +2 +1 +_ +2 +_ +_ +3 +_ +ring +bulk +loss +top +scatter +bottom +scatter +sidewalls +scatter +a +h a +h +a +a +h a += ++ ++ ++ +（ +） + +Published in Laser & Photonics Reviews. DOI: 10.1002/lpor.202200544 (2022). + + + +Table 1. The extracted surface scattering and bulk loss contribution in PECVD film. + +Bulk Loss +Surface Scattering Loss Total Loss +No Anneal +0.33 dB/cm +0.09 dB/cm + 0.42 dB/cm +Rapid Thermal Anneal 0.23 dB/cm +0.05 dB/cm + 0.28 dB/cm +Furnace Anneal +0.04 dB/cm +0.02 dB/cm + 0.06 dB/cm + +The structure fabricated without any post-fabrication thermal treatment exhibits a high +confinement of 87% and a low propagation loss of 0.42 dB/cm. High confinement is necessary for +tailoring the waveguide dispersion to achieve phase matching in nonlinear processes as well as for +tighter bends, thus allowing small footprints required in large-scale photonic systems. We compare +the confinement factor and propagation loss achieved in this work with other state-of-the-art works +realized in foundry compatible PECVD platform without any thermal treatment in Figure 6[2,3,5,27– +30]. + +Figure 6. Loss and confinement achieved in this work compared with other state- +of-the-art works based on PECVD platform. All points including this work are for +devices fabricated without any thermal treatment[2,3,5,27–30]. + +10 +(This work) +1/Loss (cm) +5 +Y. Huang, et al (2014) ++N. Sherwood-Droz, et al (2011) +C. Lacava et al, (2017) +E. A. Douglas et al, (2016) +s. Mao et al, (2008) +L.Wang, et al (2018) ++K. Ikeda, et al (2008) +0 +40 +50 +60 +70 +80 +90 +100 +Confinement Factor (%)Published in Laser & Photonics Reviews. DOI: 10.1002/lpor.202200544 (2022). + + + +4. Dispersion engineering +We show the dispersion of the devices can be tuned by post-processing with furnace anneal. In +order to engineer the dispersion, we derive the Sellmeier equations for PECVD Si3N4 films from +ellipsometry performed over 200–1690 nm and 1.7–34 μm wavelength ranges using J.A. Woollam +M-2000 and IR-VASE instruments. We show the measured spectra from 200-1750 nm before and +after annealing in Figure 7(a) and Figure 7(b). We fit the spectra over the wavelength range 300– +2000 nm to obtain the following Sellmeier equations for Si3N4 before and after furnace anneal. + + + + +𝜆 is in units of nanometer. We show the simulated dispersions based on the Sellmeier equations +for silicon nitride resonators with a cross section of 730 nm x 1500 nm and a bending radius of +115 µm before and after annealing in Figure 7(c). The dashed line separates the anomalous group- +velocity dispersion (GVD) regime and the normal GVD regime. One can see that the device with +the same cross section of 730 nm x 1500 nm exhibits normal GVD before anneal and anomalous +GVD after anneal. +3 +4 +2 +9 +2 +2 +2 +2 +2 +8 +2 +2.61 +1.11 10 +( +_ +) +1 +139.77 +2.51 10 +Si N +n +before +anneal +l +l +l +l +´ += + ++ +- +- +´ +（ +） +3 +4 +2 +9 +2 +2 +2 +2 +2 +8 +2 +2.97 +1.57 10 +( +_ +) +1 +-144.86 +- 3.80 10 +Si N +n +after +anneal +l +l +l +l +´ += + ++ +´ +（ +） + +Published in Laser & Photonics Reviews. DOI: 10.1002/lpor.202200544 (2022). + + + + + +Figure 7. (a) Refractive index n and extinction coefficient k for the wavelength +range 200–1750 nm before annealing. (b) Refractive index n and extinction +coefficient k for the wavelength range 200-1750 nm after annealing. (c) Dispersion +simulations for fundamental TE mode of a silicon nitride ring resonator with a cross +section of 730 nm ´ 1500 nm and a bending radius of 115 µm before and after +annealing. The dashed line separates the anomalous group-velocity dispersion +regime and the normal group-velocity dispersion regime. + + +Before annealing +After annealing + +(a) +2.5 +0.4 +Extinction ( +n +2.4 +Refraction, +0.3 +2.3 +n +2.2 +Coefficient k +0.2 +2.1 +of +2 +0.1 +1.8 +0 +0 +250 +500 +750 +1000 +1250 +1500 +1750 +Wavelength (nm) +(b) +2.5 +0.2 +n +2.4 +n +0.15 +2.3 +Refrac +-k +2.2 +0.1 +Coefficie +R +xepul +2.1 +0.05 +ient k +2 +1.9 +0 +0 +250 +500 +750 +1000 +1250 +1500 +1750 +Wavelength (nm) +(c) +100 +Before annealing +(wy/wu/sd) +-After annealing +50 +ispersion ( +-50 +-100 +D +-150 +200 +1000 +1200 +1400 +1600 +1800 +2000 +Wavelength (nm)Published in Laser & Photonics Reviews. DOI: 10.1002/lpor.202200544 (2022). + + + +5. Linear and nonlinear applications +We demonstrate low threshold parametric oscillation and frequency combs generation using +foundry compatible devices post-processed with furnace anneal leveraging our ability to engineer +the dispersion. We show the evolution of the comb generation process and observe transitions into +various comb states in Figure 8 using a pump wavelength of 1550 nm. As the power in the +resonator builds, we see the primary sidebands form at the parametric gain peak due to degenerate +four-wave mixing as shown in Figure 8(a). We show the transition into the mini-combs in Figure +8(b) and eventually the broadband frequency combs with an on-chip pump power of 202 mW in +Figure 8(c). The parametric oscillation threshold is measured as low as 3 mW, which is close to +the theoretical limit of 2.7 mW. + +Published in Laser & Photonics Reviews. DOI: 10.1002/lpor.202200544 (2022). + + + + +Figure 8. Evolution of the frequency comb generation process. (a) Primary +sidebands form at the parametric gain peak due to degenerate four-wave mixing. +(b) The mini-comb formation. (c) Broadband Kerr frequency comb with an on-chip +pump power of 202 mW. + +We demonstrate that modal-collapse of a multimode Fabry-Perot laser diode (FPL) can be +realized by using the same device. Therefore, we obtain a single-wavelength emission laser thanks +to the increased robustness to coupling loss of a FPL[31] and strong feedback of the high quality +factor resonator. The system is composed of a commercial single transverse-mode FPL (Thorlabs +FPL1001C) and the high quality resonator as shown in Figure 9. + +(a) +10 +0 +10 +Power (dBm) +20 +-30 +40 +50 +-60 +-70 +1450 +1500 +1550 +1600 +1650 +1700 +(b) +Wavelength (nm) +10 +0 +10 +(dBm) +20 +30 +-40 +-50 +60 +-70 +1450 +1500 +1550 +1600 +1650 +1700 +(c) +Wavelength (nm) +10 +0 +-10 +Power (dBm) +-20 +-30 +40 +50 +60 +-70 +1450 +1500 +1550 +1600 +1650 +1700 +Wavelength (nm)Published in Laser & Photonics Reviews. DOI: 10.1002/lpor.202200544 (2022). + + + + +Figure 9. Schematic of the experimental setup for lasing measurement. A +commercial single transverse-mode Fabry-Perot Laser Diode (Thorlabs +FPL1001C) is coupled to the high quality factor resonator. The spectrum of the +laser is measured with an optical spectrum analyzer (OSA). + +A feedback signal from the high quality factor resonator leads to self-injection locking of the +FPL laser resulting in a locked laser with single longitudinal-mode emission and narrow-linewidth. +The spectrum of the unlocked free-running laser and the locked laser are shown in Figure 10. The +side-mode suppression ratio (SMSR) is at least 29 dB and the linewidth is measured below +resolution limit of the optical spectrum analyzer. We have calculated the intrinsic linewidth to be +in the range of 1 - 10 kHz. For this calculation we have considered the Schawlow–Townes +linewidth of the free-running laser and the linewidth reduction due to self-injection locking +following a similar procedure as explained in Ref [31]. The coupling structure for our device here +is inverse taper and it could be optimized for coupling to FPL, so better SMSRs and even narrower +linewidths can be achieved with improved coupling. + +Figure 10. (a) Optical spectra of the unlocked free-running laser. (b) Optical +spectra of the locked narrow-linewidth laser to the ring resonator. Side-mode +suppression ratio (SMSR) is at least 29 dB. + +Chip +Fabry-Perot Laser Diode(a) +Free Running +Locked +Power (10 dB/div.) +Power (10 dB/div.) +29 dB +1520 +1524 +1528 +1532 +1536 +1540 +1520 +1524 +1528 +1532 +1536 +1540 +Wavelength (nm) +Wavelength (nm)Published in Laser & Photonics Reviews. DOI: 10.1002/lpor.202200544 (2022). + + + +6. Conclusion and Discussion +Our work demonstrates the feasibility of obtaining ultra-low loss devices directly from foundries. +We show that these foundry compatible devices with or without a simple post-processing step can +be used for linear and nonlinear applications where ultra-low loss and dispersion are required. Low +threshold parametric oscillation, broadband frequency combs and narrow-linewidth laser are +demonstrated. The fundamental limit of loss in our devices is extracted and proved to be +comparable with the loss achieved in LPCVD films. Our work provides a promising path for +scalable photonic systems based on foundries. +Recently, reactive sputtering silicon nitride films annealed at 400℃ in ambient atmosphere +have been shown to achieve propagation losses down to 0.54 dB/cm[32]. Optical frequency +combs[32] and hybrid integration with lithium niobate on insulator platforms[33,34] have been +successfully demonstrated, which makes the reactive sputtering another promising method for +producing low-loss silicon nitride films. Since the losses in reactive sputtering devices are +currently limited by scattering from the sidewall roughness rather than H-bond absorption losses[35], +these devices could further benefit from the processes and techniques we developed here. + +Acknowledgements +The authors would like to acknowledge Ron Synowicki from J.A. Woollam Co., the leading +manufacturer of spectroscopic ellipsometers for optical properties measurements. Research +reported in this work was performed in part at the Cornell NanoScale Science & Technology +Facility (CNF), a member of the National Nanotechnology Coordinated Infrastructure (NNCI) +supported by National Science Foundation (Grant NNCI-2025233). The authors acknowledge +support from the PIPES program funded by DARPA (HR0011-19-2-0014), the PINE program +funded by the ARPA-E (DE-AR0000843), and the AFOSR STTR program (FA9550-20-1-0297). + + +Published in Laser & Photonics Reviews. DOI: 10.1002/lpor.202200544 (2022). + + + +References +[1] +A. H. Atabaki, S. Moazeni, F. Pavanello, H. Gevorgyan, J. Notaros, L. Alloatti, M. T. +Wade, C. Sun, S. A. Kruger, H. Meng, K. Al Qubaisi, I. Wang, B. Zhang, A. Khilo, C. V. +Baiocco, M. A. Popović, V. M. Stojanović, R. J. Ram, Nature 2018, 556, 349. +[2] +E. A. Douglas, P. Mahony, A. Starbuck, A. Pomerene, D. C. Trotter, C. T. DeRose, +Optical Materials Express 2016, 6, 2892. +[3] +S. C. Mao, S. H. Tao, Y. L. Xu, X. W. Sun, M. B. Yu, G. Q. Lo, D. L. Kwong, Optics +Express 2008, 16, 20809. +[4] +T. Domínguez Bucio, A. Z. Khokhar, C. Lacava, S. Stankovic, G. Z. Mashanovich, P. +Petropoulos, F. Y. Gardes, Journal of Physics D: Applied Physics 2017, 50, 025106. +[5] +C. Lacava, S. Stankovic, A. Z. Khokhar, T. D. Bucio, F. Y. Gardes, G. T. Reed, D. J. +Richardson, P. Petropoulos, Scientific Reports 2017, 7, DOI 10.1038/s41598-017-00062-6. +[6] +J. Chiles, N. Nader, D. D. Hickstein, S. P. Yu, T. C. Briles, D. Carlson, H. Jung, J. M. +Shainline, S. Diddams, S. B. Papp, S. W. Nam, R. P. Mirin, Optics Letters 2018, 43, 1527. +[7] +G.-R. Yang, Y.-P. Zhao, Y. Z. Hu, T. Paul Chow, R. J. Gutmann, Thin Solid Films 1998, +333, 219. +[8] +H. Huang, K. J. Winchester, A. Suvorova, B. R. Lawn, Y. Liu, X. Z. Hu, J. M. Dell, L. +Faraone, Materials Science and Engineering: A 2006, 435–436, 453. +[9] +X. Ji, F. A. S. Barbosa, S. P. Roberts, A. Dutt, J. Cardenas, Y. Okawachi, A. Bryant, A. +L. Gaeta, M. Lipson, Optica 2017, 4, 619. +[10] +R. J. Bojko, J. Li, L. He, T. Baehr-Jones, M. Hochberg, Y. Aida, Journal of Vacuum +Science & Technology B: Microelectronics and Nanometer Structures 2011, 29, 06F309. +[11] +B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, J.- Laine, Journal of Lightwave Technology +1997, 15, 998. +[12] +W. Bogaerts, P. D. Heyn, T. V. Vaerenbergh, K. D. Vos, S. K. Selvaraja, T. Claes, P. +Dumon, P. Bienstman, D. V. Thourhout, R. Baets, Laser & Photonics Reviews 2012, 6, 47. +[13] +A. Yariv, Electronics Letters 2000, 36, 321. +[14] +A. Yariv, IEEE Photonics Technology Letters 2002, 14, 483. +[15] +M. J. Hart, A. G. R. Evans, Semiconductor Science and Technology 1988, 3, 421. +[16] +V. Trivedi, S. J. Pearton, Solid-State Electronics 2002, 46, 777. +[17] +F. L. Martínez, A. del Prado, I. Mártil, G. González-Diaz, W. Bohne, W. Fuhs, J. +Röhrich, B. Selle, I. Sieber, Phys. Rev. B 2001, 63, 245320. +[18] +R. Bousbih, W. Dimassi, I. Haddadi, H. Ezzaouia, Phys. Status Solidi C 2012, 9, 2189. +[19] +M. J. Shaw, J. Guo, G. A. Vawter, S. Habermehl, C. T. Sullivan, in Proc.SPIE (Eds.: E. +G. Johnson, G. P. Nordin, T. J. Suleski), Proc.SPIE, San Jose, CA, 2005. +[20] +Y. Xuan, Y. Liu, L. T. Varghese, A. J. Metcalf, X. Xue, P.-H. Wang, K. Han, J. A. +Jaramillo-Villegas, A. Al Noman, C. Wang, S. Kim, M. Teng, Y. J. Lee, B. Niu, L. Fan, J. +Wang, D. E. Leaird, A. M. Weiner, M. Qi, Optica 2016, 3, 1171. +[21] +K. Luke, Y. Okawachi, M. R. E. Lamont, A. L. Gaeta, M. Lipson, Optics Letters 2015, +40, 4823. +[22] +M. H. P. Pfeiffer, J. Liu, A. S. Raja, T. Morais, B. Ghadiani, T. J. Kippenberg, Optica, +OPTICA 2018, 5, 884. +[23] +X. Ji, X. Yao, A. Klenner, Y. Gan, A. L. Gaeta, C. P. Hendon, M. Lipson, Opt. Express, +OE 2019, 27, 19896. +[24] +T. Gu, M. Yu, D.-L. Kwong, C. W. Wong, Optics Express 2014, 22, 18412. + +Published in Laser & Photonics Reviews. DOI: 10.1002/lpor.202200544 (2022). + + + +[25] +T. Barwicz, H. A. Haus, Journal of Lightwave Technology 2005, 23, 2719. +[26] +F. P. Payne, J. P. R. Lacey, Optical and Quantum Electronics 1994, 26, 977. +[27] +K. Ikeda, R. E. Saperstein, N. Alic, Y. Fainman, Optics Express 2008, 16, 12987. +[28] +N. Sherwood-Droz, M. Lipson, Opt. Express, OE 2011, 19, 17758. +[29] +Y. Huang, J. Song, X. Luo, T.-Y. Liow, G.-Q. Lo, Opt. Express, OE 2014, 22, 21859. +[30] +L. Wang, W. Xie, D. V. Thourhout, Y. Zhang, H. Yu, S. Wang, Opt. Express, OE 2018, +26, 9645. +[31] +A. Gil-Molina, O. Westreich, Y. Antman, X. Ji, A. L. Gaeta, M. Lipson, in 2020 +Conference on Lasers and Electro-Optics (CLEO), 2020, pp. 1–2. +[32] +A. Frigg, A. Boes, G. Ren, T. G. Nguyen, D.-Y. Choi, S. Gees, D. Moss, A. Mitchell, +APL Photonics 2020, 5, 011302. +[33] +X. Han, Y. Jiang, A. Frigg, H. Xiao, P. Zhang, T. G. Nguyen, A. Boes, J. Yang, G. Ren, +Y. Su, A. Mitchell, Y. Tian, Laser & Photonics Reviews 2022, 16, 2100529. +[34] +Y. Jiang, X. Han, H. Huang, P. Zhang, A. Dubey, H. Xiao, M. Yuan, A. Frigg, T. G. +Nguyen, A. Boes, Y. Li, G. Ren, Y. Su, A. Mitchell, Y. Tian, Advanced Photonics Research +2022, 3, 2200121. +[35] +A. Frigg, A. Boes, G. Ren, I. Abdo, D.-Y. Choi, S. Gees, A. Mitchell, Opt. Express 2019, +27, 37795. + + diff --git a/0tE1T4oBgHgl3EQfRgNg/content/tmp_files/load_file.txt b/0tE1T4oBgHgl3EQfRgNg/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..9064319182e809574da29ebb676bf786618674db --- /dev/null +++ b/0tE1T4oBgHgl3EQfRgNg/content/tmp_files/load_file.txt @@ -0,0 +1,733 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf,len=732 +page_content='Published in Laser & Photonics Reviews.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='1002/lpor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='202200544 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Ultra-Low-Loss Silicon Nitride Photonics Based on Deposited Films Compatible with Foundries Xingchen Ji,1,3,* Yoshitomo Okawachi,2 Andres Gil-Molina,1 Mateus Corato-Zanarella,1 Samantha Roberts,1 Alexander L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Gaeta,2 and Michal Lipson1,* 1Department of Electrical Engineering, Columbia University, New York, NY, 10027, USA 2Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY, 10027, USA 3Currently at John Hopcroft Center for Computer Science, School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China *Corresponding Author: E-mail: xingchenji@sjtu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='cn and ml3745@columbia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='edu Abstract: The fabrication processes of silicon nitride (Si3N4) photonic devices used in foundries require low temperature deposition, which typically leads to high propagation losses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Here, we show that propagation loss as low as 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='42 dB/cm can be achieved using foundry compatible processes by solely reducing waveguide surface roughness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' By post-processing the fabricated devices using rapid thermal anneal (RTA) and furnace anneal, we achieve propagation losses down to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='28 dB/cm and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='06 dB/cm, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' These low losses are comparable to the conventional devices using high temperature, high-stress LPCVD films.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' We also tune the dispersion of the devices, and proved that these devices can be used for linear and nonlinear applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Low threshold parametric oscillation, broadband frequency combs and narrow-linewidth laser are demonstrated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Our work demonstrates the feasibility of scalable photonic systems based on foundries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Published in Laser & Photonics Reviews.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='1002/lpor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='202200544 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Introduction To date, ultra-low-loss silicon nitride (Si3N4) waveguides and resonators have been demonstrated almost exclusively using films deposited at high temperature, while foundries mostly rely on Si3N4 films deposited at low temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' The high temperature deposition uses low-pressure chemical vapor deposition (LPCVD), while low temperature deposition uses plasma-enhanced chemical vapor deposition (PECVD).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' PECVD Si3N4 is the most commonly used thin film in foundries as an insulator or a chemical barrier layer, however, the high propagation losses in these films limit their applications in photonics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' LPCVD Si3N4 is not used in foundries due to the high temperature required and high film stress.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Therefore, reducing losses in PECVD Si3N4 photonic devices is critical for integrating photonics devices with electronics, which could be used to realize high performance, scalable systems and realize system-level innovation[1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Previously, there have been efforts to reduce losses in PECVD Si3N4 films by chemically changing the film composition[2–5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' By lowering the ammonium concentration during the deposition, losses down to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='5 dB/cm have been shown[2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' However, these losses remain too high for most photonic applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Researchers have also substituted conventional precursors with deuterated ones to reduce the losses of the film, losses down to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='3 dB/cm have been shown[6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' However, these methods require special precursors and deposition tools, which are not commonly available in foundries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Film deposition and waveguide fabrication Here we show that low-loss can be achieved in a standard PECVD process by physically reducing waveguide surface roughness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' The fabrication process is schematically shown in Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' We deposit Si3N4 using PECVD at 350 °C in a single step onto a thermally oxidized 4-inch silicon Published in Laser & Photonics Reviews.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='1002/lpor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='202200544 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' wafer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' The gases used for deposition are a mixture of silane (SiH4: 20 sccm) diluted by nitrogen (N2: 1425 sccm) and pure ammonia (NH3: 30 sccm), with a process pressure of 1900 mTorr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' The plasma frequencies alternate between a high frequency (13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='56 MHz) with a power of 200 W and a low frequency (100 kHz) with a power of 160 W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' The time duration for the two frequencies is 8 seconds and 12 seconds, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' The above parameters ensure that the deposition of Si3N4 film has very low film stress and high uniformity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' The measured stress for the Si3N4 film on a test wafer is 93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='4 MPa and tensile, which is more than an order of magnitude lower than LPCVD Si3N4 films deposited at high temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' The low stress allows us to deposit thicker films without any cracking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Schematic of our low-temperature PECVD Si3N4 fabrication processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' The process steps here are fully compatible with CMOS electronics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' We design high confinement waveguides based on the deposited PECVD films allows for strong dispersion engineering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' One can see in Figure 2, the strong mode overlaps with the top surface that can exhibit a roughness of several nanometers for PECVD films[7,8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Si,N4 SiO2 Si,N4 SiO2 SisN4 SiO2 SiO2 SiO2 Resist Resist SiO2 SiO, Sio, SigN4 SisN4 SisN4 SiO2 SiO2 SiO2 SiO2 SisN4 SiO2Published in Laser & Photonics Reviews.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='1002/lpor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='202200544 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Mode simulation and microscope images of fabricated devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' (a) Mode simulation of 730 nm tall and 1500 nm wide waveguide showing that the mode is highly confined in the geometry we have chosen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' (b) Top view optical microscope image of a 115 µm radius ring resonator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' To reduce scattering from the top surface of PECVD Si3N4, we use chemical mechanical planarization (CMP) to smooth the surface, as roughness traditionally leads to a high loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' We show the atomic-force microscopy (AFM) scans before and after the polishing step in Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' The root-mean-squared (RMS) roughness is decreased from 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='36 nm before polishing to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='20 nm after polishing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' In order to reduce the roughness from the sidewalls and protect the polished top surface, we use a SiO2 hard mask deposited using PECVD after CMP and use a dry etching process with a much higher oxygen flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' This etching process has been proved to substantially reduce the polymerization process during etching and decreases the roughness[9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' We pattern our devices with electron beam lithography using ma-N 2403 resist and use multipass writing algorithms to further reduce sidewall roughness caused by the lithography itself[9,10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Finally, we clad the devices with 2 μm of SiO2 deposited using PECVD for waveguide protection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' The fabricated devices consist of resonators with a radius of 115 μm, a height of 730 nm and a width of 1500 nm, which are coupled to a waveguide of the same width and height.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' These dimensions ensure high confinement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' 730nm 1500 nm 100μmPublished in Laser & Photonics Reviews.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='1002/lpor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='202200544 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' AFM measurement of the top surface of PECVD Si3N4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' (a) 3D AFM scan of the top surface before CMP with RMS roughness of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='36 nm and a correlation length of 27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='6 nm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' (b) 2D image of Si3N4 top surface before CMP and scaled to - 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='0 – 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='0 nm with RMS roughness of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='36 nm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' (c) 3D image of Si3N4 top surface after CMP with RMS roughness of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='20 nm and a correlation length of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='96 nm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' (d) 2D image of Si3N4 top surface after CMP and scaled to -1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='0 – 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='0 nm with RMS roughness of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='20 nm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Note the different scale bars on (a) and (c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Fundamental loss extraction and discussion The quality factor is a measure of the sharpness of the resonance relative to its central frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' It represents how well the resonator can store energy and can be written as[11,12]: (1) The quality factor defined in Equation 1 is the loaded quality factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' The intrinsic quality factor of the cavity which is directly related to the propagation losses can be written as[13,14]: (2) 0 L Q w w = D min 2 1 L i Q Q T = ± 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='0 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='0 nm 300 nm 300 nm 100 nm 100 nm 100 nm -5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='0 5 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='0 nm 300 nm 300 nm 100 nm 100 nm -1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='0 100 nmPublished in Laser & Photonics Reviews.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='1002/lpor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='202200544 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Tmin is the on-resonance normalized transmission minimum, sign is corresponding to undercoupled and overcoupled condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' The schematic of the experimental setup for quality factor measurement and frequency comb generation is shown in Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' The resonators we fabricated and measured here have a height of 730 nm, a width of 1500 nm and a bending radius of 115 µm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' We measure an intrinsic quality factor of 724,000, corresponding to a propagation loss of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='42 dB/cm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' In Figure 5(a), we show the measured resonance and normalized transmission spectrum over a broad wavelength range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' To the best of our knowledge, this is the lowest propagation loss reported to date in a standard PECVD film compatible with foundries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Schematic of the experimental setup for measuring transmission spectra and resonator linewidth to characterize the quality factor and generate frequency combs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' FPC: fiber polarization controller;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' PD: photodetector;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' and OSA: optical spectrum analyzer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Note that amplifier is not needed for transmission measurement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' To minimize both surface scattering losses, as well as bulk loss, we post-process the films with a rapid thermal anneal (RTA).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' With RTA, we achieve an even higher intrinsic quality factor of more than 1 million, corresponding to a propagation loss of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='28 dB/cm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' RTA has been successfully applied in the microelectronics industry and it has particular relevance for CMOS technology, specifically in steps such as implant annealing, oxidation, and source and drain contact junctions[15,16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' The process reduces loss by driving out the non-bonded atomic and molecular hydrogen trapped in microvoids of the structure and further densifies the films[17,18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' We apply RTA at 800 °C for 5 mins to the cladded devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' In Figure 5(b), we show the measured resonance ± 000 Laser Amplifier ChipPublished in Laser & Photonics Reviews.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='1002/lpor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='202200544 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' and normalized transmission spectrum over a broad wavelength range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' The thermal budget is below the tolerance of most CMOS electronics and can be used to further reduce losses for devices with microheaters or dopants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' We show that by post-processing foundry-compatible devices with furnace anneal (appropriate for devices with high thermal budget), the propagation loss can be comparable to those fabricated using high temperature, high-stress LPCVD films.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Furnace anneal differs from RTA, with higher temperatures (above 1000 °C [19–24]) and longer anneal times (several hours).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' We anneal cladded devices at 1150 °C in a nitrogen atmosphere for 3 hours and no defects or cracks were observed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' We achieve a quality factor of 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='7 million, which corresponds to a propagation loss of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='06 dB/cm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' In Figure 5(c), we show the measured resonance and normalized transmission spectrum over a broad wavelength range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Published in Laser & Photonics Reviews.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='1002/lpor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='202200544 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' (a) Device without annealing shows a measured full width half maximum (FWHM) of 595 MHz around 1600 nm and measured normalized transmission spectrum over a broad wavelength range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' (b) Device after rapid thermal anneal shows a measured full width half maximum (FWHM) of 423 MHz around 1600 nm and measured normalized transmission spectrum over a broad wavelength range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' (c) Device after furnace anneal shows a measured full width half maximum (FWHM) of 52 MHz around 1600 nm and measured normalized transmission spectrum over a broad wavelength range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' We show that for as-fabricated devices, the bulk losses dominate over the surface scattering loss, and can be as low as 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='33 dB/cm, while for post-fabrication annealed devices, the bulk losses No anneal (a) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='6 ed Normalized 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='4 595 MHz 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='2 Qi = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='72 million 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='2 ION 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='0 1320 1530 1540 1550 1560 1570 1580 1590 1600 1610 1620 -2000 -1000 0 1000 2000 Wavelength (nm) Frequency (MHz) (b) Rapidthermalanneal 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='6 Normalized 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='4 423 MHz 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='2 Qi = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='1 million 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='0 -2000 -1000 0 1000 2000 Wavelength (nm) △Frequency (MHz) (c) Furnace anneal 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='6 52 MHz ed 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='4 Qi= 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='7million 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='2 Nor 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='0 1320 1530 1540 1550 1560 1570 1580 1590 1600 1610 1620 -400 -200 0 200 400 Wavelength (nm) △Frequency(MHz)Published in Laser & Photonics Reviews.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='1002/lpor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='202200544 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' are comparable to the surface scattering loss, and can be as low as 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='04 dB/cm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' We extract the loss contributions by comparing the losses between two different structures with different mode overlap with the interfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' , , are the overlap of the optical field with the waveguide core, the top and bottom surfaces, and sidewalls respectively for the two different waveguide widths[25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' These parameters are calculated using FEM simulations (performed with COMSOL).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' We also use the Payne-Lacey model[26] to relate scattering loss to the surface’s RMS roughness (σ) and the correlation length (Lc), both extracted from the AFM measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' The method used here to extract the loss contributions is similar to the one used in ref[9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' We find that for complete overlap of the mode with the interfaces, the scattering losses are ~ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='0002 dB/cm and ~ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='0024 dB/cm at the SiO2/Si3N4 top interface and Si3N4/SiO2 bottom interface, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' The estimated surface scattering and bulk loss contributions for different thermal treatments (shown in Table 1) are extracted from Equation 3 and Equation 4 below: (3) (4) We find that both bulk loss and surface scattering losses are reduced after RTA and furnace anneal, which indicates that the chemical and physical properties of the films are improved by thermal treatment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' From Table 1 and Equation 3, if the surface scattering loss were eliminated, one could reduce the propagation loss down to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='33 dB/cm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' By post-processing with RTA at 800 °C, one could reduce the propagation loss to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='23 dB/cm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' The propagation loss can be further reduced if RTA were performed at a higher temperature to break down bonded hydrogen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' By post- processing with furnace anneal, one could reduce the propagation loss in these devices to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='04 dB/cm if the surface scattering loss were eliminated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' 1 h 2 h 3 h _ top scatter a _ bottom scatter a 1 _ _ _ _ ring bulk loss top scatter bottom scatter sidewalls scatter a a a a a = + + + 2 1 _ 2 _ _ 3 _ ring bulk loss top scatter bottom scatter sidewalls scatter a h a h a a h a = + + + （ ） Published in Laser & Photonics Reviews.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='1002/lpor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='202200544 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' The extracted surface scattering and bulk loss contribution in PECVD film.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Bulk Loss Surface Scattering Loss Total Loss No Anneal 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='33 dB/cm 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='09 dB/cm 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='42 dB/cm Rapid Thermal Anneal 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='23 dB/cm 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='05 dB/cm 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='28 dB/cm Furnace Anneal 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='04 dB/cm 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='02 dB/cm 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='06 dB/cm The structure fabricated without any post-fabrication thermal treatment exhibits a high confinement of 87% and a low propagation loss of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='42 dB/cm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' High confinement is necessary for tailoring the waveguide dispersion to achieve phase matching in nonlinear processes as well as for tighter bends, thus allowing small footprints required in large-scale photonic systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' We compare the confinement factor and propagation loss achieved in this work with other state-of-the-art works realized in foundry compatible PECVD platform without any thermal treatment in Figure 6[2,3,5,27– 30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Loss and confinement achieved in this work compared with other state- of-the-art works based on PECVD platform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' All points including this work are for devices fabricated without any thermal treatment[2,3,5,27–30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' 10 (This work) 1/Loss (cm) 5 Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Huang, et al (2014) +N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Sherwood-Droz, et al (2011) C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Lacava et al, (2017) E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Douglas et al, (2016) s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Mao et al, (2008) L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='Wang, et al (2018) +K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Ikeda, et al (2008) 0 40 50 60 70 80 90 100 Confinement Factor (%)Published in Laser & Photonics Reviews.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='1002/lpor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='202200544 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Dispersion engineering We show the dispersion of the devices can be tuned by post-processing with furnace anneal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' In order to engineer the dispersion, we derive the Sellmeier equations for PECVD Si3N4 films from ellipsometry performed over 200–1690 nm and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='7–34 μm wavelength ranges using J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Woollam M-2000 and IR-VASE instruments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' We show the measured spectra from 200-1750 nm before and after annealing in Figure 7(a) and Figure 7(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' We fit the spectra over the wavelength range 300– 2000 nm to obtain the following Sellmeier equations for Si3N4 before and after furnace anneal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' 𝜆 is in units of nanometer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' We show the simulated dispersions based on the Sellmeier equations for silicon nitride resonators with a cross section of 730 nm x 1500 nm and a bending radius of 115 µm before and after annealing in Figure 7(c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' The dashed line separates the anomalous group- velocity dispersion (GVD) regime and the normal GVD regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' One can see that the device with the same cross section of 730 nm x 1500 nm exhibits normal GVD before anneal and anomalous GVD after anneal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' 3 4 2 9 2 2 2 2 2 8 2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='61 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='11 10 ( _ ) 1 139.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='77 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='51 10 Si N n before anneal l l l l ´ = + + - - ´ （ ） 3 4 2 9 2 2 2 2 2 8 2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='97 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='57 10 ( _ ) 1 -144.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='86 - 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='80 10 Si N n after anneal l l l l ´ = + + ´ （ ） Published in Laser & Photonics Reviews.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='1002/lpor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='202200544 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' (a) Refractive index n and extinction coefficient k for the wavelength range 200–1750 nm before annealing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' (b) Refractive index n and extinction coefficient k for the wavelength range 200-1750 nm after annealing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' (c) Dispersion simulations for fundamental TE mode of a silicon nitride ring resonator with a cross section of 730 nm ´ 1500 nm and a bending radius of 115 µm before and after annealing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' The dashed line separates the anomalous group-velocity dispersion regime and the normal group-velocity dispersion regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Before annealing After annealing (a) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='4 Extinction ( n 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='4 Refraction, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='3 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='3 n 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='2 Coefficient k 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='1 of 2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='8 0 0 250 500 750 1000 1250 1500 1750 Wavelength (nm) (b) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='2 n 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='4 n 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='15 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='3 Refrac -k 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='1 Coefficie R xepul 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='05 ient k 2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='9 0 0 250 500 750 1000 1250 1500 1750 Wavelength (nm) (c) 100 Before annealing (wy/wu/sd) -After annealing 50 ispersion ( -50 -100 D -150 200 1000 1200 1400 1600 1800 2000 Wavelength (nm)Published in Laser & Photonics Reviews.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='1002/lpor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='202200544 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Linear and nonlinear applications We demonstrate low threshold parametric oscillation and frequency combs generation using foundry compatible devices post-processed with furnace anneal leveraging our ability to engineer the dispersion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' We show the evolution of the comb generation process and observe transitions into various comb states in Figure 8 using a pump wavelength of 1550 nm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' As the power in the resonator builds, we see the primary sidebands form at the parametric gain peak due to degenerate four-wave mixing as shown in Figure 8(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' We show the transition into the mini-combs in Figure 8(b) and eventually the broadband frequency combs with an on-chip pump power of 202 mW in Figure 8(c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' The parametric oscillation threshold is measured as low as 3 mW, which is close to the theoretical limit of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='7 mW.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Published in Laser & Photonics Reviews.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='1002/lpor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='202200544 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Evolution of the frequency comb generation process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' (a) Primary sidebands form at the parametric gain peak due to degenerate four-wave mixing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' (b) The mini-comb formation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' (c) Broadband Kerr frequency comb with an on-chip pump power of 202 mW.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' We demonstrate that modal-collapse of a multimode Fabry-Perot laser diode (FPL) can be realized by using the same device.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Therefore, we obtain a single-wavelength emission laser thanks to the increased robustness to coupling loss of a FPL[31] and strong feedback of the high quality factor resonator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' The system is composed of a commercial single transverse-mode FPL (Thorlabs FPL1001C) and the high quality resonator as shown in Figure 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' (a) 10 0 10 Power (dBm) 20 -30 40 50 -60 -70 1450 1500 1550 1600 1650 1700 (b) Wavelength (nm) 10 0 10 (dBm) 20 30 -40 -50 60 -70 1450 1500 1550 1600 1650 1700 (c) Wavelength (nm) 10 0 -10 Power (dBm) -20 -30 40 50 60 -70 1450 1500 1550 1600 1650 1700 Wavelength (nm)Published in Laser & Photonics Reviews.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='1002/lpor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='202200544 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Figure 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Schematic of the experimental setup for lasing measurement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' A commercial single transverse-mode Fabry-Perot Laser Diode (Thorlabs FPL1001C) is coupled to the high quality factor resonator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' The spectrum of the laser is measured with an optical spectrum analyzer (OSA).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' A feedback signal from the high quality factor resonator leads to self-injection locking of the FPL laser resulting in a locked laser with single longitudinal-mode emission and narrow-linewidth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' The spectrum of the unlocked free-running laser and the locked laser are shown in Figure 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' The side-mode suppression ratio (SMSR) is at least 29 dB and the linewidth is measured below resolution limit of the optical spectrum analyzer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' We have calculated the intrinsic linewidth to be in the range of 1 - 10 kHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' For this calculation we have considered the Schawlow–Townes linewidth of the free-running laser and the linewidth reduction due to self-injection locking following a similar procedure as explained in Ref [31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' The coupling structure for our device here is inverse taper and it could be optimized for coupling to FPL, so better SMSRs and even narrower linewidths can be achieved with improved coupling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Figure 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' (a) Optical spectra of the unlocked free-running laser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' (b) Optical spectra of the locked narrow-linewidth laser to the ring resonator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Side-mode suppression ratio (SMSR) is at least 29 dB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Chip Fabry-Perot Laser Diode(a) Free Running Locked Power (10 dB/div.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=') Power (10 dB/div.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=') 29 dB 1520 1524 1528 1532 1536 1540 1520 1524 1528 1532 1536 1540 Wavelength (nm) Wavelength (nm)Published in Laser & Photonics Reviews.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='1002/lpor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='202200544 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Conclusion and Discussion Our work demonstrates the feasibility of obtaining ultra-low loss devices directly from foundries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' We show that these foundry compatible devices with or without a simple post-processing step can be used for linear and nonlinear applications where ultra-low loss and dispersion are required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Low threshold parametric oscillation, broadband frequency combs and narrow-linewidth laser are demonstrated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' The fundamental limit of loss in our devices is extracted and proved to be comparable with the loss achieved in LPCVD films.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Our work provides a promising path for scalable photonic systems based on foundries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Recently, reactive sputtering silicon nitride films annealed at 400℃ in ambient atmosphere have been shown to achieve propagation losses down to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='54 dB/cm[32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Optical frequency combs[32] and hybrid integration with lithium niobate on insulator platforms[33,34] have been successfully demonstrated, which makes the reactive sputtering another promising method for producing low-loss silicon nitride films.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Since the losses in reactive sputtering devices are currently limited by scattering from the sidewall roughness rather than H-bond absorption losses[35], these devices could further benefit from the processes and techniques we developed here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Acknowledgements The authors would like to acknowledge Ron Synowicki from J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Woollam Co.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=', the leading manufacturer of spectroscopic ellipsometers for optical properties measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Research reported in this work was performed in part at the Cornell NanoScale Science & Technology Facility (CNF), a member of the National Nanotechnology Coordinated Infrastructure (NNCI) supported by National Science Foundation (Grant NNCI-2025233).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' The authors acknowledge support from the PIPES program funded by DARPA (HR0011-19-2-0014), the PINE program funded by the ARPA-E (DE-AR0000843), and the AFOSR STTR program (FA9550-20-1-0297).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Published in Laser & Photonics Reviews.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='1002/lpor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='202200544 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' References [1] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Atabaki, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Moazeni, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Pavanello, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Gevorgyan, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Notaros, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Alloatti, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Wade, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Sun, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Kruger, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Meng, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Al Qubaisi, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Wang, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Zhang, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Khilo, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Baiocco, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Popović, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Stojanović, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Ram, Nature 2018, 556, 349.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' [2] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Douglas, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Mahony, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Starbuck, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Pomerene, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Trotter, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' DeRose, Optical Materials Express 2016, 6, 2892.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' [3] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Mao, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Tao, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Xu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Sun, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Yu, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Lo, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Kwong, Optics Express 2008, 16, 20809.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' [4] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Domínguez Bucio, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Khokhar, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Lacava, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Stankovic, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Mashanovich, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Petropoulos, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Gardes, Journal of Physics D: Applied Physics 2017, 50, 025106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' [5] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Lacava, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Stankovic, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Khokhar, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Bucio, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Gardes, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Reed, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Richardson, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Petropoulos, Scientific Reports 2017, 7, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='1038/s41598-017-00062-6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' [6] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Chiles, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Nader, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Hickstein, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Yu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Briles, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Carlson, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Jung, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Shainline, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Diddams, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Papp, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Nam, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Mirin, Optics Letters 2018, 43, 1527.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' [7] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='-R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Yang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='-P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Zhao, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Hu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Paul Chow, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Gutmann, Thin Solid Films 1998, 333, 219.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' [8] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Huang, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Winchester, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Suvorova, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Lawn, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Liu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Hu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Dell, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Faraone, Materials Science and Engineering: A 2006, 435–436, 453.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' [9] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Ji, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Barbosa, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Roberts, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Dutt, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Cardenas, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Okawachi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Bryant, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Gaeta, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Lipson, Optica 2017, 4, 619.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' [10] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Bojko, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Li, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' He, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Baehr-Jones, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Hochberg, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Aida, Journal of Vacuum Science & Technology B: Microelectronics and Nanometer Structures 2011, 29, 06F309.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' [11] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Little, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Chu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Haus, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Foresi, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='- Laine, Journal of Lightwave Technology 1997, 15, 998.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' [12] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Bogaerts, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Heyn, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Vaerenbergh, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Vos, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Selvaraja, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Claes, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Dumon, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Bienstman, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Thourhout, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Baets, Laser & Photonics Reviews 2012, 6, 47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' [13] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Yariv, Electronics Letters 2000, 36, 321.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' [14] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Yariv, IEEE Photonics Technology Letters 2002, 14, 483.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' [15] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Hart, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Evans, Semiconductor Science and Technology 1988, 3, 421.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' [16] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Trivedi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Pearton, Solid-State Electronics 2002, 46, 777.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' [17] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Martínez, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' del Prado, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Mártil, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' González-Diaz, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Bohne, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Fuhs, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Röhrich, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Selle, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Sieber, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' B 2001, 63, 245320.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' [18] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Bousbih, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Dimassi, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Haddadi, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Ezzaouia, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Status Solidi C 2012, 9, 2189.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' [19] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Shaw, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Guo, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Vawter, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Habermehl, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Sullivan, in Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='SPIE (Eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' : E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Johnson, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Nordin, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Suleski), Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='SPIE, San Jose, CA, 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' [20] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Xuan, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Liu, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Varghese, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Metcalf, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Xue, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Wang, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Han, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Jaramillo-Villegas, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Al Noman, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Wang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Kim, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Teng, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Lee, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Niu, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Fan, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Wang, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Leaird, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Weiner, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Qi, Optica 2016, 3, 1171.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' [21] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Luke, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Okawachi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Lamont, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Gaeta, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Lipson, Optics Letters 2015, 40, 4823.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' [22] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Pfeiffer, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Liu, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Raja, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Morais, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Ghadiani, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Kippenberg, Optica, OPTICA 2018, 5, 884.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' [23] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Ji, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Yao, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Klenner, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Gan, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Gaeta, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Hendon, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Lipson, Opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Express, OE 2019, 27, 19896.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' [24] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Gu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Yu, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Kwong, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Wong, Optics Express 2014, 22, 18412.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Published in Laser & Photonics Reviews.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='1002/lpor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='202200544 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' [25] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Barwicz, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Haus, Journal of Lightwave Technology 2005, 23, 2719.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' [26] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Payne, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Lacey, Optical and Quantum Electronics 1994, 26, 977.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' [27] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Ikeda, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Saperstein, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Alic, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Fainman, Optics Express 2008, 16, 12987.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' [28] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Sherwood-Droz, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Lipson, Opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Express, OE 2011, 19, 17758.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' [29] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Huang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Song, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Luo, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Liow, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='-Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Lo, Opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Express, OE 2014, 22, 21859.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' [30] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Wang, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Xie, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Thourhout, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Zhang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Yu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Wang, Opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Express, OE 2018, 26, 9645.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' [31] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Gil-Molina, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Westreich, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Antman, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Ji, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Gaeta, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Lipson, in 2020 Conference on Lasers and Electro-Optics (CLEO), 2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' 1–2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' [32] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Frigg, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Boes, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Ren, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Nguyen, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Choi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Gees, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Moss, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Mitchell, APL Photonics 2020, 5, 011302.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' [33] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Han, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Jiang, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Frigg, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Xiao, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Zhang, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Nguyen, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Boes, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Yang, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Ren, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Su, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Mitchell, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Tian, Laser & Photonics Reviews 2022, 16, 2100529.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' [34] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Jiang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Han, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Huang, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Zhang, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Dubey, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Xiao, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Yuan, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Frigg, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Nguyen, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Boes, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Li, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Ren, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Su, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Mitchell, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Tian, Advanced Photonics Research 2022, 3, 2200121.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' [35] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Frigg, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Boes, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Ren, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Abdo, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Choi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Gees, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Mitchell, Opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} +page_content=' Express 2019, 27, 37795.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tE1T4oBgHgl3EQfRgNg/content/2301.03053v1.pdf'} diff --git a/1dE4T4oBgHgl3EQfaAyc/content/tmp_files/2301.05061v1.pdf.txt b/1dE4T4oBgHgl3EQfaAyc/content/tmp_files/2301.05061v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..6ee3bf2ab9e802ec705c2b0a50ab2cbffa273541 --- /dev/null +++ b/1dE4T4oBgHgl3EQfaAyc/content/tmp_files/2301.05061v1.pdf.txt @@ -0,0 +1,5781 @@ +PREPRINT +Electroweak Phase Transition in a Right-Handed +Neutrino Superfield Extended NMSSM +Pankaj Borah,a Pradipta Ghosh,a Sourov Royb and Abhijit Kumar Sahab +aDepartment of Physics, Indian Institute of Technology Delhi, Hauz Khas 110 016, India +bSchool of Physical Sciences, Indian Association for the Cultivation of Science, 2A & 2B Raja +S.C. Mullick Road, Kolkata 700 032, India +E-mail: Pankaj.Borah@physics.iitd.ac.in, tphyspg@physics.iitd.ac.in, +tpsr@iacs.res.in, psaks2484@iacs.res.in +Abstract: Supersymmetric models with singlet extensions can accommodate single- or +multi-step first-order phase transitions (FOPT) along the various constituent field direc- +tions. Such a framework can also produce Gravitational Waves, detectable at the upcom- +ing space-based interferometers, e.g., U-DECIGO. We explore the dynamics of electroweak +phase transition and the production of Gravitational Waves in an extended set-up of the +Next-to-Minimal Supersymmetric Standard Model (NMSSM) with a Standard Model sin- +glet right-handed neutrino superfield. We examine the role of the new parameters compared +to NMSSM on the phase transition dynamics and observe that the occurrence of a FOPT, +an essential requirement for Electroweak Baryogenesis, typically favours a right-handed +sneutrino state below 125 GeV. Our investigation shows how the analysis can offer com- +plementary probes for physics beyond the Standard Model besides the collider searches. +arXiv:2301.05061v1 [hep-ph] 12 Jan 2023 + +Contents +1 +Introduction +2 +2 +The Model +5 +2.1 +A convenient basis choice +8 +2.2 +Higher order contributions +10 +2.3 +Contributions from non-zero temperature +12 +3 +Choice of parameters +13 +3.1 +Experimental Constraints +15 +4 +The EWPT and its Properties +17 +4.1 +PT in the NMSSM + one RHN model +19 +4.2 +Numerical Results +20 +4.3 +GW spectrum from SFOPT in the NMSSM + one RHN model +28 +5 +Summary and Conclusion +36 +A Field dependent mass matrices +38 +A.1 CP-even neutral scalars squared mass matrix +40 +A.2 CP-odd neutral scalars squared mass matrix +41 +A.3 Uncoloured charged scalars squared mass matrix +43 +A.4 Neutralino mass matrix +45 +A.5 Chargino mass matrix +45 +B Neutral scalar mass matrices after the EWSB +46 +B.1 +CP-even mass squared elements +46 +B.2 +CP-odd mass squared elements +47 +C Counter terms +47 +D Daisy coefficients +48 +E Minimization conditions +49 +– 1 – + +1 +Introduction +Baryon asymmetry of the Universe is a precisely measured quantity by Planck experiment +[1]. Different kinds of proposals pertaining to baryon asymmetry production mechanism in +the early Universe are prevalent in literature (for a brief summary see Ref. [2]). In recent +times, baryon asymmetry production during the Electroweak Phase Transition (EWPT), +known as the Electroweak Baryogenesis (EWBG) [3] has gained particular attention. The +EWBG occurs around the TeV scale and has the potential to be probed in collider ex- +periments [4–6]. Irrespective of different baryon asymmetry generation mechanisms, the +Sakharov conditions [7], namely, (i) baryon number violation, (ii) charge (C) and charge- +parity (CP) violation and (iii) deviation from thermal equilibrium must be satisfied. +It is well known that the Standard Model (SM) of particle physics fails to provide a +sufficient departure from thermal equilibrium [8, 9]. Moreover, C and CP violations in the +SM are not adequate enough to yield the observed baryon asymmetry of the Universe [8, 9]. +In principle, a strong first-order EWPT (SFOEWPT) in the early Universe can pave the +way for the EWBG by allowing sufficient out-of-equilibrium processes [10]. The SM of par- +ticle physics with the observed Higgs mass ∼ 125 GeV [11, 12], shows a smooth cross-over +pattern along the Higgs field direction without any PT [13–15] and thus, fails to accom- +modate the EWBG. This issue can be circumvented by introducing new scalar degrees of +freedom having sizeable coupling with the SM Higgs boson. In general, the strength of the +EW phase transition is determined by both the high and low-temperature behaviour of the +scalar potential. Computation of critical temperature reveals displacement of the global +minimum for a scalar potential when expressed as a function of the temperature (T) of +the Universe. However, a correct description of the EWPT requires the study of bubble +nucleation dynamics since PT proceeds via the nucleation of bubbles [16]. The dynamics of +bubble nucleation, during the first-order EWPT, can yield stochastic Gravitational Waves +(GWs) in the early Universe [17–22] that may appear detectable at different GW experi- +ments. In fact, the search for GWs for probing different kinds of beyond the SM (BSM) +frameworks has long been practised (see Refs. [23–26] for some of the recent works). +Supersymmetric models, having a rich scalar sector compared to the SM, carry the +necessary ingredients for exhibiting an SFOEWPT. The PT properties in the Minimal +Supersymmetric Standard Model (MSSM) (see Ref. +[27] for a review) are exercised in +Refs. [28–37]. It is shown in Ref. [37] that a strong EWPT with a 125 GeV Higgs boson +favours a hierarchical stop sector in the MSSM, i.e., one of two stops appears to be much +heavier than the EW scale while the lighter one remains around O(100 GeV) [36, 37]. The +presence of such a light stop enhances the Higgs production rate through gluon-gluon fusion +[37, 38] and confronts constraints from LHC data [11, 12]. This tension, nevertheless, can +be alleviated by considering a light neutralino with a mass lower than about 60 GeV [37]. +However, once again it is challenged by the LHC data of Higgs invisible decay width [39–42] +and neutralino searches from the stop decay [43–45]. Besides, the MSSM also suffers from +a new kind of naturalness problem known as the µ-problem [46] and, just like the SM, is +incapable of accommodating non-zero neutrino masses and mixing [47, 48] in its original +– 2 – + +form1. +The Next-to-Minimal Supersymmetric Standard Model (NMSSM) [54] provides a dy- +namical solution to the µ-problem, a challenge that has plagued the MSSM. In the NMSSM, +the scalar sector of the MSSM is further enriched by the presence of a gauge singlet scalar +S. Studies related to EWPT in the NMSSM can be found in Refs. [55–60]. It has been +observed [55–60] that in the NMSSM soft supersymmetry (SUSY) breaking term involving +S and Higgs doublets assists to form the potential barrier even at T = 0 in contrast to the +MSSM where T ̸= 0 effects are essential for barrier formation. Thus, the PT dynamics is +more involved in the NMSSM where one needs to consider a three-dimensional field space +spanned by three2 CP-even scalar fields. +The EWPT could occur either in single-step or multi-step. +In the NMSSM, both +single-step and multi-step phase transitions are possible as discussed in Ref. +[59, 60]. +These studies [59, 60] rely on an effective field theory set-up after integrating out heavy +stops which yield potentially large contributions to the one-loop effective potential. Such +an effective-theory-based approach reduces the number of degrees of freedom participating +in the EWPT dynamics. Refs. [59, 60] also showed that the NMSSM can accommodate +EWBG in some region corners of the NMSSM parameter space. +Shifting our attention to non-zero neutrino masses and mixing [47, 48, 53], another +experimentally established BSM signature, both MSSM and NMSSM, are futile just like +the SM. Extensions of these models with additional ingredients, e.g., right-handed (RH) +neutrinos, however, offer a simple elegant way to accommodate massive neutrinos using +the popular type-I see-saw mechanism [62–65]. Supersymmetric type-I seesaw mechanism, +where the MSSM superfield content is extended with RH-neutrino superfield(s) is well stud- +ied, see for example, Refs. [66–68]. Incorporating RH-neutrino superfield(s) in the NMSSM +provides a minimal model [69] where, apart from accommodating none-zero neutrino masses +and mixing, one also gets a solution for the µ-problem3. In such a framework, non-zero +neutrino masses appear through three sources: (i) type-I seesaw mechanism involving RH- +neutrino(s), generally known as the “canonical seesaw”, (ii) type-I and type-III seesaw +involving gauginos, popularly known as the “gaugino seesaw” and, (iii) seesaw involving +higgsinos, better known as “higgsino seesaw” [69]. The last two pieces arise when left- +handed (LH) and RH sneutrinos acquire vacuum expectation values (VEVs), i.e., R-parity +gets spontaneously broken [73, 74] and effective bilinear R-parity-violating [49] terms are +generated. For this study, for simplicity, we considered the NMSSM framework extended +with one RH-neutrino superfield. One, however, needs at least two RH-neutrino superfields +to accommodate the neutrino data, leaving the lightest one massless [75, 76]. The chosen +simple framework, nevertheless, offers a nice platform to investigate the PT dynamics and +subsequently the predictions for GW emission, besides providing the correct scale for the +1MSSM extended with new superfields or new symmetries or R-parity violation [49] (see Refs. [50–52] +for further reading) can accommodate neutrino data [47, 48, 53]. R-parity is defined as RP = (−1)3B+L+2s +where L(B) denotes the lepton (baryon) number and s represents the spin. +2The PT dynamics in guided by a two-dimensional field space in the MSSM [35, 61]. +3An alternative minimal framework, known as µνSSM [70–72], also solves the µ-problem and satisfies +the neutrino oscillation data simultaneously, even at the tree-level [72]. +– 3 – + +neutrino mass and the atmospheric mass-square difference [47, 48, 53]. We plan to inves- +tigate the possible correlations between the neutrino sector and the PT dynamics in the +context of NMSSM with more than one family of RH-neutrino superfields in a forthcoming +publication. +Restoring the discussion of PT dynamics, the electrically neutral uncoloured scalar +sector of the NMSSM extended with one RH-neutrino superfield set-up possesses fourteen +degrees of freedom, including the neutral Goldstone mode. However, as we will see later +in section 2, the effective degrees of freedom appear to be eight owing to weak couplings +of the LH-sneutrino states with the remaining states. Out of these eight, only four are +CP-even in nature and actively participate in the PT dynamics. Hence, the concerned field +space is four-dimensional for the chosen framework. This enhanced field space compared +to the MSSM (two-dimensional due to two Higgses) and the NMSSM (three-dimensional +owing to two Higgs doublets and one singlet), facilitates the study of EWPT, via single +steps and multi-steps. +In the numerical frontier, we adopt a benchmark-based analysis and finally select a +few benchmark points (BPs) that appear promising from the viewpoint of EWBG and +also exhibit distinct (single-step or two-steps) PT properties in the early Universe along +the various constituent field directions. +In the later part, we exploit some of the BPs +in order to further investigate the role of new parameters that appear in the setup due +to the presence of RH-neutrino superfield in the PT dynamics. We also consider various +relevant experimental constraints, e.g., collider, charged-lepton flavour violation, etc., while +choosing our BPs. In fact, null experimental evidence of sparticles to date has put stringent +lower bounds on the concerned states, especially the coloured ones [77–80]. Thus, for the +analysis of EWPT, we integrate such heavy states out and work in the context of a simplified +effective model rather than considering the full NMSSM + one RH-neutrino framework. +We have adopted both the critical and nucleation temperature analyses to describe the PT +properties in our model. This is crucial since earlier studies, e.g., Ref. [60], have reported +that the analysis of PT, solely based on critical temperature calculation does not provide +a complete picture. In fact, the critical temperature analysis does not confirm whether +a PT has indeed taken place or not. +A first-order phase transition (FOPT) proceeds +via bubble nucleation and hence computation of nucleation probability and subsequently, +nucleation temperature are vital to correctly describe the pattern of a FOPT. Finally, we +discuss the detection prospects of all our BPs in the forthcoming GW interferometers and +find that the future space-based experiments: namely, U-DECIGO and U-DECIGO-corr +[81, 82], have the required sensitivities to test a few of our BPs. This possibility gives +a complementary detection scope for the NMSSM + one RH-neutrino set-up beyond the +conventional experimental searches, e.g., collider, neutrino, flavour, etc. +The paper is organised as follows. In section 2 we discuss the model setup. Next in +section 3, we talk about the relevant model parameters that are important for studying +the PT properties and the possible experimental constraints. Subsequently in section 4, we +present the dynamics of EWPT in detail along with our numerical findings. This section +also addresses the production of the GW and the testability of our framework in upcoming +space-based interferometers, e.g., U-DECIGO. Finally, we summarize our analysis and +– 4 – + +conclude in section 5. Some useful formulae and relations are relegated to the appendices. +2 +The Model +The superpotential for the chosen framework is given by +W = W ′ +MSSM + λ �S �Hu · �Hd + κ +3 +�S3 + Y i +N � +N �Li · �Hu + λN +2 +�S � +N � +N, +(2.1) +where i = 1, 2, 3 denotes the generation indices. Eq.(2.1) is nothing but the Z3 symmet- +ric NMSSM superpotential, extended with one Right-Handed Neutrino (RHN) superfield +( ˆN), keeping the initial Z3 symmetry unbroken. Here W ′ +MSSM denotes the MSSM super- +potential (see reviews [27, 83–85]) without the bilinear µ-term, ˆHu = ( ˆH+ +u , ˆH0 +u)T , ˆHd = +( ˆH0 +d, ˆH− +d )T , ˆLi = (ˆνi, ˆli)T are the SU(2)L doublet up-type Higgs, down-type Higgs, and +lepton superfields, respectively and the “·” notation is used to express SU(2) product, e.g., +ˆLi · ˆHu = ˆνi ˆH0 +u − ˆli ˆH+ +u . The superpotential in Eq. (2.1) cannot be made invariant under +a global U(1) symmetry, e.g., U(1) of the Lepton number. This in turn ensures the disap- +pearance of a Nambu-Goldstone boson which results from the spontaneous breaking of a +global symmetry. The ˆN is considered to be odd under RP while the ˆS transforms as even. +RP is violated spontaneously in this model when, along with the other neutral scalars, the +RH-sneutrino ( � +N) also acquires a non-zero VEV. These VEVs yield the effective µ-term +(µ = λ⟨S⟩), the effective bilinear RP -violating couplings (ϵi = Y i +N⟨ � +N⟩), and the Majorana +mass term for the RHN (λN⟨S⟩). One should note the presence of four extra couplings +(three neutrino Yukawa couplings Y 1,2,3 +N +and another trilinear coupling λN) in Eq. (2.1), +apart from the known Z3 invariant NMSSM couplings, λ and κ (see for example Refs. +[54, 86]). +We would like to re-emphasize here that with only one ˆN, of course, one cannot +reproduce the observed neutrino mass squared differences and mixing [47, 48, 53], even after +including loop corrections [76]. However, even this simple choice can predict the absolute +mass scale and atmospheric mass squared difference for the active neutrinos, besides giving +interesting information about the EWPT and GW, the primary goals of this article. We +plan to explore the possible correlations between neutrino observable with the EWPT and +GW sectors in the context of a two or three ˆN scenario [69] in future work. +Following Eq. (2.1), in a similar way, we can write down Lsoft, the piece of Lagrangian +density that contains soft-SUSY breaking terms: +−Lsoft = −L′soft + m2 +S S∗S + M2 +N � +N∗ � +N + +� +λAλS Hu · Hd + h.c. +� ++ +�κAκ +3 S3 + (ANYN)i �Li · Hu � +N + AλN λN +2 +S � +N � +N + h.c. +� +, +(2.2) +where L′ +soft contains the MSSM soft-supersymmetry breaking terms, excluding the Bµ term +[27, 83–85, 87, 88]. The remaining terms are typical to that of the Z3 symmetric NMSSM, +except the terms involving � +N. Soft terms, as depicted in Eq. (2.2), are written in the +framework of supergravity mediated SUSY breaking [89]. All the trilinear A-terms and +the soft squared masses are assumed to lie in the TeV regime and consequently, all VEVs +– 5 – + +are expected to appear also in the same regime. In other words, the scale of RHN mass, +which is determined solely by the scale of soft-SUSY breaking terms will also lie in the +TeV regime assuming λN ∼ O(1). This assures neutrino mass generation via the TeV +scale seesaw mechanism which is also testable at colliders [90–95]. Further, the TeV scale +seesaw immediately suggests Y i +N ∼ O (10−6 − 10−7) and left-handed sneutrino VEVs, +⟨�νi⟩ ∼ O (10−4 − 10−5) GeV. These values of Y i +N, ⟨�νi⟩ indicate (i) tiny RP violation (∼ O +(10−3 − 10−4) GeV, typical for the bilinear RP violation [96]) and, (ii) weak mixing of the +left-handed leptons and sleptons (neutral and charged) with the concerned sectors, e.g., +charged and neutral gauginos, higgsinos, Higgses, right-handed neutrino and sneutrino, +etc. +One can use the advantage of such weak mixing to perform a simplified analysis +without the loss of generality, e.g., using a set of four fields (Hu, Hd, S, ˜N) instead of seven +(Hu, Hd, S, � +N, �Li) while investigating the PT phenomena. +The tree-level neutral scalar potential is the sum of F-term (VF ), D-term (VD) and +the soft-SUSY breaking terms and is given by +Vtree = VF + VD + Vsoft, +(2.3) +where Vsoft ≡ −Lsoft is given by Eq. (2.2). VF , following the usual prescription from Eq. +(2.1), is written as +VF += +��� − λH0 +uH0 +d + κS2 + λN +2 +� +N2��� +2 ++ |Y i +N|2 |H0 +u|2| � +N|2 + |λ|2|S|2|H0 +u|2 ++ +��� +3 +� +i=1 +Y i +N �νiH0 +u + λNS � +N +��� +2 ++ +��� +3 +� +i=1 +Y i +N �νi � +N − λSH0 +d +��� +2 +, +(2.4) +and VD, again using the standard procedure is read as +VD = g2 +1 + g2 +2 +8 +� +|H0 +d|2 + +3 +� +i=1 +|�νi|2 − |H0 +u|2 +�2 +, +(2.5) +with g1, g2 as the U(1)Y , SU(2)L gauge couplings, respectively. +The neutral CP-even scalar components4, after the EW-symmetry breaking (EWSB), +develop the following zero-temperature VEVs: +⟨H0 +u⟩ = vu, ⟨H0 +d⟩ = vd, ⟨S⟩ = vS, ⟨�νi⟩ = vi, ⟨ � +N⟩ = vN, +i = 1, 2, 3 +or +e, µ, τ. +(2.6) +The first three VEVs are typical to the NMSSM while the last two VEVs appear for the +chosen framework as a consequence of the spontaneous RP violation. One can use these +VEVs to trade off the concerned soft squared masses as depicted in Eq. (2.2). The VEVs +vS, vN, being governed by the TeV scale soft-terms, also lie in the same regime whereas vi +appears to be much smaller ∼ O(100 MeV) for vN, vS ∼ O(1 TeV) [74]. Generation of the +neutrino mass via a TeV scale seesaw mechanism, as already advocated, however, offers +4Here we adhere to CP-conservation. Further, we do not consider the possibility of charge and colour- +breaking minima for this study (see e.g., Ref. [97] in the context of the NMSSM) and hence, assign vanishing +VEVs to charged and coloured scalars. +– 6 – + +a more stringent constraint on vi (∼ O (10−4 − 10−5) GeV), similar to models studied +in Refs. [73, 98–101]. One can write down minimization conditions for vN, vi, using Eq. +(2.3), as: +∂Vtree +∂ � +N +��� +VEVs as Eq. (2.6) = λNvN +� +λvuvd + κv2 +S + λN +2 v2 +N +� ++ |Y i +N|2v2 +uvN ++λNvS +� +3 +� +i=1 +Y i +Nvivu + λNvSvN +� ++ +3 +� +i=1 +Y i +Nvi +� +3 +� +j=1 +Y j +NvjvN − λvSvd +� ++M2 +NvN + +3 +� +i=1 +(ANYN)ivivu + ANλNvSvN, +∂Vtree +∂ �νi +��� +VEVs as Eq. (2.6) = Y i +Nvu +� +3 +� +j=1 +Y j +Nvjvu + λNvSvN +� ++ Y i +NvN +� +3 +� +j=1 +Y j +NvjvN − λvSvd +� ++ +3 +� +j=1 +m2 +�Lijvj + (ANYN)ivuvN + g2 +1 + g2 +2 +4 +� +�v2 +d + +3 +� +j=1 +v2 +j − v2 +u +� +� vi, +(2.7) +where m2 +�Lij denotes soft-squared masses for sleptons [27, 83–85] and all the concerned +parameters are assumed to be real. It is apparent from Eq.(2.7) that if one neglects terms +like Y i +NY j +N, Y i +Nvi for smallness, then vS → 0 suggests vN → 0 and consequently vi → 0. +Thus, a non-zero vS is indirectly connected to a non-zero vi. The smallness of vi, compared +to vu, vd, also assures that one can still safely use the MSSM relations v2 = v2 +u + v2 +d and +tan β = vu/vd. +The presence of tiny but non-zero Y i +N, vi, as already stated, generates mixing between +left-handed neutrinos and neutral gauginos. These new mixing terms in the EW sector +enhance the size of neutral scalar, neutral pseudoscalar, charged scalar, neutral fermion and +charged fermion mass matrices. Being explicit, RP -violating mixing of H0 +u, H0 +d, S states +with � +N and three families of �νi, enlarges the NMSSM CP-even and CP-odd neutral scalar +mass matrices from 3 × 3 to 7 × 7. Similar augmentation appears (i) in the charged scalar +sector (2 × 2 in the NMSSM to 8 × 8 due to RP -violating mixing of H± +u , H∓ +d states with +the three families of left- and right-handed charged sleptons), (ii) in the neutral fermion +sector (5 × 5 in the NMSSM to 9 × 9 due to RP -violating mixing among neutral gauginos, +� +H0u, � +H0 +d, �S states with the right-handed neutrino and the three families of left-handed +neutrinos), and (iii) in the charged fermion sector (2×2 in the NMSSM to 5×5 due to RP - +violating mixing among the charged higgsino, gaugino states with the three families of the +left- and right-handed handed leptons). However, because of tiny values of Y i +N, vi, one can +easily decompose the aforesaid mass matrices in blocks for approximate analytical studies. +For example, for all practical purposes, the neutral scalar mass matrix can be decomposed +into two diagonal blocks: (i) a 4 × 4 one consisting of CP-even H0 +u, H0 +d, S, � +N states, (ii) +another 3 × 3 one consisting of CP-even left-handed sneutrino states, and off-diagonal +blocks containing tiny mixing terms between the two aforementioned states. A similar +observation holds true for the neutral pseudoscalar, charged scalar, neutralino and chargino +mass matrices, which can be effectively considered as having dimensions 3 × 3, 2 × 2, 6 × 6 +– 7 – + +and 2×2, respectively5, without any loss of generality, leaving the almost pure left-handed +CP-odd sneutrino, charged slepton, left-handed neutrino and charged leptons states aside. +For the purpose of analyzing the chosen model numerically, it is convenient to express the +aforesaid mass matrices in the extended Higgs basis [102–109] which will be introduced +subsequently. Entries of these mass matrices are detailed in appendix A, along with the +full uncoloured scalar potential. +2.1 +A convenient basis choice +We have already introduced the tree-level neutral scalar potential in Eq.(2.3), using Eqs.(2.2), +(2.4) and (2.5). However, to study the phenomena of PT we need to move beyond the tree- +level contribution. For this purpose, as we already mentioned, it is useful to work in the +extended Higgs basis [102–109], given as: +Hd = +� 1 +√ +2(cβHSM − sβHNSM) + +i +√ +2(−cβG0 + sβANSM) +−cβG− + sβH− +� +, +Hu = +� +sβG+ + cβH+ +1 +√ +2(sβHSM + cβHNSM) + +i +√ +2(sβG0 + cβANSM) +� +, +S = +1 +√ +2(HS + iAS), +� +N += +1 +√ +2(NR + i NI), +(2.8) +where cβ(sβ) = cos β(sin β) with tan β = vu/vd. +Note that one trades off the scalar, +the pseudoscalar and the charged components of the relevant four fields {Hu, Hd, S, � +N} +with the four neutral CP-even interaction states (HSM, HNSM, HS, NR), three CP-odd +interaction states (ANSM, AS, NI), one charged Higgs pairs (H±), along with the neutral +and charged Goldstone modes (G0, G±) in the extended Higgs basis. +This particular +basis choice assures the SM-like couplings between HSM with the up-type SM fermions, +the down-type SM fermions and the SM vector bosons. In addition, the aforementioned +basis choice also predicts vanishing couplings between HS, NR with the same aforesaid SM +states. Furthermore, from Eq. (2.8), in the light of Eq.(2.6) and v2 = v2 +u + v2 +d, one can +see that ⟨HSM⟩ = +√ +2v, ⟨HNSM⟩ = 0, ⟨HS⟩ = +√ +2vS and ⟨NR⟩ = +√ +2vN, i.e., non-vanishing +VEVs appear only in certain field directions leaving the SM-direction undisturbed. These +interaction states later mix to produce the mass eigenstates. However, one of the CP-even +states with a mass in the ballpark of 125 GeV (see Ref. +[110] and references therein) +contains the predominant HSM component. This alignment between the 125 GeV SM-like +Higgs in the mass basis and HSM of the extended Higgs basis implies negligible admixing +among various states in the extended Higgs basis. Mathematically, after the EWSB, in the +HSM, HNSM, HS, NR basis: +|M2 +S,1i| ≪ |M2 +S,ii − M2 +S,11|, +(2.9) +5One can easily identify the remaining three neutralinos and three chargions, lying at the bottom of the +mass spectrum, as three LH-neutrino dominated states and the charged leptons, e, µ, τ. +– 8 – + +where i = 2, 3, 4 and M2 +S,1i, the entries of the CP-even scalar squared mass matrix, are +given in appendix B. It is now apparent that in order to satisfy Eq.(2.9) one either needs +small M2 +S,1i or large |M2 +S,ii − M2 +S,11|, i.e., decoupling of HSM from the three remaining +states. The latter, in terms of the mass eigenstates, predicts three significantly heavier +states dominated by HNSM, HS, NR compositions, and one ∼ O(125 GeV) state controlled +by HSM composition. In reality, for the SFOEWPT, singlet-like states lighter than 125 +GeV are favoured. Besides, heavier singlet-dominated states create a kind of “push-down” +effect [71, 111] which makes it difficult to achieve an SM-like Higgs state around 125 GeV. +Thus, for our numerical studies, we consider regions of the parameter space that can +accommodate one or more singlet-like states lighter than 125 GeV. These light singlet- +dominated states are helpful in accommodating a 125 GeV SM-like Higgs through the +“push-up effect” [71, 111]. +One can use Eq.(2.9) subsequently to derive a few approximate relations, useful for +parameter space scanning. For example, using appendix B and assuming M2 +S,11 = m2 +h125, +the condition M2 +S,12 → 0, i.e., vanishing mixing between the HSM and HNSM states, implies +λ2 ≃ m2 +h125 − m2 +Z cos 2β +2v2 sin2 β +. +(2.10) +As mh125, mZ (mass of the SM Z0-boson), v are known, λ approximately appears to be a +function of tan β only. A similar relation like Eq.(2.10) holds also for the NMSSM [60]. +Applying the same procedure to minimize the mixing between HSM and HS states, i.e., +M2 +S,13 → 0, one gets +M2 +A ≃ +4µ2 +sin2 2β +� +1 − κ +2λsin 2β + λλNv2 +N +4µ2 +sin 2β +� +, +(2.11) +choosing M2 +A ≃ +2µ +sin 2β +� +Aλ + κµ +λ + λλNv2 +N +2µ +� +6. The last term in the Eq. (2.11) appears due +to mixing with the RH-sneutrino. In the limit of κ ≪ λ, using Eq. (2.11), it turns out that +M2 +A ≃ M2 +H ≃ M2 +H± ≃ 4µ2csc2 2β +� +1 + λλNv2 +N +4µ2 +sin 2β +� +where MH represents mass of a state +with dominant HNSM contribution. The presence of vN shows that these mass eigenstates +possess contributions from the RH-sneutrino. These kinds of mixing may appear sizable +depending on λN and vS values. +Adopting a similar analysis for M2 +S,14 → 0, i.e., effacing the mixing between HSM and +NR states, it is hardly possible to get a simple relation. A light state below 80 GeV with +dominant RH-sneutrino contribution hints for a sizable mixing between the HSM and NR +states. This effect, via one-loop, makes it easy to assure a 125 GeV SM-like Higgs, even +with stop mass below O(1 TeV) [112]. By choosing the parameters carefully, one can of +course consider a heavier stop mass to secure a 125 GeV SM-like Higgs having negligible +admixing with a lighter RH-sneutrino-dominated state. This is precisely what we have +done while scanning the parameter space since a lighter sneutrino, as also stated earlier, +is advantageous for SFOEWPT. We will discuss this aspect in detail later. We note in +6At the limit λN → 0, Eq. (2.11) reproduces the known NMSSM result [60]. If one further considers +κ → 0, Eq. (2.11) matches the well-known MSSM relation [27]. +– 9 – + +passing that so far we have discussed only the tree-level aspects of the scalar potential. +In reality, the scalar potential receives considerable contributions from radiative effects +involving various SM particles and their SUSY partners [54, 113–115]. +Some of these +higher-order contributions have observable consequences, e.g., effects of the top and stop +loops to procure a 125 GeV SM-like Higgs. +2.2 +Higher order contributions +It is relevant to investigate various sources critically before implementing higher-order ef- +fects arising from the different SM and BSM states on the tree-level scalar potential. The +effect of higher-order contributions, especially via SUSY partners, is crucial for yielding the +observed SM mass spectrum, e.g., the Higgs mass. These effects, however, are diluted for +the analysis of EWPT. Hence, we concentrate only on the leading one-loop effects which +can arise from various SM and BSM sources. +Regarding the latter, one needs to con- +sider the following facts: (i) BSM Higgs masses, i.e., states with dominant HNSM, HS, NR, +ANSM, AS and NI components, must not remain very far from the EW scale for a suc- +cessful SFOEWPT and, (ii) hitherto unseen experimental evidence of SUSY searches have +set lower limits on sparticle masses. These limits are stringent for the coloured sector, +e.g., gluinos and squarks, >∼ O (1 TeV) (see, for example, the latest CMS [77–79, 116] +and ATLAS [80, 117–119] limits). On the other hand, for the uncoloured sparticles, e.g., +sleptons, LH-sneutrinos, etc, experimental lower bounds are rather flexible [120–122]. For +convenience, however, we consider heavy sleptons and LH-sneutrinos, >∼ O (1 TeV), for +this study7. A careful range of relevant parameters was considered so that even with these +heavy sleptons one can satisfy the latest result on the anomalous magnetic moment of +muon [123] which typically favours the aforesaid states to be lighter than a TeV. +With the above mentioned facts and assumptions, one ends up with a situation where +one encounters >∼ O (1 TeV) sleptons, LH-sneutrinos, squarks & gluinos together with +other BSM states, e.g., scalar and pseudoscalar Higgses, neutralinos, and charginos, in the +ballpark of the EW scale. Clearly, now one can integrate out these >∼ O (1 TeV) states +to yield an effective theory with BSM scalar, pseudoscalar, charged Higgses, neutralinos, +charginos and, of course, the SM particles. Here we would like to point out again that +the neutralino and the chargino sector for the concerned model are enhanced compared +to the NMSSM, owing to the presence of Y i +N in the superpotential (see Eq. (2.1)) and +non-zero LH-sneutrino VEVs (see Eq. (2.6)). However, these parameters are compelled to +remain tiny (∼ O (10−6 − 10−7) and ∼ O (10−4 − 10−5) GeV), thanks to the constraints +arising from the neutrino experiments and the assumption of a TeV scale seesaw. A similar +observation, as already stated, also holds true for the BSM Higgs sector. In summary, the +effective number of contributing states are four CP-even Higgses (S0 +i ), three CP-odd Higgses +(P 0 +i ), two charged Higgses (H±), six neutralinos (�χ0 +i ), two charginos (�χ± +i ), charged and the +neutral Goldstone bosons (G±, G0), and, the relevant SM particles (t, W ±, Z0)8. This +7Unlike the coloured sector, >∼ O (1 TeV) sleptons and sneutrinos do not introduce large higher-order +corrections to the scalar sector owing to small values of the concerned lepton Yukawa couplings. +8Contributions from the remaining SM fermions are sub-leading due to the sizes of concerned Yukawa +couplings. +– 10 – + +set of nineteen particles including the two Goldstone bosons, together with the t, W ±, Z0, +will be considered as the dynamical degrees of freedom needed for the current study. One +can derive parameters of the aforesaid effective theory through the renormalization group +equation and subsequently, by matching onto the complete model at some intermediate +scale Λ which we fixed at mt, the top mass. The leading contribution to the tree-level +potential Vtree obtained using this procedure is +∆V = ∆λ2 +2 |Hu|4, +(2.12) +where ∆λ2 at one-loop level is given by [124–127], +∆λ2 = +3 +8π2 y4 +t +� +log +� +M2 +�t +m2 +t +� ++ A2 +t +M2 +�t +� +1 − +A2 +t +12M2 +�t +�� +. +(2.13) +Here yt is the top Yukawa coupling evaluated using the running top quark mass, M�t = +√m�t1m�t2 depicts the geometric mean of two stop masses and At is the soft trilinear coupling +between Higgs and stops (appears within L′ +soft of Eq. (2.2) [27]). One can of course write +down contributions like the one shown in Eq. (2.12) for other scalar states, e.g., Hd. Such +a term, however, appears due to mixing between Hu and Hd through the effective µ-term +and is usually sub-leading compared to the one shown in Eq. (2.12), as long as µ ≪ M�t +9 +and tan β value appears not too large. The quantity ∆λ2 is crucial to accommodate a 125 +GeV SM-like Higgs and can be estimated using the same. +The leftover degrees of freedom also contribute to the potential (see Eq. (2.3)) through +radiative corrections. Their collective contributions are given by Coleman-Weinberg po- +tential [129] +V 1−loop +CW += +1 +64π2 +� +i=B,F +(−1)Finim4 +i (φα) +� +log +�m2 +i (φα) +Λ2 +� +− Ci +� +, +(2.14) +where i = B (F), i.e., bosons (fermions), ni represents the relevant degrees of freedom, +FB = 0 (FF = 1), Ci is a constant with a value of 3/2 (1/2) for scalars, fermions, longitu- +dinally polarized vector bosons (transversely polarized vector bosons), Λ is the aforesaid +intermediate energy scale, fixed at mt and, m2 +i (φα) = m2 +i (HSM, HNSM, HS, NR) denotes +field-dependent masses. The latter is estimated from Vtree + ∆V (see Eq. (2.3) and Eq. +(2.12)). Contributions from Vtree are detailed in appendix A. The set of involved Bs are +given by S0 +1,..,4, P 0 +1,2,3, H±, G0, G±, Z0, W ± with nB = 4×1, 3×1, 2, 1, 2, 3, 2×3, depend- +ing on the nature of the concerned state, i.e., scalar or complex scalar or massless bosons +or massive vector bosons. A similar approach for the fermions give F = �χ0 +1,..,9, �χ± +4,5, t with +nB = 9 × 2, 2 × 2, 3 × 4 considering their electric and colour charges. One should note +that the presence of G0, G± in the Coleman-Weinberg potential yields divergent contribu- +tions. However, these can be effaced by using an infrared regulator. Finally, putting all +9Such a choice helps one parameterize radiative contributions from stops effectively, even beyond the +one-loop order [125, 127, 128]. +– 11 – + +these pieces, i.e., Vtree (see Eq. (2.3)), ∆V (see Eq. (2.12)) and V 1−loop +CW +(see Eq. (2.14)) +together, one obtains the effective scalar potential as +Veff = Vtree + V 1−loop +CW ++ ∆V. +(2.15) +Inclusion of Coleman-Weinberg contributions (see Eq. (2.15)) to the tree-level scalar poten- +tial, however, changes the position of physical minima and masses. To restore the original +position for the physical minima, keeping M2 +S,13, M2 +S,14 → 0 and maintaining the mass of +the CP-even scalar state with leading HSM composition at 125 GeV, one needs to intro- +duce appropriate counterterms, encapsulated within another contributor Vct. The latter is +normally related to a redefinition of the entries of −Lsoft (see Eq. (2.2)) [130–132] which +are depicted in appendix C. The counterterms are, thus, not arbitrary but fixed by the +aforesaid criteria. Mathematically, +∂ +∂φi +� +Veff + Vct +���� +φi=⟨φi⟩ = 0 and +∂2 +∂φi∂φj +� +Veff + Vct +���� +φi=⟨φj⟩ = 0, +(2.16) +with φi = {HSM, HNSM, HS, NR}. One can figure out ⟨φi⟩ using Eq. (2.6) and Eq. (2.8). +We note in passing that till now we have discussed modifications of the tree-level scalar +potential from higher order effects at vanishing temperature, i.e., T = 0. In reality, however, +one also needs to include contributions arising from T ̸= 0 which we will address now. +2.3 +Contributions from non-zero temperature +The one-loop temperature-dependent potential is given by [133] +V 1−loop +T̸=0 += T 4 +2π2 +� +i=B,F +(−1)FiniJB/F +�m2 +i (φα, T) +T 2 +� +, +(2.17) +where T represents the temperature, symbols FF,B, nF,B are the same as discussed in the +context of Eq. (2.14), m2 +i (φα, T) depicts thermal field-dependent masses of the ith degrees +of freedom as: +m2 +i (φα, T) = m2 +i (φα) + ciT 2, +(2.18) +with ci representing the concerned Daisy coefficients [133–137]. These coefficients appear +non-vanishing for bosons and are given in appendix D. Finally, JB/F , i.e., the thermal +function, is defined as +JB/F +� +x2 ≡ m2 +i (φα, T) +T 2 +� += ± +� ∞ +0 +dy y2 log +� +1 ∓ e−√ +x2+y2� +, +(2.19) +where + (−) sign is for bosons (fermions). One should note that at the m2 ≫ T 2 limit, +where “m” depicts a generic mass term, JB/F suffers an exponential suppression from +Boltzmann factor. These repressions ensure that massive degrees of freedom, e.g., squarks, +gluinos, etc., that are already integrated out (see subsection 2.2), do not affect T ̸= 0 +corrections. +– 12 – + +Clubbing all the pieces together, i.e., tree-level scalar potential, one-loop contributions +via Coleman-Weinberg potential, and contributions from the finite temperature part, one +gets the finite temperature effective scalar potential at the one-loop order as +VT = Vtree + ∆V + V ′1−loop +CW ++ Vct + V 1−loop +T̸=0 +≡ VT (φ, T), +(2.20) +where V ′1−loop +CW +has a form similar to Eq. (2.14) but replacing m2 +i (φα) with thermal masses +m2 +i (φα, T), as depicted in Eq. (2.18). We will use Eq. (2.20) to inquire about the PT +properties. We note in passing that the components of VT have explicit gauge dependence +[138–140]. Besides, V 1−loop +CW +(see Eq. (2.14)), and hence V ′1−loop +CW +, also has renormalization +scale (Λ) dependence which could dominate over the gauge dependence [141]. To note, +we have worked in the Landau gauge while computing the one-loop corrected potential at +both zero and non-zero temperatures. +So far we have discussed different pieces of the scalar potential needed to study the +PT dynamics. Now we will address how and to which extent various model parameters +can affect the same. +3 +Choice of parameters +The set of new parameters, compared to the NMSSM, are +Y i +N, λN, vN, (ANYN)i, AλN λN, +(3.1) +using Eq. (2.1), Eq. (2.3), Eq. (2.6), and replacing soft-SUSY breaking square mass term +M2 +N with the corresponding VEV. Now, as already discussed, Y i +Ns are associated with the +neutrino mass generation through a TeV scale seesaw and thus, are constrained to be small. +These Y i +N values, for TeV-scale trilinear terms, predicts (ANYN)i ∼ O (10−3 − 10−4) GeV. +The latter is also related to the smallness of vi, i.e, the LH-sneutrino VEVs (see Eq. (2.6)), +as guided by a TeV scale seesaw mechanism and neutrino data. Hence, for the PT analysis, +we can neglect these tiny parameters, i.e., vi, Y i +N, (ANYN)i, without any loss of generality +as they have negligible effects on the PT dynamics. Now from the discussion of section +2, it is evident that relevant “bare” parameters for the uncoloured scalar potential after +trading (see appendix E for details) soft-squared masses with the corresponding VEVs (see +Eq. (2.6)) are, +λ, λN, κ, vu, vd, vS, vN, Aλ, Aκ, AλN . +(3.2) +One can redefine this list further by trading vu, vd with v = +� +v2u + v2 +d, tan β = vu/vd and +vS with µ = λvS. As v = 174 GeV is known, Eq.(3.2) can be re-casted as +λ, λN, κ, tan β, µ, vN, Aλ, Aκ, AλN . +(3.3) +One can also trade parameter vN with the RH-neutrino mass term MN ∝ λNvN. Similar +trading is also possible for Aλ with MA, using a relation given in subsection 2.1. We, +however, do not use MA, MN for the parameter space scanning. Parameter λ can also +be exchanged using Eq.(2.10). +The same parameter can also be constrained using an +– 13 – + +upper-bound on the tree-level SM-like Higgs mass [54, 142, 143], given as m2 +Z(cos2 2β + +g−2 +2 λ2 sin2 2β). This helps us to consider small tan β ≲ 5 and λ ∼ O(0.1) or higher such +that one gets a significant contribution to the tree-level SM-like Higgs mass10. +The ranges of other parameters are also guided by certain aspects, e.g., in order to +avoid the presence of Landau pole [144, 145] below the GUT scale, i.e., 1016 GeV, one +needs to consider λ, κ values carefully at the EW scale such that +√ +λ2 + κ2 <∼ 0.7 [54]. +Besides, smaller values of κ ∼ O(10−2) are favoured as a stronger PT along a particular +field direction prefers smaller values of the quartic coupling (e.g., κ for PT along the +HS direction) and larger values of the cubic coupling (e.g., Aκ for a PT along the HS +direction), leading to an enhanced barrier height along that specific direction. A small +value of κ, together with a small Aκ value11, as already discussed in subsection 2.1, assure +the presence of light CP-even and CP-odd states below 125 GeV. These light states help +to procure a 125 GeV SM-like Higgs via the “push-up” [71, 111] effect. It is evident that +one needs to consider Aκ values carefully as for this parameter larger values are favourable +for the PT dynamics while smaller ones are useful in fixing the SM-like Higgs mass around +125 GeV. Tree-level mass of the singlet-dominated CP-even state, using Eq.(3.3) and Eq. +(B.1), is +M2 +S,33 ≡ m2 +HS = −λλNAλN v2 +N +2µ ++ κAκµ +λ ++ 4κ2µ2 +λ2 ++ λ2v2Aλ sin 2β +µ +. +(3.4) +This reduces to the known NMSSM result [143] at the limit λN → 0 with a O(λ2) correc- +tion12. It is apparent from Eq. (3.4) that how different parameters appear instrumental +in determining the mass of a CP-even singlet-dominated state in this framework. We con- +sider κ > 0, Ak < 0 in this study to ensure the formation of a barrier along the HS field +direction. The parameter µ plays a vital role in the PT dynamics and, as given in Eq. +(3.4), is also crucial for the mass and composition of a singlet-like state. Ref. [59] suggests +that a strong EWPT favours µ ≲ 300 GeV for the Z3 invariant NMSSM. We consider +similar ranges for µ in our analysis which also obey the “naturalness” criteria and the LEP +chargino bound [148–151], i.e., |µ| >∼ 103.5 GeV. This range of µ values, together with the +choice of λ ∼ O(0.1), suggests a value for vS not too far from the EW scale as required to +yield a sizable impact on the EWPT from the singlet sector. A similar observation holds +true for the RH-sneutrino VEV vN. The parameter vS also determines the mass term for +RH-neutrino, i.e., ∝ λNvS which is constrained to be around a TeV as non-zero neutrino +masses in the chosen framework arise through a TeV scale seesaw. The adaptation of a +TeV scale seesaw also put some bounds on the parameter λN that is expected to be at +most O(1) to avoid the existence of Landau pole below the GUT scale. The requirement +of having stronger PT along the NR field direction, however, suggests smaller values of +λN. This behaviour, is similar to κ, as addressed before. The role played by λN in the +10Lower λ values suggest reduced tree-level mass and hence, needs larger corrections from the stop sector. +In the NMSSM, considering the perturbative nature of λ up to the scale of the Grand Unified Theory (GUT) +one gets λ ≲ 0.7, in the limit of κ ≪ λ [54]. +11These ranges of κ, Aκ are guided by the well-known U(1)PQ, U(1)R limits [143, 146, 147] for the +NMSSM. +12This term appear to be sub-leading for small λ, tan β values together with vS ≪ v. +– 14 – + +PT dynamics is somewhat non-trivial and will be addressed later in detail. The remaining +parameters, Aλ, AλN are connected to the scale of vS, vN and thus, are expected to be in +the ballpark of a TeV. These parameters, i.e., Aλ, AλN also affect tree-level masses of the +CP-even and CP-odd scalar states as detailed in appendix B. In this analysis we consider +Aλ > 0 and AλN < 0. The latter choice helps to efface the possible existence of a tachyonic +state in the CP-odd scalar sector (see Eq. (B.2)). We note in passing that so far we have +presented a qualitative discussion in the context of the chosen independent parameters, +as depicted in Eq. (3.3). For finding BPs through numerical analysis, one, however, also +needs to consider all the relevant present and anticipated experimental bounds which we +will address in the next subsection. +3.1 +Experimental Constraints +A viable phenomenological analysis must satisfy all the concerned experimental limits, the +existing and the projected ones. The inclusion of these bounds reduces the size of the +available parameter space. In this analysis, apart from considering sensitivity reaches of +the existing [152–154] and upcoming [81, 155, 156] GW detection setups, we also consid- +ered constraints arising from (i) analysis of the SM-like Higgs boson properties and BSM +Higgs searches at colliders, (ii) other BSM searches at the colliders, (iii) flavour-violating +processes, (iv) neutrino experiments, (v) muon anomalous magnetic moment, etc. In order +to employ these constraints in our numerical analysis, we first implemented the concerned +model in SARAH 4.14.5 [157–164]. Subsequently, we use SPheno-4.0.5 [158, 162, 164–171] +to get the mass spectrum and decay widths. The output of SPheno-4.0.5 also provides +branching fractions for various flavour-violating processes, BSM contributions to the muon +anomalous magnetic moment [166], several LHC observables like reduced Higgs couplings, +etc. We will now discuss the aforesaid constraints one by one in further detail. +(i) Analysis of the SM-like Higgs boson properties and BSM Higgs searches at colliders: +Here one needs to consider two aspects: (a) SM-like Higgs analyses, and (b) the BSM Higgs +searches. Concerning the first, important constraints appear from the measured mass, i.e., +≈ 125 GeV [42, 172], and couplings [39–42, 173–177]. We have used these results to assure +the existence of an SM-like 125 GeV Higgs in our analysis. Besides, to assure the SM- +like nature we also put a lower limit (80%) on the Hu composition of the 125 GeV mass +eigenstate. +Regarding the BSM Higgs searches, i.e., for states with leading HNSM, HS +components, and the charged Higgs, we consider the concerned experimental bounds, see +for example Ref. [178] and references therein. We used HiggsBounds [179] 5.10.2 [180] to +implement experimental constraints from the SM and BSM Higgs searches in our numerical +study. +(ii) Other BSM searches at the colliders: We already discussed in subsection 2.2 that +we are working in an effective framework after integrating out heavy degrees of freedom like +gluinos, squarks and even charged sleptons and LH-sneutrinos. We consider these states +to remain heavier than 1 TeV. Such assumptions, especially for gluinos and squarks are +supported by the experimental findings. In this study, we consider gluino mass >∼ 1.8 TeV +and squark masses >∼ 1.2 TeV. These choices are guided by the present CMS [77–79, 116] +and ATLAS [80, 117–119] observations. Experimental lower bounds on the charged slepton +– 15 – + +and LH-sneutrino masses are somewhat less [120–122]. However, we also considered them +to be heavier than a TeV and integrate them out. In our numerical study, the lightest +neutralino mass varies from 3 GeV to 120 GeV. However, this does not contradict any +experimental bounds, e.g., SM-like Higgs decaying to a pair of neutralinos, (see for example +Refs. [80, 121, 181–184]) as its predominant composition (≳ 90%) is from the singlino and +the RH-neutrino. For charginos, we used a lower bound of 103.5 GeV [148–151] in our +analysis. It is important to note that experimental lower bounds are often interpreted in +the context of simplified models and hence, they may not directly restrict the concerned +model parameter space. +(iii) Flavour-violating processes: The presence of BSM states can significantly enhance +branching fractions (BR) of certain flavour-violating processes, e.g., B → Xsγ, B0 +s → µ+µ− +(see Refs. [185–191] and references therein), etc., compared to the SM predictions. One can +minimize these new contributions by taking tan β <∼ 5 and fixing squarks, gluinos, sleptons, +etc., masses to be heavier than a TeV. However, finite BSM contributions to these pro- +cesses still appear through the EW scale uncoloured neutral scalars, neutral pseudoscalars, +charged scalars, charginos and neutralinos, as required for the EWPT. Thus, we consider +the following 2σ bounds +BR(B → Xsγ) = (3.49 ± 0.38) × 10−4, +BR(B0 +s → µ+µ−) = (3.45 ± 0.58) × 10−9. +(3.5) +We note in passing that BR(B → Xsγ), BR(B0 +s → µ+µ−) also receive extra contributions +due to R-parity breaking [192, 193]. However, given the framework of a TeV scale seesaw, +the size of R-parity violating couplings, i.e., Y i +NvN, appears to be ∼ O(10−3 − 10−4) GeV +and hence, hardly yield any significant contributions. +We consider charged Yukawa couplings to be diagonal for this work which helps to +bypass constraints from the flavour-violating Higgs decays [194, 195]. One can also con- +sider slepton soft squared masses to be diagonal to minimize mixing among sleptons (both +charged and neutral). With these choices, the effective bilinear R-parity violating cou- +plings, i.e., Y i +NvN, and the LH-sneutrino VEVs appear to be main sources for the various +charged lepton flavour violating (cLFV) processes like µ → eγ, µ → eee, etc. However, the +scale of these couplings, i.e., ∼ O(10−3 − 10−4) GeV, as required for a TeV scale seesaw, +can easily evade these bounds. This behaviour is very similar to the SUSY models with +bilinear R-parity violation [196–198]. We note in passing that in our numerical studies +we emphasized on the cLFV processes for the µ over the similar ones from τ as the con- +cerned existing and upcoming experimental sensitivities are much more stringent for µ. +Nevertheless, we also include constraints for cLFV processes involving a τ in our analysis, +e.g., BR(τ → µγ) < 4.4 × 10−8 [199]. The µ-based cLFV bounds included in the current +analysis are given by +BR(µ → eγ) < 4.2 × 10−13 [200], +BR(µ → eee) < 1.0 × 10−12 [201], +CR(µN → eN∗) < 7 × 10−13 [202], +– 16 – + +where CR(µN → eN∗) represents muon to electron conversion ratio in atomic nuclei with +N (N∗) representing the nucleus in the normal (excited) state. The given number, i.e., +7 × 10−13 is for the gold nuclei. +(iv) Neutrino experiments: With one generation of RH-neutrino, as already stated in +section 2, it is not possible to accommodate the experimentally observed three-flavour neu- +trino masses and mixing [47, 48, 53], even with the inclusion of loop effects [76]. Thus, one +will get one massive and two nearly massless neutrinos in this model. Nevertheless, even in +such a scenario, we used constraints from the atmospheric mass squared difference ∆m2 +atm, +i.e., 2.430(−2.574) × 10−3 − 2.593(−2.410) × 10−3 eV2 for normal (inverted) hierarchy, and +the sum of three neutrino masses ≲ 1.2 eV [1, 203]. +(v) Muon anomalous magnetic moment: Just like the flavour violating processes, the +anomalous magnetic moment of muon also receives extra contributions over the SM from +new parameters and the BSM states (see Refs. [204, 205] and references therein). +The +recent comprehensive SM prediction of the muon anomaly is 116591810 (43) × 10−11 (0.37 +ppm) [206] while the experimental average13 is 116592061(41) × 10−11 (0.35 ppm). These +numbers, adding errors in quadrature, gives ∆aµ = (251±59)×10−11 which is arising from +the BSM sources. This, in 4σ span, gives (1.5 − 48.7) × 10−10. The BSM contributions, +especially involving charged sleptons states below a TeV [208–210], can affect this process +significantly and can easily accommodate the latest experimental observation [123]. In our +analysis, as already discussed in subsection 2.2, we kept charged slepton masses around a +TeV. Nevertheless, by playing with the other concerned parameters we checked that the +aforesaid ∆aµ range, i.e., (1.5 − 48.7) × 10−10 is not violated in our BPs. In fact, the +choice of slepton, squark masses around a TeV or more yields suppressed cLFV processes +and smaller BSM contributions to the anomalous magnetic moment of the muon. All the +chosen BPs respect all the five aforesaid classes of constraints. We now discuss this study’s +key objectives in detail, i.e., PT properties and GW production. +4 +The EWPT and its Properties +As we already discussed, understanding the EWPT properties in the early Universe in +a Particle Physics model has twofold advantages. Firstly, it can be confirmed whether +the model carries the prospect to explain the origin of EWBG at some corner of the +parameter space. Secondly, it provides scope to test the model at GW detectors beyond +the conventional BSM searches. One of the prerequisites of EWBG is the FOPT with +sufficient strength along the SU(2)L field directions so that it can suppress the processes +which wash out the baryon asymmetry after it is produced, namely SU(2)L sphalerons [2]. +The same FOPT may yield a detectable amount of GWs that could be accessible by future +GW interferometers. +The structure of the thermal effective potential for a PT reveals that at very high +temperatures the Universe would be in a symmetric phase with the relevant field (say φi) +being located at zero. As the Universe cools down, the symmetric vacuum may disappear +13Here we have used combined experimental average obtained from the FNAL [123] and the BNL E821 +[207] results. +– 17 – + +and the corresponding field values could be finite. Additionally, a second minimum can +be formed at some higher field value which becomes degenerate with the previous one at +T = Tc, known as critical temperature. At temperature below Tc, the transition from the +high-T VEVs (say v′ +X) to the low-T VEVs (say vX) can take place. Here X = u, d, S, i, N +as depicted in Eq. (2.6). We should note here that a high-T (low-T) phase means an +unstable (stable) vacuum below Tc or above nucleation temperature. Therefore, to have +an in-depth understanding of PT dynamics, an estimate of critical temperature Tc and the +strength of PT are enormously important. +Theoretically, the critical temperature can be obtained from the following equality: +VT (v′ +X, Tc) = VT (vX, Tc), +(4.1) +where v′ +X and vX represent high-T and low-T VEVs, respectively, along a particular field +direction. We also need to ensure the existence of high- and low-T vacua which can be +confirmed by the following equalities, +∂φαVT (v′ +X, Tc) = 0, ∂φαVT (vX, Tc) = 0, +(4.2) +where φα = {HSM, HNSM, HS, NR}. In many cases, including ours, analytical solutions of +Eq. (4.1) and Eq. (4.2) are almost impossible to derive in order to obtain the estimates of +the relevant parameters to study the PT properties. We have used the publicly available +package cosmoTransitions [211] to carry out the numerical calculation for our model in +consideration. +A FOPT proceeds via bubble nucleation and the nucleation rate (Γ) per unit volume +(V ) at finite temperature is given by Γ +V ∝ T 4e−SE/T , where SE is the three-dimensional +effective Euclidean action known as bounce action. The criterion which set the condition +for the onset of bubble nucleation is given by [16, 212], +SE(Tn) +Tn +≃ 140, +(4.3) +where Tn is the nucleation temperature. If it happens that the quantity SE(Tn) +Tn +> 140, then +the transition does not occur due to low tunnelling probability. +As mentioned earlier, we use cosmoTransitions [211] to compute SE and Tn, which +also allows for estimating the probability of a transition taking place. Since we have four- +dimensional field space, relevant to EWPT, a detailed scan of the model parameter space +is challenging and numerically expensive as well. Therefore in the present work, we first +provide a representative BP-based study which will be detailed subsequently. We will see +that such BPs are sufficient to understand the parameter space of NMSSM + one RHN +framework that can potentially give rise to an SFOPT and can also be interesting from +the viewpoint of EWBG. Subsequently, we discuss the impact of new parameters in the +present setup compared to the NMSSM on PT strength along different field directions by +providing a scan of the relevant parameter spaces. +Before we proceed further, let us now define different criteria to consider a PT to be a +strong one. Conventionally, in the critical temperature analysis, the order parameter that +– 18 – + +decides the fate of PT is given by, +γc ≡ vc(Tc) +Tc += +� +⟨HSM⟩2 + ⟨HNSM⟩2 +Tc +≳ 1.0, +(4.4) +where vc(Tc) denotes VEVs of the SU(2)L Higgs fields, i.e., HSM, HNSM, at Tc. For the nu- +cleation temperature calculation, we define an SFOPT along the respective field directions +as follows: +• Along SU(2)L doublet Higgs direction: +∆φSU(2) +Tn += +� +( +� +HlT +SM +� +− +� +HhT +SM +� +)2 + ( +� +HlT +NSM +� +− +� +HhT +NSM +� +)2 +Tn +≳ 1.0 +(4.5) +• Along the SU(2)L singlet Higgs and the RH-sneutrino direction: +∆φS +Tn += +� +( +� +HlT +S +� +− +� +HhT +S +� +)2 +Tn +≳ 1.0 ; +∆φ � +N +Tn += +� +( +� +NlT +R +� +− +� +NhT +R +� +)2 +Tn +≳ 1.0, +(4.6) +where +∆φSU(2) +Tn +, ∆φS +Tn +and +∆φ � +N +Tn +represent PT strength along the SU(2)L-doublet, SU(2)L- +singlet and the RH-sneutrino field direction, respectively. The notation, +� +ΦlT� +denotes the +low temperature minimum while +� +ΦhT� +is the high temperature minimum of a scalar field +(Φ) before nucleation. A favourable condition to yield the observed baryon asymmetry +of the Universe via the EWBG is ( +� +HhT +SM +� +, +� +HhT +NSM +� +) = (0, 0) with +∆φSU(2) +Tn +≳ 1. In con- +trast, when ( +� +HhT +SM +� +, +� +HhT +NSM +� +) ̸= (0, 0), the sphaleron processes outside the bubble gets +substantially suppressed which lead to inefficient production of the baryon asymmetry of +the Universe from the EWBG. +4.1 +PT in the NMSSM + one RHN model +As we already specified, the field space relevant to the PT analysis is four-dimensional in +the present framework. This opens up the possibility of obtaining a richer PT pattern +compared to the case of the NMSSM. We define the high-temperature symmetric vacuum +of the scalar potential as Ω0. In principle, one can have many distinct PT patterns in the +whole parameter region of the NMSSM + one RHN framework. Here we summarise a few +such possibilities that advocate some unique PT patterns along the various field directions: +• Type-I: As already stated, at T ≫ Tc, the Universe remains in the symmetric phase +where each of the four fields has zero VEV. The simplest possibility for a PT is that +at critical temperature the symmetry-breaking minimum of the total scalar potential +appears only along the HSM direction. Then the PT happens from symmetric to the +broken phase directly in that direction. We denote this by Ω0 +PT +−−→ ΩHSM where ΩHSM +represents the vacuum along SM Higgs direction. +• Type-IIa: This pattern involves displacement of the HS field VEV (at T > Tc) from +the initial zero value as the Universe cools down. We label it as Type II. Below Tc, +the PT occurs along both the HSM and HS field directions. We denote this particular +pattern (IIa) as Ω0 → Ω′ +HS +PT +−−→ ΩHSM + ΩHS. +– 19 – + +• Type-IIb: This is similar to the earlier case where for T > Tc, a shift of the HS field +value from zero vacuum appears. Below the critical temperature, the transition also +takes place along the HS direction only and is represented by Ω0 → Ω′ +HS +PT +−−→ ΩHS. +• Type-IIc: This case also falls under the Type II category. However, below critical +temperature, the PT happens along both HS and NR field directions as indicated by +Ω0 → Ω′ +HS +PT +−−→ ΩHS + ΩNR. +• Type-IIIa: In this category, for T > Tc, the shifts of HSM and HS VEVs from the +initial zero values take place. When T < Tc, PT also occurs along the same field +directions. This pattern is represented by Ω0 → Ω′ +HSM + Ω′ +HS +PT +−−→ ΩHSM+ΩHS. +• Type-IIIb: In this category, at T > Tc, the behaviour of the scalar potential is +similar to the last one. However, at T < Tc, the PT occurs along HSM, HS and NR +directions as indicated by Ω0 → Ω′ +HSM + Ω′ +HS +PT +−−→ ΩHSM +ΩHS+ΩNR. +• Type-IV: This category is defined to indicate a particular PT pattern where at a +T > Tc, the symmetric vacuum of the total scalar potential gets displaced along +the S and NR field directions. The PT occurs below Tc along any of the four field +directions. +As described earlier, any BP showing either of the type-I or type-IIa PT pattern is +preferred in view of efficient EWBG, provided the corresponding PT strength satisfies the +condition +∆φSU(2) +Tn +≳ 1. Whereas, the rest of the types as listed above may not lead to +EWBG due to non-satisfaction of either of the conditions, +�� +HhT +SM +� +, +� +HhT +NSM +�� +̸= (0, 0) or +∆φSU(2) +Tn +≳ 1. The PT types that do not favour EWBG, can be still interesting if it triggers +an SFOPT along the SU(2)L doublet or singlet field directions and subsequently radiates +GW at a detectable amount. +4.2 +Numerical Results +As earlier mentioned, we would like to begin with a benchmark-based study of EWPT in +the present work. In the later part, we will be discussing explicitly the dependence of new +parameters in the current setup compared to the NMSSM. We first tabulate six BPs in +Table 1 that are consistent with all relevant theoretical and experimental constraints, as +discussed in subsection 3.1. We select the BPs in such a way that they show distinct PT +characteristics with some of them favouring EWBG and carrying good to moderate detec- +tion prospects at GW detectors. Note that we have four soft-SUSY breaking parameters +(i.e., Aλ, Aκ, AλN , AN) in our model. We discuss the possible role of all the A− parameters +in section 3. Recall that one of the soft parameters AN does not contribute much to the +PT dynamics since it is always associated with the tiny neutrino Yukawa coupling Y i +N as +earlier clarified. We keep AN above the TeV scale for all BPs, which ensures slepton masses +≳ O(1 TeV). In Table 1, we provide the eigenvalues of the four CP-even mass eigenstates, +i.e., mh125, mH, mHS, m � +N, corresponding to each BPs. The leading composition in these +states are coming from the HSM, HNSM, HS and NR fields, respectively. We have explicitly +– 20 – + +checked that all the BPs evade the relevant experimental bounds as detailed in subsection +3.1. Nevertheless, we have explicitly shown values of the various flavour-violating processes +∆aµ and ∆m2 +atm for the sake of completeness. In Table 2 and Table 3, we have summarised +the PT outputs of the BPs as obtained from the cosmoTransitions [211] package. Below +we discuss the PT characteristics for each of the BPs in detail. +BP-I +BP-II +BP-III +BP-IV +BP-V +BP-VI +tan β +2.90 +2.74 +2.90 +5.77 +4.79 +5.86 +λ +0.416 +0.412 +0.416 +0.384 +0.118 +0.111 +κ +0.022 +0.019 +0.022 +0.012 +0.013 +0.051 +λN +0.146 +0.142 +0.146 +0.130 +0.260 +0.238 +Y 1 +N × 107 +0.9 +0.65 +1.1 +1.0 +3.6 +4.3 +Y 2 +N × 107 +0.9 +0.65 +1.1 +1.0 +3.6 +4.3 +Y 3 +N × 107 +0.9 +0.65 +1.1 +1.0 +3.6 +4.3 +Aλ [GeV] +775.48 +705.32 +775.48 +1184.87 +988.08 +920.08 +Aκ [GeV] +-62.75 +-25.37 +-95.61 +-107.08 +-11.70 +-41.61 +AλN [GeV] +-349.68 +-337.77 +-326.60 +-363.16 +-1358.30 +-1528.57 +AN [GeV] +-16000.0 +-12000.0 +-8500.0 +-12000.0 +-6500.0 +-5000.0 +µ [GeV] +224.56 +220.86 +224.56 +203.12 +153.59 +162.64 +vN [GeV] +308.80 +325.21 +284.50 +386.45 +136.57 +355.66 +v1 × 104 [GeV] +1.0 +0.55 +1.0 +1.2 +1.0 +1.0 +v2 × 104 [GeV] +1.0 +0.55 +1.0 +1.2 +1.0 +1.0 +v3 × 104 [GeV] +1.0 +0.55 +1.0 +1.2 +1.0 +1.0 +mh125 [GeV] +126.02 +124.80 +125.64 +125.63 +126.28 +124.05 +mH [GeV] +772.36 +718.07 +772.73 +1213.76 +897.40 +1012.14 +mHS [GeV] +83.60 +88.98 +69.48 +109.54 +97.31 +195.41 +m � +N [GeV] +48.60 +51.65 +51.89 +27.65 +65.18 +115.63 +BR(B → Xsγ) × 104 +3.61 +3.70 +3.62 +3.47 +3.59 +3.55 +BR(B0 +s → µ+µ−) × 109 +3.24 +3.26 +3.24 +3.19 +3.20 +3.19 +BR(µ → eγ) × 1030 +394 +0.61 +4.98 +51.4 +404 +173 +BR(µ → eee) × 1029 +113.0 +363.7 +44.6 +53.9 +2.04 +2.04 +CR(µN → eN∗) × 1028 +1.81 +0.11 +2.49 +4.43 +4.85 +7.31 +∆m2 +atm × 103 eV2 +2.51 +2.57 +2.58 +2.54 +2.58 +2.46 +∆aµ × 1010 +3.88 +0.75 +3.42 +1.94 +1.54 +3.24 +Table 1. +The representative BPs that we will use to study the PT patterns in the present +framework. +Apart from the parameters mentioned above, we fix the gaugino mass parameters +M1 = 300 GeV, M2 = 2M1, M3 = 6M1, trilinear soft coupling At around 2 TeV. We also consider +RH-slepton soft masses above 1 TeV and squarks soft masses M � +Qi, M�uc +i , M � +dc +i all above 1.2 TeV. +With the chosen values of parameters Y i +N, vi and AN, the LH-sneutrino and LH-slepton masses also +appear in the ballpark of a TeV. As already stated in subsection 3.1, suppressed cLFV processes +and smaller BSM contributions to the anomalous magnetic moment of muon are evident now due to +slepton, squark masses around a TeV or more. In fact, for BP-II, ∆aµ remains below the aforesaid +4σ range. CR(µ N → e N ∗) value is estimated for the gold nuclei. +• BP-I and BP-II : Out of these two representative BPs, BP-I shows an SFOPT along +both the SU(2)L-doublet and singlet field directions. +On the other hand, we obtain a +weaker FOPT for BP-II in the SU(2)L doublet directions whereas a stronger one along the +SU(2)L singlet direction. In Figure 1, we have shown the evolution of the phase structures +along the HSM (left) and the HS (right) field directions as a function of temperature for +BP-I. The critical temperature for BP-I is 117.8 GeV as noted in Table 2. Above the critical +– 21 – + +BP-I +BP-II +BP-III +Transition Type +Type-IIa +Type-IIa +Type-IIIa +vc/Tc +1.30 (In); 0 (Out) +0.73 (I); 0 (O) +1.83 (I); 0.61 (O) +∆φSU(2)/Tn +1.58 +0.81 +1.28 +∆φS/Tn +4.70 +1.16 +7.61 +∆φ � +N/Tn +0 +0 +0 +Tc (GeV) +117.8 +127.2 +101.6 +Tn (GeV) +109.9 +126.7 +82.9 +high-Tn VEVs +(0, 0, 113.8, 0) +(0, 0, 341.6, 0) +(105.8, 32.5, 88.8, 0) +low-Tn VEVs +(173.1, 9.5, 631.3, 0) +(102.3, 11.3, 488.7, 0) +(208.1, 4.8, 719.7, 0) +high-Tc VEVs +(0, 0, 72.6, 0) +(0, 0, 333.1, 0) +(62.4, 20.9, 35.6, 0) +low-Tc VEVs +(152.9, 11.8, 572.5, 0) +(92.5, 10.1, 467.7, 0) +(186.4, 10.6, 625.4, 0) +Table 2. The PT properties for first three BPs as tabulated in Table 1. +temperature HSM is located at zero (as pointed by the legend phase 3, red coloured, in +Figure 1). At T = Tc, we find another degenerate minimum along the same field direction, +which is ⟨HSM⟩ = 152.9 GeV (as marked by phase 2, green coloured). The black coloured +line with the arrow connects the high-T and low-T VEVs indicating a possible FOPT. The +bubble nucleation occurs afterwards and it ends at 109.9 GeV which we have highlighted +in orange colour (also labelled as phase 1). A similar pattern can be observed along HS +direction too as shown in the right panel of Figure 1. The interesting point to mention +here is that the ⟨HS⟩ starts to get displaced from zero value even at a temperature above +Tc. This is in contrast to the evolution of phase structure along HSM direction for this +particular BP. The BP-II shows similar characteristics although the strong PT occurs only +along the HS direction. The high-temperature behaviour of the total scalar potential leads +us to identify the PT properties for both BP-I and BP-II as Type-IIa. For BP-I, we observe +from Table 2, that the PT strength at T = Tc is greater than one inside the bubble and +zero outside the bubble. Therefore a baryon number may be generated in the broken phase +and the wash-out effects are likely to be suppressed. In view of this, BP-I is favoured in +order to address EWBG. However, BP-II shows a weaker FOPT in the SU(2)L doublet +directions and hence is not suitable to address the question of EWBG. In subsection 4.3 we +will discuss the strength of emitted GW spectrum during bubble nucleation for both BP-I +and BP-II in view of the proposed sensitivities of a few forthcoming GW experiments. +• BP-III: The BP-III falls into Type-IIIa category. +It implies that at a temperature +above Tc, both HSM and HS attain non-zero VEVs. The critical temperature for this BP +comes out to be 101.6 GeV. At this temperature, the presence of two degenerate vacua is +noticed having nonzero field values for both SU(2)L doublet and singlet fields, which set +the possibility of a PT. We obtain SFOPT along both the SU(2)L-doublet and singlet field +directions where the PT strength turns out to be larger than one. However, the quantity φc +Tc +becomes non-zero both inside and outside the bubble. This gives rise to a stronger wash- +out effect which is likely to suppress the yield of baryon asymmetry and hence seemingly +disfavored in view of EWBG. Nevertheless, it carries good detection prospects in the GW +detectors due to relatively larger PT strength ∆φS +Tn +compared to BP-I. +– 22 – + +0 +50 +100 +150 +200 +250 +⟨HSM⟩ [GeV] +0 +50 +100 +150 +200 +250 +300 +T [GeV] +phase3 +phase2 +phase1 +phase0 +0 +200 +400 +600 +800 +⟨HS⟩ [GeV] +0 +50 +100 +150 +200 +250 +300 +T [GeV] +phase3 +phase2 +phase1 +phase0 +Figure 1. +Phase structures as a function of temperature along the HSM and HS field directions +for BP-I. Different colours represent the locations of a particular field as a function of temperature. +The black coloured line with the arrow connects two degenerate phases at T = Tc and the direction +of the arrow indicates a possible FOPT. +0 +200 +400 +600 +⟨HS⟩ [GeV] +0 +200 +400 +600 +800 +1000 +T [GeV] +phase3 +phase2 +phase1 +phase0 +−500 +−400 +−300 +−200 +−100 +0 +⟨NR⟩ [GeV] +0 +200 +400 +600 +800 +1000 +T [GeV] +phase3 +phase2 +phase1 +phase0 +Figure 2. +Phase structures as function of temperature along HS and NR field directions for +BP-IV. Different colours show the evolution of minimum along a particular field direction with +temperature. The line with the arrow connects two degenerate phases at T = Tc and the direction +of the arrow indicates a possible FOPT. +• BP-IV: The BP-IV in Table 1 shows type-IIc PT pattern. The numerical estimates of +the relevant parameters that govern the PT dynamics for BP-IV are listed in Table 3. We +find SOFPT along both the HS and NR directions. Clearly, this BP is not preferred to +address EWBG. In Figure 2, we show the phase structure along HS and NR directions for +BP-IV as a function of temperature. At temperature above Tc = 184.5 GeV, HS takes a +non-zero field value which is the typical type-II feature. The black coloured line with arrow +in Figure 2 connects two degenerate phases at the critical temperature and paves the way +for the PTs in the respective singlet field directions. +• BP-V: This BP is unique in the sense that we obtain FOPT below the critical tempera- +ture along the directions of SU(2)L fields, HS and NR at the same time. This BP falls into +– 23 – + +the type-III category since at temperature above Tc, we find high-T VEV to be non-zero for +both HSM and HS fields. Although this particular BP shows FOPT along HSM direction, +the strength is relatively weaker as can be seen from Table 3. Therefore, the possibility +of EWBG remains unlikely for this BP. Nevertheless, we obtain SFOPT along HS and ˜N +directions in contrast to weaker FOPT in the HSM direction. +BP-IV +BP-V +BP-VI +Transition Type +Type-IIc +Type-IIIb +Type-IV +vc/Tc +0.0 (In) ; 0.0 (Out) +0.0 (I); 0.0 (O) +2nd: 0.54 (In); 0.0 (Out) +1st: 0.0 (In) ; 0.0 (Out) +∆φSU(2)/Tn +0 +0.04 +1st: 0 ; 2nd: 0.57 +∆φS/Tn +1.01 +1.56 +1st: 0; 2nd: 0 +∆φ � +N/Tn +2.81 +1.71 +1st: 0.2; 2nd: 0.13 +Tc (GeV) +184.5 +177.9 +2nd: 206.3 +1st: 232.8 +Tn (GeV) +165.8 +144.3 +2nd: 204.6 +1st: 232.6 +high-Tn VEVs +(0, 0, 529.9, 0) +(137.9, 3.5, 1606.9, 0) +2nd: (0, 0, 2087.9, −720.9) +1st: (0, 0, 2087.7, −845.4) +low-Tn VEVs +(0, 0, 696.6, −465.28) +(143.2, 0, 1832.7, 247.2) +2nd: (117.2, 0, 2088.1, −747.6) +1st: (0, 0, 2087.7, -807.2) +high-Tc VEVs +(0, 0, 459.9, 0) +(0, 0, 1484.6, 0) +2nd: (0, 0, 2087.9, −724.6) +1st: (0, 0, 2087.7, −846.2) +low-Tc VEVs +(0, 0, 671.2, −429.5) +(0, 0, 1827.6, 275.9) +2nd: (112.3, 0, 2088.1, −749.3) +1st: (0, 0, 2087.4, −808.5) +Table 3. The PT properties for the last three BPs as tabulated in Table 1. +• BP-VI: So far, for all the BPs we have obtained single-step FOPT. In contrast, BP-VI +shows a two-step FOPT. The outputs are tabulated in Table 3. In both steps, the high- +temperature behaviour of the scalar potential closely follows the Type-IV pattern. On the +other hand, in the first step FOPT occurs along the NR direction only, while in the second +step, we find FOPT in both the NR and HSM directions. Note that, this BP shows a weaker +FOPT and hence, is not suitable for the EWBG. +Recall from section 3 that the new physics parameters, relevant for the study of PT in +the current framework are {λN, AλN , vN} compared to the Z3 symmetric NMSSM. In the +subsequent analysis, we like to inquire about the impact of these new parameters on the +PT strength along different field directions. Also, note that a FOPT apparently favours a +lighter RH-sneutrino-like state below 125 GeV as we observe from the BP-based study of +PT and their outcomes. This characteristic is likely to be further confirmed while we vary +the new parameters and obtain the sensitivity of PT strength on these parameters. +First, in Figure 3 we show the impact of vN (left) and λN (right) on the PT strength +vc +Tc . In each of the sub-figures, we have fixed the other relevant parameters as in BP-I of +Table 1. We find the PT strength decreases with the rise of both vN and λN. We repeat +the analysis for the same BP as shown in the top panel of Figure 4 considering nucleation +temperature calculation. In particular, we estimate the PT strength in the SU(2)L field +– 24 – + +150 +200 +250 +300 +350 +400 +vN (GeV) +0.9 +1.0 +1.1 +1.2 +1.3 +1.4 +1.5 +vc/Tc +0.14 +0.16 +0.18 +0.20 +0.22 +0.24 +0.26 +λN +0.5 +0.6 +0.7 +0.8 +0.9 +1.0 +1.1 +1.2 +1.3 +vc/Tc +Figure 3. These plots show the dependence of PT strength on vN (left) and λN (right) in the Tc +calculation. Parameters Y i +N, vi and AN have no significant effect in PT dynamics and thus, we keep +their values ∼ O(10−7), ∼ O(10−4 GeV), ∼ O(1 TeV), respectively. Other relevant parameters are +fixed as in BP-I of Table 1, except vN and λN. +directions, i.e., ∆φSU(2)/Tn as function of vN and λN and notice similar trends as in +Figure 3. Now a smaller λN or vN implies lighter sneutrino following the CP-even mass +matrices mentioned in Appendix B. Hence, Figures 3 and 4 further reinforce the fact that +a comparatively lighter RH-snuetrino is indeed preferred to trigger a possible FOPT along +the SU(2)L doublet field directions in the present framework. Now the remaining new +parameter AλN is expected to show a minor impact on the ∆φSU(2)/Tn. This is because it +is not directly connected to the relevant terms at the tree level in the Lagrangian involving +the SU(2) doublet Higgs fields. Indeed, in our analysis, we have found that the ∆φSU(2)/Tn +remains more or less unaltered upon varying AλN as shown in the bottom panel of Fig. 4. +Next, we like to examine the impact of the new physics parameters as earlier specified +on the PT strength along SU(2)L-singlet field direction ∆φS/Tn while the other parameters +are set according to BP-III of Table 1. In top panel of Figure 5 we depict the variation of +∆φS/Tn as function of vN (left) and λN (right). We observe that the quantity ∆φS/Tn +increases upon lowering λN when vN is fixed. In the other case when we fix λN and vary +vN, the ∆φS/Tn gets enhanced for a smaller vN. Once again, these observations further +strengthen our earlier finding that a lighter RH-sneutrino below 125 GeV is favoured for +the occurrence of an SFOPT in the SU(2)L-singlet, i.e., HS direction as well. On the +other hand, we also notice that the ∆φS/Tn increases with the rise of AλN as shown in +the bottom panel of Figure 5. Note that AλN is appearing as the coefficient of the cubic +interaction S � +N � +N (see Eq. (2.2)). Hence a larger AλN is expected to increase the barrier +height which results in a stronger ∆φS/Tn. +Previously, we have found that BP-IV provides us with a SOFPT along the NR field +direction ∆φ � +N/Tn. We would like to utilize this particular BP to enquire about the de- +pendence of new parameters on ∆φ � +N/Tn. In top left of Figure 6, we show the dependence +of ∆φ � +N/Tn on vN. We find that for vN ≲ 500 GeV, the ∆φ � +N/Tn remains more or less +– 25 – + +320 +340 +360 +380 +400 +vN (GeV) +1.0 +1.1 +1.2 +1.3 +1.4 +1.5 +∆φSU(2)/Tn +0.14 +0.16 +0.18 +0.20 +0.22 +0.24 +0.26 +λN +0.6 +0.8 +1.0 +1.2 +1.4 +1.6 +∆φSU(2)/Tn +−1400 −1200 −1000 −800 +−600 +−400 +−200 +AλN +0.08 +0.09 +0.10 +0.11 +0.12 +0.13 +0.14 +0.15 +0.16 +∆φSU(2)/Tn +Figure 4. These plots show the dependence of PT strength ∆φSU(2)/Tn on vN (top left), λN (top +right) and AλN (bottom) along the SU(2)L field direction, in the Tn calculation. Here, orders of +parameters Y i +N, vi and AN are chosen as in Figure 3 and the other relevant parameters are fixed as +in BP-I of Table 1, except vN, λN and AλN . +constant, however, decreases while we increase vN further. Additionally, from top right +of Figure 6 the ∆φ � +N/Tn gets reduced as well upon increasing λN. The reason for this is +twofold. As we mentioned earlier, a smaller λN leads to lighter RH-sneutrino states below +125 GeV which in turn enhances the ∆φ � +N/Tn. Moreover, a smaller λN also assists in +increasing the barrier height and hence results in enhanced ∆φ � +N/Tn. In bottom panel of +Figure 6, we have shown the ∆φ � +N/Tn strength gets enhanced upon increasing AλN . This +is once again caused by the enhanced barrier height for a larger AλN similar to the earlier +case. +After examining the individual dependence of new parameters on PT strength, we +now give a random scan on new physics parameters highlighting the region allowed by +the experimental constraints and favouring an SFOPT along SU(2)L field directions. We +vary (λN, vN) and fix the other relevant parameters in Eq. (3.3) following BP-I. However, +orders of parameters Y i +N, vi and AN are chosen as ∼ O(10−7), ∼ O(10−4 GeV), ∼ O(1 +– 26 – + +150 +200 +250 +300 +350 +400 +vN (GeV) +2 +3 +4 +5 +6 +∆φS/Tn +0.14 +0.16 +0.18 +0.20 +0.22 +0.24 +0.26 +λN +1 +2 +3 +4 +5 +∆φS/Tn +−800 +−700 +−600 +−500 +−400 +−300 +−200 +AλN +0.8 +0.9 +1.0 +1.1 +1.2 +1.3 +1.4 +∆φS/Tn +Figure 5. These plots show the dependence of PT strength ∆φS/Tn on vN (top left), λN (top +right) and AλN (bottom) along the SU(2)L-singlet field direction, in the Tn calculation. Here, +orders of parameters Y i +N, vi and AN are chosen as in Figure 3 and the other relevant parameters +are fixed as in BP-III of Table 1, except vN, λN and AλN . +TeV), respectively, as they hardly affect the PT dynamics. We have randomly generated +pairs of (λN, vN) and pass through all the experimental bounds mentioned in subsection +3.1. We first sort out the points that pass all the experimental constraints as shown in +green colour in Figure 7. Next, we apply the condition of SFOPT along the SU(2)L field +direction and pin down the points that favour SFOPT only and SFOPT with possible +EWBG having minimal wash-out effects. We have marked them in Figure 7 by coloured +‘▲’ and ‘■’, respectively. These points depict the variation of ∆φSU(2)/Tn in the vN - λN +plane. +Next in Figure 8, we made a scenario similar to that of Figure 7, however, in the HS +field direction in the context of BP-IV, as shown in Table 3. Here, points which undergo +SFOPT are marked by ‘⋆’. We also compute the ∆φS/Tn strength and find that the +∆φS/Tn strength is maximum when both λN and vN are small, which is in agreement with +our earlier observations. +– 27 – + +400 +500 +600 +700 +800 +900 +1000 +vN (GeV) +2.0 +2.2 +2.4 +2.6 +2.8 +3.0 +∆φ� +N/Tn +0.15 +0.20 +0.25 +0.30 +0.35 +λN +0.0 +0.5 +1.0 +1.5 +2.0 +2.5 +3.0 +∆φ� +N/Tn +−1000 +−800 +−600 +−400 +−200 +AλN +2.6 +2.8 +3.0 +3.2 +3.4 +3.6 +3.8 +∆φ� +N/Tn +Figure 6. These plots show the dependence of PT strength ∆φ � +N/Tn on vN (top left), on λN +(top right) and on AλN (bottom) along the NR direction, in the Tn calculation. Here, orders of +parameters Y i +N, vi and AN are chosen as in Figure 3 and the other relevant parameters are fixed as +in BP-IV of Table 1, except vN, λN and AλN . +Finally, in Figure 9 we perform an analogous exercise to show the variation of ∆φ � +N/Tn +in the vN - λN plane. In this case, we have utilized the BP-IV of Table 3 once again to fix +the other relevant parameters, except vN and λN. The green-coloured points are allowed +by the various experimental constraints as stated in subsection 3.1. We mark the points +that favour SFOPT in the NR direction by coloured ‘⋆’. Once again, we find that the +∆φ � +N/Tn is maximum for simultaneous lower values of vN and λN, consistent with our +earlier findings. +4.3 +GW spectrum from SFOPT in the NMSSM + one RHN model +A cosmological FOPT can produce GWs in the early Universe that contains information +about the strength of different model parameters. In the preceding section, we have dis- +cussed different PT characteristics in the proposed framework and computed the relevant +quantities that determine the strength of a PT. In the current section, we will be talking +– 28 – + +220 +240 +260 +280 +300 +320 +340 +vN (GeV) +0.135 +0.140 +0.145 +0.150 +0.155 +0.160 +0.165 +0.170 +λN +tan β = 2.90, λ = 0.416, κ = 0.022, µ = 224.56 GeV, +Aλ = 775.48 GeV, Aκ = −62.75 GeV, AλN = −349.68 GeV +Allowed by experimental bounds +SFOPT and no EWBG +SFOPT and possible EWBG +1.50 +1.75 +2.00 +2.25 +2.50 +2.75 +3.00 +3.25 +3.50 +∆φSU(2)/Tn +Figure 7. This figure shows variations of ∆φSU(2)/Tn in the vN - λN plane. The green-coloured +points pass all the experimental constraints as discussed in subsection 3.1. The points favoured for +SFOPT along the SU(2)L field direction without and with EWBG are marked by coloured ‘▲’ and +‘■’ symbols, respectively. Orders of parameters Y i +N, vi and AN are chosen as in Figure 3 and the +other relevant parameters are fixed as in BP-I of Table 1. +about the production of GW and its detection prospects within our model setup. +As we have mentioned earlier, a FOPT is characterized by critical temperature Tc, +and nucleation temperature Tn. The critical temperature indicates the moment when the +location of the global minimum changes from one vacuum phase to another. However, +the critical temperature analysis does not assure that the associated PT is indeed taking +place. On the other hand, FOPT proceeds via bubble nucleation, and hence calculation of +nucleation temperature is very crucial in order to obtain the phenomenological parameters +that are important from the standpoint of estimating GW spectra. When the nucleation +happens, at a temperature below Tc, the probability of tunnelling Γ(T) from the false +vacuum to the true one is given by [213], +Γ(T) ≈ T 4 +� SE +2πT +�3/2 +e− SE +T , +(4.7) +where SE is the bounce action corresponding to the critical bubble and can be written as +[212], +SE = +� ∞ +0 +4πr2dr +� +VT (φ, T) + 1 +2 +�dφ(r) +dr +�2� +, +(4.8) +with r being the radial coordinate and φ corresponding to the scalar dynamical fields +present in a model framework. The scalar field solution φ can be derived by solving the +– 29 – + +340 +360 +380 +400 +420 +440 +460 +vN +0.12 +0.13 +0.14 +0.15 +0.16 +0.17 +0.18 +0.19 +0.20 +λN +tan β = 5.77, λ = 0.384, κ = 0.012, µ = 203.12 GeV, +Aλ = 1184.87 GeV, Aκ = −107.08 GeV, AλN = −363.16 GeV +Allowed by experimental bounds +SFOPT along HS direction +1.0 +1.2 +1.4 +1.6 +1.8 +2.0 +2.2 +∆φS/Tn +Figure 8. This figure shows variations of ∆φS/Tn in the vN - λN plane. The green-coloured points +pass all the experimental constraints as discussed in subsection 3.1. The points favoured for SFOPT +along the HS field direction are marked by coloured ‘⋆’. Orders of parameters Y i +N, vi and AN are +chosen as in Figure 3 and the other relevant parameters are fixed following BP-IV of Table 1. +classical field equation [212, 214, 215] +d2φ +dr2 + 2 +r +dφ +dr = dVT (φ, T) +dr +, +(4.9) +and subsequently applying proper boundary conditions: +dφ +dr = 0 when r → 0 and φ(r) → +φfalse when r → ∞, where φfalse represents the four-dimensional field values at the false +vacua. We reiterate here that in order to solve the differential equation and the bounce +action numerically, we have implemented our model in the cosmoTransitions [211] pack- +age. +The essential parameters that are required for the estimation of GW spectra from +FOPT are relative change in energy density during the PT (α), and the inverse of the +duration of the PT (β). Both the parameters, α, and β, are defined at the nucleation +temperature Tn. The first parameter, α, is computed from [216], +α = ∆ρ +ρrad +, +(4.10) +where ∆ρ is the released latent heat and it is expressed as [217], +∆ρ = +� +VT (φ0, T) − T dVT (φ0, T) +dT +� +T=Tn +− +� +VT (φn, T) − T dVT (φn, T) +dT +� +T=Tn +, +(4.11) +– 30 – + +340 +360 +380 +400 +420 +440 +460 +vN (GeV) +0.12 +0.13 +0.14 +0.15 +0.16 +0.17 +0.18 +0.19 +0.20 +λN +tan β = 5.77, λ = 0.384, κ = 0.012, µ = 203.12 GeV, +Aλ = 1184.87 GeV, Aκ = −107.08 GeV, AλN = −363.16 GeV +Allowed by experimental bounds +SFOPT along � +N direction +1.6 +1.8 +2.0 +2.2 +2.4 +2.6 +2.8 +∆φ� +N/Tn +Figure 9. This figure shows variations of ∆φ � +N/Tn in the vN - λN plane. The green-coloured +points pass all the experimental constraints as discussed in subsection 3.1. The points favoured +for SFOPT along the NR field direction are marked by coloured ‘⋆’. Orders of parameters Y i +N, vi +and AN are chosen as in Figure 3 and the other relevant parameters are fixed following BP-IV of +Table 1. +with φ0 and φn represent, in our case, the four-dimensional field values at the false and true +vacua, respectively, and VT (φ, T) is the finite-temperature effective potential as mentioned +in Eq. (2.20). We should note here that the quantity ∆ρ measures the strength of a PT, the +larger value of the same corresponds to a stronger FOPT. In Eq. (4.10), ρrad corresponds +to the radiation energy in the plasma and it is expressed as, ρrad = π2g∗ +30 T 4 +n, with g∗ being a +temperature-dependent quantity that counts the total number of relativistic energy degrees +of freedom. +The parameter β is defined as [218], +β +H∗ += T d +dT +�SE +T +� ����� +T=T∗ +≡ T d +dT +�SE +T +� ����� +T=Tn +, +(4.12) +where H∗ is the expansion rate of the Universe during the PT and T∗ stands for the PT +temperature. We have considered T∗ ≃ Tn in the present work. We have tabulated the +obtained values of α and β in Table 4 for different BPs shown in Table 1. As stated earlier, +the quantity α is proportional to the energy released during the PT and hence a larger PT +strength should lead to a larger α value. In fact, this is exactly the case where we find the +largest α for the BP-III (see Table 4) having ∆φS/Tn = 7.61 (see Table 2.) We obtain the +lowest α for the first-step PT of BP-VI since the corresponding ∆φ � +N/Tn is weakest among +all as can be seen from Tables 2 and 3. +– 31 – + +BPs +α +β/H∗ +BP-I +0.0456 +37535.2 +BP-II +0.0121 +143931.0 +BP-III +0.0870 +11729.8 +BP-IV +0.0101 +7596.0 +BP-V +0.0027 +4611.3 +BP-VI-I +0.0002 +516911.0 +BP-VI-II +0.0017 +63837.8 +Table 4. Estimates of the parameters α and β as defined in Eq. (4.10) and Eq. (4.12), respectively +for the six BPs listed in Table 1. Note that the BP-VI-I shows two-step PT patterns and we have +made the estimates of α and β in both steps. +There are mainly three different processes that trigger the emission of GWs in a FOPT: +(i) bubble wall collisions, (ii) sound waves, and (iii) magneto-hydrodynamic (MHD) tur- +bulence in the plasma. +Therefore, the total energy spectrum of the emitted GW can +approximately be given as a sum of these three contributions [155, 219], +ΩGWh2 ≈ Ωcolh2 + Ωswh2 + Ωturh2, respectively, +(4.13) +where, h = H0/(100 km · sec−1 · Mpc−1) [220] with H0 corresponding to Hubble’s constant +at the present epoch. The contribution to the total GW energy density from the bubble +wall collision can be computed using the envelope approximation and it can be estimated +as a function of frequency “f” as [221], +Ωcolh2 = 1.67 × 10−5 +� β +H∗ +�−2 � κcα +1 + α +�2 �100 +g∗ +�1/3 � 0.11v3 +w +0.42 + v2w +� +3.8 (f/fcol)2.8 +1 + 2.8 (f/fcol)3.8 , +(4.14) +where vw is the bubble wall velocity and κc is the efficiency factor of bubble collision, given +as, +κc = +0.715α + 4 +27 +� +3α +2 +1 + 0.715α +. +(4.15) +The red-shifted peak frequency fcol [221] is expressed as (with the approximation T∗ ≈ Tn), +fcol = 16.5 × 10−6 +�f∗ +β +� � β +H∗ +� � +Tn +100 GeV +� � g∗ +100 +�1/6 +Hz, +(4.16) +where the fitting function, f∗/β, at the time of the PT is given by, +f∗ +β = +0.62 +1.8 − 0.1vw + v2w +. +(4.17) +In order to obtain a GW spectrum with higher strength, it is generally assumed that the +expanding bubbles attain a relativistic terminal velocity in the plasma and we consider +– 32 – + +vw ≃ 1 in our calculations 14. However, there is a note of caution that runway bubble walls +are generally undesirable in view of the successful yield of a sizeable amount of EWBG 15. +The contribution to the total GW density from sound waves can be parameterized as +[230–233], +Ωswh2 = 2.65×10−6 Υ(τsw) +� β +H∗ +�−1 +vw +� κswα +1 + α +�2 � g∗ +100 +�1/3 � f +fsw +�3 � +7 +4 + 3 (f/fsw)2 +�7/2 +, +(4.18) +where κsw is the efficiency factor for the sound wave contribution representing the fraction +of the energy (latent heat) that gets converted into the bulk motion of the plasma and +subsequently emits gravitational waves as given by (in the limit vw → 1) +κsw ≃ +� +α +0.73 + 0.083√α + α +� +. +(4.19) +The quantity fsw corresponds to the present peak frequency for the sound wave contribution +to the total GW energy density, expressed as +fsw = 1.9 × 10−5 +� 1 +vw +� � β +H∗ +� � +Tn +100 GeV +� � g∗ +100 +�1/6 +Hz. +(4.20) +The parameter Υ(τsw) appears due to the finite lifetime of the sound waves which suppresses +their contributions to the GW energy density as written as +Υ(τsw) = 1 − +1 +√1 + 2τswH∗ +, +(4.21) +with τsw being the lifetime of the sound waves. The onset of the turbulence takes place at +this timescale and disrupts the sound wave source. Following Ref. [232], we write τsw ≈ +R∗/U f, where R∗ = (8π)1/3 vw/β and U f = +� +3κswα/4 are the mean bubble separation and +the root-mean-squared fluid velocity which can be obtained from a hydrodynamic analysis, +respectively. +At the time of PT, the plasma is fully ionized and due to the resulting MHD turbulence, +it leads to another source of GWs. The MHD turbulence contribution to the total GW +energy density is modelled as [235] +Ωturh2 = 3.35 × 10−4 +� β +H∗ +�−1 +vw +�κturα +1 + α +�3/2 �100 +g∗ +�1/3 +� +� +(f/ftur)3 +[1 + (f/ftur)]11/3 � +1 + 8πf +h∗ +� +� +� , +(4.22) +14A precise determination of bubble wall velocity is non-trivial [222–226] and out of scope of the present +analysis. Instead, we consider here vw as an input parameter. +15Recently, an improved analysis on bubble wall dynamics has reported that EWBG may be possible +even for supersonic vw [227–229] which is in contrast with our traditional notion. +– 33 – + +U-DECIGO +U-DECIGO-corr +DECIGO-corr +BP-I +BP-II +BP-III +10-7 +10-5 +0.001 +0.100 +10 +10-28 +10-23 +10-18 +10-13 +10-8 +Figure 10. +Prediction of GW energy density as a function of the frequency for the first three BPs +as shown in Table 1. We have also highlighted the regions that indicate the proposed sensitivities +of the GW experiments namely U-DECIGO and U-DECIGO corr [81, 82]. The sensitivity curves +for DECIGO and U-DECIGO with correlation analyses are taken from Ref. [234]. +. +where h∗ = 16.5 × +� +Tn +100 GeV +� � +g∗ +100 +�1/6 +Hz, the inverse Hubble time during GW production, +red-shifted to today. The peak frequency ftur is given by, +ftur = 2.7 × 10−5 1 +vw +� β +H∗ +� � +Tn +100 GeV +� � g∗ +100 +�1/6 +Hz. +(4.23) +We set κtur = ϵκsw where ϵ stands for the fraction of the bulk motion which is turbulent. +Simulations suggest κtur = 0.1κsw which we have considered in our numerical calculations. +U-DECIGO +U-DECIGO-corr +DECIGO-corr +BP-IV +BP-V +BP-VI-I +BP-VI-II +10-7 +10-5 +0.001 +0.100 +10 +10-28 +10-23 +10-18 +10-13 +10-8 +Figure 11. Prediction of GW energy density as a function of the frequency for the last three BPs +from Table 1. We have also highlighted the regions that indicate the proposed sensitivities of the +GW experiments namely DECIGO-corr, U-DECIGO and U-DECIGO corr [81, 82]. +With these details, in Figure 10 we present the estimates of GW energy density spec- +trum as a function of frequency for the first three BPs as shown in Table 1. The predictions +– 34 – + +of ΩGWh2 for the last three BPs of Table 1 are shown in Figure 11. We notice from Eq. +(4.14), Eq. (4.18) and Eq. (4.22), that each individual contribution to the total GW energy +density, ΩGWh2 (as defined in Eq.(4.13)) is an increasing function of α 16. This feature in +turn makes ΩGWh2 rise as well for a relatively larger α. In contrast, a larger +β +H∗ reduces +the amount of ΩGWh2. Earlier, in Table 4, we observed that BP-III yields the largest value +of α among the six BPs of Table 1 with relatively smaller +β +H∗ ratio. Consequently, we find +the corresponding peak amplitude of ΩGWh2 to be ∼ O(10−17) for BP-III, which turns +out to be the largest as well. This feature is depicted in Figure 10. The lowest peak am- +plitude of ΩGWh2 that we obtain is for the first-step PT of BP-VI which is ∼ O(10−25) +as shown in Figure 11. The massive suppression to ΩGWh2 for BP-VI-I is caused by the +simultaneous presence of a large +β +H∗ value together with a small α value as shown in Table +4. The second-step PT of BP-VI produces a peak having amplitude ∼ O(10−22) which is +relatively less suppressed due to a smaller value of +β +H∗ compared to BP-VI-I as shown in +Table 4. +In view of such estimates, the proposed future GW interferometers namely U-DECIGO +and U-DECIGO correlation have the required sensitivities to probe all the BPs, except +BP-VI-I, considered in our analysis including BP-I which is preferred in order to address +EWBG. We also find it pertinent to mention that the peak frequency of each contribution +to GW energy density is linearly proportional to the ratio +β +H∗ as evident from Eqs. (4.16), +(4.20) and (4.23). +It is numerically found that the frequency fmax where ΩGWh2 (see +Eq.(4.13)) attains maximum, also emerges to be an increasing function of +β +H∗ ratio. As +already noted in Table 4, that BP-VI-I produces the largest +β +H∗ ratio among all the BPs. +This makes the peak frequency fmax of the corresponding GW spectrum for BP-VI-I the +largest among all BPs. +−1.5 +−1.0 +−0.5 +0.0 +0.5 +log10α +2 +3 +4 +5 +6 +7 +log10(β/H∗) +SFOPT and possible EWBG +SFOPT and no EWBG +1.5 +2.0 +2.5 +3.0 +3.5 +∆φSU(2)/Tn +−1.5 +−1.0 +−0.5 +0.0 +0.5 +log10α +2 +3 +4 +5 +6 +7 +log10(β/H∗) +SFOPT and possible EWBG +SFOPT and no EWBG +20 +40 +60 +80 +100 +120 +140 +160 +Tn +Figure 12. Values of α and +β +H∗ as a function of ∆φSU(2)/Tn (right) and nucleation temperature Tn +(left) for the points in Figure 7 that satisfy the criteria of SFOPT with possible EWBG (depicted +by coloured ‘■’) and SFOPT without EWBG (depicted by coloured ‘▲’). +16For α ≫ 1, Ωcolh2, Ωswh2 and Ωturh2 are expected to turn insensitive to the change of α. +– 35 – + +Earlier in Figure 7 we have identified points in the vN − λN plane that exhibits strong +PT along the SU(2)L doublet direction, i.e., ∆φSU(2)/Tn > 1, with and without favouring +EWBG as highlighted by coloured ‘■’ and ‘▲’ symbols, respectively. Recollect that, in +order to prepare Figure 7, we have utilised the fixed values of the other relevant independent +parameters as in BP-I, except vN and λN. In Figure 12, we show the estimates of α and +β/H∗, corresponding to the same parameter corner, that is relevant to estimate ΩGWh2 as a +function of ∆φSU(2)/Tn (left) and the nucleation temperature Tn (right), respectively. Note +that we are giving particular emphasis on analysing Figure 7 further to compute the GW +energy density since it offers the scope of realising EWBG while exhibiting ∆φSU(2)/Tn > 1 +(traceable at GW interferometers) at the same time. The Figure 12 illustrates the fact that +the points, favoured for EWBG require relatively higher β/H∗ and lower α values compared +to the points that do not favour EWBG. This essentially suppresses the peak amplitude +of ΩGWh2 for the points favouring EWBG and simultaneously increase the peak frequency +fmax. The right panel of Figure 12 indicates that a lower Tn tends to increase α which +in turn enhance the ∆φSU(2)/Tn leading to larger Ωpeak +GW h2. Such features are imprinted +in Figure 13 where we have shown the estimates of ΩGWh2 as a function of f for both +the coloured ‘■’ and ‘▲’ shaped points, present in Figure 7. We clearly observe that the +points which are not favoured for possible EWBG, produce a larger amount of ΩGWh2 at a +particular f and may even fall within the sensitivity curves of LISA [236] and BBO [156]. +However, the discovery scopes of those points purely depend on the signal-to-noise ratio of +the corresponding experiments [237]. +10−5 +10−4 +10−3 +10−2 +10−1 +100 +101 +102 +103 +f [Hz] +10−28 +10−25 +10−22 +10−19 +10−16 +10−13 +10−10 +10−7 +ΩGWh2(f) +LISA +BBO +DECIGO-corr +U-DECIGO +U-DECIGO-corr +BP-I +SFOPT and EWBG +0.020 +0.025 +0.030 +0.035 +0.040 +0.045 +α +10−5 +10−4 +10−3 +10−2 +10−1 +100 +101 +102 +103 +f [Hz] +10−28 +10−25 +10−22 +10−19 +10−16 +10−13 +10−10 +10−7 +ΩGWh2(f) +LISA +BBO +DECIGO-corr +U-DECIGO +U-DECIGO-corr +SFOPT and no EWBG +0.2 +0.4 +0.6 +0.8 +1.0 +1.2 +1.4 +1.6 +α +Figure 13. GW spectra for the points that show SFOPT in the SU(2)L doublet field directions +with (left) and without (right) possible EWBG. Note that these points are marked by ‘ ■’ and ‘ ▲’ +in Figure 7. For both figures, we keep α as a variable. +5 +Summary and Conclusion +In the present work, we have addressed the properties of EWPT in the RHN superfield +extended setup of Z3 invariant NMSSM. The RHN extended Z3 invariant NMSSM is cap- +tivating due to its ability to provide solutions to the µ−problem of the MSSM and non- +– 36 – + +vanishing neutrino masses and mixing simultaneously. In particular, we consider the case +where both the LH- and RH-sneutrino receive non-zero VEVs, leading to a spontaneous R- +parity-violating scenario. We have worked in an effective field theory set-up by integrating +out the heavier squarks, gluinos, as well as sleptons. Additionally, a simple parametriza- +tion of the TeV scale seesaw dictates the LH-sneutrino fields to weakly couple to the other +relevant fields and thus, is expected to contribute negligibly to the PT dynamics. These +facts effectively lead to a four-dimensional field space spanned by the four CP-even Higgses +which is of interest in order to explore the PT characteristics in the present framework. +Without going into the numerical details, one can naively anticipate that in the current +setup having a four-dimensional field space, the PT dynamics is likely to be more involved +than in the NMSSM where the relevant field space is three-dimensional. +The EWPT +properties and estimate of GW spectrum in the NMSSM have been extensively studied in +literature where the roles of NMSSM parameters on the PT strength are also detailed. In +this work, we scrutinize the role served by the new parameters that appear in theory due +to the presence of the RHN superfield on the PT dynamics. In particular, we find that +three new parameters λN, AλN and vN leave a non-trivial impact on determining the PT +strength. +In the beginning, we describe the model details and successively develop the tools re- +quired to study the behaviour of the scalar potential as a function of temperature. We +then demonstrate the possible experimental constraints that are of utmost importance to +obtain a viable parameter space. Specifically, we undertake constraints arising from the +validation of SM Higgs boson properties, BSM Higgs and SUSY searches at colliders, var- +ious flavour-violating processes, neutrino experiments and the muon anomalous magnetic +moment. Since extensive scanning of full parameter space considering a four-dimensional +field space, relevant for PT is numerically challenging, we first adopt a benchmark-based +analysis. We provide six BPs that pass through all the experimental constraints and exhibit +distinct kinds of FOPT patterns along the different field directions. We have discussed the +PT dynamics corresponding to each BP in detail. +An SFOPT is a prerequisite for EWBG with distinct high-temperature behaviour of +the total scalar potential along the SU(2)L field directions. We have shown that BP-I is +the preferred BP that exhibits the essential features required for a possible EWBG. On +the other hand, BP-II - BP-V showing SFOPT along the different SU(2)L doublet and +singlet field directions in single-step, however, are not suitable for successful EWBG. We +find multi-step FOPT for BP-VI. All the BPs listed have one particular feature in common +which is the preference for a lighter RH-sneutrino-dominated state below 125 GeV for the +occurrence of a FOPT. Next, we utilize a few of the BPs to inquire about the role of new +parameters on PT strength. Two of the new parameters vN and λN show similar impacts +on the PT strength along either of the SU(2)L doublet or singlet field directions. It turns +out that the PT strength increases with the decrease of either vN or λN. The remaining +parameter AλN has a minor role in the PT along SU(2)L doublet field directions whereas +the PT strengths in the SU(2)L singlet field directions get enhanced with the increase of +|AλN |. The possible reasons for such unique properties are associated with the impact of +the new parameters on the barrier height in the constituent field directions and also the +– 37 – + +lightness of the RH-sneutrino state. +Finally, we examine the testability of the BPs by computing the GW energy density +corresponding to each BP. We have considered all possible sources that trigger GW emis- +sion in a FOPT namely, bubble wall collisions, sound waves and magneto-hydrodynamic +turbulence. The highest peak amplitude of the GW energy density that we obtain is for +BP-III which lies within the proposed sensitivity of DECIGO correlation data. The peak +amplitude of ΩGWh2 for other BPs is relatively weaker, however, within the reach of U- +DECIGO and U-DECIGO-corr sensitivities. It is to be noted that a TeV scale canonical +seesaw model with RHN weakly coupled to SM particles is extremely difficult to probe +at collider experiments. Our analysis infers an alternative albeit promising pathway to +validate a TeV scale seesaw model at future GW interferometers beyond colliders. +In the present work, we have not performed an exact prediction of the baryon asym- +metry of the Universe. +Instead, we find the corner of the parameter space that shows +SFOPT along the SU(2)L doublet field directions and facilitates EWBG. Improvement of +our analysis is possible by precise computation of bubble wall profile, bubble wall velocity, +and CP-violation that decide the final amount of baryon asymmetry of the Universe, which +is also correlated with NMSSM + RHN model parameters. In an R-parity violating theory +like the present one, gravitino can be a potential decaying dark matter candidate. Future +works may also include investigating the correspondence between gravitino dark matter +phenomenology and NMSSM + RHN parameter space, favouring an SFOPT. +Acknowledgements +P. B. acknowledges the financial support received from the Indian Institute of Technology, +Delhi (IITD) as a Senior Research Fellow. P. G. acknowledges the IITD SEED grant sup- +port IITD/Plg/budget/2018-2019/21924, continued as IITD/Plg/budget/2019- +2020/173965, IITD Equipment Matching Grant IITD/IRD/MI02120/208794, and +Start-up Research Grant (SRG) support SRG/2019/000064 from the Science and Engi- +neering Research Board (SERB), Department of Science and Technology, Government of +India. A.K.S. is supported by NPDF grant PDF/2020/000797 from the SERB, Govern- +ment of India. P.B. and A.K.S. also acknowledge Mikael Chala, Bo-Qiang Lu, Jiang Zhu +and Kaius Loos for useful communications regarding cosmoTransitions code. +A +Field dependent mass matrices +Our numerical studies are based on the field-dependent masses (see subsection 2.1). The +corresponding scalar squared mass terms are evaluated at T = 0 using the tree-level un- +coloured scalar potential Vscalar (see below), including only the dominant higher-order con- +tributions ∆V (see Eq. (2.12)). Mathematically, for the uncoloured scalar squared mass +matrices +M2 +X,ij = M2 +φαφβ(HSM, HNSM, HS, NR) ≡ ∂2Vscalar +∂φα∂φβ +���� +φα̸=0 +, +(A.1) +where X = S (for the CP-even neutral scalar) or A (for the CP-odd neutral scalar) and +i, j = 1, ....., 7. Further, φα(β) = HSM, HNSM, HS, NR, ℜ(�ν1,2,3) for the CP-even neutral +– 38 – + +scalar and φα(β) = ANSM, AS, G0, NI, ℑ(�ν1,2,3) for the CP-even neutral scalar, respectively. +For the uncoloured electrically charged scalar, X = C with i, j = 1, ....., 8 and φα(β) ≡ C+ = +H+, G+, �e+ +L, �µ+ +L, �τ + +L , �e+ +R, �µ+ +R, �τ + +R . Here, we have used +�νi = ℜ�νi + iℑ�νi +√ +2 +≡ νRi + i�νIi +√ +2 +with +i = 1, 2, 3 ≡ e, µ, τ. +(A.2) +The full uncoloured scalar potential is given by +Vscalar = +����� +3 +� +i=1 +Y i +N �νi � +N − λSH0 +d +����� +2 ++ +������ +3 +� +i,j=1 +Y ij +e �li�ec +j − λSH0 +u +������ +2 ++ +������ +Y i +NH0 +u � +N − +3 +� +j=1 +Y ij +e H− +d �ec +j +������ +2 ++ +����λHu · Hd + κS2 + λN +2 +� +N 2 +���� +2 ++ +����� +3 +� +i=1 +Y i +N �Li · Hu + λNS � +N +����� +2 ++ +����� +3 +� +i=1 +Y ij +e Hd · �Li +����� +2 ++ +������ +λSH+ +u − +3 +� +i,j=1 +Y ij +e �νi�ec +j +������ +2 ++ +�����λSH− +d − +3 +� +i=1 +Y i +N�li � +N +����� +2 ++ +������ +3 +� +j=1 +Y ij +e H0 +d�ec +j − Y i +NH+ +u � +N +������ +2 ++ g2 +1 +8 (|Hd|2 − |Hu|2 + |�Li|2 − 2|�ec +i|2)2 + g2 +2 +2 +3 +� +a=1 +� +H† +d +τ a +2 Hd + H† +u +τ a +2 Hu + �L† +i +τ a +2 +�Li +�2 ++ m2 +Hd|Hd|2 + m2 +Hu|Hu|2 + m2 +S|S|2 + M 2 +N| � +N|2 + +3 +� +i,j=1 +m2 +�Lij �Lm∗ +i +�Lm +j + +3 +� +i,j=1 +m2 +�ec +ij�ecm∗ +i +�ecm +j ++ +3 +� +i=1 +(AeYe)ijHd · �Li�ec +j + λAλSHu · Hd + (ANYN)i�Li · Hu � +N + κAκ +3 S3 + λNAλN +2 +S � +N 2 ++ h.c. +(A.3) +Here Y ij +e +belongs to W ′ +MSSM (see Eq. +(2.1)) and m2 +Hd, m2 +Hu, m2 +�Lij, m2 +�ec +ij, (AeYe)ij are +encapsulated within −L′ +soft (see Eq. (2.2)). Further, i, j are generation indices, τ as are +Pauli spin matrices and m = 1, 2, as per the standard notation (see Refs. [27, 83–85, 87, 88] +for details). +In a similar way, one can derive field-dependent mass matrices for the uncoloured elec- +trically neutral and electrically charged fermions, i.e., neutralinos and charginos, directly +from the superpotential W (see Eq. (2.1)). Mathematically, the generic mass term for the +neutralino sector and the chargino sector are given by +− 1 +2 +� +ψ0T +i M0ijψ0 +j + h.c. +� +, +−1 +2(ψ+, ψ−)T Mχ±(ψ+, ψ−) + h.c., +(A.4) +respectively. Here basis for the neutralino sector is given by ψ0T = { �B0, � +W 0 +3 , �H0 +d, �H0 +u, �S, N, +ν1, ν2, ν3} involving neutral U(1)Y , SU(2)L gauginos ( �B0, � +W 0 +3 ), neutral higgsinos ( �H0 +d, �H0 +u), +singlino (�S), RH-neutrino (N) and LH-neutrinos (ν1,2,3). For charginos, including charged +SU(2)L gauginos (� +W ±), charged higgsinos ( �H+ +u , �H− +d ) and charged leptons (e± +L, R, µ± +L, R, +τ ± +L, R), one gets ψ+T = {� +W +, �H+ +u , e+ +R, µ+ +R, τ + +R } and ψ−T = {� +W −, �H− +d , e− +L, µ− +L, τ − +L }, respec- +– 39 – + +tively. We will start with the scalar mass squared matrices and will discuss the fermionic +sector subsequently.17 +A.1 +CP-even neutral scalars squared mass matrix +In the basis HSM, HNSM, HS, NR, ℜ(�ν1,2,3), non-zero entries of the symmetric M2 +S,ij are +M2 +S,11 ≃ +1 +16vuvd +� +8λvSv2 (Aλ + κvS) + 2λ2vuvd +� +−4 +� +v2 + 2v2 +S +� ++ H2 +NSM + 4H2 +S + 3H2 +SM +� ++vuvd +� +3∆λ2 + G2� � +H2 +NSM + 3H2 +SM +� +−4 cos 2β +� +v2 cos 2β +� +2λvS (Aλ + κvS) + vuvd +� +G − 2λ2� +vu +� ++ 3∆λ2vuvdH2 +SM +� ++vuvd +� +(4 sin 2β +� +3∆λ2HNSMHSM − 2λHS +�√ +2Aλ + κHS +�� +−3 +� +∆λ2 + G − 2λ2� � +2 sin 4β HNSMHSM + cos 4β +� +H2 +NSM − H2 +SM +�� �� +− 1 +2v +�λNv +2 +sin 2β +� +N2 +R − 2v2 +N +�� +, +(A.5) +M2 +S,12 ≃ +1 +16vuvd +�2v2 sin 4β +� +2λvS (Aλ + κvS) + vuvd +� +G − 2λ2�� +vuvd +−8λ cos 2β HS +�√ +2Aλ + κHS +� ++ 3 sin 4β +� +∆λ2 + G − 2λ2� � +H2 +NSM − H2 +SM +� +−6 cos 4β HNSMHSM +� +∆λ2 + G − 2λ2� ++ 2HNSMHSM +� +3∆λ2 + G + 2λ2� ++6∆λ2 sin 2β +� +H2 +NSM + H2 +SM +� � +− 1 +4 +� +λ cos 2β λN +� +N2 +R − 2v2 +N +� � +, +(A.6) +M2 +S,13 ≃ λ2HSHSM − 1 +2λ +�√ +2Aλ + 2κHS +� +(cos 2β HNSM + sin 2β HSM) , +(A.7) +M2 +S,14 ≃ −1 +2λλNNR (cos 2β HNSM + sin 2β HSM), +(A.8) +M2 +S,1 (4+i) ≃ 1 +2NRY i +N +�√ +2AN sin β + HS (λ cos β + λN sin β) +� +, +(A.9) +M2 +S,22 ≃ +1 +16vuvd +� +8λvSv2 (Aλ + κvS) + vuvd (3∆λ2 + G) +� +3H2 +NSM + H2 +SM +� ++2λ2vuvd +� +−4 +� +v2 + 2v2 +S +� ++ 3H2 +NSM + 4H2 +S + H2 +SM +� ++4 cos 2β +� +v2 cos 2β +� +2λvS (Aλ + κvS) + vdvu +� +G − 2λ2�� ++ 3∆λ2vdH2 +NSMvu +� ++vdvu +� +4 sin 2β +� +2λHS +�√ +2Aλ + κHS +� ++ 3∆λ2HNSMHSM +� ++3 +� +∆λ2 + G − 2λ2� � +2 sin 4β HNSMHSM + cos 4β +� +H2 +NSM − H2 +SM +�� �� ++ 1 +8v +� +cos β cot βλN +� +λv(cos 4β + 3) sec3 βv2 +N + 4λv sin β tan β N2 +R +�� +, +(A.10) +17While writing field-dependent masses, we ignore terms that are quadratic in vi, Y i +N and terms like +3� +i=1 +viY i +N, keeping in mind their smallness. Besides, as already stated, these terms do not play any crucial +role in the EWPT. Nevertheless, we have kept all these terms in our numerical analysis. +– 40 – + +M2 +S,23 ≃ 1 +2λ +�√ +2Aλ + 2κHS +� +(sin 2β HNSM − cos 2β HSM) + λ2HNSMHS,(A.11) +M2 +S,24 ≃ 1 +2λλNNR (sin 2β HNSM − cos 2β HSM), +(A.12) +M2 +S,2 (4+i) ≃ 1 +2NRY i +N +�√ +2AN cos β + HS (cos β λN − λ sin β ) +� +, +(A.13) +M2 +S,33 ≃ λvuvd (Aλ + 2κvS) +vS ++ κ +� +Aκ +�√ +2HS − vS +� ++ κ +� +3H2 +S − 2v2 +S +�� +− λ2v2 ++λ2 +2 +� +H2 +NSM + H2 +SM +� +− λκ cos 2β HNSMHSM + λκ +2 sin 2β +� +H2 +NSM − H2 +SM +� ++ 1 +2vS +� +λN +� +(κ + λN) vS +� +N2 +R − 2v2 +N +� +− v2 +NAλN +�� +, +(A.14) +M2 +S,34 ≃ 1 +2λNNR +�√ +2AλN + 2 (κ + λN) HS +� +, +(A.15) +M2 +S,3 (4+i) ≃ 1 +2Y i +NNR (HNSM (λN cos βλ sin β ) + HSM (λ cos β + λN sin β )), +(A.16) +M2 +S,44 ≃ +1 +4vN +� +− 2λλN cos 2β HNSMHSMvN+λ sin 2β vNλN +� +H2 +NSM − H2 +SM + 2v2� ++λNvN +� +2AλN +�√ +2HS − 2vS +� ++ 2 (κ + λN) H2 +S +� ++λNvN +� +λN +� +3N2 +R − 2v2 +N +� +− 4 (κ + λN) v2 +S +� � +, +(A.17) +M2 +S,4 (4+i) ≃ 1 +2Y i +N +�√ +2AN (cos β HNSM + sin β HSM) + HS +� +HNSM (λN cos β − λ sin β) ++HSM (λ cos β + λN sin β) +�� +, +(A.18) +M2 +S,(4+i) (4+j) ≃ δij +8 +� +− 2G sin 2β HNSMHSM − G cos 2β +� +H2 +NSM − H2 +SM +� +−8vNY i +N (vu (AN + λNvS) + λvdvS) +vi +− 2Gv2 cos 2β +� +−1 +4g2 +2 (sin β HNSM − cos β HSM) 2, +(A.19) +where we have used G = g2 +1 + g2 +2, v2 +u + v2 +d = v2 and i = 1, 2, 3 are generational indices. +A.2 +CP-odd neutral scalars squared mass matrix +In the basis ANSM, AS, G0, NI, ℑ(�ν1,2,3), non-zero entries of the symmetric M2 +A,ij are +M2 +A,11 ≃ +1 +16vdvu +� +8λvSv2 (Aλ + κvS) + Gvdvu +� +H2 +NSM − H2 +SM +� ++2λ2vdvu +� +−4 +� +v2 + 2v2 +S +� ++ H2 +NSM + 4H2 +S + 3H2 +SM +� ++ ∆λ2vdvu +� +3H2 +NSM + H2 +SM +� ++4 cos 2β +� +v2 cos 2β +� +2λvS (Aλ + κvS) + vuvd +� +G − 2λ2�� ++ ∆λ2vuvdH2 +NSM +� ++vuvd +� +4 sin 2β +� +2λHS +�√ +2Aλ + κHS +� ++ ∆λ2HNSMHSM +� ++ +� +∆λ2 + G − 2λ2� � +2 sin 4β HNSMHSM + cos 4β +� +H2 +NSM − H2 +SM +�� �� ++ 1 +8v +� +cos β cot β λN +� +λv(cos 4β + 3) sec3 β v2 +N + 4λv sin β tan β N2 +R +�� +, +(A.20) +– 41 – + +M2 +A,12 ≃ 1 +2λHSM +�√ +2Aλ − 2κHS +� +, +(A.21) +M2 +A,13 ≃ 1 +16 +�2v2 sin 4β +� +2λvS (Aλ + κvS) + +� +G − 2λ2� +vuvd +� +vuvd +−8λ cos 2β HS +�√ +2Aλ + κHS +� ++ 2∆λ2 sin 2β +� +H2 +NSM + H2 +SM +� ++2HNSMHSM +� +∆λ2 + G − 2λ2� +− 2 cos 4β HNSMHSM +� +∆λ2 + G − 2λ2� ++ sin 4β +� +∆λ2 + G − 2λ2� +(HNSM − HSM) (HNSM + HSM) +� +− 1 +4v +� +λλNv cos 2β +� +N2 +R − 2v2 +N +� � +, +(A.22) +M2 +A,14 ≃ −1 +2λλNHSMNR, +(A.23) +M2 +A,1 (4+i) ≃ −1 +2Y i +NNR +�√ +2AN cos β + HS (cos β λN − λ sin β ) +� +, +(A.24) +M2 +A,22 ≃ λvuvd (Aλ + 2κvS) +vS +− κAκ +�√ +2HS + vS +� +− 1 +2λ2 � +2v2 + H2 +NSM + H2 +SM +� ++λκ cos 2β HNSMHSM + λκ sin β cos β +� +H2 +SM − H2 +NSM +� ++ κ2 � +H2 +S − 2v2 +S +� +− 1 +2vS +� +λN +� +(v2 +NAλN + vS +� +2v2 +N (κ + λN) + N2 +R (κ − λN) +� �� +, +(A.25) +M2 +A,23 ≃ −1 +2λHNSM +�√ +2Aλ − 2κHS +� +, +(A.26) +M2 +A,24 = −1 +2λNNR +�√ +2AλN − 2κHS +� +, +(A.27) +M2 +A,2 (4+i) ≃ Y i +N +2 NR (HNSM (λN cos β − λ sin β) + HSM (λ cos β + λN sin β)), +(A.28) +M2 +A,33 ≃ +1 +16vuvd +� +8λvSv2 (Aλ + κvS) − Gvuvd +� +H2 +NSM − H2 +SM +� ++2λ2vuvd +� +−4 +� +v2 + 2v2 +S +� ++ 3H2 +NSM + 4H2 +S + H2 +SM +� ++ ∆λ2vuvd +� +H2 +NSM + 3H2 +SM +� +−4 cos 2β +� +v2 cos 2β +� +2λvS (Aλ + κvS) + vuvd +� +G − 2λ2�� ++ ∆λ2vdH2 +SMvu +� ++vuvd +� +4 sin 2β +� +∆λ2HNSMHSM − 2λHS +�√ +2Aλ + κHS +�� +− +� +∆λ2 + G − 2λ2� � +2 sin 4β HNSMHSM + cos 4β +� +H2 +NSM − H2 +SM +�� �� +− 1 +2v +� +λλNv sin β cos β +� +N2 +R − 2v2 +N +�� +, +(A.29) +M2 +A,34 ≃ 1 +2λλNHNSMNR, +(A.30) +M2 +A,3 (4+i) ≃ −Y i +N +2 NR +�√ +2AN sin β + HS (λ cos β + sin β λN) +� +, +(A.31) +– 42 – + +M2 +A,44 ≃ +1 +4vN +� +2λλN cos 2βHNSMHSMvN ++λλN sin 2βvN +� +−H2 +NSM + H2 +SM + 2v2� ++λNvN +� +− 2AλN +�√ +2HS + 2vS +� ++ 2 (λN − κ) H2 +S +� ++λNvN +� +λN +� +N2 +R − 2v2 +N +� +− 4v2 +S (κ + λN) +�� +, +(A.32) +M2 +A,4 (4+i) ≃ Y i +N +2 +� +HS +� +HNSM (λ sin β + λN cos β) + HSM (λN sin β − λ cos β) +� +− +√ +2AN (cos βHNSM + sin β HSM) +� +, +(A.33) +M2 +A, (4+i)(4+j) ≃ − δij +8vj +� +G cos 2βvj +� +H2 +NSM − H2 +SM + 2v2� ++ 2Gvj sin 2β HNSMHSM ++8v sin β vNY j +N (AN + λNvS) + 8λv cos β vNY j +NvS +� +−1 +4g2 +2 (sin β HNSM − cos β HSM)2, +(A.34) +M2 +A, 56 ≃ Y 1 +NY 2 +N +2 +(cos βHNSM + sin βHSM)2 , +(A.35) +M2 +A, 57 ≃ Y 1 +NY 3 +N +2 +(cos βHNSM + sin βHSM)2 +(A.36) +M2 +A,67 ≃ Y 2 +NY 3 +N +2 +(cos β HNSM + sin β HSM)2 . +(A.37) +where we have used G = g2 +1+g2 +2, v2 +u+v2 +d = v2 and i = 1, 2, 3 are generational indices. At the +physical vacuum, i.e., +� +⟨HSM⟩, ⟨HNSM⟩, ⟨HS⟩, ⟨NR⟩ +� += +�√ +2v, 0, +√ +2vS, +√ +2vN +� +, neglecting +terms like v2 +i , Y i2 +N , +3� +i=1 +viY i +N, the Goldstone mode appears massless and decouples from the +other CP-odd states. +A.3 +Uncoloured charged scalars squared mass matrix +Non-zero entries for the uncoloured symmetric charged scalar mass squared matrix, i.e., +C+MCC−, in the basis C+ = H+, G+, �e+ +L, �µ+ +L, �τ + +L , �e+ +R, �µ+ +R, �τ + +R are +M2 +C,11 ≃ 1 +16 +� +2 cos 2βg2 +1 +� +2 sin 2βHNSMHSM + cos 2β(2v2 + H2 +NSM − H2 +SM) +� ++g2 +2 +� +(1 + cos 4β)H2 +NSM + 2 sin 4βHNSMHSM − (−3 + cos 4β)H2 +SM + 2v2(1 + cos 4β) ++4 cos 2β +� +− 4v2λ2(3 + cos 4β) + 2λ2(4H2 +S + (−1 + cos 4β)H2 +SM) − 16λ2v2 +s ++2∆λ2 sin2 2βH2 +SM ++4(λ2 sin2 2β + ∆λ22 cos4 β)H2 +SM + 4(λ2 sin 4β − 4∆λ2 cos3 β sin β)HNSMHSM ++4λvSAλ(3 + cos 4β) csc β sec β + 4λ sin β +� +2HS( +√ +2Aλ + κHS + λNN2 +R) +� ++4λ(3 + cos 4β) csc 2β(2κv2 +S + v2 +NλN) +� +, +(A.38) +– 43 – + +M2 +C,12 ≃ 1 +16 +� � +2 cos 4β(2λ2 − G − ∆λ2) + 2(2λ2 + g2 +1 − g2 +2 + ∆λ2) +� +HNSMHSM ++2 sin 2β∆λ2(H2 +NSM + (1 + 2 sin2 β)H2 +SM) ++ sin 4β +� +(G − 2λ2)(2v2 + H2 +NSM − H2 +SM) + (H2 +NSM − H2 +SM)∆λ2 +� ++8λ cos 2β +� +κH2 +S + Aλ( +√ +2HS − 2vS) − 2κv2 +S + λN +2 (N2 +R − 2v2 +N) +� � +,(A.39) +M2 +C1, (2+i) ≃ δij +4 +� +vj +� � +g2 +2 cos 2β + 2(Y ij +e )2 sin2 β +� +HNSM + sin 2β +� +g2 +2 − (Y ij +e )2� +HSM +� +−2Y j +NNR +�√ +2AN cos β + cos β +� +λNHS − Y ij +e (sin βHNSM +− cos βHSM) +� ++ λ sin βHS +�� +, +(A.40) +M2 +C,1 (5+i) ≃ − 1 +√ +2AeY ij +e vj sin β − 1 +2Y ij +e Y j +N sin β(NR) (cos βHNSM + sin βHSM) , +(A.41) +M2 +C,22 ≃ 1 +16 +� +2G cos2 β(H2 +SM − 2v2) + 4λ2 sin2 2β(H2 +SM − 2v2) + 8λ2(H2 +S − 2v2 +S) ++ +� +− 2g2 +1 cos2 2β + g2 +2(cos 4β − 3) + (cos 4β − 1)(2λ2 − ∆λ2) +� +H2 +NSM ++2 +� +sin 4β(2λ2 − G)8 cos β sin3 β∆λ2 +� +HSMHNSM + 4λ sin 2β +� +− 2κH2 +S ++4κv2 +S + Aλ +� +−2 +√ +2HS + 4vS − λN(N2 +R − 2v2 +N) +� �� +, +(A.42) +M2 +C2, (2+i) ≃ δij +4 +� +vj +� � +−g2 +2 cos 2β − 2(Y ij +e )2 sin2 β +� +HSM + sin 2β +� +g2 +2 − (Y ij +e )2� +HNSM +� +−2Y j +NNR +�√ +2AN sin β + sin β +� +λNHS − Y ij +e (sin βHNSM +− cos βHSM) +� +− λ cos βHS +�� +, +(A.43) +M2 +C,2 (5+i) ≃ −(AeYe)ij +√ +2 +vj cos β − 1 +2Y ij +e Y j +NNR +� +cos2 βHNSM + sin 2β +2 +HSM +� +, (A.44) +M2 +C,(2+i)(2+j) ≃ m2 +�Lij + δij +8 +� +(g2 +1 − g2 +2)(cos 2β(H2 +SM − H2 +NSM) − 2 sin 2βHSMHNSM) ++4(Y ij +e )2(cos βHSM − sin βHNSM)2 +� +, +(A.45) +M2 +C,(2+i)(5+j) ≃ δij(AeYe)ij +√ +2 +(cos βHSM − sin βHNSM) +−δijλY ij +e +2 +(cos βHNSM + sin βHSM)HS, +(A.46) +M2 +C,(5+i)(5+j) ≃ m2 +�ec +ij − δij +4 +� +g2 +1(cos 2β(H2 +SM − H2 +NSM) − 2 sin 2βHSMHNSM) +−2(Y ij +e )2(cos βHSM − sin βHNSM)2 +� +, +(A.47) +– 44 – + +where we have used G = g2 +1+g2 +2, v2 +u+v2 +d = v2 and i = 1, 2, 3 are generational indices. At the +physical vacuum, i.e., +� +⟨HSM⟩, ⟨HNSM⟩, ⟨HS⟩, ⟨NR⟩ +� += +�√ +2v, 0, +√ +2vS, +√ +2vN +� +, neglecting +terms like v2 +i , Y i2 +N , +3� +i=1 +viY i +N, the Goldstone mode appears massless and decouples from the +other charged states. +A.4 +Neutralino mass matrix +In the basis of ψ0T = { �B0, � +W 0 +3 , �H0 +d, �H0 +u, �S, N, ν1, ν2, ν3}, the matrix M0 (see Eq. (A.4)) is +given as +M0 = +� +� +� +M6×6 m6×3 +mT +3×6 03×3 +� +� +� , +(A.48) +where we have used ⟨�νi⟩ = vi (see Eq. (2.6)) as the LH-sneutrinos are not dynamical in +nature (see subsection 2.1). Further, matrices mT +3×6 and M6×6, using Eq. (2.8), are given +as +mT +3×6 = +� +� +� +� +� +� +� +� +� +−g1ve +√ +2 +g2ve +√ +2 0 Y 1 +NNR +√ +2 +0 Y 1 +N +√ +2Y +−g1vµ +√ +2 +g2vµ +√ +2 0 Y 2 +NNR +√ +2 +0 Y 2 +N +√ +2Y +−g1vτ +√ +2 +g2vτ +√ +2 0 Y 3 +NNR +√ +2 +0 Y 3 +N +√ +2Y +� +� +� +� +� +� +� +� +� +, +(A.49) +with Y = +� +sβHSM + cβHNSM +� +and the symmetric matrix M6×6 is given as, +� +� +� +� +� +� +� +� +� +� +� +� +� +� +� +� +� +� +� +� +� +� +M1 +0 +− g1 +2 X +g1 +2 Y +0 +0 +M2 +g2 +2 X +− g2 +2 Y +0 +0 +0 +− λ +√ +2HS − λ +√ +2Y +0 +0 +− λ +√ +2X +0 +√ +2κHS +λN +2 +√ +2NR +λN +√ +2HS +� +� +� +� +� +� +� +� +� +� +� +� +� +� +� +� +� +� +� +� +� +� +, +(A.50) +where we have omitted symmetric entries, i.e., M0ij = M0ji for ̸= j and X = +� +cβHSM − +sβHNSM +� +. +A.5 +Chargino mass matrix +Using a similar approach, in the basis ψ+T = {� +W +, �H+ +u , e+ +R, µ+ +R, τ + +R } and ψ−T = {� +W −, +�H− +d , e− +L, µ− +L, τ − +L }, the matrix M± is given as +M± = +� +0 XT +X +0 +� +, +(A.51) +– 45 – + +where the 5 × 5 matrix X is given by +� +� +� +� +� +� +� +� +� +� +� +� +� +� +� +� +� +� +M2 +g2 +√ +2Y +0 +0 +0 +g2 +√ +2X +λ +√ +2HS +−Y 11 +e ve −Y 22 +e ve −Y 33 +e vτ +g2ve − +Y 1 +N NR +√ +2 +Y 11 +e +√ +2 X +0 +0 +g2vµ − +Y 2 +N NR +√ +2 +0 +Y 22 +e +√ +2 X +0 +g2vτ − +Y 3 +N NR +√ +2 +0 +0 +Y 33 +e +√ +2 X +� +� +� +� +� +� +� +� +� +� +� +� +� +� +� +� +� +� +. +(A.52) +Here we have used Y ij +e += Y ii +e δij. +B +Neutral scalar mass matrices after the EWSB +Weak couplings among the LH-handed sneutrino states and the remaining states, as already +discussed in section 2, suggest that one can safely decouple the LH-sneutrino-dominated +states from the CP-even and CP-odd scalar squared mass matrices without any loss of +generality. +After the aforesaid detachment, both CP-even and CP-odd scalar squared +mass matrices appear to be 4 × 4 in size. +The full 7 × 7 squared mass matrices are +given in subsections A.1 & A.2, including LH-sneutrino states. In this section, squared +mass matrices of the CP-even and the CP-odd Higgses are given after the EW symmetry +breaking, i.e., using relations given in subsections A.1 & A.2 and considering ⟨HSM⟩ = +√ +2v, +⟨HNSM⟩ = 0, ⟨HS⟩ = +√ +2vS, ⟨NR⟩ = +√ +2vN, ⟨ANSM⟩ = 0, ⟨AS⟩ = 0, ⟨NI⟩ = 0 (see +subsection 2.1). For the CP-even states, we consider the {HSM, HNSM, HS, NR} basis while +for the CP-odd ones we use {ANSM, AS, G0, AN} basis. +B.1 +CP-even mass squared elements +M2 +S,11 = λ2v2 sin2 2β + (g2 +1 + g2 +2)v2 +2 +cos2 2β, M2 +S,12 = λ2v2 +2 +sin 4β − (g2 +1 + g2 +2)v2 +4 +sin 4β, +M2 +S,13 = 2λ2vvS − λv(Aλ + 2κvS) sin 2β, +M2 +S,14 = −λλNvN sin 2β, +M2 +S,22 = 2λvS(Aλ + κvS) csc 2β + λλNv2 +N csc 2β − λ2v2 sin2 2β + (g2 +1 + g2 +2)v2 +2 +sin2 2β, +M2 +S,23 = −λv(Aλ + 2κvS) cos 2β, +M2 +S,24 = −λλNvvN cos 2β, +M2 +S,33 = κvS(Aκ + 4κvS) + λv2Aλ +2vS +sin 2β − λNv2 +NAλN +2vS +, +M2 +S,34 = λNvNAλN + 2λNκvSvN + 2λ2 +NvSvN, +M2 +S,44 = λ2 +Nv2 +N, +(B.1) +where we have used the symmetric nature of these entries, i.e., M2 +S,ij = M2 +S,ji for i ̸= j. +– 46 – + +B.2 +CP-odd mass squared elements +M2 +A,11 = λλNv2 +N csc 2β + 2λvS(Aλ + κvS) csc 2β, +M2 +A,12 = λvAλ − 2λκvvS, +M2 +A,13 = 0, +M2 +A,14 = −λλNvvN, +M2 +A,22 = κ(2λv2 sin 2β − 3vSAκ) + λv2Aλ +2vS +sin 2β − λNv2 +N +2vS +(AλN + 4κvS), +M2 +A,23 = 0, +M2 +A,24 = 2λNκvSvN − λNvNAλN , +M2 +A,33 = 0, +M2 +A,34 = 0, +M2 +A,44 = λλNv2 sin 2β − 2λNvS(AλN + κvS), +(B.2) +where we have used the symmetric nature of these entries, i.e., M2 +A,ij = M2 +A,ji for i ̸= j. +C +Counter terms +As already addressed in subsection 2.2, after including Coleman-Weinberg contributions +(see Eq. (2.15)), counter terms are necessary to restore the original physical minima and +masses. These terms are encapsulated within Vct which is written as +Vct = δm2 +Hd |Hd|2 + δm2 +Hu |Hu|2 + δm2 +S |S|2 + δM2 +N | � +N|2 + δλAλ (SHu · Hd + h.c.) ++δλNAλN (S � +N � +N + h.c.) + δλ2 +2 +|Hu|4, +(C.1) +where δm2 +Hd, δm2 +Hu, δm2 +S, δM2 +N , δλAλ, δλNAλN , δλ2 are counter terms corresponding to en- +tries given by Eq. (2.2) and Eq. (2.12). Entries corresponding to δm2 +Hd, δm2 +Hu are encapsu- +lated within −L′ +soft of Eq. (2.2). In order to maintain the location of the physical minima +solutions for the counter-terms must satisfy the following relations: +δm2 +Hd += +1 +√ +2v +� +tan β +∂Veff +∂HNSM +− ∂Veff +∂HSM +� ++ µ sec2 β +2λv +∂2Veff +∂HS∂HSM +, +δm2 +Hu += csc2 β +4vλ +∂ +∂HSM +�√ +2λ(cos 2β − 2) Veff + 2µ∂Veff +∂HS ++ 2λv ∂Veff +∂HSM +� +− 1 +√ +2v cot β +∂Veff +∂HNSM +, +δm2 +S += λ +2µ +∂ +∂HS +� +v ∂Veff +∂HSM ++ vN +∂Veff +∂NR +− +√ +2 Veff +� +, +δM2 +N += − 1 +2vN +∂ +∂NR +�√ +2 Veff − 2µ +λ +∂Veff +∂HS +� +, +δλAλ += csc 2β +v +∂2Veff +∂HS∂HSM +, +δλNAλN += − 1 +2vN +∂2Veff +∂HS∂NR +, +δλ2 = csc4 β +4v3 +∂ +∂HSM +�√ +2 Veff − 2v ∂Veff +∂HSM +� +. +(C.2) +– 47 – + +Identifying δλ2 as a counter term for ∆λ2, a quartic coupling among Hu as given in Eq. +(2.12), seems inconsistent. However, in reality, ∆λ2 is connected to the soft SUSY-breaking +terms as the estimation of ∆λ2 includes soft SUSY-breaking terms of the stop sector (see +Eq. (2.13)). +D +Daisy coefficients +The Daisy coefficients [133–137], ci, using Eq. (2.18) is given by +ci = m2 +i (φα, T) − m2 +i (φα) +T +, +(D.1) +and can be estimated using the high-temperature limit, i.e., T 2 ≫ m2 (m depicts a generic +mass term involved in the calculation) [133], of the thermal corrections from V T̸=0 +1−loop (see +Eq. (2.17)) as +1 +T 2 +∂2V 1−loop +T̸=0 +∂φi∂φj +. +(D.2) +Daisy coefficients are calculated at the T 2 ≫ m2 limit which helps to efface gauge depen- +dence for these coefficients although V 1−loop +T̸=0 +, as already discussed in subsection 2.3, has +explicit gauge dependence. The form of Eq. (D.2), except the 1/T 2 factor, looks similar to +relations that are conventionally used for the computation of i, j-th entry of the different +scalar mass matrices from the concerned potential. For the calculation of Daisy coefficients +we use V 1−loop +T̸=0 +as a function of m2 +i (φα) and not as a function of m2 +i (φα, T). However, +while computing V 1−loop +T̸=0 +and V ′1−loop +CW +(see Eq. (2.20)) we use thermal masses m2 +i (φα, T). +Expanding thermal function JB/F (see Eq. (2.19)), in the limit T 2 ≫ m2, one gets in the +leading order [137, 238] +V T̸=0 +1−loop +∼ +T 2 +48 +� +2 +� +i=B +nim2 +i + +� +i=F +nim2 +i +� +, +(D.3) +where B(F) represents boson (fermion) and ni depicts the associated degrees of freedom, +as already detailed in subsection 2.2. It is also apparent from Eq. (D.3) that contribu- +tions from the bosonic sources are the leading ones. Also, as detailed in Ref.[137], cubic +contributions in the V T̸=0 +1−loop appears only via bosons. Further, quartic contributions from +fermions are suppressed compared to the same from bosons and do not affect the shift in +the VEVs [137]. Thus, we neglect contributions from the relevant fermionic sources (see +Ref. [239] for a similar discussion in the context of the NMSSM.). In light of Eq. (D.2) +and Eq. (D.3), non-zero Daisy coefficients are given below where field-dependent masses +– 48 – + +are considered as a function of all bosonic degrees of freedom. +cHSMHSM = cG0G0 = λ2 +4 + (3m2 +Z + 4m2 +W ) +8v2 ++ m2 +Z +4v2 sin2 θw cos2 β + m2 +t +4v2 + ∆λ2 +4v2 , +cHSMHNSM = cHNSMG0 = m2 +t +4v2 +1 +tan2 β + ∆λ2 sin 2β +8 +− m2 +Z +8v2 sin2 θw sin 2β, +cHNSMHNSM = cANSMANSM = λ2 +4 + (m2 +Z + 4m2 +W ) +8v2 ++ +m2 +t +4v2 tan2 β + m2 +Z +4v2 sin2 θw sin2 β ++ ∆λ2 +4 cos2 β, +cHSHS = λ2 + κ2 +2 ++ λ2 +N +8 , cASAS = λ2 + κ2 +3 ++ λ2 +N +12 , cNRNR = λ2 +N +4 , cNINI = λ2 +N +6 , +cH+H− = λ2 +6 + (m2 +Z + 8m2 +W ) +24v2 +− m2 +Z +4v2 sin2 θw sin2 β + +m2 +t +4v2 tan2 β +1 +tan2 β + ∆λ2 +4 cos2 β, +cH+G− = +m2 +t +4v2 tan2 β +1 +tan2β + ∆λ2 sin 2β +8 +− m2 +Z +8v2 sin2 θw sin 2β, +cG+G− = λ2 +6 + (7m2 +Z + 8m2 +W ) +24v2 +− m2 +Z +4v2 sin2 θw sin2 β + m2 +t +4v2 + ∆λ2 +4 sin2 β, +(D.4) +where mW , mZ represent masses for the W ±, Z0 bosons, respectively and θw is Weinberg +angle [110]. +Longitudinal modes of the massive gauge bosons also yield non-zero Daisy coefficients +[240, 241] +cW + +L W − +L = cW 3 +LW 3 +L = 5 +2g2 +2, +cBLBL = 13 +6 g2 +1, +(D.5) +where W ± +L , W 3 +L, BL correspond to longitudinal modes of the SM SU(2)L, U(1)Y gauge +bosons. These results are the same as the Z3-invariant NMSSM as gauge sector of the +chosen NMSSM + one RH-neutrino framework remains exactly the same as the Z3-invariant +NMSSM. Finally, at T ̸= 0 the photon (γ) also gets a temperature-dependent mass, i.e., a +non-vanishing longitudinal component, which should also be included in the field-dependent +mass matrix used to evaluate eigenvalues of the electrically neutral EW gauge bosons, γ, Z0 +at T ̸= 0. +m2 +ZLγL(HSM, HNSM, HS, NR, T) = +� +� +� +g2 +2 +H2 +SM+H2 +NSM +4 ++ 5 +2g2 +2T 2 +−g1g2 +H2 +SM+H2 +NSM +4 +−g1g2 +H2 +SM+H2 +NSM +4 +g2 +1 +H2 +SM+H2 +NSM +4 ++ 13 +6 g2 +1T 2 +� +� +� . +(D.6) +E +Minimization conditions +As already stated in section 3 that one can trade different soft-masses, i.e., m2 +Hu, m2 +Hd, +m2 +�Lij, m2 +S, M2 +N (see Eq. (2.2)) with the corresponding VEVs (see Eq. (2.6)) using min- +imization conditions of the Vtree (see Eq. (2.3)). One can also use the neutral part of +Vscalar as depicted in Eq. (A.3). Mathematically, the minimization condition gives a set of +– 49 – + +equations like +�∂Vtree +∂Xi +����� +X=⟨X⟩ += 0, +(E.1) +where Xi = H0 +u, H0 +d, �νi, S, � +N, and ⟨X⟩ represents all the concerned VEVs as given in Eq. +(2.6). In detail, assuming all superpotential couplings (see Eq. (2.1)) to be real, one gets +�∂Vtree +∂H0u +����� +VEVs += λvd +� +λvuvd − κv2 +S − λN +2 v2 +N +� ++ Y i2 +N v2 +Nvu + λ2v2 +Svu + m2 +Huvu ++ +3 +� +j=1 +Y j +Nvj +� 3 +� +i=1 +Y i +Nvivu + λNvSvN +� ++ g2 +1 + g2 +2 +4 +� +v2 +d + +3 +� +i=1 +v2 +i − v2 +u +� +vu ++ λAλvSvd + +3 +� +i=1 +(ANYN)ivivN, +(E.2) +�∂Vtree +∂H0 +d +����� +VEVs += λvu +� +λvuvd − κv2 +S − λN +2 v2 +N +� ++ λvS +� +λvSvd − +3 +� +i=1 +Y i +NvivN +� ++ g2 +1 + g2 +2 +4 +� +v2 +d + +3 +� +i=1 +v2 +i − v2 +u +� +vd + m2 +Hdvd + λAλvSvu, +(E.3) +�∂Vtree +∂ �νi +����� +VEVs += Y i +Nvu +� +� +3 +� +j=1 +Y j +Nvjvu + λNvSvN +� +� + Y i +NvN +� +� +3 +� +j=1 +Y j +NvjvN − λvdvS +� +� ++ g2 +1 + g2 +2 +4 +� +v2 +d + +3 +� +i=1 +v2 +i − v2 +u +� +vi + (ANYN)ivuvN + +3 +� +j=1 +m2 +�Lijvj, +(E.4) +�∂Vtree +∂S +����� +VEVs += 2κvS +� +−λvuvd + κv2 +S + λN +2 v2 +N +� ++ λvd +� +λvSvd − +3 +� +i +Y i +NvivN +� ++ λNvN +� 3 +� +i=1 +Y i +Nvivu + λNvSvN +� ++ λ2v2 +uvS + m2 +SvS + λAλvuvd ++ κAκv2 +S + λNAλN +2 +v2 +N, +(E.5) +�∂Vtree +∂ � +N +����� +VEVs += λNvN +� +−λvuvd + κv2 +S + λN +2 v2 +N +� ++ λNvS +� 3 +� +i=1 +Y i +Nvivu + λNvSvN +� ++ +3 +� +j=1 +Y j +Nvj +� 3 +� +i=1 +Y i +NvivN − λvSvd +� ++ Y i2 +N v2 +uvN + M2 +NvN ++ +3 +� +i=1 +(ANYN)ivivu + λAλN vSvN. +(E.6) +– 50 – + +References +[1] Planck collaboration, Planck 2018 results. VI. Cosmological parameters, Astron. +Astrophys. 641 (2020) A6 [1807.06209]. +[2] J. M. Cline, Baryogenesis, in Les Houches Summer School - Session 86: Particle Physics +and Cosmology: The Fabric of Spacetime, 9, 2006, hep-ph/0609145. +[3] G. W. Anderson and L. J. Hall, The Electroweak phase transition and baryogenesis, Phys. +Rev. D 45 (1992) 2685. +[4] D. Curtin, P. Meade and C.-T. Yu, Testing Electroweak Baryogenesis with Future Colliders, +JHEP 11 (2014) 127 [1409.0005]. +[5] M. Artymowski, M. Lewicki and J. D. Wells, Gravitational wave and collider implications of +electroweak baryogenesis aided by non-standard cosmology, JHEP 03 (2017) 066 +[1609.07143]. +[6] T. Modak and E. Senaha, Probing Electroweak Baryogenesis induced by extra bottom +Yukawa coupling via EDMs and collider signatures, JHEP 11 (2020) 025 [2005.09928]. +[7] A. D. Sakharov, Violation of CP Invariance, C asymmetry, and baryon asymmetry of the +universe, Pisma Zh. Eksp. Teor. Fiz. 5 (1967) 32. +[8] M. B. Gavela, P. Hernandez, J. Orloff, O. Pene and C. Quimbay, Standard model CP +violation and baryon asymmetry. Part 2: Finite temperature, Nucl. Phys. B 430 (1994) 382 +[hep-ph/9406289]. +[9] W. Bernreuther, CP violation and baryogenesis, Lect. Notes Phys. 591 (2002) 237 +[hep-ph/0205279]. +[10] D. E. Morrissey and M. J. Ramsey-Musolf, Electroweak baryogenesis, New J. Phys. 14 +(2012) 125003 [1206.2942]. +[11] ATLAS collaboration, Observation of a new particle in the search for the Standard Model +Higgs boson with the ATLAS detector at the LHC, Phys. Lett. B 716 (2012) 1 [1207.7214]. +[12] CMS collaboration, Observation of a New Boson at a Mass of 125 GeV with the CMS +Experiment at the LHC, Phys. Lett. B 716 (2012) 30 [1207.7235]. +[13] K. Kajantie, M. Laine, K. Rummukainen and M. E. Shaposhnikov, Is there a hot +electroweak phase transition at mH ≳ mW ?, Phys. Rev. Lett. 77 (1996) 2887 +[hep-ph/9605288]. +[14] K. Rummukainen, M. Tsypin, K. Kajantie, M. Laine and M. E. Shaposhnikov, The +Universality class of the electroweak theory, Nucl. Phys. B 532 (1998) 283 +[hep-lat/9805013]. +[15] F. Csikor, Z. Fodor and J. Heitger, Endpoint of the hot electroweak phase transition, Phys. +Rev. Lett. 82 (1999) 21 [hep-ph/9809291]. +[16] A. Mazumdar and G. White, Review of cosmic phase transitions: their significance and +experimental signatures, Rept. Prog. Phys. 82 (2019) 076901 [1811.01948]. +[17] R. Apreda, M. Maggiore, A. Nicolis and A. Riotto, Gravitational waves from electroweak +phase transitions, Nucl. Phys. B 631 (2002) 342 [gr-qc/0107033]. +[18] C. Grojean, G. Servant and J. D. Wells, First-order electroweak phase transition in the +standard model with a low cutoff, Phys. Rev. D 71 (2005) 036001 [hep-ph/0407019]. +– 51 – + +[19] D. J. Weir, Gravitational waves from a first order electroweak phase transition: a brief +review, Phil. Trans. Roy. Soc. Lond. A 376 (2018) 20170126 [1705.01783]. +[20] J. Ellis, M. Lewicki and J. M. No, On the Maximal Strength of a First-Order Electroweak +Phase Transition and its Gravitational Wave Signal, JCAP 04 (2019) 003 [1809.08242]. +[21] T. Alanne, T. Hugle, M. Platscher and K. Schmitz, A fresh look at the gravitational-wave +signal from cosmological phase transitions, JHEP 03 (2020) 004 [1909.11356]. +[22] C. Caprini et al., Detecting gravitational waves from cosmological phase transitions with +LISA: an update, JCAP 03 (2020) 024 [1910.13125]. +[23] F. Costa, S. Khan and J. Kim, A two-component dark matter model and its associated +gravitational waves, JHEP 06 (2022) 026 [2202.13126]. +[24] A. Ahriche, K. Hashino, S. Kanemura and S. Nasri, Gravitational Waves from Phase +Transitions in Models with Charged Singlets, Phys. Lett. B 789 (2019) 119 [1809.09883]. +[25] V. R. Shajiee and A. Tofighi, Electroweak Phase Transition, Gravitational Waves and Dark +Matter in Two Scalar Singlet Extension of The Standard Model, Eur. Phys. J. C 79 (2019) +360 [1811.09807]. +[26] A. Alves, T. Ghosh, H.-K. Guo, K. Sinha and D. Vagie, Collider and Gravitational Wave +Complementarity in Exploring the Singlet Extension of the Standard Model, JHEP 04 +(2019) 052 [1812.09333]. +[27] H. E. Haber and G. L. Kane, The Search for Supersymmetry: Probing Physics Beyond the +Standard Model, Phys. Rept. 117 (1985) 75. +[28] J. R. Espinosa, M. Quiros and F. Zwirner, On the electroweak phase transition in the +minimal supersymmetric Standard Model, Phys. Lett. B 307 (1993) 106 [hep-ph/9303317]. +[29] M. Carena, M. Quiros and C. E. M. Wagner, Opening the window for electroweak +baryogenesis, Phys. Lett. B 380 (1996) 81 [hep-ph/9603420]. +[30] D. Delepine, J. M. Gerard, R. Gonzalez Felipe and J. Weyers, A Light stop and electroweak +baryogenesis, Phys. Lett. B 386 (1996) 183 [hep-ph/9604440]. +[31] M. Laine and K. Rummukainen, The MSSM electroweak phase transition on the lattice, +Nucl. Phys. B 535 (1998) 423 [hep-lat/9804019]. +[32] J. M. Cline and G. D. Moore, Supersymmetric electroweak phase transition: Baryogenesis +versus experimental constraints, Phys. Rev. Lett. 81 (1998) 3315 [hep-ph/9806354]. +[33] C. Balazs, M. Carena, A. Menon, D. E. Morrissey and C. E. M. Wagner, The +Supersymmetric origin of matter, Phys. Rev. D 71 (2005) 075002 [hep-ph/0412264]. +[34] C. Lee, V. Cirigliano and M. J. Ramsey-Musolf, Resonant relaxation in electroweak +baryogenesis, Phys. Rev. D 71 (2005) 075010 [hep-ph/0412354]. +[35] M. Carena, G. Nardini, M. Quiros and C. E. M. Wagner, The Baryogenesis Window in the +MSSM, Nucl. Phys. B 812 (2009) 243 [0809.3760]. +[36] A. Menon and D. E. Morrissey, Higgs Boson Signatures of MSSM Electroweak +Baryogenesis, Phys. Rev. D 79 (2009) 115020 [0903.3038]. +[37] M. Carena, G. Nardini, M. Quiros and C. E. M. Wagner, MSSM Electroweak Baryogenesis +and LHC Data, JHEP 02 (2013) 001 [1207.6330]. +– 52 – + +[38] D. Curtin, P. Jaiswal and P. Meade, Excluding Electroweak Baryogenesis in the MSSM, +JHEP 08 (2012) 005 [1203.2932]. +[39] ATLAS collaboration, Search for associated production of a Z boson with an invisibly +decaying Higgs boson or dark matter candidates at √s =13 TeV with the ATLAS detector, +Phys. Lett. B 829 (2022) 137066 [2111.08372]. +[40] CMS collaboration, Search for invisible decays of the Higgs boson produced via vector boson +fusion in proton-proton collisions at √s=13 TeV, Phys. Rev. D 105 (2022) 092007 +[2201.11585]. +[41] ATLAS collaboration, Search for invisible Higgs-boson decays in events with vector-boson +fusion signatures using 139 fb−1 of proton-proton data recorded by the ATLAS experiment, +JHEP 08 (2022) 104 [2202.07953]. +[42] CMS collaboration, A portrait of the Higgs boson by the CMS experiment ten years after +the discovery, Nature 607 (2022) 60 [2207.00043]. +[43] K. Krizka, A. Kumar and D. E. Morrissey, Very Light Scalar Top Quarks at the LHC, Phys. +Rev. D 87 (2013) 095016 [1212.4856]. +[44] A. Delgado, G. F. Giudice, G. Isidori, M. Pierini and A. Strumia, The light stop window, +Eur. Phys. J. C 73 (2013) 2370 [1212.6847]. +[45] R. Gr¨ober, M. M. M¨uhlleitner, E. Popenda and A. Wlotzka, Light Stop Decays: +Implications for LHC Searches, Eur. Phys. J. C 75 (2015) 420 [1408.4662]. +[46] J. E. Kim and H. P. Nilles, The mu Problem and the Strong CP Problem, Phys. Lett. B 138 +(1984) 150. +[47] I. Esteban, M. C. Gonzalez-Garcia, M. Maltoni, T. Schwetz and A. Zhou, The fate of hints: +updated global analysis of three-flavor neutrino oscillations, JHEP 09 (2020) 178 +[2007.14792]. +[48] M. C. Gonzalez-Garcia, M. Maltoni and T. Schwetz, NuFIT: Three-Flavour Global Analyses +of Neutrino Oscillation Experiments, Universe 7 (2021) 459 [2111.03086]. +[49] L. J. Hall and M. Suzuki, Explicit R-Parity Breaking in Supersymmetric Models, Nucl. +Phys. B 231 (1984) 419. +[50] M. Hirsch and J. W. F. Valle, Supersymmetric origin of neutrino mass, New J. Phys. 6 +(2004) 76 [hep-ph/0405015]. +[51] R. Barbier et al., R-parity violating supersymmetry, Phys. Rept. 420 (2005) 1 +[hep-ph/0406039]. +[52] R. N. Mohapatra et al., Theory of neutrinos: A White paper, Rept. Prog. Phys. 70 (2007) +1757 [hep-ph/0510213]. +[53] P. F. de Salas, D. V. Forero, S. Gariazzo, P. Mart´ınez-Mirav´e, O. Mena, C. A. Ternes et al., +2020 global reassessment of the neutrino oscillation picture, JHEP 02 (2021) 071 +[2006.11237]. +[54] U. Ellwanger, C. Hugonie and A. M. Teixeira, The Next-to-Minimal Supersymmetric +Standard Model, Phys. Rept. 496 (2010) 1 [0910.1785]. +[55] M. Pietroni, The Electroweak phase transition in a nonminimal supersymmetric model, +Nucl. Phys. B 402 (1993) 27 [hep-ph/9207227]. +– 53 – + +[56] A. T. Davies, C. D. Froggatt and R. G. Moorhouse, Electroweak baryogenesis in the +next-to-minimal supersymmetric model, Phys. Lett. B 372 (1996) 88 [hep-ph/9603388]. +[57] S. J. Huber, T. Konstandin, T. Prokopec and M. G. Schmidt, Electroweak Phase Transition +and Baryogenesis in the nMSSM, Nucl. Phys. B 757 (2006) 172 [hep-ph/0606298]. +[58] W. Huang, Z. Kang, J. Shu, P. Wu and J. M. Yang, New insights in the electroweak phase +transition in the NMSSM, Phys. Rev. D 91 (2015) 025006 [1405.1152]. +[59] J. Kozaczuk, S. Profumo, L. S. Haskins and C. L. Wainwright, Cosmological Phase +Transitions and their Properties in the NMSSM, JHEP 01 (2015) 144 [1407.4134]. +[60] S. Baum, M. Carena, N. R. Shah, C. E. M. Wagner and Y. Wang, Nucleation is more than +critical: A case study of the electroweak phase transition in the NMSSM, JHEP 03 (2021) +055 [2009.10743]. +[61] M. Carena, G. Nardini, M. Quiros and C. E. M. Wagner, The Effective Theory of the Light +Stop Scenario, JHEP 10 (2008) 062 [0806.4297]. +[62] P. Minkowski, µ → eγ at a Rate of One Out of 109 Muon Decays?, Phys. Lett. B 67 (1977) +421. +[63] T. Yanagida, Horizontal gauge symmetry and masses of neutrinos, Conf. Proc. C 7902131 +(1979) 95. +[64] M. Gell-Mann, P. Ramond and R. Slansky, Complex Spinors and Unified Theories, Conf. +Proc. C 790927 (1979) 315 [1306.4669]. +[65] R. N. Mohapatra and G. Senjanovic, Neutrino Mass and Spontaneous Parity +Nonconservation, Phys. Rev. Lett. 44 (1980) 912. +[66] J. Hisano, T. Moroi, K. Tobe and M. Yamaguchi, Lepton flavor violation via right-handed +neutrino Yukawa couplings in supersymmetric standard model, Phys. Rev. D 53 (1996) +2442 [hep-ph/9510309]. +[67] J. Hisano, T. Moroi, K. Tobe, M. Yamaguchi and T. Yanagida, Lepton flavor violation in +the supersymmetric standard model with seesaw induced neutrino masses, Phys. Lett. B 357 +(1995) 579 [hep-ph/9501407]. +[68] J. R. Ellis, J. Hisano, M. Raidal and Y. Shimizu, A New parametrization of the seesaw +mechanism and applications in supersymmetric models, Phys. Rev. D 66 (2002) 115013 +[hep-ph/0206110]. +[69] R. Kitano and K.-y. Oda, Neutrino masses in the supersymmetric standard model with +right-handed neutrinos and spontaneous R-parity violation, Phys. Rev. D 61 (2000) 113001 +[hep-ph/9911327]. +[70] D. E. Lopez-Fogliani and C. Munoz, Proposal for a Supersymmetric Standard Model, Phys. +Rev. Lett. 97 (2006) 041801 [hep-ph/0508297]. +[71] N. Escudero, D. E. Lopez-Fogliani, C. Munoz and R. Ruiz de Austri, Analysis of the +parameter space and spectrum of the mu nu SSM, JHEP 12 (2008) 099 [0810.1507]. +[72] P. Ghosh and S. Roy, Neutrino masses and mixing, lightest neutralino decays and a solution +to the mu problem in supersymmetry, JHEP 04 (2009) 069 [0812.0084]. +[73] C. S. Aulakh and R. N. Mohapatra, Neutrino as the Supersymmetric Partner of the +Majoron, Phys. Lett. B 119 (1982) 136. +– 54 – + +[74] A. Masiero and J. W. F. Valle, A Model for Spontaneous R Parity Breaking, Phys. Lett. B +251 (1990) 273. +[75] S. F. King, Large mixing angle MSW and atmospheric neutrinos from single right-handed +neutrino dominance and U(1) family symmetry, Nucl. Phys. B 576 (2000) 85 +[hep-ph/9912492]. +[76] A. Ibarra and G. G. Ross, Neutrino phenomenology: The Case of two right-handed +neutrinos, Phys. Lett. B 591 (2004) 285 [hep-ph/0312138]. +[77] CMS collaboration, Search for top squarks decaying via the four-body mode in single-lepton +final states from Run 2 of the LHC, CMS-PAS-SUS-21-003 (2022) . +[78] CMS collaboration, Search for top squark pair production in a final state with one or two +tau leptons in proton-proton collisions at √s = 13 TeV, CMS-PAS-SUS-21-004 (2022) . +[79] CMS collaboration, Search for supersymmetry in final states with a single electron or muon +using angular correlations and heavy object tagging in proton-proton collisions at +√s = 13 TeV, CMS-PAS-SUS-21-007 (2022) . +[80] ATLAS collaboration, SUSY Summary Plots March 2022, ATL-PHYS-PUB-2022-013 +(2022) . +[81] H. Kudoh, A. Taruya, T. Hiramatsu and Y. Himemoto, Detecting a gravitational-wave +background with next-generation space interferometers, Phys. Rev. D 73 (2006) 064006 +[gr-qc/0511145]. +[82] K. Yagi and N. Seto, Detector configuration of DECIGO/BBO and identification of +cosmological neutron-star binaries, Phys. Rev. D 83 (2011) 044011 [1101.3940]. +[83] H. P. Nilles, Supersymmetry, Supergravity and Particle Physics, Phys. Rept. 110 (1984) 1. +[84] M. F. Sohnius, Introducing Supersymmetry, Phys. Rept. 128 (1985) 39. +[85] S. P. Martin, A Supersymmetry primer, Adv. Ser. Direct. High Energy Phys. 18 (1998) 1 +[hep-ph/9709356]. +[86] M. Maniatis, The Next-to-Minimal Supersymmetric extension of the Standard Model +reviewed, Int. J. Mod. Phys. A 25 (2010) 3505 [0906.0777]. +[87] I. Simonsen, A Review of minimal supersymmetric electroweak theory, hep-ph/9506369. +[88] M. Drees, R. Godbole and P. Roy, Theory and phenomenology of sparticles: An account of +four-dimensional N=1 supersymmetry in high energy physics. World Scientific Publishing +Co Pvt Ltd, 2004. +[89] L. J. Hall, J. D. Lykken and S. Weinberg, Supergravity as the Messenger of Supersymmetry +Breaking, Phys. Rev. D 27 (1983) 2359. +[90] S. Roy and B. Mukhopadhyaya, Some implications of a supersymmetric model with R-parity +breaking bilinear interactions, Phys. Rev. D 55 (1997) 7020 [hep-ph/9612447]. +[91] W. Porod, M. Hirsch, J. Romao and J. W. F. Valle, Testing neutrino mixing at future +collider experiments, Phys. Rev. D 63 (2001) 115004 [hep-ph/0011248]. +[92] M. Hirsch, A. Vicente and W. Porod, Spontaneous R-parity violation: Lightest neutralino +decays and neutrino mixing angles at future colliders, Phys. Rev. D 77 (2008) 075005 +[0802.2896]. +– 55 – + +[93] A. Bartl, M. Hirsch, A. Vicente, S. Liebler and W. Porod, LHC phenomenology of the mu +nu SSM, JHEP 05 (2009) 120 [0903.3596]. +[94] J. Fidalgo, D. E. Lopez-Fogliani, C. Munoz and R. Ruiz de Austri, The Higgs sector of the +µνSSM and collider physics, JHEP 10 (2011) 020 [1107.4614]. +[95] P. Ghosh, D. E. Lopez-Fogliani, V. A. Mitsou, C. Munoz and R. Ruiz de Austri, Probing +the µ-from-ν supersymmetric standard model with displaced multileptons from the decay of a +Higgs boson at the LHC, Phys. Rev. D 88 (2013) 015009 [1211.3177]. +[96] M. Hirsch, M. A. Diaz, W. Porod, J. C. Romao and J. W. F. Valle, Neutrino masses and +mixings from supersymmetry with bilinear R parity violation: A Theory for solar and +atmospheric neutrino oscillations, Phys. Rev. D 62 (2000) 113008 [hep-ph/0004115]. +[97] M. E. Krauss, T. Opferkuch and F. Staub, Spontaneous Charge Breaking in the NMSSM - +Dangerous or not?, Eur. Phys. J. C 77 (2017) 331 [1703.05329]. +[98] H. M. Georgi, S. L. Glashow and S. Nussinov, Unconventional Model of Neutrino Masses, +Nucl. Phys. B 193 (1981) 297. +[99] A. Santamaria and J. W. F. Valle, Spontaneous R-Parity Violation in Supersymmetry: A +Model for Solar Neutrino Oscillations, Phys. Lett. B 195 (1987) 423. +[100] A. Santamaria and J. W. F. Valle, Supersymmetric Majoron Signatures and Solar Neutrino +Oscillations, Phys. Rev. Lett. 60 (1988) 397. +[101] A. Santamaria and J. W. F. Valle, Solar Neutrino Oscillation Parameters and the Broken R +Parity Majoron, Phys. Rev. D 39 (1989) 1780. +[102] M. Carena, H. E. Haber, I. Low, N. R. Shah and C. E. M. Wagner, Alignment limit of the +NMSSM Higgs sector, Phys. Rev. D 93 (2016) 035013 [1510.09137]. +[103] H. Georgi and D. V. Nanopoulos, Suppression of Flavor Changing Effects From Neutral +Spinless Meson Exchange in Gauge Theories, Phys. Lett. B 82 (1979) 95. +[104] J. F. Donoghue and L. F. Li, Properties of Charged Higgs Bosons, Phys. Rev. D 19 (1979) +945. +[105] L. Lavoura and J. P. Silva, Fundamental CP violating quantities in a SU(2) x U(1) model +with many Higgs doublets, Phys. Rev. D 50 (1994) 4619 [hep-ph/9404276]. +[106] F. J. Botella and J. P. Silva, Jarlskog - like invariants for theories with scalars and +fermions, Phys. Rev. D 51 (1995) 3870 [hep-ph/9411288]. +[107] J. F. Gunion and H. E. Haber, The CP conserving two Higgs doublet model: The Approach +to the decoupling limit, Phys. Rev. D 67 (2003) 075019 [hep-ph/0207010]. +[108] J. F. Gunion, H. E. Haber, G. L. Kane and S. Dawson, The Higgs Hunter’s Guide, vol. 80. +CRC Pressv, 2000. +[109] J. F. Gunion, H. E. Haber, G. L. Kane and S. Dawson, Errata for the Higgs hunter’s guide, +hep-ph/9302272. +[110] Particle Data Group collaboration, Review of Particle Physics, PTEP 2022 (2022) +083C01. +[111] P. Ghosh, D. E. Lopez-Fogliani, V. A. Mitsou, C. Munoz and R. Ruiz de Austri, Probing +the µνSSM with light scalars, pseudoscalars and neutralinos from the decay of a SM-like +Higgs boson at the LHC, JHEP 11 (2014) 102 [1410.2070]. +– 56 – + +[112] K. Huitu and H. Waltari, Higgs sector in NMSSM with right-handed neutrinos and +spontaneous R-parity violation, JHEP 11 (2014) 053 [1405.5330]. +[113] J. P. Derendinger and C. A. Savoy, Quantum Effects and SU(2) x U(1) Breaking in +Supergravity Gauge Theories, Nucl. Phys. B 237 (1984) 307. +[114] S. F. King and P. L. White, Resolving the constrained minimal and next-to-minimal +supersymmetric standard models, Phys. Rev. D 52 (1995) 4183 [hep-ph/9505326]. +[115] M. Masip, R. Munoz-Tapia and A. Pomarol, Limits on the mass of the lightest Higgs in +supersymmetric models, Phys. Rev. D 57 (1998) R5340 [hep-ph/9801437]. +[116] CMS collaboration, Search for top squark production in fully-hadronic final states in +proton-proton collisions at √s = 13 TeV, Phys. Rev. D 104 (2021) 052001 [2103.01290]. +[117] ATLAS collaboration, Search for squarks and gluinos in final states with one isolated +lepton, jets, and missing transverse momentum at √s = 13 with the ATLAS detector, Eur. +Phys. J. C 81 (2021) 600 [2101.01629]. +[118] ATLAS collaboration, Search for R-parity violating supersymmetry in a final state +containing leptons and many jets with the ATLAS experiment using √s = 13 TeV +proton-proton collision data, ATLAS-CONF-2021-007 (2021) . +[119] ATLAS collaboration, Search for supersymmetry in final states with missing transverse +momentum and three or more b-jets in 139 fb−1 of proton−proton collisions at √s = 13 +TeV with the ATLAS detector, 2211.08028. +[120] ATLAS collaboration, Search for direct stau production in events with two hadronic +τ-leptons in √s = 13 TeV pp collisions with the ATLAS detector, Phys. Rev. D 101 (2020) +032009 [1911.06660]. +[121] CMS collaboration, Search for electroweak production of supersymmetric particles in final +states containing hadronic decays of WW, WZ, or WH and missing transverse momentum, +CMS-PAS-SUS-21-002 (2021) . +[122] ATLAS collaboration, Search for direct pair production of sleptons and charginos decaying +to two leptons and neutralinos with mass splittings near the W-boson mass in √s = 13 TeV +pp collisions with the ATLAS detector, 2209.13935. +[123] Muon g-2 collaboration, Measurement of the Positive Muon Anomalous Magnetic Moment +to 0.46 ppm, Phys. Rev. Lett. 126 (2021) 141801 [2104.03281]. +[124] J. R. Ellis, G. Ridolfi and F. Zwirner, On radiative corrections to supersymmetric Higgs +boson masses and their implications for LEP searches, Phys. Lett. B 262 (1991) 477. +[125] H. E. Haber and R. Hempfling, The Renormalization group improved Higgs sector of the +minimal supersymmetric model, Phys. Rev. D 48 (1993) 4280 [hep-ph/9307201]. +[126] J. A. Casas, J. R. Espinosa, M. Quiros and A. Riotto, The Lightest Higgs boson mass in the +minimal supersymmetric standard model, Nucl. Phys. B 436 (1995) 3 [hep-ph/9407389]. +[127] M. Carena, J. R. Espinosa, M. Quiros and C. E. M. Wagner, Analytical expressions for +radiatively corrected Higgs masses and couplings in the MSSM, Phys. Lett. B 355 (1995) +209 [hep-ph/9504316]. +[128] G. Lee and C. E. M. Wagner, Higgs bosons in heavy supersymmetry with an intermediate +mA, Phys. Rev. D 92 (2015) 075032 [1508.00576]. +– 57 – + +[129] S. R. Coleman and E. J. Weinberg, Radiative Corrections as the Origin of Spontaneous +Symmetry Breaking, Phys. Rev. D 7 (1973) 1888. +[130] X.-J. Bi, L. Bian, W. Huang, J. Shu and P.-F. Yin, Interpretation of the Galactic Center +excess and electroweak phase transition in the NMSSM, Phys. Rev. D 92 (2015) 023507 +[1503.03749]. +[131] S. J. Huber, T. Konstandin, G. Nardini and I. Rues, Detectable Gravitational Waves from +Very Strong Phase Transitions in the General NMSSM, JCAP 03 (2016) 036 [1512.06357]. +[132] L. Bian, H.-K. Guo and J. Shu, Gravitational Waves, baryon asymmetry of the universe +and electric dipole moment in the CP-violating NMSSM, Chin. Phys. C 42 (2018) 093106 +[1704.02488]. +[133] L. Dolan and R. Jackiw, Symmetry Behavior at Finite Temperature, Phys. Rev. D 9 (1974) +3320. +[134] D. A. Kirzhnits and A. D. Linde, Symmetry Behavior in Gauge Theories, Annals Phys. 101 +(1976) 195. +[135] R. R. Parwani, Resummation in a hot scalar field theory, Phys. Rev. D 45 (1992) 4695 +[hep-ph/9204216]. +[136] J. R. Espinosa, M. Quiros and F. Zwirner, On the phase transition in the scalar theory, +Phys. Lett. B 291 (1992) 115 [hep-ph/9206227]. +[137] P. B. Arnold and O. Espinosa, The Effective potential and first-order phase transitions: +Beyond leading-order, Phys. Rev. D 47 (1993) 3546 [hep-ph/9212235]. +[138] N. K. Nielsen, On the Gauge Dependence of Spontaneous Symmetry Breaking in Gauge +Theories, Nucl. Phys. B 101 (1975) 173. +[139] H. H. Patel and M. J. Ramsey-Musolf, Baryon Washout, Electroweak Phase Transition, and +Perturbation Theory, JHEP 07 (2011) 029 [1101.4665]. +[140] L. Di Luzio and L. Mihaila, On the gauge dependence of the Standard Model vacuum +instability scale, JHEP 06 (2014) 079 [1404.7450]. +[141] M. Laine, M. Meyer and G. Nardini, Thermal phase transition with full 2-loop effective +potential, Nucl. Phys. B 920 (2017) 565 [1702.07479]. +[142] M. Drees, Supersymmetric Models with Extended Higgs Sector, Int. J. Mod. Phys. A 4 +(1989) 3635. +[143] J. R. Ellis, J. F. Gunion, H. E. Haber, L. Roszkowski and F. Zwirner, Higgs Bosons in a +Nonminimal Supersymmetric Model, Phys. Rev. D 39 (1989) 844. +[144] L. D. Landau, A. A. Abrikosov and I. M. Khalatnikov, An asymptotic expression for the +photon Green function in quantum electrodynamics, Dokl. Akad. Nauk SSSR 95 (1954) +1177. +[145] L. D. Landau, On the quantum field theory, Niels Bohr and the Development of Physics, ed. +W. Pauli. Pergamon Press, London, 1955. +[146] B. A. Dobrescu, G. L. Landsberg and K. T. Matchev, Higgs boson decays to CP odd scalars +at the Tevatron and beyond, Phys. Rev. D 63 (2001) 075003 [hep-ph/0005308]. +[147] B. A. Dobrescu and K. T. Matchev, Light axion within the next-to-minimal supersymmetric +standard model, JHEP 09 (2000) 031 [hep-ph/0008192]. +– 58 – + +[148] L3 collaboration, Search for charginos and neutralinos in e+e− collisions at √s = 189 +GeV, Phys. Lett. B 472 (2000) 420 [hep-ex/9910007]. +[149] ALEPH collaboration, Absolute mass lower limit for the lightest neutralino of the MSSM +from e+e− data at √s up to 209 GeV, Phys. Lett. B 583 (2004) 247. +[150] DELPHI collaboration, Searches for supersymmetric particles in e+e− collisions up to 208 +GeV and interpretation of the results within the MSSM, Eur. Phys. J. C 31 (2003) 421 +[hep-ex/0311019]. +[151] OPAL collaboration, Search for chargino and neutralino production at √s = 192 - 209 +GeV at LEP, Eur. Phys. J. C 35 (2004) 1 [hep-ex/0401026]. +[152] L. Lentati et al., European Pulsar Timing Array Limits On An Isotropic Stochastic +Gravitational-Wave Background, Mon. Not. Roy. Astron. Soc. 453 (2015) 2576 +[1504.03692]. +[153] NANOGRAV collaboration, The NANOGrav 11-year Data Set: Pulsar-timing Constraints +On The Stochastic Gravitational-wave Background, Astrophys. J. 859 (2018) 47 +[1801.02617]. +[154] LIGO Scientific, VIRGO collaboration, Characterization of the LIGO detectors during +their sixth science run, Class. Quant. Grav. 32 (2015) 115012 [1410.7764]. +[155] C. Caprini et al., Science with the space-based interferometer eLISA. II: Gravitational +waves from cosmological phase transitions, JCAP 04 (2016) 001 [1512.06239]. +[156] V. Corbin and N. J. Cornish, Detecting the cosmic gravitational wave background with the +big bang observer, Class. Quant. Grav. 23 (2006) 2435 [gr-qc/0512039]. +[157] F. Staub, SARAH, 0806.0538. +[158] F. Staub, T. Ohl, W. Porod and C. Speckner, A Tool Box for Implementing +Supersymmetric Models, Comput. Phys. Commun. 183 (2012) 2165 [1109.5147]. +[159] F. Staub, SARAH 3.2: Dirac Gauginos, UFO output, and more, Comput. Phys. Commun. +184 (2013) 1792 [1207.0906]. +[160] H. Dreiner, K. Nickel, W. Porod and F. Staub, Full 1-loop calculation of BR(B0 +s,d → ℓ¯ℓ) in +models beyond the MSSM with SARAH and SPheno, Comput. Phys. Commun. 184 (2013) +2604 [1212.5074]. +[161] F. Staub, SARAH 4 : A tool for (not only SUSY) model builders, Comput. Phys. Commun. +185 (2014) 1773 [1309.7223]. +[162] M. D. Goodsell, K. Nickel and F. Staub, Two-Loop Higgs mass calculations in +supersymmetric models beyond the MSSM with SARAH and SPheno, Eur. Phys. J. C 75 +(2015) 32 [1411.0675]. +[163] F. Staub, Exploring new models in all detail with SARAH, Adv. High Energy Phys. 2015 +(2015) 840780 [1503.04200]. +[164] M. D. Goodsell and F. Staub, Unitarity constraints on general scalar couplings with +SARAH, Eur. Phys. J. C 78 (2018) 649 [1805.07306]. +[165] W. Porod, SPheno, a program for calculating supersymmetric spectra, SUSY particle decays +and SUSY particle production at e+e− colliders, Comput. Phys. Commun. 153 (2003) 275 +[hep-ph/0301101]. +– 59 – + +[166] W. Porod and F. Staub, SPheno 3.1: Extensions including flavour, CP-phases and models +beyond the MSSM, Comput. Phys. Commun. 183 (2012) 2458 [1104.1573]. +[167] W. Porod, F. Staub and A. Vicente, A Flavor Kit for BSM models, Eur. Phys. J. C 74 +(2014) 2992 [1405.1434]. +[168] M. Goodsell, K. Nickel and F. Staub, Generic two-loop Higgs mass calculation from a +diagrammatic approach, Eur. Phys. J. C 75 (2015) 290 [1503.03098]. +[169] M. D. Goodsell and F. Staub, The Higgs mass in the CP violating MSSM, NMSSM, and +beyond, Eur. Phys. J. C 77 (2017) 46 [1604.05335]. +[170] J. Braathen, M. D. Goodsell and F. Staub, Supersymmetric and non-supersymmetric +models without catastrophic Goldstone bosons, Eur. Phys. J. C 77 (2017) 757 [1706.05372]. +[171] M. D. Goodsell and R. Moutafis, How heavy can dark matter be? Constraining colourful +unitarity with SARAH, Eur. Phys. J. C 81 (2021) 808 [2012.09022]. +[172] ATLAS collaboration, Measurement of the Higgs boson mass in the H → ZZ∗ → 4ℓ decay +channel using 139 fb−1 of √s = 13 TeV pp collisions recorded by the ATLAS detector at the +LHC, 2207.00320. +[173] ATLAS collaboration, Constraints on Higgs boson production with large transverse +momentum using H → b¯b decays in the ATLAS detector, Phys. Rev. D 105 (2022) 092003 +[2111.08340]. +[174] ATLAS collaboration, Measurements of Higgs boson production cross-sections in +the H → τ +τ − decay channel in pp collisions at √s = 13 TeV with the ATLAS detector, +JHEP 08 (2022) 175 [2201.08269]. +[175] ATLAS collaboration, Direct constraint on the Higgs-charm coupling from a search for +Higgs boson decays into charm quarks with the ATLAS detector, Eur. Phys. J. C 82 (2022) +717 [2201.11428]. +[176] ATLAS collaboration, Measurement of the properties of Higgs boson production at √s = 13 +TeV in the H → γγ channel using 139 fb−1 of pp collision data with the ATLAS +experiment, 2207.00348. +[177] ATLAS collaboration, Combined measurement of the total and differential cross sections in +the H → γγ and the H → ZZ∗ → 4ℓ decay channels at √s = 13 TeV with the ATLAS +detector, ATLAS-CONF-2022-002 (2022) . +[178] ATLAS and CMS collaboration, Rare and BSM Higgs Searches, CMS-CR-2022-179 +(2022) . +[179] P. Bechtle, O. Brein, S. Heinemeyer, G. Weiglein and K. E. Williams, HiggsBounds: +Confronting Arbitrary Higgs Sectors with Exclusion Bounds from LEP and the Tevatron, +Comput. Phys. Commun. 181 (2010) 138 [0811.4169]. +[180] P. Bechtle, D. Dercks, S. Heinemeyer, T. Klingl, T. Stefaniak, G. Weiglein et al., +HiggsBounds-5: Testing Higgs Sectors in the LHC 13 TeV Era, Eur. Phys. J. C 80 (2020) +1211 [2006.06007]. +[181] CMS collaboration, Search for electroweak production of charginos and neutralinos in +proton-proton collisions at √s = 13 TeV, JHEP 04 (2022) 147 [2106.14246]. +[182] CMS collaboration, Search for charging-neutralino production in events with Higgs and W +– 60 – + +bosons using 137 fb−1 of proton-proton collisions at √s = 13 TeV, JHEP 10 (2021) 045 +[2107.12553]. +[183] ATLAS collaboration, Search for charginos and neutralinos in final states with two boosted +hadronically decaying bosons and missing transverse momentum in pp collisions at √s = 13 +TeV with the ATLAS detector, Phys. Rev. D 104 (2021) 112010 [2108.07586]. +[184] ATLAS collaboration, SUSY March 2021 Summary Plot Update, +ATL-PHYS-PUB-2021-007 (2021) . +[185] S. Bertolini, F. Borzumati and A. Masiero, New Constraints on Squark and Gluino Masses +from Radiative b Decays, Phys. Lett. B 192 (1987) 437. +[186] S. Bertolini, F. Borzumati, A. Masiero and G. Ridolfi, Effects of supergravity induced +electroweak breaking on rare B decays and mixings, Nucl. Phys. B 353 (1991) 591. +[187] M. Ciuchini, G. Degrassi, P. Gambino and G. F. Giudice, Next-to-leading QCD corrections +to B → Xsγ in supersymmetry, Nucl. Phys. B 534 (1998) 3 [hep-ph/9806308]. +[188] F. Borzumati, C. Greub and Y. Yamada, Beyond leading order corrections to B → Xsγ at +large tan β: The Charged Higgs contribution, Phys. Rev. D 69 (2004) 055005 +[hep-ph/0311151]. +[189] G. Degrassi, P. Gambino and P. Slavich, QCD corrections to radiative B decays in the +MSSM with minimal flavor violation, Phys. Lett. B 635 (2006) 335 [hep-ph/0601135]. +[190] F. Domingo and U. Ellwanger, Updated Constraints from B Physics on the MSSM and the +NMSSM, JHEP 12 (2007) 090 [0710.3714]. +[191] A. Arbey, M. Battaglia, F. Mahmoudi and D. Mart´ınez Santos, Supersymmetry confronts +Bs → µ+µ− : Present and future status, Phys. Rev. D 87 (2013) 035026 [1212.4887]. +[192] O. C. W. Kong and R. Vaidya, tan beta enhanced contributions to b → s + γ in SUSY +without R-parity, hep-ph/0411165. +[193] Y.-G. Xu, R.-M. Wang and Y.-D. Yang, Probe R-parity violating supersymmetry effects in +B → K∗ℓ+ℓ− and Bs → ℓ+ℓ−decays, Phys. Rev. D 74 (2006) 114019 [hep-ph/0610338]. +[194] ATLAS collaboration, Searches for lepton-flavour-violating decays of the Higgs boson in +√s = 13 TeV pp collisions with the ATLAS detector, Phys. Lett. B 800 (2020) 135069 +[1907.06131]. +[195] CMS collaboration, Search for lepton-flavor violating decays of the Higgs boson in the µτ +and eτ final states in proton-proton collisions at √s = 13 TeV, Phys. Rev. D 104 (2021) +032013 [2105.03007]. +[196] M. Frank, Bilinear R-parity violation parameters from µ → eγ, Phys. Rev. D 62 (2000) +015006. +[197] K.-m. Cheung and O. C. W. Kong, µ → eγ from supersymmetry without R parity, Phys. +Rev. D 64 (2001) 095007 [hep-ph/0101347]. +[198] D. F. Carvalho, M. E. Gomez and J. C. Romao, Charged lepton flavor violation in +supersymmetry with bilinear R-parity violation, Phys. Rev. D 65 (2002) 093013 +[hep-ph/0202054]. +[199] BaBar collaboration, Searches for Lepton Flavor Violation in the Decays τ ± → e±γ and +τ ± → µ±γ, Phys. Rev. Lett. 104 (2010) 021802 [0908.2381]. +– 61 – + +[200] MEG collaboration, Search for the lepton flavour violating decay µ+ → e+γ with the full +dataset of the MEG experiment, Eur. Phys. J. C 76 (2016) 434 [1605.05081]. +[201] SINDRUM collaboration, Search for the Decay µ+ → e+e+e−, Nucl. Phys. B 299 (1988) 1. +[202] SINDRUM II collaboration, A Search for muon to electron conversion in muonic gold, +Eur. Phys. J. C 47 (2006) 337. +[203] M. M. Ivanov, M. Simonovi´c and M. Zaldarriaga, Cosmological Parameters and Neutrino +Masses from the Final Planck and Full-Shape BOSS Data, Phys. Rev. D 101 (2020) 083504 +[1912.08208]. +[204] A. Kobakhidze, M. Talia and L. Wu, Probing the MSSM explanation of the muon g-2 +anomaly in dark matter experiments and at a 100 TeV pp collider, Phys. Rev. D 95 (2017) +055023 [1608.03641]. +[205] R. S. Hundi, Constraints from neutrino masses and muon (g-2) in the bilinear R-parity +violating supersymmetric model, Phys. Rev. D 83 (2011) 115019 [1101.2810]. +[206] T. Aoyama et al., The anomalous magnetic moment of the muon in the Standard Model, +Phys. Rept. 887 (2020) 1 [2006.04822]. +[207] Muon g-2 collaboration, Final Report of the Muon E821 Anomalous Magnetic Moment +Measurement at BNL, Phys. Rev. D 73 (2006) 072003 [hep-ex/0602035]. +[208] M. Chakraborti, S. Heinemeyer and I. Saha, The new “MUON G-2” result and +supersymmetry, Eur. Phys. J. C 81 (2021) 1114 [2104.03287]. +[209] M. Badziak and K. Sakurai, Explanation of electron and muon g − 2 anomalies in the +MSSM, JHEP 10 (2019) 024 [1908.03607]. +[210] F. Domingo and U. Ellwanger, Constraints from the Muon g-2 on the Parameter Space of +the NMSSM, JHEP 07 (2008) 079 [0806.0733]. +[211] C. L. Wainwright, CosmoTransitions: Computing Cosmological Phase Transition +Temperatures and Bubble Profiles with Multiple Fields, Comput. Phys. Commun. 183 +(2012) 2006 [1109.4189]. +[212] A. D. Linde, Decay of the False Vacuum at Finite Temperature, Nucl. Phys. B 216 (1983) +421. +[213] C. Grojean and G. Servant, Gravitational Waves from Phase Transitions at the Electroweak +Scale and Beyond, Phys. Rev. D 75 (2007) 043507 [hep-ph/0607107]. +[214] I. Affleck, Quantum Statistical Metastability, Phys. Rev. Lett. 46 (1981) 388. +[215] A. D. Linde, On the Vacuum Instability and the Higgs Meson Mass, Phys. Lett. B 70 +(1977) 306. +[216] M. Kamionkowski, A. Kosowsky and M. S. Turner, Gravitational radiation from first order +phase transitions, Phys. Rev. D 49 (1994) 2837 [astro-ph/9310044]. +[217] J. Kehayias and S. Profumo, Semi-Analytic Calculation of the Gravitational Wave Signal +From the Electroweak Phase Transition for General Quartic Scalar Effective Potentials, +JCAP 03 (2010) 003 [0911.0687]. +[218] A. Nicolis, Relic gravitational waves from colliding bubbles and cosmic turbulence, Class. +Quant. Grav. 21 (2004) L27 [gr-qc/0303084]. +– 62 – + +[219] J. Ellis, M. Lewicki and J. M. No, Gravitational waves from first-order cosmological phase +transitions: lifetime of the sound wave source, JCAP 07 (2020) 050 [2003.07360]. +[220] DES collaboration, Dark Energy Survey Year 1 Results: A Precise H0 Estimate from DES +Y1, BAO, and D/H Data, Mon. Not. Roy. Astron. Soc. 480 (2018) 3879 [1711.00403]. +[221] R. Jinno and M. Takimoto, Gravitational waves from bubble collisions: An analytic +derivation, Phys. Rev. D 95 (2017) 024009 [1605.01403]. +[222] M. Dine, R. G. Leigh, P. Y. Huet, A. D. Linde and D. A. Linde, Towards the theory of the +electroweak phase transition, Phys. Rev. D 46 (1992) 550 [hep-ph/9203203]. +[223] J. Ignatius, K. Kajantie, H. Kurki-Suonio and M. Laine, The growth of bubbles in +cosmological phase transitions, Phys. Rev. D 49 (1994) 3854 [astro-ph/9309059]. +[224] G. D. Moore and T. Prokopec, How fast can the wall move? A Study of the electroweak +phase transition dynamics, Phys. Rev. D 52 (1995) 7182 [hep-ph/9506475]. +[225] G. D. Moore and T. Prokopec, Bubble wall velocity in a first order electroweak phase +transition, Phys. Rev. Lett. 75 (1995) 777 [hep-ph/9503296]. +[226] G. D. Moore, Electroweak bubble wall friction: Analytic results, JHEP 03 (2000) 006 +[hep-ph/0001274]. +[227] J. M. Cline and K. Kainulainen, Electroweak baryogenesis at high bubble wall velocities, +Phys. Rev. D 101 (2020) 063525 [2001.00568]. +[228] G. C. Dorsch, S. J. Huber and T. Konstandin, A sonic boom in bubble wall friction, JCAP +04 (2022) 010 [2112.12548]. +[229] G. C. Dorsch, S. J. Huber and T. Konstandin, On the wall velocity dependence of +electroweak baryogenesis, JCAP 08 (2021) 020 [2106.06547]. +[230] M. Hindmarsh, S. J. Huber, K. Rummukainen and D. J. Weir, Gravitational waves from the +sound of a first order phase transition, Phys. Rev. Lett. 112 (2014) 041301 [1304.2433]. +[231] M. Hindmarsh, Sound shell model for acoustic gravitational wave production at a first-order +phase transition in the early Universe, Phys. Rev. Lett. 120 (2018) 071301 [1608.04735]. +[232] M. Hindmarsh, S. J. Huber, K. Rummukainen and D. J. Weir, Shape of the acoustic +gravitational wave power spectrum from a first order phase transition, Phys. Rev. D 96 +(2017) 103520 [1704.05871]. +[233] H.-K. Guo, K. Sinha, D. Vagie and G. White, Phase Transitions in an Expanding Universe: +Stochastic Gravitational Waves in Standard and Non-Standard Histories, JCAP 01 (2021) +001 [2007.08537]. +[234] K. Nakayama and J. Yokoyama, Gravitational Wave Background and Non-Gaussianity as a +Probe of the Curvaton Scenario, JCAP 01 (2010) 010 [0910.0715]. +[235] C. Caprini, R. Durrer and G. Servant, The stochastic gravitational wave background from +turbulence and magnetic fields generated by a first-order phase transition, JCAP 12 (2009) +024 [0909.0622]. +[236] LIGO Scientific collaboration, Advanced LIGO: The next generation of gravitational +wave detectors, Class. Quant. Grav. 27 (2010) 084006. +[237] A. Kosowsky, M. S. Turner and R. Watkins, Gravitational radiation from colliding vacuum +bubbles, Phys. Rev. D 45 (1992) 4514. +– 63 – + +[238] D. Curtin, P. Meade and H. Ramani, Thermal Resummation and Phase Transitions, Eur. +Phys. J. C 78 (2018) 787 [1612.00466]. +[239] P. Athron, C. Balazs, A. Fowlie, G. Pozzo, G. White and Y. Zhang, Strong first-order phase +transitions in the NMSSM - a comprehensive survey, JHEP 11 (2019) 151 [1908.11847]. +[240] M. E. Carrington, The Effective potential at finite temperature in the Standard Model, Phys. +Rev. D 45 (1992) 2933. +[241] D. Comelli and J. R. Espinosa, Bosonic thermal masses in supersymmetry, Phys. Rev. D +55 (1997) 6253 [hep-ph/9606438]. +– 64 – + diff --git a/1dE4T4oBgHgl3EQfaAyc/content/tmp_files/load_file.txt b/1dE4T4oBgHgl3EQfaAyc/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..6246a2e44a2351250f09a19c84e4cc5f8f911fe1 --- /dev/null +++ b/1dE4T4oBgHgl3EQfaAyc/content/tmp_files/load_file.txt @@ -0,0 +1,3432 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf,len=3431 +page_content='PREPRINT Electroweak Phase Transition in a Right-Handed Neutrino Superfield Extended NMSSM Pankaj Borah,a Pradipta Ghosh,a Sourov Royb and Abhijit Kumar Sahab aDepartment of Physics, Indian Institute of Technology Delhi, Hauz Khas 110 016, India bSchool of Physical Sciences, Indian Association for the Cultivation of Science, 2A & 2B Raja S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Mullick Road, Kolkata 700 032, India E-mail: Pankaj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='Borah@physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='iitd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='in, tphyspg@physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='iitd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='in, tpsr@iacs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='in, psaks2484@iacs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='in Abstract: Supersymmetric models with singlet extensions can accommodate single- or multi-step first-order phase transitions (FOPT) along the various constituent field direc- tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Such a framework can also produce Gravitational Waves, detectable at the upcom- ing space-based interferometers, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', U-DECIGO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We explore the dynamics of electroweak phase transition and the production of Gravitational Waves in an extended set-up of the Next-to-Minimal Supersymmetric Standard Model (NMSSM) with a Standard Model sin- glet right-handed neutrino superfield.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We examine the role of the new parameters compared to NMSSM on the phase transition dynamics and observe that the occurrence of a FOPT, an essential requirement for Electroweak Baryogenesis, typically favours a right-handed sneutrino state below 125 GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Our investigation shows how the analysis can offer com- plementary probes for physics beyond the Standard Model besides the collider searches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='05061v1 [hep-ph] 12 Jan 2023 Contents 1 Introduction 2 2 The Model 5 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1 A convenient basis choice 8 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 Higher order contributions 10 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3 Contributions from non-zero temperature 12 3 Choice of parameters 13 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1 Experimental Constraints 15 4 The EWPT and its Properties 17 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1 PT in the NMSSM + one RHN model 19 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 Numerical Results 20 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3 GW spectrum from SFOPT in the NMSSM + one RHN model 28 5 Summary and Conclusion 36 A Field dependent mass matrices 38 A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1 CP-even neutral scalars squared mass matrix 40 A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 CP-odd neutral scalars squared mass matrix 41 A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3 Uncoloured charged scalars squared mass matrix 43 A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4 Neutralino mass matrix 45 A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5 Chargino mass matrix 45 B Neutral scalar mass matrices after the EWSB 46 B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1 CP-even mass squared elements 46 B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 CP-odd mass squared elements 47 C Counter terms 47 D Daisy coefficients 48 E Minimization conditions 49 – 1 – 1 Introduction Baryon asymmetry of the Universe is a precisely measured quantity by Planck experiment [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Different kinds of proposals pertaining to baryon asymmetry production mechanism in the early Universe are prevalent in literature (for a brief summary see Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [2]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In recent times, baryon asymmetry production during the Electroweak Phase Transition (EWPT), known as the Electroweak Baryogenesis (EWBG) [3] has gained particular attention.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The EWBG occurs around the TeV scale and has the potential to be probed in collider ex- periments [4–6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Irrespective of different baryon asymmetry generation mechanisms, the Sakharov conditions [7], namely, (i) baryon number violation, (ii) charge (C) and charge- parity (CP) violation and (iii) deviation from thermal equilibrium must be satisfied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' It is well known that the Standard Model (SM) of particle physics fails to provide a sufficient departure from thermal equilibrium [8, 9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Moreover, C and CP violations in the SM are not adequate enough to yield the observed baryon asymmetry of the Universe [8, 9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In principle, a strong first-order EWPT (SFOEWPT) in the early Universe can pave the way for the EWBG by allowing sufficient out-of-equilibrium processes [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The SM of par- ticle physics with the observed Higgs mass ∼ 125 GeV [11, 12], shows a smooth cross-over pattern along the Higgs field direction without any PT [13–15] and thus, fails to accom- modate the EWBG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This issue can be circumvented by introducing new scalar degrees of freedom having sizeable coupling with the SM Higgs boson.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In general, the strength of the EW phase transition is determined by both the high and low-temperature behaviour of the scalar potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Computation of critical temperature reveals displacement of the global minimum for a scalar potential when expressed as a function of the temperature (T) of the Universe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' However, a correct description of the EWPT requires the study of bubble nucleation dynamics since PT proceeds via the nucleation of bubbles [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The dynamics of bubble nucleation, during the first-order EWPT, can yield stochastic Gravitational Waves (GWs) in the early Universe [17–22] that may appear detectable at different GW experi- ments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In fact, the search for GWs for probing different kinds of beyond the SM (BSM) frameworks has long been practised (see Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [23–26] for some of the recent works).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Supersymmetric models, having a rich scalar sector compared to the SM, carry the necessary ingredients for exhibiting an SFOEWPT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The PT properties in the Minimal Supersymmetric Standard Model (MSSM) (see Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [27] for a review) are exercised in Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [28–37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' It is shown in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [37] that a strong EWPT with a 125 GeV Higgs boson favours a hierarchical stop sector in the MSSM, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', one of two stops appears to be much heavier than the EW scale while the lighter one remains around O(100 GeV) [36, 37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The presence of such a light stop enhances the Higgs production rate through gluon-gluon fusion [37, 38] and confronts constraints from LHC data [11, 12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This tension, nevertheless, can be alleviated by considering a light neutralino with a mass lower than about 60 GeV [37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' However, once again it is challenged by the LHC data of Higgs invisible decay width [39–42] and neutralino searches from the stop decay [43–45].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Besides, the MSSM also suffers from a new kind of naturalness problem known as the µ-problem [46] and, just like the SM, is incapable of accommodating non-zero neutrino masses and mixing [47, 48] in its original – 2 – form1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The Next-to-Minimal Supersymmetric Standard Model (NMSSM) [54] provides a dy- namical solution to the µ-problem, a challenge that has plagued the MSSM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In the NMSSM, the scalar sector of the MSSM is further enriched by the presence of a gauge singlet scalar S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Studies related to EWPT in the NMSSM can be found in Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [55–60].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' It has been observed [55–60] that in the NMSSM soft supersymmetry (SUSY) breaking term involving S and Higgs doublets assists to form the potential barrier even at T = 0 in contrast to the MSSM where T ̸= 0 effects are essential for barrier formation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Thus, the PT dynamics is more involved in the NMSSM where one needs to consider a three-dimensional field space spanned by three2 CP-even scalar fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The EWPT could occur either in single-step or multi-step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In the NMSSM, both single-step and multi-step phase transitions are possible as discussed in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [59, 60].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' These studies [59, 60] rely on an effective field theory set-up after integrating out heavy stops which yield potentially large contributions to the one-loop effective potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Such an effective-theory-based approach reduces the number of degrees of freedom participating in the EWPT dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [59, 60] also showed that the NMSSM can accommodate EWBG in some region corners of the NMSSM parameter space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Shifting our attention to non-zero neutrino masses and mixing [47, 48, 53], another experimentally established BSM signature, both MSSM and NMSSM, are futile just like the SM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Extensions of these models with additional ingredients, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', right-handed (RH) neutrinos, however, offer a simple elegant way to accommodate massive neutrinos using the popular type-I see-saw mechanism [62–65].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Supersymmetric type-I seesaw mechanism, where the MSSM superfield content is extended with RH-neutrino superfield(s) is well stud- ied, see for example, Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [66–68].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Incorporating RH-neutrino superfield(s) in the NMSSM provides a minimal model [69] where, apart from accommodating none-zero neutrino masses and mixing, one also gets a solution for the µ-problem3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In such a framework, non-zero neutrino masses appear through three sources: (i) type-I seesaw mechanism involving RH- neutrino(s), generally known as the “canonical seesaw”, (ii) type-I and type-III seesaw involving gauginos, popularly known as the “gaugino seesaw” and, (iii) seesaw involving higgsinos, better known as “higgsino seesaw” [69].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The last two pieces arise when left- handed (LH) and RH sneutrinos acquire vacuum expectation values (VEVs), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', R-parity gets spontaneously broken [73, 74] and effective bilinear R-parity-violating [49] terms are generated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' For this study, for simplicity, we considered the NMSSM framework extended with one RH-neutrino superfield.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' One, however, needs at least two RH-neutrino superfields to accommodate the neutrino data, leaving the lightest one massless [75, 76].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The chosen simple framework, nevertheless, offers a nice platform to investigate the PT dynamics and subsequently the predictions for GW emission, besides providing the correct scale for the 1MSSM extended with new superfields or new symmetries or R-parity violation [49] (see Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [50–52] for further reading) can accommodate neutrino data [47, 48, 53].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' R-parity is defined as RP = (−1)3B+L+2s where L(B) denotes the lepton (baryon) number and s represents the spin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 2The PT dynamics in guided by a two-dimensional field space in the MSSM [35, 61].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 3An alternative minimal framework, known as µνSSM [70–72], also solves the µ-problem and satisfies the neutrino oscillation data simultaneously, even at the tree-level [72].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' – 3 – neutrino mass and the atmospheric mass-square difference [47, 48, 53].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We plan to inves- tigate the possible correlations between the neutrino sector and the PT dynamics in the context of NMSSM with more than one family of RH-neutrino superfields in a forthcoming publication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Restoring the discussion of PT dynamics, the electrically neutral uncoloured scalar sector of the NMSSM extended with one RH-neutrino superfield set-up possesses fourteen degrees of freedom, including the neutral Goldstone mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' However, as we will see later in section 2, the effective degrees of freedom appear to be eight owing to weak couplings of the LH-sneutrino states with the remaining states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Out of these eight, only four are CP-even in nature and actively participate in the PT dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Hence, the concerned field space is four-dimensional for the chosen framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This enhanced field space compared to the MSSM (two-dimensional due to two Higgses) and the NMSSM (three-dimensional owing to two Higgs doublets and one singlet), facilitates the study of EWPT, via single steps and multi-steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In the numerical frontier, we adopt a benchmark-based analysis and finally select a few benchmark points (BPs) that appear promising from the viewpoint of EWBG and also exhibit distinct (single-step or two-steps) PT properties in the early Universe along the various constituent field directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In the later part, we exploit some of the BPs in order to further investigate the role of new parameters that appear in the setup due to the presence of RH-neutrino superfield in the PT dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We also consider various relevant experimental constraints, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', collider, charged-lepton flavour violation, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', while choosing our BPs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In fact, null experimental evidence of sparticles to date has put stringent lower bounds on the concerned states, especially the coloured ones [77–80].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Thus, for the analysis of EWPT, we integrate such heavy states out and work in the context of a simplified effective model rather than considering the full NMSSM + one RH-neutrino framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We have adopted both the critical and nucleation temperature analyses to describe the PT properties in our model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This is crucial since earlier studies, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [60], have reported that the analysis of PT, solely based on critical temperature calculation does not provide a complete picture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In fact, the critical temperature analysis does not confirm whether a PT has indeed taken place or not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' A first-order phase transition (FOPT) proceeds via bubble nucleation and hence computation of nucleation probability and subsequently, nucleation temperature are vital to correctly describe the pattern of a FOPT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Finally, we discuss the detection prospects of all our BPs in the forthcoming GW interferometers and find that the future space-based experiments: namely, U-DECIGO and U-DECIGO-corr [81, 82], have the required sensitivities to test a few of our BPs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This possibility gives a complementary detection scope for the NMSSM + one RH-neutrino set-up beyond the conventional experimental searches, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', collider, neutrino, flavour, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The paper is organised as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In section 2 we discuss the model setup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Next in section 3, we talk about the relevant model parameters that are important for studying the PT properties and the possible experimental constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Subsequently in section 4, we present the dynamics of EWPT in detail along with our numerical findings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This section also addresses the production of the GW and the testability of our framework in upcoming space-based interferometers, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', U-DECIGO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Finally, we summarize our analysis and – 4 – conclude in section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Some useful formulae and relations are relegated to the appendices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 2 The Model The superpotential for the chosen framework is given by W = W ′ MSSM + λ �S �Hu · �Hd + κ 3 �S3 + Y i N � N �Li · �Hu + λN 2 �S � N � N, (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1) where i = 1, 2, 3 denotes the generation indices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1) is nothing but the Z3 symmet- ric NMSSM superpotential, extended with one Right-Handed Neutrino (RHN) superfield ( ˆN), keeping the initial Z3 symmetry unbroken.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Here W ′ MSSM denotes the MSSM super- potential (see reviews [27, 83–85]) without the bilinear µ-term, ˆHu = ( ˆH+ u , ˆH0 u)T , ˆHd = ( ˆH0 d, ˆH− d )T , ˆLi = (ˆνi, ˆli)T are the SU(2)L doublet up-type Higgs, down-type Higgs, and lepton superfields, respectively and the “·” notation is used to express SU(2) product, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', ˆLi · ˆHu = ˆνi ˆH0 u − ˆli ˆH+ u .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The superpotential in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1) cannot be made invariant under a global U(1) symmetry, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', U(1) of the Lepton number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This in turn ensures the disap- pearance of a Nambu-Goldstone boson which results from the spontaneous breaking of a global symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The ˆN is considered to be odd under RP while the ˆS transforms as even.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' RP is violated spontaneously in this model when, along with the other neutral scalars, the RH-sneutrino ( � N) also acquires a non-zero VEV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' These VEVs yield the effective µ-term (µ = λ⟨S⟩), the effective bilinear RP -violating couplings (ϵi = Y i N⟨ � N⟩), and the Majorana mass term for the RHN (λN⟨S⟩).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' One should note the presence of four extra couplings (three neutrino Yukawa couplings Y 1,2,3 N and another trilinear coupling λN) in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1), apart from the known Z3 invariant NMSSM couplings, λ and κ (see for example Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [54, 86]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We would like to re-emphasize here that with only one ˆN, of course, one cannot reproduce the observed neutrino mass squared differences and mixing [47, 48, 53], even after including loop corrections [76].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' However, even this simple choice can predict the absolute mass scale and atmospheric mass squared difference for the active neutrinos, besides giving interesting information about the EWPT and GW, the primary goals of this article.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We plan to explore the possible correlations between neutrino observable with the EWPT and GW sectors in the context of a two or three ˆN scenario [69] in future work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Following Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1), in a similar way, we can write down Lsoft, the piece of Lagrangian density that contains soft-SUSY breaking terms: −Lsoft = −L′soft + m2 S S∗S + M2 N � N∗ � N + � λAλS Hu · Hd + h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' � + �κAκ 3 S3 + (ANYN)i �Li · Hu � N + AλN λN 2 S � N � N + h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' � , (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2) where L′ soft contains the MSSM soft-supersymmetry breaking terms, excluding the Bµ term [27, 83–85, 87, 88].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The remaining terms are typical to that of the Z3 symmetric NMSSM, except the terms involving � N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Soft terms, as depicted in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2), are written in the framework of supergravity mediated SUSY breaking [89].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' All the trilinear A-terms and the soft squared masses are assumed to lie in the TeV regime and consequently, all VEVs – 5 – are expected to appear also in the same regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In other words, the scale of RHN mass, which is determined solely by the scale of soft-SUSY breaking terms will also lie in the TeV regime assuming λN ∼ O(1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This assures neutrino mass generation via the TeV scale seesaw mechanism which is also testable at colliders [90–95].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Further, the TeV scale seesaw immediately suggests Y i N ∼ O (10−6 − 10−7) and left-handed sneutrino VEVs, ⟨�νi⟩ ∼ O (10−4 − 10−5) GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' These values of Y i N, ⟨�νi⟩ indicate (i) tiny RP violation (∼ O (10−3 − 10−4) GeV, typical for the bilinear RP violation [96]) and, (ii) weak mixing of the left-handed leptons and sleptons (neutral and charged) with the concerned sectors, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', charged and neutral gauginos, higgsinos, Higgses, right-handed neutrino and sneutrino, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' One can use the advantage of such weak mixing to perform a simplified analysis without the loss of generality, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', using a set of four fields (Hu, Hd, S, ˜N) instead of seven (Hu, Hd, S, � N, �Li) while investigating the PT phenomena.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The tree-level neutral scalar potential is the sum of F-term (VF ), D-term (VD) and the soft-SUSY breaking terms and is given by Vtree = VF + VD + Vsoft, (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3) where Vsoft ≡ −Lsoft is given by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' VF , following the usual prescription from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1), is written as VF = ��� − λH0 uH0 d + κS2 + λN 2 � N2��� 2 + |Y i N|2 |H0 u|2| � N|2 + |λ|2|S|2|H0 u|2 + ��� 3 � i=1 Y i N �νiH0 u + λNS � N ��� 2 + ��� 3 � i=1 Y i N �νi � N − λSH0 d ��� 2 , (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4) and VD, again using the standard procedure is read as VD = g2 1 + g2 2 8 � |H0 d|2 + 3 � i=1 |�νi|2 − |H0 u|2 �2 , (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5) with g1, g2 as the U(1)Y , SU(2)L gauge couplings, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The neutral CP-even scalar components4, after the EW-symmetry breaking (EWSB), develop the following zero-temperature VEVs: ⟨H0 u⟩ = vu, ⟨H0 d⟩ = vd, ⟨S⟩ = vS, ⟨�νi⟩ = vi, ⟨ � N⟩ = vN, i = 1, 2, 3 or e, µ, τ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6) The first three VEVs are typical to the NMSSM while the last two VEVs appear for the chosen framework as a consequence of the spontaneous RP violation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' One can use these VEVs to trade off the concerned soft squared masses as depicted in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The VEVs vS, vN, being governed by the TeV scale soft-terms, also lie in the same regime whereas vi appears to be much smaller ∼ O(100 MeV) for vN, vS ∼ O(1 TeV) [74].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Generation of the neutrino mass via a TeV scale seesaw mechanism, as already advocated, however, offers 4Here we adhere to CP-conservation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Further, we do not consider the possibility of charge and colour- breaking minima for this study (see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [97] in the context of the NMSSM) and hence, assign vanishing VEVs to charged and coloured scalars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' – 6 – a more stringent constraint on vi (∼ O (10−4 − 10−5) GeV), similar to models studied in Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [73, 98–101].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' One can write down minimization conditions for vN, vi, using Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3), as: ∂Vtree ∂ � N ��� VEVs as Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6) = λNvN � λvuvd + κv2 S + λN 2 v2 N � + |Y i N|2v2 uvN +λNvS � 3 � i=1 Y i Nvivu + λNvSvN � + 3 � i=1 Y i Nvi � 3 � j=1 Y j NvjvN − λvSvd � +M2 NvN + 3 � i=1 (ANYN)ivivu + ANλNvSvN, ∂Vtree ∂ �νi ��� VEVs as Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6) = Y i Nvu � 3 � j=1 Y j Nvjvu + λNvSvN � + Y i NvN � 3 � j=1 Y j NvjvN − λvSvd � + 3 � j=1 m2 �Lijvj + (ANYN)ivuvN + g2 1 + g2 2 4 � �v2 d + 3 � j=1 v2 j − v2 u � � vi, (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='7) where m2 �Lij denotes soft-squared masses for sleptons [27, 83–85] and all the concerned parameters are assumed to be real.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' It is apparent from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='7) that if one neglects terms like Y i NY j N, Y i Nvi for smallness, then vS → 0 suggests vN → 0 and consequently vi → 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Thus, a non-zero vS is indirectly connected to a non-zero vi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The smallness of vi, compared to vu, vd, also assures that one can still safely use the MSSM relations v2 = v2 u + v2 d and tan β = vu/vd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The presence of tiny but non-zero Y i N, vi, as already stated, generates mixing between left-handed neutrinos and neutral gauginos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' These new mixing terms in the EW sector enhance the size of neutral scalar, neutral pseudoscalar, charged scalar, neutral fermion and charged fermion mass matrices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Being explicit, RP -violating mixing of H0 u, H0 d, S states with � N and three families of �νi, enlarges the NMSSM CP-even and CP-odd neutral scalar mass matrices from 3 × 3 to 7 × 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Similar augmentation appears (i) in the charged scalar sector (2 × 2 in the NMSSM to 8 × 8 due to RP -violating mixing of H± u ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' H∓ d states with the three families of left- and right-handed charged sleptons),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (ii) in the neutral fermion sector (5 × 5 in the NMSSM to 9 × 9 due to RP -violating mixing among neutral gauginos,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' � H0u,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' � H0 d,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' �S states with the right-handed neutrino and the three families of left-handed neutrinos),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' and (iii) in the charged fermion sector (2×2 in the NMSSM to 5×5 due to RP - violating mixing among the charged higgsino,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' gaugino states with the three families of the left- and right-handed handed leptons).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' However, because of tiny values of Y i N, vi, one can easily decompose the aforesaid mass matrices in blocks for approximate analytical studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' For example, for all practical purposes, the neutral scalar mass matrix can be decomposed into two diagonal blocks: (i) a 4 × 4 one consisting of CP-even H0 u, H0 d, S, � N states, (ii) another 3 × 3 one consisting of CP-even left-handed sneutrino states, and off-diagonal blocks containing tiny mixing terms between the two aforementioned states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' A similar observation holds true for the neutral pseudoscalar, charged scalar, neutralino and chargino mass matrices, which can be effectively considered as having dimensions 3 × 3, 2 × 2, 6 × 6 – 7 – and 2×2, respectively5, without any loss of generality, leaving the almost pure left-handed CP-odd sneutrino, charged slepton, left-handed neutrino and charged leptons states aside.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' For the purpose of analyzing the chosen model numerically, it is convenient to express the aforesaid mass matrices in the extended Higgs basis [102–109] which will be introduced subsequently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Entries of these mass matrices are detailed in appendix A, along with the full uncoloured scalar potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1 A convenient basis choice We have already introduced the tree-level neutral scalar potential in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3), using Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2), (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4) and (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' However, to study the phenomena of PT we need to move beyond the tree- level contribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' For this purpose, as we already mentioned, it is useful to work in the extended Higgs basis [102–109], given as: Hd = � 1 √ 2(cβHSM − sβHNSM) + i √ 2(−cβG0 + sβANSM) −cβG− + sβH− � , Hu = � sβG+ + cβH+ 1 √ 2(sβHSM + cβHNSM) + i √ 2(sβG0 + cβANSM) � , S = 1 √ 2(HS + iAS), � N = 1 √ 2(NR + i NI), (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8) where cβ(sβ) = cos β(sin β) with tan β = vu/vd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Note that one trades off the scalar, the pseudoscalar and the charged components of the relevant four fields {Hu, Hd, S, � N} with the four neutral CP-even interaction states (HSM, HNSM, HS, NR), three CP-odd interaction states (ANSM, AS, NI), one charged Higgs pairs (H±), along with the neutral and charged Goldstone modes (G0, G±) in the extended Higgs basis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This particular basis choice assures the SM-like couplings between HSM with the up-type SM fermions, the down-type SM fermions and the SM vector bosons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In addition, the aforementioned basis choice also predicts vanishing couplings between HS, NR with the same aforesaid SM states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Furthermore, from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8), in the light of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6) and v2 = v2 u + v2 d, one can see that ⟨HSM⟩ = √ 2v, ⟨HNSM⟩ = 0, ⟨HS⟩ = √ 2vS and ⟨NR⟩ = √ 2vN, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', non-vanishing VEVs appear only in certain field directions leaving the SM-direction undisturbed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' These interaction states later mix to produce the mass eigenstates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' However, one of the CP-even states with a mass in the ballpark of 125 GeV (see Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [110] and references therein) contains the predominant HSM component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This alignment between the 125 GeV SM-like Higgs in the mass basis and HSM of the extended Higgs basis implies negligible admixing among various states in the extended Higgs basis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Mathematically, after the EWSB, in the HSM, HNSM, HS, NR basis: |M2 S,1i| ≪ |M2 S,ii − M2 S,11|, (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='9) 5One can easily identify the remaining three neutralinos and three chargions, lying at the bottom of the mass spectrum, as three LH-neutrino dominated states and the charged leptons, e, µ, τ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' – 8 – where i = 2, 3, 4 and M2 S,1i, the entries of the CP-even scalar squared mass matrix, are given in appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' It is now apparent that in order to satisfy Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='9) one either needs small M2 S,1i or large |M2 S,ii − M2 S,11|, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', decoupling of HSM from the three remaining states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The latter, in terms of the mass eigenstates, predicts three significantly heavier states dominated by HNSM, HS, NR compositions, and one ∼ O(125 GeV) state controlled by HSM composition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In reality, for the SFOEWPT, singlet-like states lighter than 125 GeV are favoured.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Besides, heavier singlet-dominated states create a kind of “push-down” effect [71, 111] which makes it difficult to achieve an SM-like Higgs state around 125 GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Thus, for our numerical studies, we consider regions of the parameter space that can accommodate one or more singlet-like states lighter than 125 GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' These light singlet- dominated states are helpful in accommodating a 125 GeV SM-like Higgs through the “push-up effect” [71, 111].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' One can use Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='9) subsequently to derive a few approximate relations, useful for parameter space scanning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' For example, using appendix B and assuming M2 S,11 = m2 h125, the condition M2 S,12 → 0, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', vanishing mixing between the HSM and HNSM states, implies λ2 ≃ m2 h125 − m2 Z cos 2β 2v2 sin2 β .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='10) As mh125, mZ (mass of the SM Z0-boson), v are known, λ approximately appears to be a function of tan β only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' A similar relation like Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='10) holds also for the NMSSM [60].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Applying the same procedure to minimize the mixing between HSM and HS states, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', M2 S,13 → 0, one gets M2 A ≃ 4µ2 sin2 2β � 1 − κ 2λsin 2β + λλNv2 N 4µ2 sin 2β � , (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='11) choosing M2 A ≃ 2µ sin 2β � Aλ + κµ λ + λλNv2 N 2µ � 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The last term in the Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='11) appears due to mixing with the RH-sneutrino.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In the limit of κ ≪ λ, using Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='11), it turns out that M2 A ≃ M2 H ≃ M2 H± ≃ 4µ2csc2 2β � 1 + λλNv2 N 4µ2 sin 2β � where MH represents mass of a state with dominant HNSM contribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The presence of vN shows that these mass eigenstates possess contributions from the RH-sneutrino.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' These kinds of mixing may appear sizable depending on λN and vS values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Adopting a similar analysis for M2 S,14 → 0, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', effacing the mixing between HSM and NR states, it is hardly possible to get a simple relation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' A light state below 80 GeV with dominant RH-sneutrino contribution hints for a sizable mixing between the HSM and NR states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This effect, via one-loop, makes it easy to assure a 125 GeV SM-like Higgs, even with stop mass below O(1 TeV) [112].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' By choosing the parameters carefully, one can of course consider a heavier stop mass to secure a 125 GeV SM-like Higgs having negligible admixing with a lighter RH-sneutrino-dominated state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This is precisely what we have done while scanning the parameter space since a lighter sneutrino, as also stated earlier, is advantageous for SFOEWPT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We will discuss this aspect in detail later.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We note in 6At the limit λN → 0, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='11) reproduces the known NMSSM result [60].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' If one further considers κ → 0, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='11) matches the well-known MSSM relation [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' – 9 – passing that so far we have discussed only the tree-level aspects of the scalar potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In reality, the scalar potential receives considerable contributions from radiative effects involving various SM particles and their SUSY partners [54, 113–115].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Some of these higher-order contributions have observable consequences, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', effects of the top and stop loops to procure a 125 GeV SM-like Higgs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 Higher order contributions It is relevant to investigate various sources critically before implementing higher-order ef- fects arising from the different SM and BSM states on the tree-level scalar potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The effect of higher-order contributions, especially via SUSY partners, is crucial for yielding the observed SM mass spectrum, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', the Higgs mass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' These effects, however, are diluted for the analysis of EWPT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Hence, we concentrate only on the leading one-loop effects which can arise from various SM and BSM sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Regarding the latter, one needs to con- sider the following facts: (i) BSM Higgs masses, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', states with dominant HNSM, HS, NR, ANSM, AS and NI components, must not remain very far from the EW scale for a suc- cessful SFOEWPT and, (ii) hitherto unseen experimental evidence of SUSY searches have set lower limits on sparticle masses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' These limits are stringent for the coloured sector, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', gluinos and squarks, >∼ O (1 TeV) (see, for example, the latest CMS [77–79, 116] and ATLAS [80, 117–119] limits).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' On the other hand, for the uncoloured sparticles, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', sleptons, LH-sneutrinos, etc, experimental lower bounds are rather flexible [120–122].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' For convenience, however, we consider heavy sleptons and LH-sneutrinos, >∼ O (1 TeV), for this study7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' A careful range of relevant parameters was considered so that even with these heavy sleptons one can satisfy the latest result on the anomalous magnetic moment of muon [123] which typically favours the aforesaid states to be lighter than a TeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' With the above mentioned facts and assumptions, one ends up with a situation where one encounters >∼ O (1 TeV) sleptons, LH-sneutrinos, squarks & gluinos together with other BSM states, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', scalar and pseudoscalar Higgses, neutralinos, and charginos, in the ballpark of the EW scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Clearly, now one can integrate out these >∼ O (1 TeV) states to yield an effective theory with BSM scalar, pseudoscalar, charged Higgses, neutralinos, charginos and, of course, the SM particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Here we would like to point out again that the neutralino and the chargino sector for the concerned model are enhanced compared to the NMSSM, owing to the presence of Y i N in the superpotential (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1)) and non-zero LH-sneutrino VEVs (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' However, these parameters are compelled to remain tiny (∼ O (10−6 − 10−7) and ∼ O (10−4 − 10−5) GeV), thanks to the constraints arising from the neutrino experiments and the assumption of a TeV scale seesaw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' A similar observation, as already stated, also holds true for the BSM Higgs sector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In summary, the effective number of contributing states are four CP-even Higgses (S0 i ), three CP-odd Higgses (P 0 i ), two charged Higgses (H±), six neutralinos (�χ0 i ), two charginos (�χ± i ), charged and the neutral Goldstone bosons (G±, G0), and, the relevant SM particles (t, W ±, Z0)8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This 7Unlike the coloured sector, >∼ O (1 TeV) sleptons and sneutrinos do not introduce large higher-order corrections to the scalar sector owing to small values of the concerned lepton Yukawa couplings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 8Contributions from the remaining SM fermions are sub-leading due to the sizes of concerned Yukawa couplings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' – 10 – set of nineteen particles including the two Goldstone bosons, together with the t, W ±, Z0, will be considered as the dynamical degrees of freedom needed for the current study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' One can derive parameters of the aforesaid effective theory through the renormalization group equation and subsequently, by matching onto the complete model at some intermediate scale Λ which we fixed at mt, the top mass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The leading contribution to the tree-level potential Vtree obtained using this procedure is ∆V = ∆λ2 2 |Hu|4, (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='12) where ∆λ2 at one-loop level is given by [124–127], ∆λ2 = 3 8π2 y4 t � log � M2 �t m2 t � + A2 t M2 �t � 1 − A2 t 12M2 �t �� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='13) Here yt is the top Yukawa coupling evaluated using the running top quark mass, M�t = √m�t1m�t2 depicts the geometric mean of two stop masses and At is the soft trilinear coupling between Higgs and stops (appears within L′ soft of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2) [27]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' One can of course write down contributions like the one shown in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='12) for other scalar states, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', Hd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Such a term, however, appears due to mixing between Hu and Hd through the effective µ-term and is usually sub-leading compared to the one shown in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='12), as long as µ ≪ M�t 9 and tan β value appears not too large.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The quantity ∆λ2 is crucial to accommodate a 125 GeV SM-like Higgs and can be estimated using the same.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The leftover degrees of freedom also contribute to the potential (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3)) through radiative corrections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Their collective contributions are given by Coleman-Weinberg po- tential [129] V 1−loop CW = 1 64π2 � i=B,F (−1)Finim4 i (φα) � log �m2 i (φα) Λ2 � − Ci � , (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='14) where i = B (F), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', bosons (fermions), ni represents the relevant degrees of freedom, FB = 0 (FF = 1), Ci is a constant with a value of 3/2 (1/2) for scalars, fermions, longitu- dinally polarized vector bosons (transversely polarized vector bosons), Λ is the aforesaid intermediate energy scale, fixed at mt and, m2 i (φα) = m2 i (HSM, HNSM, HS, NR) denotes field-dependent masses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The latter is estimated from Vtree + ∆V (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3) and Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='12)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Contributions from Vtree are detailed in appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The set of involved Bs are given by S0 1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='.,4, P 0 1,2,3, H±, G0, G±, Z0, W ± with nB = 4×1, 3×1, 2, 1, 2, 3, 2×3, depend- ing on the nature of the concerned state, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', scalar or complex scalar or massless bosons or massive vector bosons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' A similar approach for the fermions give F = �χ0 1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='.,9, �χ± 4,5, t with nB = 9 × 2, 2 × 2, 3 × 4 considering their electric and colour charges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' One should note that the presence of G0, G± in the Coleman-Weinberg potential yields divergent contribu- tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' However, these can be effaced by using an infrared regulator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Finally, putting all 9Such a choice helps one parameterize radiative contributions from stops effectively, even beyond the one-loop order [125, 127, 128].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' – 11 – these pieces, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', Vtree (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3)), ∆V (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='12)) and V 1−loop CW (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='14)) together, one obtains the effective scalar potential as Veff = Vtree + V 1−loop CW + ∆V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='15) Inclusion of Coleman-Weinberg contributions (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='15)) to the tree-level scalar poten- tial, however, changes the position of physical minima and masses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' To restore the original position for the physical minima, keeping M2 S,13, M2 S,14 → 0 and maintaining the mass of the CP-even scalar state with leading HSM composition at 125 GeV, one needs to intro- duce appropriate counterterms, encapsulated within another contributor Vct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The latter is normally related to a redefinition of the entries of −Lsoft (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2)) [130–132] which are depicted in appendix C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The counterterms are, thus, not arbitrary but fixed by the aforesaid criteria.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Mathematically, ∂ ∂φi � Veff + Vct ���� φi=⟨φi⟩ = 0 and ∂2 ∂φi∂φj � Veff + Vct ���� φi=⟨φj⟩ = 0, (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='16) with φi = {HSM, HNSM, HS, NR}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' One can figure out ⟨φi⟩ using Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6) and Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We note in passing that till now we have discussed modifications of the tree-level scalar potential from higher order effects at vanishing temperature, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', T = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In reality, however, one also needs to include contributions arising from T ̸= 0 which we will address now.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3 Contributions from non-zero temperature The one-loop temperature-dependent potential is given by [133] V 1−loop T̸=0 = T 4 2π2 � i=B,F (−1)FiniJB/F �m2 i (φα, T) T 2 � , (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='17) where T represents the temperature, symbols FF,B, nF,B are the same as discussed in the context of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='14), m2 i (φα, T) depicts thermal field-dependent masses of the ith degrees of freedom as: m2 i (φα, T) = m2 i (φα) + ciT 2, (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='18) with ci representing the concerned Daisy coefficients [133–137].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' These coefficients appear non-vanishing for bosons and are given in appendix D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Finally, JB/F , i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', the thermal function, is defined as JB/F � x2 ≡ m2 i (φα, T) T 2 � = ± � ∞ 0 dy y2 log � 1 ∓ e−√ x2+y2� , (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='19) where + (−) sign is for bosons (fermions).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' One should note that at the m2 ≫ T 2 limit, where “m” depicts a generic mass term, JB/F suffers an exponential suppression from Boltzmann factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' These repressions ensure that massive degrees of freedom, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', squarks, gluinos, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', that are already integrated out (see subsection 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2), do not affect T ̸= 0 corrections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' – 12 – Clubbing all the pieces together, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', tree-level scalar potential, one-loop contributions via Coleman-Weinberg potential, and contributions from the finite temperature part, one gets the finite temperature effective scalar potential at the one-loop order as VT = Vtree + ∆V + V ′1−loop CW + Vct + V 1−loop T̸=0 ≡ VT (φ, T), (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='20) where V ′1−loop CW has a form similar to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='14) but replacing m2 i (φα) with thermal masses m2 i (φα, T), as depicted in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='18).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We will use Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='20) to inquire about the PT properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We note in passing that the components of VT have explicit gauge dependence [138–140].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Besides, V 1−loop CW (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='14)), and hence V ′1−loop CW , also has renormalization scale (Λ) dependence which could dominate over the gauge dependence [141].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' To note, we have worked in the Landau gauge while computing the one-loop corrected potential at both zero and non-zero temperatures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' So far we have discussed different pieces of the scalar potential needed to study the PT dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Now we will address how and to which extent various model parameters can affect the same.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 3 Choice of parameters The set of new parameters, compared to the NMSSM, are Y i N, λN, vN, (ANYN)i, AλN λN, (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1) using Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1), Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3), Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6), and replacing soft-SUSY breaking square mass term M2 N with the corresponding VEV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Now, as already discussed, Y i Ns are associated with the neutrino mass generation through a TeV scale seesaw and thus, are constrained to be small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' These Y i N values, for TeV-scale trilinear terms, predicts (ANYN)i ∼ O (10−3 − 10−4) GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The latter is also related to the smallness of vi, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e, the LH-sneutrino VEVs (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6)), as guided by a TeV scale seesaw mechanism and neutrino data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Hence, for the PT analysis, we can neglect these tiny parameters, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', vi, Y i N, (ANYN)i, without any loss of generality as they have negligible effects on the PT dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Now from the discussion of section 2, it is evident that relevant “bare” parameters for the uncoloured scalar potential after trading (see appendix E for details) soft-squared masses with the corresponding VEVs (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6)) are, λ, λN, κ, vu, vd, vS, vN, Aλ, Aκ, AλN .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2) One can redefine this list further by trading vu, vd with v = � v2u + v2 d, tan β = vu/vd and vS with µ = λvS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' As v = 174 GeV is known, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2) can be re-casted as λ, λN, κ, tan β, µ, vN, Aλ, Aκ, AλN .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3) One can also trade parameter vN with the RH-neutrino mass term MN ∝ λNvN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Similar trading is also possible for Aλ with MA, using a relation given in subsection 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We, however, do not use MA, MN for the parameter space scanning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Parameter λ can also be exchanged using Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The same parameter can also be constrained using an – 13 – upper-bound on the tree-level SM-like Higgs mass [54, 142, 143], given as m2 Z(cos2 2β + g−2 2 λ2 sin2 2β).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This helps us to consider small tan β ≲ 5 and λ ∼ O(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1) or higher such that one gets a significant contribution to the tree-level SM-like Higgs mass10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The ranges of other parameters are also guided by certain aspects, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', in order to avoid the presence of Landau pole [144, 145] below the GUT scale, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', 1016 GeV, one needs to consider λ, κ values carefully at the EW scale such that √ λ2 + κ2 <∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='7 [54].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Besides, smaller values of κ ∼ O(10−2) are favoured as a stronger PT along a particular field direction prefers smaller values of the quartic coupling (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', κ for PT along the HS direction) and larger values of the cubic coupling (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', Aκ for a PT along the HS direction), leading to an enhanced barrier height along that specific direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' A small value of κ, together with a small Aκ value11, as already discussed in subsection 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1, assure the presence of light CP-even and CP-odd states below 125 GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' These light states help to procure a 125 GeV SM-like Higgs via the “push-up” [71, 111] effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' It is evident that one needs to consider Aκ values carefully as for this parameter larger values are favourable for the PT dynamics while smaller ones are useful in fixing the SM-like Higgs mass around 125 GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Tree-level mass of the singlet-dominated CP-even state, using Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3) and Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1), is M2 S,33 ≡ m2 HS = −λλNAλN v2 N 2µ + κAκµ λ + 4κ2µ2 λ2 + λ2v2Aλ sin 2β µ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4) This reduces to the known NMSSM result [143] at the limit λN → 0 with a O(λ2) correc- tion12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' It is apparent from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4) that how different parameters appear instrumental in determining the mass of a CP-even singlet-dominated state in this framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We con- sider κ > 0, Ak < 0 in this study to ensure the formation of a barrier along the HS field direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The parameter µ plays a vital role in the PT dynamics and, as given in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4), is also crucial for the mass and composition of a singlet-like state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [59] suggests that a strong EWPT favours µ ≲ 300 GeV for the Z3 invariant NMSSM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We consider similar ranges for µ in our analysis which also obey the “naturalness” criteria and the LEP chargino bound [148–151], i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', |µ| >∼ 103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5 GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This range of µ values, together with the choice of λ ∼ O(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1), suggests a value for vS not too far from the EW scale as required to yield a sizable impact on the EWPT from the singlet sector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' A similar observation holds true for the RH-sneutrino VEV vN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The parameter vS also determines the mass term for RH-neutrino, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', ∝ λNvS which is constrained to be around a TeV as non-zero neutrino masses in the chosen framework arise through a TeV scale seesaw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The adaptation of a TeV scale seesaw also put some bounds on the parameter λN that is expected to be at most O(1) to avoid the existence of Landau pole below the GUT scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The requirement of having stronger PT along the NR field direction, however, suggests smaller values of λN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This behaviour, is similar to κ, as addressed before.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The role played by λN in the 10Lower λ values suggest reduced tree-level mass and hence, needs larger corrections from the stop sector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In the NMSSM, considering the perturbative nature of λ up to the scale of the Grand Unified Theory (GUT) one gets λ ≲ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='7, in the limit of κ ≪ λ [54].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 11These ranges of κ, Aκ are guided by the well-known U(1)PQ, U(1)R limits [143, 146, 147] for the NMSSM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 12This term appear to be sub-leading for small λ, tan β values together with vS ≪ v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' – 14 – PT dynamics is somewhat non-trivial and will be addressed later in detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The remaining parameters, Aλ, AλN are connected to the scale of vS, vN and thus, are expected to be in the ballpark of a TeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' These parameters, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', Aλ, AλN also affect tree-level masses of the CP-even and CP-odd scalar states as detailed in appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In this analysis we consider Aλ > 0 and AλN < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The latter choice helps to efface the possible existence of a tachyonic state in the CP-odd scalar sector (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We note in passing that so far we have presented a qualitative discussion in the context of the chosen independent parameters, as depicted in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' For finding BPs through numerical analysis, one, however, also needs to consider all the relevant present and anticipated experimental bounds which we will address in the next subsection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1 Experimental Constraints A viable phenomenological analysis must satisfy all the concerned experimental limits, the existing and the projected ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The inclusion of these bounds reduces the size of the available parameter space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In this analysis, apart from considering sensitivity reaches of the existing [152–154] and upcoming [81, 155, 156] GW detection setups, we also consid- ered constraints arising from (i) analysis of the SM-like Higgs boson properties and BSM Higgs searches at colliders, (ii) other BSM searches at the colliders, (iii) flavour-violating processes, (iv) neutrino experiments, (v) muon anomalous magnetic moment, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In order to employ these constraints in our numerical analysis, we first implemented the concerned model in SARAH 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5 [157–164].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Subsequently, we use SPheno-4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5 [158, 162, 164–171] to get the mass spectrum and decay widths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The output of SPheno-4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5 also provides branching fractions for various flavour-violating processes, BSM contributions to the muon anomalous magnetic moment [166], several LHC observables like reduced Higgs couplings, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We will now discuss the aforesaid constraints one by one in further detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (i) Analysis of the SM-like Higgs boson properties and BSM Higgs searches at colliders: Here one needs to consider two aspects: (a) SM-like Higgs analyses, and (b) the BSM Higgs searches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Concerning the first, important constraints appear from the measured mass, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', ≈ 125 GeV [42, 172], and couplings [39–42, 173–177].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We have used these results to assure the existence of an SM-like 125 GeV Higgs in our analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Besides, to assure the SM- like nature we also put a lower limit (80%) on the Hu composition of the 125 GeV mass eigenstate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Regarding the BSM Higgs searches, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', for states with leading HNSM, HS components, and the charged Higgs, we consider the concerned experimental bounds, see for example Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [178] and references therein.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We used HiggsBounds [179] 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 [180] to implement experimental constraints from the SM and BSM Higgs searches in our numerical study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (ii) Other BSM searches at the colliders: We already discussed in subsection 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 that we are working in an effective framework after integrating out heavy degrees of freedom like gluinos, squarks and even charged sleptons and LH-sneutrinos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We consider these states to remain heavier than 1 TeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Such assumptions, especially for gluinos and squarks are supported by the experimental findings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In this study, we consider gluino mass >∼ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8 TeV and squark masses >∼ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 TeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' These choices are guided by the present CMS [77–79, 116] and ATLAS [80, 117–119] observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Experimental lower bounds on the charged slepton – 15 – and LH-sneutrino masses are somewhat less [120–122].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' However, we also considered them to be heavier than a TeV and integrate them out.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In our numerical study, the lightest neutralino mass varies from 3 GeV to 120 GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' However, this does not contradict any experimental bounds, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', SM-like Higgs decaying to a pair of neutralinos, (see for example Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [80, 121, 181–184]) as its predominant composition (≳ 90%) is from the singlino and the RH-neutrino.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' For charginos, we used a lower bound of 103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5 GeV [148–151] in our analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' It is important to note that experimental lower bounds are often interpreted in the context of simplified models and hence, they may not directly restrict the concerned model parameter space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (iii) Flavour-violating processes: The presence of BSM states can significantly enhance branching fractions (BR) of certain flavour-violating processes, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', B → Xsγ, B0 s → µ+µ− (see Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [185–191] and references therein), etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', compared to the SM predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' One can minimize these new contributions by taking tan β <∼ 5 and fixing squarks, gluinos, sleptons, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', masses to be heavier than a TeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' However, finite BSM contributions to these pro- cesses still appear through the EW scale uncoloured neutral scalars, neutral pseudoscalars, charged scalars, charginos and neutralinos, as required for the EWPT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Thus, we consider the following 2σ bounds BR(B → Xsγ) = (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='49 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='38) × 10−4, BR(B0 s → µ+µ−) = (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='45 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='58) × 10−9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5) We note in passing that BR(B → Xsγ), BR(B0 s → µ+µ−) also receive extra contributions due to R-parity breaking [192, 193].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' However, given the framework of a TeV scale seesaw, the size of R-parity violating couplings, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', Y i NvN, appears to be ∼ O(10−3 − 10−4) GeV and hence, hardly yield any significant contributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We consider charged Yukawa couplings to be diagonal for this work which helps to bypass constraints from the flavour-violating Higgs decays [194, 195].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' One can also con- sider slepton soft squared masses to be diagonal to minimize mixing among sleptons (both charged and neutral).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' With these choices, the effective bilinear R-parity violating cou- plings, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', Y i NvN, and the LH-sneutrino VEVs appear to be main sources for the various charged lepton flavour violating (cLFV) processes like µ → eγ, µ → eee, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' However, the scale of these couplings, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', ∼ O(10−3 − 10−4) GeV, as required for a TeV scale seesaw, can easily evade these bounds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This behaviour is very similar to the SUSY models with bilinear R-parity violation [196–198].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We note in passing that in our numerical studies we emphasized on the cLFV processes for the µ over the similar ones from τ as the con- cerned existing and upcoming experimental sensitivities are much more stringent for µ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Nevertheless, we also include constraints for cLFV processes involving a τ in our analysis, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', BR(τ → µγ) < 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4 × 10−8 [199].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The µ-based cLFV bounds included in the current analysis are given by BR(µ → eγ) < 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 × 10−13 [200], BR(µ → eee) < 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 × 10−12 [201], CR(µN → eN∗) < 7 × 10−13 [202], – 16 – where CR(µN → eN∗) represents muon to electron conversion ratio in atomic nuclei with N (N∗) representing the nucleus in the normal (excited) state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The given number, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', 7 × 10−13 is for the gold nuclei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (iv) Neutrino experiments: With one generation of RH-neutrino, as already stated in section 2, it is not possible to accommodate the experimentally observed three-flavour neu- trino masses and mixing [47, 48, 53], even with the inclusion of loop effects [76].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Thus, one will get one massive and two nearly massless neutrinos in this model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Nevertheless, even in such a scenario, we used constraints from the atmospheric mass squared difference ∆m2 atm, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='430(−2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='574) × 10−3 − 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='593(−2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='410) × 10−3 eV2 for normal (inverted) hierarchy, and the sum of three neutrino masses ≲ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 eV [1, 203].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (v) Muon anomalous magnetic moment: Just like the flavour violating processes, the anomalous magnetic moment of muon also receives extra contributions over the SM from new parameters and the BSM states (see Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [204, 205] and references therein).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The recent comprehensive SM prediction of the muon anomaly is 116591810 (43) × 10−11 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='37 ppm) [206] while the experimental average13 is 116592061(41) × 10−11 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='35 ppm).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' These numbers, adding errors in quadrature, gives ∆aµ = (251±59)×10−11 which is arising from the BSM sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This, in 4σ span, gives (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5 − 48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='7) × 10−10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The BSM contributions, especially involving charged sleptons states below a TeV [208–210], can affect this process significantly and can easily accommodate the latest experimental observation [123].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In our analysis, as already discussed in subsection 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2, we kept charged slepton masses around a TeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Nevertheless, by playing with the other concerned parameters we checked that the aforesaid ∆aµ range, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5 − 48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='7) × 10−10 is not violated in our BPs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In fact, the choice of slepton, squark masses around a TeV or more yields suppressed cLFV processes and smaller BSM contributions to the anomalous magnetic moment of the muon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' All the chosen BPs respect all the five aforesaid classes of constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We now discuss this study’s key objectives in detail, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', PT properties and GW production.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 4 The EWPT and its Properties As we already discussed, understanding the EWPT properties in the early Universe in a Particle Physics model has twofold advantages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Firstly, it can be confirmed whether the model carries the prospect to explain the origin of EWBG at some corner of the parameter space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Secondly, it provides scope to test the model at GW detectors beyond the conventional BSM searches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' One of the prerequisites of EWBG is the FOPT with sufficient strength along the SU(2)L field directions so that it can suppress the processes which wash out the baryon asymmetry after it is produced, namely SU(2)L sphalerons [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The same FOPT may yield a detectable amount of GWs that could be accessible by future GW interferometers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The structure of the thermal effective potential for a PT reveals that at very high temperatures the Universe would be in a symmetric phase with the relevant field (say φi) being located at zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' As the Universe cools down, the symmetric vacuum may disappear 13Here we have used combined experimental average obtained from the FNAL [123] and the BNL E821 [207] results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' – 17 – and the corresponding field values could be finite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Additionally, a second minimum can be formed at some higher field value which becomes degenerate with the previous one at T = Tc, known as critical temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' At temperature below Tc, the transition from the high-T VEVs (say v′ X) to the low-T VEVs (say vX) can take place.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Here X = u, d, S, i, N as depicted in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We should note here that a high-T (low-T) phase means an unstable (stable) vacuum below Tc or above nucleation temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Therefore, to have an in-depth understanding of PT dynamics, an estimate of critical temperature Tc and the strength of PT are enormously important.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Theoretically, the critical temperature can be obtained from the following equality: VT (v′ X, Tc) = VT (vX, Tc), (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1) where v′ X and vX represent high-T and low-T VEVs, respectively, along a particular field direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We also need to ensure the existence of high- and low-T vacua which can be confirmed by the following equalities, ∂φαVT (v′ X, Tc) = 0, ∂φαVT (vX, Tc) = 0, (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2) where φα = {HSM, HNSM, HS, NR}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In many cases, including ours, analytical solutions of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1) and Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2) are almost impossible to derive in order to obtain the estimates of the relevant parameters to study the PT properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We have used the publicly available package cosmoTransitions [211] to carry out the numerical calculation for our model in consideration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' A FOPT proceeds via bubble nucleation and the nucleation rate (Γ) per unit volume (V ) at finite temperature is given by Γ V ∝ T 4e−SE/T , where SE is the three-dimensional effective Euclidean action known as bounce action.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The criterion which set the condition for the onset of bubble nucleation is given by [16, 212], SE(Tn) Tn ≃ 140, (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3) where Tn is the nucleation temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' If it happens that the quantity SE(Tn) Tn > 140, then the transition does not occur due to low tunnelling probability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' As mentioned earlier, we use cosmoTransitions [211] to compute SE and Tn, which also allows for estimating the probability of a transition taking place.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Since we have four- dimensional field space, relevant to EWPT, a detailed scan of the model parameter space is challenging and numerically expensive as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Therefore in the present work, we first provide a representative BP-based study which will be detailed subsequently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We will see that such BPs are sufficient to understand the parameter space of NMSSM + one RHN framework that can potentially give rise to an SFOPT and can also be interesting from the viewpoint of EWBG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Subsequently, we discuss the impact of new parameters in the present setup compared to the NMSSM on PT strength along different field directions by providing a scan of the relevant parameter spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Before we proceed further, let us now define different criteria to consider a PT to be a strong one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Conventionally, in the critical temperature analysis, the order parameter that – 18 – decides the fate of PT is given by, γc ≡ vc(Tc) Tc = � ⟨HSM⟩2 + ⟨HNSM⟩2 Tc ≳ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0, (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4) where vc(Tc) denotes VEVs of the SU(2)L Higgs fields, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', HSM, HNSM, at Tc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' For the nu- cleation temperature calculation, we define an SFOPT along the respective field directions as follows: Along SU(2)L doublet Higgs direction: ∆φSU(2) Tn = � ( � HlT SM � − � HhT SM � )2 + ( � HlT NSM � − � HhT NSM � )2 Tn ≳ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5) Along the SU(2)L singlet Higgs and the RH-sneutrino direction: ∆φS Tn = � ( � HlT S � − � HhT S � )2 Tn ≳ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' ∆φ � N Tn = � ( � NlT R � − � NhT R � )2 Tn ≳ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0, (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6) where ∆φSU(2) Tn , ∆φS Tn and ∆φ � N Tn represent PT strength along the SU(2)L-doublet, SU(2)L- singlet and the RH-sneutrino field direction, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The notation, � ΦlT� denotes the low temperature minimum while � ΦhT� is the high temperature minimum of a scalar field (Φ) before nucleation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' A favourable condition to yield the observed baryon asymmetry of the Universe via the EWBG is ( � HhT SM � , � HhT NSM � ) = (0, 0) with ∆φSU(2) Tn ≳ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In con- trast, when ( � HhT SM � , � HhT NSM � ) ̸= (0, 0), the sphaleron processes outside the bubble gets substantially suppressed which lead to inefficient production of the baryon asymmetry of the Universe from the EWBG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1 PT in the NMSSM + one RHN model As we already specified, the field space relevant to the PT analysis is four-dimensional in the present framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This opens up the possibility of obtaining a richer PT pattern compared to the case of the NMSSM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We define the high-temperature symmetric vacuum of the scalar potential as Ω0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In principle, one can have many distinct PT patterns in the whole parameter region of the NMSSM + one RHN framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Here we summarise a few such possibilities that advocate some unique PT patterns along the various field directions: Type-I: As already stated, at T ≫ Tc, the Universe remains in the symmetric phase where each of the four fields has zero VEV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The simplest possibility for a PT is that at critical temperature the symmetry-breaking minimum of the total scalar potential appears only along the HSM direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Then the PT happens from symmetric to the broken phase directly in that direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We denote this by Ω0 PT −−→ ΩHSM where ΩHSM represents the vacuum along SM Higgs direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Type-IIa: This pattern involves displacement of the HS field VEV (at T > Tc) from the initial zero value as the Universe cools down.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We label it as Type II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Below Tc, the PT occurs along both the HSM and HS field directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We denote this particular pattern (IIa) as Ω0 → Ω′ HS PT −−→ ΩHSM + ΩHS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' – 19 – Type-IIb: This is similar to the earlier case where for T > Tc, a shift of the HS field value from zero vacuum appears.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Below the critical temperature, the transition also takes place along the HS direction only and is represented by Ω0 → Ω′ HS PT −−→ ΩHS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Type-IIc: This case also falls under the Type II category.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' However, below critical temperature, the PT happens along both HS and NR field directions as indicated by Ω0 → Ω′ HS PT −−→ ΩHS + ΩNR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Type-IIIa: In this category, for T > Tc, the shifts of HSM and HS VEVs from the initial zero values take place.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' When T < Tc, PT also occurs along the same field directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This pattern is represented by Ω0 → Ω′ HSM + Ω′ HS PT −−→ ΩHSM+ΩHS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Type-IIIb: In this category, at T > Tc, the behaviour of the scalar potential is similar to the last one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' However, at T < Tc, the PT occurs along HSM, HS and NR directions as indicated by Ω0 → Ω′ HSM + Ω′ HS PT −−→ ΩHSM +ΩHS+ΩNR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Type-IV: This category is defined to indicate a particular PT pattern where at a T > Tc, the symmetric vacuum of the total scalar potential gets displaced along the S and NR field directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The PT occurs below Tc along any of the four field directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' As described earlier, any BP showing either of the type-I or type-IIa PT pattern is preferred in view of efficient EWBG, provided the corresponding PT strength satisfies the condition ∆φSU(2) Tn ≳ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Whereas, the rest of the types as listed above may not lead to EWBG due to non-satisfaction of either of the conditions, �� HhT SM � , � HhT NSM �� ̸= (0, 0) or ∆φSU(2) Tn ≳ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The PT types that do not favour EWBG, can be still interesting if it triggers an SFOPT along the SU(2)L doublet or singlet field directions and subsequently radiates GW at a detectable amount.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 Numerical Results As earlier mentioned, we would like to begin with a benchmark-based study of EWPT in the present work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In the later part, we will be discussing explicitly the dependence of new parameters in the current setup compared to the NMSSM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We first tabulate six BPs in Table 1 that are consistent with all relevant theoretical and experimental constraints, as discussed in subsection 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We select the BPs in such a way that they show distinct PT characteristics with some of them favouring EWBG and carrying good to moderate detec- tion prospects at GW detectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Note that we have four soft-SUSY breaking parameters (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', Aλ, Aκ, AλN , AN) in our model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We discuss the possible role of all the A− parameters in section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Recall that one of the soft parameters AN does not contribute much to the PT dynamics since it is always associated with the tiny neutrino Yukawa coupling Y i N as earlier clarified.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We keep AN above the TeV scale for all BPs, which ensures slepton masses ≳ O(1 TeV).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In Table 1, we provide the eigenvalues of the four CP-even mass eigenstates, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', mh125, mH, mHS, m � N, corresponding to each BPs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The leading composition in these states are coming from the HSM, HNSM, HS and NR fields, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We have explicitly – 20 – checked that all the BPs evade the relevant experimental bounds as detailed in subsection 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Nevertheless, we have explicitly shown values of the various flavour-violating processes ∆aµ and ∆m2 atm for the sake of completeness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In Table 2 and Table 3, we have summarised the PT outputs of the BPs as obtained from the cosmoTransitions [211] package.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Below we discuss the PT characteristics for each of the BPs in detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' BP-I BP-II BP-III BP-IV BP-V BP-VI tan β 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='90 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='74 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='90 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='77 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='79 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='86 λ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='416 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='412 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='416 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='384 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='118 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='111 κ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='022 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='019 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='022 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='012 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='013 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='051 λN 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='146 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='142 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='146 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='130 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='260 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='238 Y 1 N × 107 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='9 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='65 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3 Y 2 N × 107 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='9 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='65 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3 Y 3 N × 107 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='9 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='65 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3 Aλ [GeV] 775.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='48 705.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='32 775.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='48 1184.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='87 988.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='08 920.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='08 Aκ [GeV] 62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='75 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='37 95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='61 107.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='08 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='70 41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='61 AλN [GeV] 349.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='68 337.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='77 326.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='60 363.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='16 1358.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='30 1528.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='57 AN [GeV] 16000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 12000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 8500.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 12000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 6500.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 5000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 µ [GeV] 224.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='56 220.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='86 224.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='56 203.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='12 153.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='59 162.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='64 vN [GeV] 308.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='80 325.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='21 284.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='50 386.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='45 136.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='57 355.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='66 v1 × 104 [GeV] 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='55 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 v2 × 104 [GeV] 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='55 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 v3 × 104 [GeV] 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='55 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 mh125 [GeV] 126.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='02 124.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='80 125.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='64 125.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='63 126.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='28 124.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='05 mH [GeV] 772.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='36 718.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='07 772.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='73 1213.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='76 897.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='40 1012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='14 mHS [GeV] 83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='60 88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='98 69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='48 109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='54 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='31 195.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='41 m � N [GeV] 48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='60 51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='65 51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='89 27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='65 65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='18 115.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='63 BR(B → Xsγ) × 104 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='61 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='70 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='62 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='47 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='59 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='55 BR(B0 s → µ+µ−) × 109 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='24 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='26 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='24 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='19 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='20 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='19 BR(µ → eγ) × 1030 394 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='61 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='98 51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4 404 173 BR(µ → eee) × 1029 113.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 363.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='7 44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6 53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='9 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='04 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='04 CR(µN → eN∗) × 1028 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='81 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='11 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='49 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='43 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='85 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='31 ∆m2 atm × 103 eV2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='51 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='57 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='58 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='54 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='58 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='46 ∆aµ × 1010 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='88 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='75 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='42 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='94 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='54 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='24 Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The representative BPs that we will use to study the PT patterns in the present framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Apart from the parameters mentioned above, we fix the gaugino mass parameters M1 = 300 GeV, M2 = 2M1, M3 = 6M1, trilinear soft coupling At around 2 TeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We also consider RH-slepton soft masses above 1 TeV and squarks soft masses M � Qi, M�uc i , M � dc i all above 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 TeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' With the chosen values of parameters Y i N, vi and AN, the LH-sneutrino and LH-slepton masses also appear in the ballpark of a TeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' As already stated in subsection 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1, suppressed cLFV processes and smaller BSM contributions to the anomalous magnetic moment of muon are evident now due to slepton, squark masses around a TeV or more.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In fact, for BP-II, ∆aµ remains below the aforesaid 4σ range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' CR(µ N → e N ∗) value is estimated for the gold nuclei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' BP-I and BP-II : Out of these two representative BPs, BP-I shows an SFOPT along both the SU(2)L-doublet and singlet field directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' On the other hand, we obtain a weaker FOPT for BP-II in the SU(2)L doublet directions whereas a stronger one along the SU(2)L singlet direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In Figure 1, we have shown the evolution of the phase structures along the HSM (left) and the HS (right) field directions as a function of temperature for BP-I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The critical temperature for BP-I is 117.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8 GeV as noted in Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Above the critical – 21 – BP-I BP-II BP-III Transition Type Type-IIa Type-IIa Type-IIIa vc/Tc 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='30 (In);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 0 (Out) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='73 (I);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 0 (O) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='83 (I);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='61 (O) ∆φSU(2)/Tn 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='58 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='81 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='28 ∆φS/Tn 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='70 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='16 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='61 ∆φ � N/Tn 0 0 0 Tc (GeV) 117.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8 127.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 101.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6 Tn (GeV) 109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='9 126.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='7 82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='9 high-Tn VEVs (0, 0, 113.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8, 0) (0, 0, 341.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6, 0) (105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8, 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5, 88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8, 0) low-Tn VEVs (173.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1, 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5, 631.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3, 0) (102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3, 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3, 488.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='7, 0) (208.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8, 719.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='7, 0) high-Tc VEVs (0, 0, 72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6, 0) (0, 0, 333.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1, 0) (62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4, 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='9, 35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6, 0) low-Tc VEVs (152.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='9, 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8, 572.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5, 0) (92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5, 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1, 467.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='7, 0) (186.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4, 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6, 625.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4, 0) Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The PT properties for first three BPs as tabulated in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' temperature HSM is located at zero (as pointed by the legend phase 3, red coloured, in Figure 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' At T = Tc, we find another degenerate minimum along the same field direction, which is ⟨HSM⟩ = 152.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='9 GeV (as marked by phase 2, green coloured).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The black coloured line with the arrow connects the high-T and low-T VEVs indicating a possible FOPT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The bubble nucleation occurs afterwards and it ends at 109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='9 GeV which we have highlighted in orange colour (also labelled as phase 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' A similar pattern can be observed along HS direction too as shown in the right panel of Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The interesting point to mention here is that the ⟨HS⟩ starts to get displaced from zero value even at a temperature above Tc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This is in contrast to the evolution of phase structure along HSM direction for this particular BP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The BP-II shows similar characteristics although the strong PT occurs only along the HS direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The high-temperature behaviour of the total scalar potential leads us to identify the PT properties for both BP-I and BP-II as Type-IIa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' For BP-I, we observe from Table 2, that the PT strength at T = Tc is greater than one inside the bubble and zero outside the bubble.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Therefore a baryon number may be generated in the broken phase and the wash-out effects are likely to be suppressed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In view of this, BP-I is favoured in order to address EWBG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' However, BP-II shows a weaker FOPT in the SU(2)L doublet directions and hence is not suitable to address the question of EWBG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In subsection 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3 we will discuss the strength of emitted GW spectrum during bubble nucleation for both BP-I and BP-II in view of the proposed sensitivities of a few forthcoming GW experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' BP-III: The BP-III falls into Type-IIIa category.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' It implies that at a temperature above Tc, both HSM and HS attain non-zero VEVs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The critical temperature for this BP comes out to be 101.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6 GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' At this temperature, the presence of two degenerate vacua is noticed having nonzero field values for both SU(2)L doublet and singlet fields, which set the possibility of a PT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We obtain SFOPT along both the SU(2)L-doublet and singlet field directions where the PT strength turns out to be larger than one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' However, the quantity φc Tc becomes non-zero both inside and outside the bubble.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This gives rise to a stronger wash- out effect which is likely to suppress the yield of baryon asymmetry and hence seemingly disfavored in view of EWBG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Nevertheless, it carries good detection prospects in the GW detectors due to relatively larger PT strength ∆φS Tn compared to BP-I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' – 22 – 0 50 100 150 200 250 ⟨HSM⟩ [GeV] 0 50 100 150 200 250 300 T [GeV] phase3 phase2 phase1 phase0 0 200 400 600 800 ⟨HS⟩ [GeV] 0 50 100 150 200 250 300 T [GeV] phase3 phase2 phase1 phase0 Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Phase structures as a function of temperature along the HSM and HS field directions for BP-I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Different colours represent the locations of a particular field as a function of temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The black coloured line with the arrow connects two degenerate phases at T = Tc and the direction of the arrow indicates a possible FOPT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 0 200 400 600 ⟨HS⟩ [GeV] 0 200 400 600 800 1000 T [GeV] phase3 phase2 phase1 phase0 −500 −400 −300 −200 −100 0 ⟨NR⟩ [GeV] 0 200 400 600 800 1000 T [GeV] phase3 phase2 phase1 phase0 Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Phase structures as function of temperature along HS and NR field directions for BP-IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Different colours show the evolution of minimum along a particular field direction with temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The line with the arrow connects two degenerate phases at T = Tc and the direction of the arrow indicates a possible FOPT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' BP-IV: The BP-IV in Table 1 shows type-IIc PT pattern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The numerical estimates of the relevant parameters that govern the PT dynamics for BP-IV are listed in Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We find SOFPT along both the HS and NR directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Clearly, this BP is not preferred to address EWBG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In Figure 2, we show the phase structure along HS and NR directions for BP-IV as a function of temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' At temperature above Tc = 184.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5 GeV, HS takes a non-zero field value which is the typical type-II feature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The black coloured line with arrow in Figure 2 connects two degenerate phases at the critical temperature and paves the way for the PTs in the respective singlet field directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' BP-V: This BP is unique in the sense that we obtain FOPT below the critical tempera- ture along the directions of SU(2)L fields, HS and NR at the same time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This BP falls into – 23 – the type-III category since at temperature above Tc, we find high-T VEV to be non-zero for both HSM and HS fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Although this particular BP shows FOPT along HSM direction, the strength is relatively weaker as can be seen from Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Therefore, the possibility of EWBG remains unlikely for this BP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Nevertheless, we obtain SFOPT along HS and ˜N directions in contrast to weaker FOPT in the HSM direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' BP-IV BP-V BP-VI Transition Type Type-IIc Type-IIIb Type-IV vc/Tc 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 (In) ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 (Out) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 (I);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 (O) 2nd: 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='54 (In);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 (Out) 1st: 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 (In) ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 (Out) ∆φSU(2)/Tn 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='04 1st: 0 ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 2nd: 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='57 ∆φS/Tn 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='01 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='56 1st: 0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 2nd: 0 ∆φ � N/Tn 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='81 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='71 1st: 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 2nd: 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='13 Tc (GeV) 184.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5 177.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='9 2nd: 206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3 1st: 232.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8 Tn (GeV) 165.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8 144.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3 2nd: 204.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6 1st: 232.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6 high-Tn VEVs (0, 0, 529.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='9, 0) (137.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='9, 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5, 1606.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='9, 0) 2nd: (0, 0, 2087.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='9, −720.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='9) 1st: (0, 0, 2087.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='7, −845.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4) low-Tn VEVs (0, 0, 696.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6, −465.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='28) (143.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2, 0, 1832.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='7, 247.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2) 2nd: (117.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2, 0, 2088.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1, −747.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6) 1st: (0, 0, 2087.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='7, -807.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2) high-Tc VEVs (0, 0, 459.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='9, 0) (0, 0, 1484.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6, 0) 2nd: (0, 0, 2087.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='9, −724.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6) 1st: (0, 0, 2087.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='7, −846.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2) low-Tc VEVs (0, 0, 671.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2, −429.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5) (0, 0, 1827.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6, 275.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='9) 2nd: (112.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3, 0, 2088.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1, −749.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3) 1st: (0, 0, 2087.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4, −808.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5) Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The PT properties for the last three BPs as tabulated in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' BP-VI: So far, for all the BPs we have obtained single-step FOPT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In contrast, BP-VI shows a two-step FOPT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The outputs are tabulated in Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In both steps, the high- temperature behaviour of the scalar potential closely follows the Type-IV pattern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' On the other hand, in the first step FOPT occurs along the NR direction only, while in the second step, we find FOPT in both the NR and HSM directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Note that, this BP shows a weaker FOPT and hence, is not suitable for the EWBG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Recall from section 3 that the new physics parameters, relevant for the study of PT in the current framework are {λN, AλN , vN} compared to the Z3 symmetric NMSSM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In the subsequent analysis, we like to inquire about the impact of these new parameters on the PT strength along different field directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Also, note that a FOPT apparently favours a lighter RH-sneutrino-like state below 125 GeV as we observe from the BP-based study of PT and their outcomes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This characteristic is likely to be further confirmed while we vary the new parameters and obtain the sensitivity of PT strength on these parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' First, in Figure 3 we show the impact of vN (left) and λN (right) on the PT strength vc Tc .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In each of the sub-figures, we have fixed the other relevant parameters as in BP-I of Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We find the PT strength decreases with the rise of both vN and λN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We repeat the analysis for the same BP as shown in the top panel of Figure 4 considering nucleation temperature calculation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In particular, we estimate the PT strength in the SU(2)L field – 24 – 150 200 250 300 350 400 vN (GeV) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='9 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5 vc/Tc 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='14 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='16 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='18 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='22 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='24 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='26 λN 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='9 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3 vc/Tc Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' These plots show the dependence of PT strength on vN (left) and λN (right) in the Tc calculation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Parameters Y i N, vi and AN have no significant effect in PT dynamics and thus, we keep their values ∼ O(10−7), ∼ O(10−4 GeV), ∼ O(1 TeV), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Other relevant parameters are fixed as in BP-I of Table 1, except vN and λN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' directions, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', ∆φSU(2)/Tn as function of vN and λN and notice similar trends as in Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Now a smaller λN or vN implies lighter sneutrino following the CP-even mass matrices mentioned in Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Hence, Figures 3 and 4 further reinforce the fact that a comparatively lighter RH-snuetrino is indeed preferred to trigger a possible FOPT along the SU(2)L doublet field directions in the present framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Now the remaining new parameter AλN is expected to show a minor impact on the ∆φSU(2)/Tn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This is because it is not directly connected to the relevant terms at the tree level in the Lagrangian involving the SU(2) doublet Higgs fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Indeed, in our analysis, we have found that the ∆φSU(2)/Tn remains more or less unaltered upon varying AλN as shown in the bottom panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Next, we like to examine the impact of the new physics parameters as earlier specified on the PT strength along SU(2)L-singlet field direction ∆φS/Tn while the other parameters are set according to BP-III of Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In top panel of Figure 5 we depict the variation of ∆φS/Tn as function of vN (left) and λN (right).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We observe that the quantity ∆φS/Tn increases upon lowering λN when vN is fixed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In the other case when we fix λN and vary vN, the ∆φS/Tn gets enhanced for a smaller vN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Once again, these observations further strengthen our earlier finding that a lighter RH-sneutrino below 125 GeV is favoured for the occurrence of an SFOPT in the SU(2)L-singlet, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', HS direction as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' On the other hand, we also notice that the ∆φS/Tn increases with the rise of AλN as shown in the bottom panel of Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Note that AλN is appearing as the coefficient of the cubic interaction S � N � N (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Hence a larger AλN is expected to increase the barrier height which results in a stronger ∆φS/Tn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Previously, we have found that BP-IV provides us with a SOFPT along the NR field direction ∆φ � N/Tn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We would like to utilize this particular BP to enquire about the de- pendence of new parameters on ∆φ � N/Tn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In top left of Figure 6, we show the dependence of ∆φ � N/Tn on vN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We find that for vN ≲ 500 GeV, the ∆φ � N/Tn remains more or less – 25 – 320 340 360 380 400 vN (GeV) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5 ∆φSU(2)/Tn 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='14 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='16 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='18 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='22 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='24 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='26 λN 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6 ∆φSU(2)/Tn −1400 −1200 −1000 −800 −600 −400 −200 AλN 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='08 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='09 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='11 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='12 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='13 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='14 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='16 ∆φSU(2)/Tn Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' These plots show the dependence of PT strength ∆φSU(2)/Tn on vN (top left), λN (top right) and AλN (bottom) along the SU(2)L field direction, in the Tn calculation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Here, orders of parameters Y i N, vi and AN are chosen as in Figure 3 and the other relevant parameters are fixed as in BP-I of Table 1, except vN, λN and AλN .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' constant, however, decreases while we increase vN further.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Additionally, from top right of Figure 6 the ∆φ � N/Tn gets reduced as well upon increasing λN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The reason for this is twofold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' As we mentioned earlier, a smaller λN leads to lighter RH-sneutrino states below 125 GeV which in turn enhances the ∆φ � N/Tn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Moreover, a smaller λN also assists in increasing the barrier height and hence results in enhanced ∆φ � N/Tn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In bottom panel of Figure 6, we have shown the ∆φ � N/Tn strength gets enhanced upon increasing AλN .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This is once again caused by the enhanced barrier height for a larger AλN similar to the earlier case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' After examining the individual dependence of new parameters on PT strength, we now give a random scan on new physics parameters highlighting the region allowed by the experimental constraints and favouring an SFOPT along SU(2)L field directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We vary (λN, vN) and fix the other relevant parameters in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3) following BP-I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' However, orders of parameters Y i N, vi and AN are chosen as ∼ O(10−7), ∼ O(10−4 GeV), ∼ O(1 – 26 – 150 200 250 300 350 400 vN (GeV) 2 3 4 5 6 ∆φS/Tn 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='14 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='16 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='18 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='22 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='24 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='26 λN 1 2 3 4 5 ∆φS/Tn −800 −700 −600 −500 −400 −300 −200 AλN 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='9 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4 ∆φS/Tn Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' These plots show the dependence of PT strength ∆φS/Tn on vN (top left), λN (top right) and AλN (bottom) along the SU(2)L-singlet field direction, in the Tn calculation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Here, orders of parameters Y i N, vi and AN are chosen as in Figure 3 and the other relevant parameters are fixed as in BP-III of Table 1, except vN, λN and AλN .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' TeV), respectively, as they hardly affect the PT dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We have randomly generated pairs of (λN, vN) and pass through all the experimental bounds mentioned in subsection 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We first sort out the points that pass all the experimental constraints as shown in green colour in Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Next, we apply the condition of SFOPT along the SU(2)L field direction and pin down the points that favour SFOPT only and SFOPT with possible EWBG having minimal wash-out effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We have marked them in Figure 7 by coloured ‘▲’ and ‘■’, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' These points depict the variation of ∆φSU(2)/Tn in the vN - λN plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Next in Figure 8, we made a scenario similar to that of Figure 7, however, in the HS field direction in the context of BP-IV, as shown in Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Here, points which undergo SFOPT are marked by ‘⋆’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We also compute the ∆φS/Tn strength and find that the ∆φS/Tn strength is maximum when both λN and vN are small, which is in agreement with our earlier observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' – 27 – 400 500 600 700 800 900 1000 vN (GeV) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 ∆φ� N/Tn 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='30 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='35 λN 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 ∆φ� N/Tn −1000 −800 −600 −400 −200 AλN 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8 ∆φ� N/Tn Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' These plots show the dependence of PT strength ∆φ � N/Tn on vN (top left), on λN (top right) and on AλN (bottom) along the NR direction, in the Tn calculation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Here, orders of parameters Y i N, vi and AN are chosen as in Figure 3 and the other relevant parameters are fixed as in BP-IV of Table 1, except vN, λN and AλN .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Finally, in Figure 9 we perform an analogous exercise to show the variation of ∆φ � N/Tn in the vN - λN plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In this case, we have utilized the BP-IV of Table 3 once again to fix the other relevant parameters, except vN and λN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The green-coloured points are allowed by the various experimental constraints as stated in subsection 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We mark the points that favour SFOPT in the NR direction by coloured ‘⋆’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Once again, we find that the ∆φ � N/Tn is maximum for simultaneous lower values of vN and λN, consistent with our earlier findings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3 GW spectrum from SFOPT in the NMSSM + one RHN model A cosmological FOPT can produce GWs in the early Universe that contains information about the strength of different model parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In the preceding section, we have dis- cussed different PT characteristics in the proposed framework and computed the relevant quantities that determine the strength of a PT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In the current section, we will be talking – 28 – 220 240 260 280 300 320 340 vN (GeV) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='135 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='140 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='145 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='150 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='155 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='160 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='165 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='170 λN tan β = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='90, λ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='416, κ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='022, µ = 224.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='56 GeV, Aλ = 775.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='48 GeV, Aκ = −62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='75 GeV, AλN = −349.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='68 GeV Allowed by experimental bounds SFOPT and no EWBG SFOPT and possible EWBG 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='50 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='75 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='00 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='25 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='50 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='75 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='00 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='25 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='50 ∆φSU(2)/Tn Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This figure shows variations of ∆φSU(2)/Tn in the vN - λN plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The green-coloured points pass all the experimental constraints as discussed in subsection 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The points favoured for SFOPT along the SU(2)L field direction without and with EWBG are marked by coloured ‘▲’ and ‘■’ symbols, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Orders of parameters Y i N, vi and AN are chosen as in Figure 3 and the other relevant parameters are fixed as in BP-I of Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' about the production of GW and its detection prospects within our model setup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' As we have mentioned earlier, a FOPT is characterized by critical temperature Tc, and nucleation temperature Tn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The critical temperature indicates the moment when the location of the global minimum changes from one vacuum phase to another.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' However, the critical temperature analysis does not assure that the associated PT is indeed taking place.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' On the other hand, FOPT proceeds via bubble nucleation, and hence calculation of nucleation temperature is very crucial in order to obtain the phenomenological parameters that are important from the standpoint of estimating GW spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' When the nucleation happens, at a temperature below Tc, the probability of tunnelling Γ(T) from the false vacuum to the true one is given by [213], Γ(T) ≈ T 4 � SE 2πT �3/2 e− SE T , (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='7) where SE is the bounce action corresponding to the critical bubble and can be written as [212], SE = � ∞ 0 4πr2dr � VT (φ, T) + 1 2 �dφ(r) dr �2� , (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8) with r being the radial coordinate and φ corresponding to the scalar dynamical fields present in a model framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The scalar field solution φ can be derived by solving the – 29 – 340 360 380 400 420 440 460 vN 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='12 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='13 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='14 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='16 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='17 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='18 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='19 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='20 λN tan β = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='77, λ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='384, κ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='012, µ = 203.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='12 GeV, Aλ = 1184.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='87 GeV, Aκ = −107.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='08 GeV, AλN = −363.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='16 GeV Allowed by experimental bounds SFOPT along HS direction 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 ∆φS/Tn Figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This figure shows variations of ∆φS/Tn in the vN - λN plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The green-coloured points pass all the experimental constraints as discussed in subsection 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The points favoured for SFOPT along the HS field direction are marked by coloured ‘⋆’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Orders of parameters Y i N, vi and AN are chosen as in Figure 3 and the other relevant parameters are fixed following BP-IV of Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' classical field equation [212, 214, 215] d2φ dr2 + 2 r dφ dr = dVT (φ, T) dr , (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='9) and subsequently applying proper boundary conditions: dφ dr = 0 when r → 0 and φ(r) → φfalse when r → ∞, where φfalse represents the four-dimensional field values at the false vacua.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We reiterate here that in order to solve the differential equation and the bounce action numerically, we have implemented our model in the cosmoTransitions [211] pack- age.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The essential parameters that are required for the estimation of GW spectra from FOPT are relative change in energy density during the PT (α), and the inverse of the duration of the PT (β).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Both the parameters, α, and β, are defined at the nucleation temperature Tn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The first parameter, α, is computed from [216], α = ∆ρ ρrad , (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='10) where ∆ρ is the released latent heat and it is expressed as [217], ∆ρ = � VT (φ0, T) − T dVT (φ0, T) dT � T=Tn − � VT (φn, T) − T dVT (φn, T) dT � T=Tn , (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='11) – 30 – 340 360 380 400 420 440 460 vN (GeV) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='12 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='13 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='14 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='16 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='17 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='18 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='19 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='20 λN tan β = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='77, λ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='384, κ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='012, µ = 203.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='12 GeV, Aλ = 1184.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='87 GeV, Aκ = −107.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='08 GeV, AλN = −363.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='16 GeV Allowed by experimental bounds SFOPT along � N direction 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8 ∆φ� N/Tn Figure 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This figure shows variations of ∆φ � N/Tn in the vN - λN plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The green-coloured points pass all the experimental constraints as discussed in subsection 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The points favoured for SFOPT along the NR field direction are marked by coloured ‘⋆’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Orders of parameters Y i N, vi and AN are chosen as in Figure 3 and the other relevant parameters are fixed following BP-IV of Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' with φ0 and φn represent, in our case, the four-dimensional field values at the false and true vacua, respectively, and VT (φ, T) is the finite-temperature effective potential as mentioned in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='20).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We should note here that the quantity ∆ρ measures the strength of a PT, the larger value of the same corresponds to a stronger FOPT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='10), ρrad corresponds to the radiation energy in the plasma and it is expressed as, ρrad = π2g∗ 30 T 4 n, with g∗ being a temperature-dependent quantity that counts the total number of relativistic energy degrees of freedom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The parameter β is defined as [218], β H∗ = T d dT �SE T � ����� T=T∗ ≡ T d dT �SE T � ����� T=Tn , (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='12) where H∗ is the expansion rate of the Universe during the PT and T∗ stands for the PT temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We have considered T∗ ≃ Tn in the present work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We have tabulated the obtained values of α and β in Table 4 for different BPs shown in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' As stated earlier, the quantity α is proportional to the energy released during the PT and hence a larger PT strength should lead to a larger α value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In fact, this is exactly the case where we find the largest α for the BP-III (see Table 4) having ∆φS/Tn = 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='61 (see Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=') We obtain the lowest α for the first-step PT of BP-VI since the corresponding ∆φ � N/Tn is weakest among all as can be seen from Tables 2 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' – 31 – BPs α β/H∗ BP-I 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0456 37535.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 BP-II 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0121 143931.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 BP-III 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0870 11729.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8 BP-IV 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0101 7596.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 BP-V 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0027 4611.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3 BP-VI-I 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0002 516911.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 BP-VI-II 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0017 63837.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8 Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Estimates of the parameters α and β as defined in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='10) and Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='12), respectively for the six BPs listed in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Note that the BP-VI-I shows two-step PT patterns and we have made the estimates of α and β in both steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' There are mainly three different processes that trigger the emission of GWs in a FOPT: (i) bubble wall collisions, (ii) sound waves, and (iii) magneto-hydrodynamic (MHD) tur- bulence in the plasma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Therefore, the total energy spectrum of the emitted GW can approximately be given as a sum of these three contributions [155, 219], ΩGWh2 ≈ Ωcolh2 + Ωswh2 + Ωturh2, respectively, (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='13) where, h = H0/(100 km · sec−1 · Mpc−1) [220] with H0 corresponding to Hubble’s constant at the present epoch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The contribution to the total GW energy density from the bubble wall collision can be computed using the envelope approximation and it can be estimated as a function of frequency “f” as [221], Ωcolh2 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='67 × 10−5 � β H∗ �−2 � κcα 1 + α �2 �100 g∗ �1/3 � 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='11v3 w 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='42 + v2w � 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8 (f/fcol)2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8 1 + 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8 (f/fcol)3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8 , (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='14) where vw is the bubble wall velocity and κc is the efficiency factor of bubble collision, given as, κc = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='715α + 4 27 � 3α 2 1 + 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='715α .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='15) The red-shifted peak frequency fcol [221] is expressed as (with the approximation T∗ ≈ Tn), fcol = 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5 × 10−6 �f∗ β � � β H∗ � � Tn 100 GeV � � g∗ 100 �1/6 Hz, (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='16) where the fitting function, f∗/β, at the time of the PT is given by, f∗ β = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='62 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8 − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1vw + v2w .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='17) In order to obtain a GW spectrum with higher strength, it is generally assumed that the expanding bubbles attain a relativistic terminal velocity in the plasma and we consider – 32 – vw ≃ 1 in our calculations 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' However, there is a note of caution that runway bubble walls are generally undesirable in view of the successful yield of a sizeable amount of EWBG 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The contribution to the total GW density from sound waves can be parameterized as [230–233], Ωswh2 = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='65×10−6 Υ(τsw) � β H∗ �−1 vw � κswα 1 + α �2 � g∗ 100 �1/3 � f fsw �3 � 7 4 + 3 (f/fsw)2 �7/2 , (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='18) where κsw is the efficiency factor for the sound wave contribution representing the fraction of the energy (latent heat) that gets converted into the bulk motion of the plasma and subsequently emits gravitational waves as given by (in the limit vw → 1) κsw ≃ � α 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='73 + 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='083√α + α � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='19) The quantity fsw corresponds to the present peak frequency for the sound wave contribution to the total GW energy density, expressed as fsw = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='9 × 10−5 � 1 vw � � β H∗ � � Tn 100 GeV � � g∗ 100 �1/6 Hz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='20) The parameter Υ(τsw) appears due to the finite lifetime of the sound waves which suppresses their contributions to the GW energy density as written as Υ(τsw) = 1 − 1 √1 + 2τswH∗ , (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='21) with τsw being the lifetime of the sound waves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The onset of the turbulence takes place at this timescale and disrupts the sound wave source.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Following Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [232], we write τsw ≈ R∗/U f, where R∗ = (8π)1/3 vw/β and U f = � 3κswα/4 are the mean bubble separation and the root-mean-squared fluid velocity which can be obtained from a hydrodynamic analysis, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' At the time of PT, the plasma is fully ionized and due to the resulting MHD turbulence, it leads to another source of GWs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The MHD turbulence contribution to the total GW energy density is modelled as [235] Ωturh2 = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='35 × 10−4 � β H∗ �−1 vw �κturα 1 + α �3/2 �100 g∗ �1/3 � � (f/ftur)3 [1 + (f/ftur)]11/3 � 1 + 8πf h∗ � � � , (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='22) 14A precise determination of bubble wall velocity is non-trivial [222–226] and out of scope of the present analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Instead, we consider here vw as an input parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 15Recently, an improved analysis on bubble wall dynamics has reported that EWBG may be possible even for supersonic vw [227–229] which is in contrast with our traditional notion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' – 33 – U-DECIGO U-DECIGO-corr DECIGO-corr BP-I BP-II BP-III 10-7 10-5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='001 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='100 10 10-28 10-23 10-18 10-13 10-8 Figure 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Prediction of GW energy density as a function of the frequency for the first three BPs as shown in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We have also highlighted the regions that indicate the proposed sensitivities of the GW experiments namely U-DECIGO and U-DECIGO corr [81, 82].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The sensitivity curves for DECIGO and U-DECIGO with correlation analyses are taken from Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [234].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' where h∗ = 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5 × � Tn 100 GeV � � g∗ 100 �1/6 Hz, the inverse Hubble time during GW production, red-shifted to today.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The peak frequency ftur is given by, ftur = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='7 × 10−5 1 vw � β H∗ � � Tn 100 GeV � � g∗ 100 �1/6 Hz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='23) We set κtur = ϵκsw where ϵ stands for the fraction of the bulk motion which is turbulent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Simulations suggest κtur = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1κsw which we have considered in our numerical calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' U-DECIGO U-DECIGO-corr DECIGO-corr BP-IV BP-V BP-VI-I BP-VI-II 10-7 10-5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='001 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='100 10 10-28 10-23 10-18 10-13 10-8 Figure 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Prediction of GW energy density as a function of the frequency for the last three BPs from Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We have also highlighted the regions that indicate the proposed sensitivities of the GW experiments namely DECIGO-corr, U-DECIGO and U-DECIGO corr [81, 82].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' With these details, in Figure 10 we present the estimates of GW energy density spec- trum as a function of frequency for the first three BPs as shown in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The predictions – 34 – of ΩGWh2 for the last three BPs of Table 1 are shown in Figure 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We notice from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='14), Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='18) and Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='22), that each individual contribution to the total GW energy density, ΩGWh2 (as defined in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='13)) is an increasing function of α 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This feature in turn makes ΩGWh2 rise as well for a relatively larger α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In contrast, a larger β H∗ reduces the amount of ΩGWh2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Earlier, in Table 4, we observed that BP-III yields the largest value of α among the six BPs of Table 1 with relatively smaller β H∗ ratio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Consequently, we find the corresponding peak amplitude of ΩGWh2 to be ∼ O(10−17) for BP-III, which turns out to be the largest as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This feature is depicted in Figure 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The lowest peak am- plitude of ΩGWh2 that we obtain is for the first-step PT of BP-VI which is ∼ O(10−25) as shown in Figure 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The massive suppression to ΩGWh2 for BP-VI-I is caused by the simultaneous presence of a large β H∗ value together with a small α value as shown in Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The second-step PT of BP-VI produces a peak having amplitude ∼ O(10−22) which is relatively less suppressed due to a smaller value of β H∗ compared to BP-VI-I as shown in Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In view of such estimates, the proposed future GW interferometers namely U-DECIGO and U-DECIGO correlation have the required sensitivities to probe all the BPs, except BP-VI-I, considered in our analysis including BP-I which is preferred in order to address EWBG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We also find it pertinent to mention that the peak frequency of each contribution to GW energy density is linearly proportional to the ratio β H∗ as evident from Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='16), (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='20) and (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='23).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' It is numerically found that the frequency fmax where ΩGWh2 (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='13)) attains maximum, also emerges to be an increasing function of β H∗ ratio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' As already noted in Table 4, that BP-VI-I produces the largest β H∗ ratio among all the BPs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This makes the peak frequency fmax of the corresponding GW spectrum for BP-VI-I the largest among all BPs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5 −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5 log10α 2 3 4 5 6 7 log10(β/H∗) SFOPT and possible EWBG SFOPT and no EWBG 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5 ∆φSU(2)/Tn −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5 −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5 log10α 2 3 4 5 6 7 log10(β/H∗) SFOPT and possible EWBG SFOPT and no EWBG 20 40 60 80 100 120 140 160 Tn Figure 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Values of α and β H∗ as a function of ∆φSU(2)/Tn (right) and nucleation temperature Tn (left) for the points in Figure 7 that satisfy the criteria of SFOPT with possible EWBG (depicted by coloured ‘■’) and SFOPT without EWBG (depicted by coloured ‘▲’).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 16For α ≫ 1, Ωcolh2, Ωswh2 and Ωturh2 are expected to turn insensitive to the change of α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' – 35 – Earlier in Figure 7 we have identified points in the vN − λN plane that exhibits strong PT along the SU(2)L doublet direction, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', ∆φSU(2)/Tn > 1, with and without favouring EWBG as highlighted by coloured ‘■’ and ‘▲’ symbols, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Recollect that, in order to prepare Figure 7, we have utilised the fixed values of the other relevant independent parameters as in BP-I, except vN and λN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In Figure 12, we show the estimates of α and β/H∗, corresponding to the same parameter corner, that is relevant to estimate ΩGWh2 as a function of ∆φSU(2)/Tn (left) and the nucleation temperature Tn (right), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Note that we are giving particular emphasis on analysing Figure 7 further to compute the GW energy density since it offers the scope of realising EWBG while exhibiting ∆φSU(2)/Tn > 1 (traceable at GW interferometers) at the same time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The Figure 12 illustrates the fact that the points, favoured for EWBG require relatively higher β/H∗ and lower α values compared to the points that do not favour EWBG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' This essentially suppresses the peak amplitude of ΩGWh2 for the points favouring EWBG and simultaneously increase the peak frequency fmax.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The right panel of Figure 12 indicates that a lower Tn tends to increase α which in turn enhance the ∆φSU(2)/Tn leading to larger Ωpeak GW h2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Such features are imprinted in Figure 13 where we have shown the estimates of ΩGWh2 as a function of f for both the coloured ‘■’ and ‘▲’ shaped points, present in Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We clearly observe that the points which are not favoured for possible EWBG, produce a larger amount of ΩGWh2 at a particular f and may even fall within the sensitivity curves of LISA [236] and BBO [156].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' However, the discovery scopes of those points purely depend on the signal-to-noise ratio of the corresponding experiments [237].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 10−5 10−4 10−3 10−2 10−1 100 101 102 103 f [Hz] 10−28 10−25 10−22 10−19 10−16 10−13 10−10 10−7 ΩGWh2(f) LISA BBO DECIGO-corr U-DECIGO U-DECIGO-corr BP-I SFOPT and EWBG 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='020 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='025 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='030 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='035 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='040 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='045 α 10−5 10−4 10−3 10−2 10−1 100 101 102 103 f [Hz] 10−28 10−25 10−22 10−19 10−16 10−13 10−10 10−7 ΩGWh2(f) LISA BBO DECIGO-corr U-DECIGO U-DECIGO-corr SFOPT and no EWBG 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6 α Figure 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' GW spectra for the points that show SFOPT in the SU(2)L doublet field directions with (left) and without (right) possible EWBG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Note that these points are marked by ‘ ■’ and ‘ ▲’ in Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' For both figures, we keep α as a variable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 5 Summary and Conclusion In the present work, we have addressed the properties of EWPT in the RHN superfield extended setup of Z3 invariant NMSSM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The RHN extended Z3 invariant NMSSM is cap- tivating due to its ability to provide solutions to the µ−problem of the MSSM and non- – 36 – vanishing neutrino masses and mixing simultaneously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In particular, we consider the case where both the LH- and RH-sneutrino receive non-zero VEVs, leading to a spontaneous R- parity-violating scenario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We have worked in an effective field theory set-up by integrating out the heavier squarks, gluinos, as well as sleptons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Additionally, a simple parametriza- tion of the TeV scale seesaw dictates the LH-sneutrino fields to weakly couple to the other relevant fields and thus, is expected to contribute negligibly to the PT dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' These facts effectively lead to a four-dimensional field space spanned by the four CP-even Higgses which is of interest in order to explore the PT characteristics in the present framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Without going into the numerical details, one can naively anticipate that in the current setup having a four-dimensional field space, the PT dynamics is likely to be more involved than in the NMSSM where the relevant field space is three-dimensional.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The EWPT properties and estimate of GW spectrum in the NMSSM have been extensively studied in literature where the roles of NMSSM parameters on the PT strength are also detailed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In this work, we scrutinize the role served by the new parameters that appear in theory due to the presence of the RHN superfield on the PT dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In particular, we find that three new parameters λN, AλN and vN leave a non-trivial impact on determining the PT strength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In the beginning, we describe the model details and successively develop the tools re- quired to study the behaviour of the scalar potential as a function of temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We then demonstrate the possible experimental constraints that are of utmost importance to obtain a viable parameter space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Specifically, we undertake constraints arising from the validation of SM Higgs boson properties, BSM Higgs and SUSY searches at colliders, var- ious flavour-violating processes, neutrino experiments and the muon anomalous magnetic moment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Since extensive scanning of full parameter space considering a four-dimensional field space, relevant for PT is numerically challenging, we first adopt a benchmark-based analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We provide six BPs that pass through all the experimental constraints and exhibit distinct kinds of FOPT patterns along the different field directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We have discussed the PT dynamics corresponding to each BP in detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' An SFOPT is a prerequisite for EWBG with distinct high-temperature behaviour of the total scalar potential along the SU(2)L field directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We have shown that BP-I is the preferred BP that exhibits the essential features required for a possible EWBG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' On the other hand, BP-II - BP-V showing SFOPT along the different SU(2)L doublet and singlet field directions in single-step, however, are not suitable for successful EWBG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We find multi-step FOPT for BP-VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' All the BPs listed have one particular feature in common which is the preference for a lighter RH-sneutrino-dominated state below 125 GeV for the occurrence of a FOPT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Next, we utilize a few of the BPs to inquire about the role of new parameters on PT strength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Two of the new parameters vN and λN show similar impacts on the PT strength along either of the SU(2)L doublet or singlet field directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' It turns out that the PT strength increases with the decrease of either vN or λN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The remaining parameter AλN has a minor role in the PT along SU(2)L doublet field directions whereas the PT strengths in the SU(2)L singlet field directions get enhanced with the increase of |AλN |.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The possible reasons for such unique properties are associated with the impact of the new parameters on the barrier height in the constituent field directions and also the – 37 – lightness of the RH-sneutrino state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Finally, we examine the testability of the BPs by computing the GW energy density corresponding to each BP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We have considered all possible sources that trigger GW emis- sion in a FOPT namely, bubble wall collisions, sound waves and magneto-hydrodynamic turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The highest peak amplitude of the GW energy density that we obtain is for BP-III which lies within the proposed sensitivity of DECIGO correlation data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The peak amplitude of ΩGWh2 for other BPs is relatively weaker, however, within the reach of U- DECIGO and U-DECIGO-corr sensitivities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' It is to be noted that a TeV scale canonical seesaw model with RHN weakly coupled to SM particles is extremely difficult to probe at collider experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Our analysis infers an alternative albeit promising pathway to validate a TeV scale seesaw model at future GW interferometers beyond colliders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In the present work, we have not performed an exact prediction of the baryon asym- metry of the Universe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Instead, we find the corner of the parameter space that shows SFOPT along the SU(2)L doublet field directions and facilitates EWBG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Improvement of our analysis is possible by precise computation of bubble wall profile, bubble wall velocity, and CP-violation that decide the final amount of baryon asymmetry of the Universe, which is also correlated with NMSSM + RHN model parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In an R-parity violating theory like the present one, gravitino can be a potential decaying dark matter candidate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Future works may also include investigating the correspondence between gravitino dark matter phenomenology and NMSSM + RHN parameter space, favouring an SFOPT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Acknowledgements P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' acknowledges the financial support received from the Indian Institute of Technology, Delhi (IITD) as a Senior Research Fellow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' acknowledges the IITD SEED grant sup- port IITD/Plg/budget/2018-2019/21924, continued as IITD/Plg/budget/2019- 2020/173965, IITD Equipment Matching Grant IITD/IRD/MI02120/208794, and Start-up Research Grant (SRG) support SRG/2019/000064 from the Science and Engi- neering Research Board (SERB), Department of Science and Technology, Government of India.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' is supported by NPDF grant PDF/2020/000797 from the SERB, Govern- ment of India.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' also acknowledge Mikael Chala, Bo-Qiang Lu, Jiang Zhu and Kaius Loos for useful communications regarding cosmoTransitions code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' A Field dependent mass matrices Our numerical studies are based on the field-dependent masses (see subsection 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The corresponding scalar squared mass terms are evaluated at T = 0 using the tree-level un- coloured scalar potential Vscalar (see below), including only the dominant higher-order con- tributions ∆V (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='12)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Mathematically, for the uncoloured scalar squared mass matrices M2 X,ij = M2 φαφβ(HSM, HNSM, HS, NR) ≡ ∂2Vscalar ∂φα∂φβ ���� φα̸=0 , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1) where X = S (for the CP-even neutral scalar) or A (for the CP-odd neutral scalar) and i, j = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Further, φα(β) = HSM, HNSM, HS, NR, ℜ(�ν1,2,3) for the CP-even neutral – 38 – scalar and φα(β) = ANSM, AS, G0, NI, ℑ(�ν1,2,3) for the CP-even neutral scalar, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' For the uncoloured electrically charged scalar, X = C with i, j = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', 8 and φα(β) ≡ C+ = H+, G+, �e+ L, �µ+ L, �τ + L , �e+ R, �µ+ R, �τ + R .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Here, we have used �νi = ℜ�νi + iℑ�νi √ 2 ≡ νRi + i�νIi √ 2 with i = 1, 2, 3 ≡ e, µ, τ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2) The full uncoloured scalar potential is given by Vscalar = ����� 3 � i=1 Y i N �νi � N − λSH0 d ����� 2 + ������ 3 � i,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='j=1 Y ij e �li�ec j − λSH0 u ������ 2 + ������ Y i NH0 u � N − 3 � j=1 Y ij e H− d �ec j ������ 2 + ����λHu · Hd + κS2 + λN 2 � N 2 ���� 2 + ����� 3 � i=1 Y i N �Li · Hu + λNS � N ����� 2 + ����� 3 � i=1 Y ij e Hd · �Li ����� 2 + ������ λSH+ u − 3 � i,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='j=1 Y ij e �νi�ec j ������ 2 + �����λSH− d − 3 � i=1 Y i N�li � N ����� 2 + ������ 3 � j=1 Y ij e H0 d�ec j − Y i NH+ u � N ������ 2 + g2 1 8 (|Hd|2 − |Hu|2 + |�Li|2 − 2|�ec i|2)2 + g2 2 2 3 � a=1 � H† d τ a 2 Hd + H† u τ a 2 Hu + �L† i τ a 2 �Li �2 + m2 Hd|Hd|2 + m2 Hu|Hu|2 + m2 S|S|2 + M 2 N| � N|2 + 3 � i,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='j=1 m2 �Lij �Lm∗ i �Lm j + 3 � i,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='j=1 m2 �ec ij�ecm∗ i �ecm j + 3 � i=1 (AeYe)ijHd · �Li�ec j + λAλSHu · Hd + (ANYN)i�Li · Hu � N + κAκ 3 S3 + λNAλN 2 S � N 2 + h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3) Here Y ij e belongs to W ′ MSSM (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1)) and m2 Hd, m2 Hu, m2 �Lij, m2 �ec ij, (AeYe)ij are encapsulated within −L′ soft (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Further, i, j are generation indices, τ as are Pauli spin matrices and m = 1, 2, as per the standard notation (see Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [27, 83–85, 87, 88] for details).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In a similar way, one can derive field-dependent mass matrices for the uncoloured elec- trically neutral and electrically charged fermions, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', neutralinos and charginos, directly from the superpotential W (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Mathematically, the generic mass term for the neutralino sector and the chargino sector are given by − 1 2 � ψ0T i M0ijψ0 j + h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' � , −1 2(ψ+, ψ−)T Mχ±(ψ+, ψ−) + h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4) respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Here basis for the neutralino sector is given by ψ0T = { �B0, � W 0 3 , �H0 d, �H0 u, �S, N, ν1, ν2, ν3} involving neutral U(1)Y , SU(2)L gauginos ( �B0, � W 0 3 ), neutral higgsinos ( �H0 d, �H0 u), singlino (�S), RH-neutrino (N) and LH-neutrinos (ν1,2,3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' For charginos, including charged SU(2)L gauginos (� W ±), charged higgsinos ( �H+ u , �H− d ) and charged leptons (e± L, R, µ± L, R, τ ± L, R), one gets ψ+T = {� W +, �H+ u , e+ R, µ+ R, τ + R } and ψ−T = {� W −, �H− d , e− L, µ− L, τ − L }, respec- – 39 – tively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' We will start with the scalar mass squared matrices and will discuss the fermionic sector subsequently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='17 A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1 CP-even neutral scalars squared mass matrix In the basis HSM,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' HNSM,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' HS,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' NR,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' ℜ(�ν1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' non-zero entries of the symmetric M2 S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='ij are M2 S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='11 ≃ 1 16vuvd � 8λvSv2 (Aλ + κvS) + 2λ2vuvd � −4 � v2 + 2v2 S � + H2 NSM + 4H2 S + 3H2 SM � +vuvd � 3∆λ2 + G2� � H2 NSM + 3H2 SM � −4 cos 2β � v2 cos 2β � 2λvS (Aλ + κvS) + vuvd � G − 2λ2� vu � + 3∆λ2vuvdH2 SM � +vuvd � (4 sin 2β � 3∆λ2HNSMHSM − 2λHS �√ 2Aλ + κHS �� −3 � ∆λ2 + G − 2λ2� � 2 sin 4β HNSMHSM + cos 4β � H2 NSM − H2 SM �� �� − 1 2v �λNv 2 sin 2β � N2 R − 2v2 N �� ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5) M2 S,12 ≃ 1 16vuvd �2v2 sin 4β � 2λvS (Aλ + κvS) + vuvd � G − 2λ2�� vuvd −8λ cos 2β HS �√ 2Aλ + κHS � + 3 sin 4β � ∆λ2 + G − 2λ2� � H2 NSM − H2 SM � −6 cos 4β HNSMHSM � ∆λ2 + G − 2λ2� + 2HNSMHSM � 3∆λ2 + G + 2λ2� +6∆λ2 sin 2β � H2 NSM + H2 SM � � − 1 4 � λ cos 2β λN � N2 R − 2v2 N � � , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6) M2 S,13 ≃ λ2HSHSM − 1 2λ �√ 2Aλ + 2κHS � (cos 2β HNSM + sin 2β HSM) , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='7) M2 S,14 ≃ −1 2λλNNR (cos 2β HNSM + sin 2β HSM), (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8) M2 S,1 (4+i) ≃ 1 2NRY i N �√ 2AN sin β + HS (λ cos β + λN sin β) � , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='9) M2 S,22 ≃ 1 16vuvd � 8λvSv2 (Aλ + κvS) + vuvd (3∆λ2 + G) � 3H2 NSM + H2 SM � +2λ2vuvd � −4 � v2 + 2v2 S � + 3H2 NSM + 4H2 S + H2 SM � +4 cos 2β � v2 cos 2β � 2λvS (Aλ + κvS) + vdvu � G − 2λ2�� + 3∆λ2vdH2 NSMvu � +vdvu � 4 sin 2β � 2λHS �√ 2Aλ + κHS � + 3∆λ2HNSMHSM � +3 � ∆λ2 + G − 2λ2� � 2 sin 4β HNSMHSM + cos 4β � H2 NSM − H2 SM �� �� + 1 8v � cos β cot βλN � λv(cos 4β + 3) sec3 βv2 N + 4λv sin β tan β N2 R �� , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='10) 17While writing field-dependent masses, we ignore terms that are quadratic in vi, Y i N and terms like 3� i=1 viY i N, keeping in mind their smallness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Besides, as already stated, these terms do not play any crucial role in the EWPT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Nevertheless, we have kept all these terms in our numerical analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' – 40 – M2 S,23 ≃ 1 2λ �√ 2Aλ + 2κHS � (sin 2β HNSM − cos 2β HSM) + λ2HNSMHS,(A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='11) M2 S,24 ≃ 1 2λλNNR (sin 2β HNSM − cos 2β HSM), (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='12) M2 S,2 (4+i) ≃ 1 2NRY i N �√ 2AN cos β + HS (cos β λN − λ sin β ) � , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='13) M2 S,33 ≃ λvuvd (Aλ + 2κvS) vS + κ � Aκ �√ 2HS − vS � + κ � 3H2 S − 2v2 S �� − λ2v2 +λ2 2 � H2 NSM + H2 SM � − λκ cos 2β HNSMHSM + λκ 2 sin 2β � H2 NSM − H2 SM � + 1 2vS � λN � (κ + λN) vS � N2 R − 2v2 N � − v2 NAλN �� , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='14) M2 S,34 ≃ 1 2λNNR �√ 2AλN + 2 (κ + λN) HS � , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='15) M2 S,3 (4+i) ≃ 1 2Y i NNR (HNSM (λN cos βλ sin β ) + HSM (λ cos β + λN sin β )), (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='16) M2 S,44 ≃ 1 4vN � − 2λλN cos 2β HNSMHSMvN+λ sin 2β vNλN � H2 NSM − H2 SM + 2v2� +λNvN � 2AλN �√ 2HS − 2vS � + 2 (κ + λN) H2 S � +λNvN � λN � 3N2 R − 2v2 N � − 4 (κ + λN) v2 S � � , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='17) M2 S,4 (4+i) ≃ 1 2Y i N �√ 2AN (cos β HNSM + sin β HSM) + HS � HNSM (λN cos β − λ sin β) +HSM (λ cos β + λN sin β) �� , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='18) M2 S,(4+i) (4+j) ≃ δij 8 � − 2G sin 2β HNSMHSM − G cos 2β � H2 NSM − H2 SM � −8vNY i N (vu (AN + λNvS) + λvdvS) vi − 2Gv2 cos 2β � −1 4g2 2 (sin β HNSM − cos β HSM) 2, (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='19) where we have used G = g2 1 + g2 2, v2 u + v2 d = v2 and i = 1, 2, 3 are generational indices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 CP-odd neutral scalars squared mass matrix In the basis ANSM,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' AS,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' G0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' NI,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' ℑ(�ν1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' non-zero entries of the symmetric M2 A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='ij are M2 A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='11 ≃ 1 16vdvu � 8λvSv2 (Aλ + κvS) + Gvdvu � H2 NSM − H2 SM � +2λ2vdvu � −4 � v2 + 2v2 S � + H2 NSM + 4H2 S + 3H2 SM � + ∆λ2vdvu � 3H2 NSM + H2 SM � +4 cos 2β � v2 cos 2β � 2λvS (Aλ + κvS) + vuvd � G − 2λ2�� + ∆λ2vuvdH2 NSM � +vuvd � 4 sin 2β � 2λHS �√ 2Aλ + κHS � + ∆λ2HNSMHSM � + � ∆λ2 + G − 2λ2� � 2 sin 4β HNSMHSM + cos 4β � H2 NSM − H2 SM �� �� + 1 8v � cos β cot β λN � λv(cos 4β + 3) sec3 β v2 N + 4λv sin β tan β N2 R �� ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='20) – 41 – M2 A,12 ≃ 1 2λHSM �√ 2Aλ − 2κHS � , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='21) M2 A,13 ≃ 1 16 �2v2 sin 4β � 2λvS (Aλ + κvS) + � G − 2λ2� vuvd � vuvd −8λ cos 2β HS �√ 2Aλ + κHS � + 2∆λ2 sin 2β � H2 NSM + H2 SM � +2HNSMHSM � ∆λ2 + G − 2λ2� − 2 cos 4β HNSMHSM � ∆λ2 + G − 2λ2� + sin 4β � ∆λ2 + G − 2λ2� (HNSM − HSM) (HNSM + HSM) � − 1 4v � λλNv cos 2β � N2 R − 2v2 N � � , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='22) M2 A,14 ≃ −1 2λλNHSMNR, (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='23) M2 A,1 (4+i) ≃ −1 2Y i NNR �√ 2AN cos β + HS (cos β λN − λ sin β ) � , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='24) M2 A,22 ≃ λvuvd (Aλ + 2κvS) vS − κAκ �√ 2HS + vS � − 1 2λ2 � 2v2 + H2 NSM + H2 SM � +λκ cos 2β HNSMHSM + λκ sin β cos β � H2 SM − H2 NSM � + κ2 � H2 S − 2v2 S � − 1 2vS � λN � (v2 NAλN + vS � 2v2 N (κ + λN) + N2 R (κ − λN) � �� , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='25) M2 A,23 ≃ −1 2λHNSM �√ 2Aλ − 2κHS � , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='26) M2 A,24 = −1 2λNNR �√ 2AλN − 2κHS � , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='27) M2 A,2 (4+i) ≃ Y i N 2 NR (HNSM (λN cos β − λ sin β) + HSM (λ cos β + λN sin β)), (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='28) M2 A,33 ≃ 1 16vuvd � 8λvSv2 (Aλ + κvS) − Gvuvd � H2 NSM − H2 SM � +2λ2vuvd � −4 � v2 + 2v2 S � + 3H2 NSM + 4H2 S + H2 SM � + ∆λ2vuvd � H2 NSM + 3H2 SM � −4 cos 2β � v2 cos 2β � 2λvS (Aλ + κvS) + vuvd � G − 2λ2�� + ∆λ2vdH2 SMvu � +vuvd � 4 sin 2β � ∆λ2HNSMHSM − 2λHS �√ 2Aλ + κHS �� − � ∆λ2 + G − 2λ2� � 2 sin 4β HNSMHSM + cos 4β � H2 NSM − H2 SM �� �� − 1 2v � λλNv sin β cos β � N2 R − 2v2 N �� , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='29) M2 A,34 ≃ 1 2λλNHNSMNR, (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='30) M2 A,3 (4+i) ≃ −Y i N 2 NR �√ 2AN sin β + HS (λ cos β + sin β λN) � , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='31) – 42 – M2 A,44 ≃ 1 4vN � 2λλN cos 2βHNSMHSMvN +λλN sin 2βvN � −H2 NSM + H2 SM + 2v2� +λNvN � − 2AλN �√ 2HS + 2vS � + 2 (λN − κ) H2 S � +λNvN � λN � N2 R − 2v2 N � − 4v2 S (κ + λN) �� , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='32) M2 A,4 (4+i) ≃ Y i N 2 � HS � HNSM (λ sin β + λN cos β) + HSM (λN sin β − λ cos β) � − √ 2AN (cos βHNSM + sin β HSM) � , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='33) M2 A, (4+i)(4+j) ≃ − δij 8vj � G cos 2βvj � H2 NSM − H2 SM + 2v2� + 2Gvj sin 2β HNSMHSM +8v sin β vNY j N (AN + λNvS) + 8λv cos β vNY j NvS � −1 4g2 2 (sin β HNSM − cos β HSM)2, (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='34) M2 A, 56 ≃ Y 1 NY 2 N 2 (cos βHNSM + sin βHSM)2 , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='35) M2 A, 57 ≃ Y 1 NY 3 N 2 (cos βHNSM + sin βHSM)2 (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='36) M2 A,67 ≃ Y 2 NY 3 N 2 (cos β HNSM + sin β HSM)2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='37) where we have used G = g2 1+g2 2, v2 u+v2 d = v2 and i = 1, 2, 3 are generational indices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' At the physical vacuum, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', � ⟨HSM⟩, ⟨HNSM⟩, ⟨HS⟩, ⟨NR⟩ � = �√ 2v, 0, √ 2vS, √ 2vN � , neglecting terms like v2 i , Y i2 N , 3� i=1 viY i N, the Goldstone mode appears massless and decouples from the other CP-odd states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3 Uncoloured charged scalars squared mass matrix Non-zero entries for the uncoloured symmetric charged scalar mass squared matrix, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=',' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' C+MCC−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' in the basis C+ = H+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' G+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' �e+ L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' �µ+ L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' �τ + L ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' �e+ R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' �µ+ R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' �τ + R are M2 C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='11 ≃ 1 16 � 2 cos 2βg2 1 � 2 sin 2βHNSMHSM + cos 2β(2v2 + H2 NSM − H2 SM) � +g2 2 � (1 + cos 4β)H2 NSM + 2 sin 4βHNSMHSM − (−3 + cos 4β)H2 SM + 2v2(1 + cos 4β) +4 cos 2β � − 4v2λ2(3 + cos 4β) + 2λ2(4H2 S + (−1 + cos 4β)H2 SM) − 16λ2v2 s +2∆λ2 sin2 2βH2 SM +4(λ2 sin2 2β + ∆λ22 cos4 β)H2 SM + 4(λ2 sin 4β − 4∆λ2 cos3 β sin β)HNSMHSM +4λvSAλ(3 + cos 4β) csc β sec β + 4λ sin β � 2HS( √ 2Aλ + κHS + λNN2 R) � +4λ(3 + cos 4β) csc 2β(2κv2 S + v2 NλN) � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='38) – 43 – M2 C,12 ≃ 1 16 � � 2 cos 4β(2λ2 − G − ∆λ2) + 2(2λ2 + g2 1 − g2 2 + ∆λ2) � HNSMHSM +2 sin 2β∆λ2(H2 NSM + (1 + 2 sin2 β)H2 SM) + sin 4β � (G − 2λ2)(2v2 + H2 NSM − H2 SM) + (H2 NSM − H2 SM)∆λ2 � +8λ cos 2β � κH2 S + Aλ( √ 2HS − 2vS) − 2κv2 S + λN 2 (N2 R − 2v2 N) � � ,(A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='39) M2 C1, (2+i) ≃ δij 4 � vj � � g2 2 cos 2β + 2(Y ij e )2 sin2 β � HNSM + sin 2β � g2 2 − (Y ij e )2� HSM � −2Y j NNR �√ 2AN cos β + cos β � λNHS − Y ij e (sin βHNSM − cos βHSM) � + λ sin βHS �� , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='40) M2 C,1 (5+i) ≃ − 1 √ 2AeY ij e vj sin β − 1 2Y ij e Y j N sin β(NR) (cos βHNSM + sin βHSM) , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='41) M2 C,22 ≃ 1 16 � 2G cos2 β(H2 SM − 2v2) + 4λ2 sin2 2β(H2 SM − 2v2) + 8λ2(H2 S − 2v2 S) + � − 2g2 1 cos2 2β + g2 2(cos 4β − 3) + (cos 4β − 1)(2λ2 − ∆λ2) � H2 NSM +2 � sin 4β(2λ2 − G)8 cos β sin3 β∆λ2 � HSMHNSM + 4λ sin 2β � − 2κH2 S +4κv2 S + Aλ � −2 √ 2HS + 4vS − λN(N2 R − 2v2 N) � �� , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='42) M2 C2, (2+i) ≃ δij 4 � vj � � −g2 2 cos 2β − 2(Y ij e )2 sin2 β � HSM + sin 2β � g2 2 − (Y ij e )2� HNSM � −2Y j NNR �√ 2AN sin β + sin β � λNHS − Y ij e (sin βHNSM − cos βHSM) � − λ cos βHS �� , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='43) M2 C,2 (5+i) ≃ −(AeYe)ij √ 2 vj cos β − 1 2Y ij e Y j NNR � cos2 βHNSM + sin 2β 2 HSM � , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='44) M2 C,(2+i)(2+j) ≃ m2 �Lij + δij 8 � (g2 1 − g2 2)(cos 2β(H2 SM − H2 NSM) − 2 sin 2βHSMHNSM) +4(Y ij e )2(cos βHSM − sin βHNSM)2 � , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='45) M2 C,(2+i)(5+j) ≃ δij(AeYe)ij √ 2 (cos βHSM − sin βHNSM) −δijλY ij e 2 (cos βHNSM + sin βHSM)HS, (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='46) M2 C,(5+i)(5+j) ≃ m2 �ec ij − δij 4 � g2 1(cos 2β(H2 SM − H2 NSM) − 2 sin 2βHSMHNSM) −2(Y ij e )2(cos βHSM − sin βHNSM)2 � , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='47) – 44 – where we have used G = g2 1+g2 2, v2 u+v2 d = v2 and i = 1, 2, 3 are generational indices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' At the physical vacuum, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', � ⟨HSM⟩, ⟨HNSM⟩, ⟨HS⟩, ⟨NR⟩ � = �√ 2v, 0, √ 2vS, √ 2vN � , neglecting terms like v2 i , Y i2 N , 3� i=1 viY i N, the Goldstone mode appears massless and decouples from the other charged states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4 Neutralino mass matrix In the basis of ψ0T = { �B0, � W 0 3 , �H0 d, �H0 u, �S, N, ν1, ν2, ν3}, the matrix M0 (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4)) is given as M0 = � � � M6×6 m6×3 mT 3×6 03×3 � � � , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='48) where we have used ⟨�νi⟩ = vi (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6)) as the LH-sneutrinos are not dynamical in nature (see subsection 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Further, matrices mT 3×6 and M6×6, using Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='8), are given as mT 3×6 = � � � � � � � � � −g1ve √ 2 g2ve √ 2 0 Y 1 NNR √ 2 0 Y 1 N √ 2Y −g1vµ √ 2 g2vµ √ 2 0 Y 2 NNR √ 2 0 Y 2 N √ 2Y −g1vτ √ 2 g2vτ √ 2 0 Y 3 NNR √ 2 0 Y 3 N √ 2Y � � � � � � � � � , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='49) with Y = � sβHSM + cβHNSM � and the symmetric matrix M6×6 is given as, � � � � � � � � � � � � � � � � � � � � � � M1 0 − g1 2 X g1 2 Y 0 0 M2 g2 2 X − g2 2 Y 0 0 0 − λ √ 2HS − λ √ 2Y 0 0 − λ √ 2X 0 √ 2κHS λN 2 √ 2NR λN √ 2HS � � � � � � � � � � � � � � � � � � � � � � , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='50) where we have omitted symmetric entries, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', M0ij = M0ji for ̸= j and X = � cβHSM − sβHNSM � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5 Chargino mass matrix Using a similar approach, in the basis ψ+T = {� W +, �H+ u , e+ R, µ+ R, τ + R } and ψ−T = {� W −, �H− d , e− L, µ− L, τ − L }, the matrix M± is given as M± = � 0 XT X 0 � , (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='51) – 45 – where the 5 × 5 matrix X is given by � � � � � � � � � � � � � � � � � � M2 g2 √ 2Y 0 0 0 g2 √ 2X λ √ 2HS −Y 11 e ve −Y 22 e ve −Y 33 e vτ g2ve − Y 1 N NR √ 2 Y 11 e √ 2 X 0 0 g2vµ − Y 2 N NR √ 2 0 Y 22 e √ 2 X 0 g2vτ − Y 3 N NR √ 2 0 0 Y 33 e √ 2 X � � � � � � � � � � � � � � � � � � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='52) Here we have used Y ij e = Y ii e δij.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' B Neutral scalar mass matrices after the EWSB Weak couplings among the LH-handed sneutrino states and the remaining states, as already discussed in section 2, suggest that one can safely decouple the LH-sneutrino-dominated states from the CP-even and CP-odd scalar squared mass matrices without any loss of generality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' After the aforesaid detachment, both CP-even and CP-odd scalar squared mass matrices appear to be 4 × 4 in size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The full 7 × 7 squared mass matrices are given in subsections A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1 & A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2, including LH-sneutrino states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In this section, squared mass matrices of the CP-even and the CP-odd Higgses are given after the EW symmetry breaking, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', using relations given in subsections A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1 & A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 and considering ⟨HSM⟩ = √ 2v, ⟨HNSM⟩ = 0, ⟨HS⟩ = √ 2vS, ⟨NR⟩ = √ 2vN, ⟨ANSM⟩ = 0, ⟨AS⟩ = 0, ⟨NI⟩ = 0 (see subsection 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' For the CP-even states, we consider the {HSM, HNSM, HS, NR} basis while for the CP-odd ones we use {ANSM, AS, G0, AN} basis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1 CP-even mass squared elements M2 S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='11 = λ2v2 sin2 2β + (g2 1 + g2 2)v2 2 cos2 2β,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' M2 S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='12 = λ2v2 2 sin 4β − (g2 1 + g2 2)v2 4 sin 4β,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' M2 S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='13 = 2λ2vvS − λv(Aλ + 2κvS) sin 2β,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' M2 S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='14 = −λλNvN sin 2β,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' M2 S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='22 = 2λvS(Aλ + κvS) csc 2β + λλNv2 N csc 2β − λ2v2 sin2 2β + (g2 1 + g2 2)v2 2 sin2 2β,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' M2 S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='23 = −λv(Aλ + 2κvS) cos 2β,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' M2 S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='24 = −λλNvvN cos 2β,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' M2 S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='33 = κvS(Aκ + 4κvS) + λv2Aλ 2vS sin 2β − λNv2 NAλN 2vS ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' M2 S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='34 = λNvNAλN + 2λNκvSvN + 2λ2 NvSvN,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' M2 S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='44 = λ2 Nv2 N,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1) where we have used the symmetric nature of these entries, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', M2 S,ij = M2 S,ji for i ̸= j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' – 46 – B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2 CP-odd mass squared elements M2 A,11 = λλNv2 N csc 2β + 2λvS(Aλ + κvS) csc 2β, M2 A,12 = λvAλ − 2λκvvS, M2 A,13 = 0, M2 A,14 = −λλNvvN, M2 A,22 = κ(2λv2 sin 2β − 3vSAκ) + λv2Aλ 2vS sin 2β − λNv2 N 2vS (AλN + 4κvS), M2 A,23 = 0, M2 A,24 = 2λNκvSvN − λNvNAλN , M2 A,33 = 0, M2 A,34 = 0, M2 A,44 = λλNv2 sin 2β − 2λNvS(AλN + κvS), (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2) where we have used the symmetric nature of these entries, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', M2 A,ij = M2 A,ji for i ̸= j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' C Counter terms As already addressed in subsection 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2, after including Coleman-Weinberg contributions (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='15)), counter terms are necessary to restore the original physical minima and masses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' These terms are encapsulated within Vct which is written as Vct = δm2 Hd |Hd|2 + δm2 Hu |Hu|2 + δm2 S |S|2 + δM2 N | � N|2 + δλAλ (SHu · Hd + h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=') +δλNAλN (S � N � N + h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=') + δλ2 2 |Hu|4, (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1) where δm2 Hd, δm2 Hu, δm2 S, δM2 N , δλAλ, δλNAλN , δλ2 are counter terms corresponding to en- tries given by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2) and Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='12).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Entries corresponding to δm2 Hd, δm2 Hu are encapsu- lated within −L′ soft of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In order to maintain the location of the physical minima solutions for the counter-terms must satisfy the following relations: δm2 Hd = 1 √ 2v � tan β ∂Veff ∂HNSM − ∂Veff ∂HSM � + µ sec2 β 2λv ∂2Veff ∂HS∂HSM ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' δm2 Hu = csc2 β 4vλ ∂ ∂HSM �√ 2λ(cos 2β − 2) Veff + 2µ∂Veff ∂HS + 2λv ∂Veff ∂HSM � − 1 √ 2v cot β ∂Veff ∂HNSM ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' δm2 S = λ 2µ ∂ ∂HS � v ∂Veff ∂HSM + vN ∂Veff ∂NR − √ 2 Veff � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' δM2 N = − 1 2vN ∂ ∂NR �√ 2 Veff − 2µ λ ∂Veff ∂HS � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' δλAλ = csc 2β v ∂2Veff ∂HS∂HSM ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' δλNAλN = − 1 2vN ∂2Veff ∂HS∂NR ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' δλ2 = csc4 β 4v3 ∂ ∂HSM �√ 2 Veff − 2v ∂Veff ∂HSM � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2) – 47 – Identifying δλ2 as a counter term for ∆λ2, a quartic coupling among Hu as given in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='12), seems inconsistent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' However, in reality, ∆λ2 is connected to the soft SUSY-breaking terms as the estimation of ∆λ2 includes soft SUSY-breaking terms of the stop sector (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='13)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D Daisy coefficients The Daisy coefficients [133–137], ci, using Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='18) is given by ci = m2 i (φα, T) − m2 i (φα) T , (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1) and can be estimated using the high-temperature limit, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', T 2 ≫ m2 (m depicts a generic mass term involved in the calculation) [133], of the thermal corrections from V T̸=0 1−loop (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='17)) as 1 T 2 ∂2V 1−loop T̸=0 ∂φi∂φj .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2) Daisy coefficients are calculated at the T 2 ≫ m2 limit which helps to efface gauge depen- dence for these coefficients although V 1−loop T̸=0 , as already discussed in subsection 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3, has explicit gauge dependence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' The form of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2), except the 1/T 2 factor, looks similar to relations that are conventionally used for the computation of i, j-th entry of the different scalar mass matrices from the concerned potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' For the calculation of Daisy coefficients we use V 1−loop T̸=0 as a function of m2 i (φα) and not as a function of m2 i (φα, T).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' However, while computing V 1−loop T̸=0 and V ′1−loop CW (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='20)) we use thermal masses m2 i (φα, T).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Expanding thermal function JB/F (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='19)), in the limit T 2 ≫ m2, one gets in the leading order [137, 238] V T̸=0 1−loop ∼ T 2 48 � 2 � i=B nim2 i + � i=F nim2 i � , (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3) where B(F) represents boson (fermion) and ni depicts the associated degrees of freedom, as already detailed in subsection 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' It is also apparent from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3) that contribu- tions from the bosonic sources are the leading ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Also, as detailed in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [137], cubic contributions in the V T̸=0 1−loop appears only via bosons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Further, quartic contributions from fermions are suppressed compared to the same from bosons and do not affect the shift in the VEVs [137].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Thus, we neglect contributions from the relevant fermionic sources (see Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [239] for a similar discussion in the context of the NMSSM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=').' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In light of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2) and Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3), non-zero Daisy coefficients are given below where field-dependent masses – 48 – are considered as a function of all bosonic degrees of freedom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' cHSMHSM = cG0G0 = λ2 4 + (3m2 Z + 4m2 W ) 8v2 + m2 Z 4v2 sin2 θw cos2 β + m2 t 4v2 + ∆λ2 4v2 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' cHSMHNSM = cHNSMG0 = m2 t 4v2 1 tan2 β + ∆λ2 sin 2β 8 − m2 Z 8v2 sin2 θw sin 2β,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' cHNSMHNSM = cANSMANSM = λ2 4 + (m2 Z + 4m2 W ) 8v2 + m2 t 4v2 tan2 β + m2 Z 4v2 sin2 θw sin2 β + ∆λ2 4 cos2 β,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' cHSHS = λ2 + κ2 2 + λ2 N 8 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' cASAS = λ2 + κ2 3 + λ2 N 12 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' cNRNR = λ2 N 4 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' cNINI = λ2 N 6 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' cH+H− = λ2 6 + (m2 Z + 8m2 W ) 24v2 − m2 Z 4v2 sin2 θw sin2 β + m2 t 4v2 tan2 β 1 tan2 β + ∆λ2 4 cos2 β,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' cH+G− = m2 t 4v2 tan2 β 1 tan2β + ∆λ2 sin 2β 8 − m2 Z 8v2 sin2 θw sin 2β,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' cG+G− = λ2 6 + (7m2 Z + 8m2 W ) 24v2 − m2 Z 4v2 sin2 θw sin2 β + m2 t 4v2 + ∆λ2 4 sin2 β,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4) where mW , mZ represent masses for the W ±, Z0 bosons, respectively and θw is Weinberg angle [110].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Longitudinal modes of the massive gauge bosons also yield non-zero Daisy coefficients [240, 241] cW + L W − L = cW 3 LW 3 L = 5 2g2 2, cBLBL = 13 6 g2 1, (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5) where W ± L , W 3 L, BL correspond to longitudinal modes of the SM SU(2)L, U(1)Y gauge bosons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' These results are the same as the Z3-invariant NMSSM as gauge sector of the chosen NMSSM + one RH-neutrino framework remains exactly the same as the Z3-invariant NMSSM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Finally, at T ̸= 0 the photon (γ) also gets a temperature-dependent mass, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', a non-vanishing longitudinal component, which should also be included in the field-dependent mass matrix used to evaluate eigenvalues of the electrically neutral EW gauge bosons, γ, Z0 at T ̸= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' m2 ZLγL(HSM, HNSM, HS, NR, T) = � � � g2 2 H2 SM+H2 NSM 4 + 5 2g2 2T 2 −g1g2 H2 SM+H2 NSM 4 −g1g2 H2 SM+H2 NSM 4 g2 1 H2 SM+H2 NSM 4 + 13 6 g2 1T 2 � � � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6) E Minimization conditions As already stated in section 3 that one can trade different soft-masses, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', m2 Hu, m2 Hd, m2 �Lij, m2 S, M2 N (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2)) with the corresponding VEVs (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6)) using min- imization conditions of the Vtree (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' One can also use the neutral part of Vscalar as depicted in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Mathematically, the minimization condition gives a set of – 49 – equations like �∂Vtree ∂Xi ����� X=⟨X⟩ = 0, (E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1) where Xi = H0 u, H0 d, �νi, S, � N, and ⟨X⟩ represents all the concerned VEVs as given in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' In detail, assuming all superpotential couplings (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1)) to be real, one gets �∂Vtree ∂H0u ����� VEVs = λvd � λvuvd − κv2 S − λN 2 v2 N � + Y i2 N v2 Nvu + λ2v2 Svu + m2 Huvu + 3 � j=1 Y j Nvj � 3 � i=1 Y i Nvivu + λNvSvN � + g2 1 + g2 2 4 � v2 d + 3 � i=1 v2 i − v2 u � vu + λAλvSvd + 3 � i=1 (ANYN)ivivN, (E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2) �∂Vtree ∂H0 d ����� VEVs = λvu � λvuvd − κv2 S − λN 2 v2 N � + λvS � λvSvd − 3 � i=1 Y i NvivN � + g2 1 + g2 2 4 � v2 d + 3 � i=1 v2 i − v2 u � vd + m2 Hdvd + λAλvSvu, (E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3) �∂Vtree ∂ �νi ����� VEVs = Y i Nvu � � 3 � j=1 Y j Nvjvu + λNvSvN � � + Y i NvN � � 3 � j=1 Y j NvjvN − λvdvS � � + g2 1 + g2 2 4 � v2 d + 3 � i=1 v2 i − v2 u � vi + (ANYN)ivuvN + 3 � j=1 m2 �Lijvj, (E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4) �∂Vtree ∂S ����� VEVs = 2κvS � −λvuvd + κv2 S + λN 2 v2 N � + λvd � λvSvd − 3 � i Y i NvivN � + λNvN � 3 � i=1 Y i Nvivu + λNvSvN � + λ2v2 uvS + m2 SvS + λAλvuvd + κAκv2 S + λNAλN 2 v2 N, (E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5) �∂Vtree ∂ � N ����� VEVs = λNvN � −λvuvd + κv2 S + λN 2 v2 N � + λNvS � 3 � i=1 Y i Nvivu + λNvSvN � + 3 � j=1 Y j Nvj � 3 � i=1 Y i NvivN − λvSvd � + Y i2 N v2 uvN + M2 NvN + 3 � i=1 (ANYN)ivivu + λAλN vSvN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' (E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6) – 50 – References [1] Planck collaboration, Planck 2018 results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Cosmological parameters, Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 641 (2020) A6 [1807.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='06209].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [2] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Cline, Baryogenesis, in Les Houches Summer School - Session 86: Particle Physics and Cosmology: The Fabric of Spacetime, 9, 2006, hep-ph/0609145.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [3] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Anderson and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Hall, The Electroweak phase transition and baryogenesis, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D 45 (1992) 2685.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [4] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Curtin, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Meade and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='-T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Yu, Testing Electroweak Baryogenesis with Future Colliders, JHEP 11 (2014) 127 [1409.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0005].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [5] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Artymowski, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Lewicki and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Wells, Gravitational wave and collider implications of electroweak baryogenesis aided by non-standard cosmology, JHEP 03 (2017) 066 [1609.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='07143].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [6] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Modak and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Senaha, Probing Electroweak Baryogenesis induced by extra bottom Yukawa coupling via EDMs and collider signatures, JHEP 11 (2020) 025 [2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='09928].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [7] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Sakharov, Violation of CP Invariance, C asymmetry, and baryon asymmetry of the universe, Pisma Zh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Eksp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Teor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Fiz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 5 (1967) 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [8] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Gavela, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Hernandez, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Orloff, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Pene and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Quimbay, Standard model CP violation and baryon asymmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Part 2: Finite temperature, Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' B 430 (1994) 382 [hep-ph/9406289].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [9] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Bernreuther, CP violation and baryogenesis, Lect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Notes Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 591 (2002) 237 [hep-ph/0205279].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [10] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Morrissey and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Ramsey-Musolf, Electroweak baryogenesis, New J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 14 (2012) 125003 [1206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2942].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [11] ATLAS collaboration, Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' B 716 (2012) 1 [1207.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='7214].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [12] CMS collaboration, Observation of a New Boson at a Mass of 125 GeV with the CMS Experiment at the LHC, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' B 716 (2012) 30 [1207.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='7235].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [13] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Kajantie, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Laine, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rummukainen and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Shaposhnikov, Is there a hot electroweak phase transition at mH ≳ mW ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 77 (1996) 2887 [hep-ph/9605288].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [14] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rummukainen, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Tsypin, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Kajantie, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Laine and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Shaposhnikov, The Universality class of the electroweak theory, Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' B 532 (1998) 283 [hep-lat/9805013].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [15] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Csikor, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Fodor and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Heitger, Endpoint of the hot electroweak phase transition, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 82 (1999) 21 [hep-ph/9809291].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [16] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Mazumdar and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' White, Review of cosmic phase transitions: their significance and experimental signatures, Rept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Prog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 82 (2019) 076901 [1811.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='01948].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [17] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Apreda, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Maggiore, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Nicolis and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Riotto, Gravitational waves from electroweak phase transitions, Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' B 631 (2002) 342 [gr-qc/0107033].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [18] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Grojean, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Servant and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Wells, First-order electroweak phase transition in the standard model with a low cutoff, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D 71 (2005) 036001 [hep-ph/0407019].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' – 51 – [19] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Weir, Gravitational waves from a first order electroweak phase transition: a brief review, Phil.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Roy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Lond.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' A 376 (2018) 20170126 [1705.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='01783].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [20] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Ellis, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Lewicki and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' No, On the Maximal Strength of a First-Order Electroweak Phase Transition and its Gravitational Wave Signal, JCAP 04 (2019) 003 [1809.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='08242].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [21] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Alanne, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Hugle, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Platscher and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Schmitz, A fresh look at the gravitational-wave signal from cosmological phase transitions, JHEP 03 (2020) 004 [1909.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='11356].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [22] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Caprini et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', Detecting gravitational waves from cosmological phase transitions with LISA: an update, JCAP 03 (2020) 024 [1910.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='13125].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [23] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Costa, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Khan and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Kim, A two-component dark matter model and its associated gravitational waves, JHEP 06 (2022) 026 [2202.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='13126].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [24] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Ahriche, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Hashino, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Kanemura and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Nasri, Gravitational Waves from Phase Transitions in Models with Charged Singlets, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' B 789 (2019) 119 [1809.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='09883].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [25] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Shajiee and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Tofighi, Electroweak Phase Transition, Gravitational Waves and Dark Matter in Two Scalar Singlet Extension of The Standard Model, Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' C 79 (2019) 360 [1811.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='09807].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [26] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Alves, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Ghosh, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='-K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Guo, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Sinha and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Vagie, Collider and Gravitational Wave Complementarity in Exploring the Singlet Extension of the Standard Model, JHEP 04 (2019) 052 [1812.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='09333].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [27] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Haber and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Kane, The Search for Supersymmetry: Probing Physics Beyond the Standard Model, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 117 (1985) 75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [28] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Espinosa, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Quiros and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Zwirner, On the electroweak phase transition in the minimal supersymmetric Standard Model, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' B 307 (1993) 106 [hep-ph/9303317].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [29] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Carena, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Quiros and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Wagner, Opening the window for electroweak baryogenesis, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' B 380 (1996) 81 [hep-ph/9603420].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [30] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Delepine, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Gerard, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Gonzalez Felipe and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Weyers, A Light stop and electroweak baryogenesis, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' B 386 (1996) 183 [hep-ph/9604440].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [31] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Laine and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rummukainen, The MSSM electroweak phase transition on the lattice, Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' B 535 (1998) 423 [hep-lat/9804019].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [32] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Cline and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Moore, Supersymmetric electroweak phase transition: Baryogenesis versus experimental constraints, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 81 (1998) 3315 [hep-ph/9806354].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [33] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Balazs, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Carena, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Menon, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Morrissey and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Wagner, The Supersymmetric origin of matter, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D 71 (2005) 075002 [hep-ph/0412264].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [34] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Lee, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Cirigliano and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Ramsey-Musolf, Resonant relaxation in electroweak baryogenesis, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D 71 (2005) 075010 [hep-ph/0412354].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [35] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Carena, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Nardini, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Quiros and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Wagner, The Baryogenesis Window in the MSSM, Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' B 812 (2009) 243 [0809.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3760].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [36] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Menon and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Morrissey, Higgs Boson Signatures of MSSM Electroweak Baryogenesis, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D 79 (2009) 115020 [0903.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3038].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [37] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Carena, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Nardini, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Quiros and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Wagner, MSSM Electroweak Baryogenesis and LHC Data, JHEP 02 (2013) 001 [1207.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6330].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' – 52 – [38] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Curtin, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Jaiswal and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Meade, Excluding Electroweak Baryogenesis in the MSSM, JHEP 08 (2012) 005 [1203.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2932].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [39] ATLAS collaboration, Search for associated production of a Z boson with an invisibly decaying Higgs boson or dark matter candidates at √s =13 TeV with the ATLAS detector, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' B 829 (2022) 137066 [2111.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='08372].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [40] CMS collaboration, Search for invisible decays of the Higgs boson produced via vector boson fusion in proton-proton collisions at √s=13 TeV, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D 105 (2022) 092007 [2201.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='11585].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [41] ATLAS collaboration, Search for invisible Higgs-boson decays in events with vector-boson fusion signatures using 139 fb−1 of proton-proton data recorded by the ATLAS experiment, JHEP 08 (2022) 104 [2202.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='07953].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [42] CMS collaboration, A portrait of the Higgs boson by the CMS experiment ten years after the discovery, Nature 607 (2022) 60 [2207.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='00043].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [43] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Krizka, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Kumar and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Morrissey, Very Light Scalar Top Quarks at the LHC, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D 87 (2013) 095016 [1212.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4856].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [44] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Delgado, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Giudice, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Isidori, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Pierini and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Strumia, The light stop window, Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' C 73 (2013) 2370 [1212.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='6847].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [45] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Gr¨ober, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' M¨uhlleitner, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Popenda and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Wlotzka, Light Stop Decays: Implications for LHC Searches, Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' C 75 (2015) 420 [1408.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4662].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [46] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Kim and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Nilles, The mu Problem and the Strong CP Problem, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' B 138 (1984) 150.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [47] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Esteban, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Gonzalez-Garcia, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Maltoni, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Schwetz and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Zhou, The fate of hints: updated global analysis of three-flavor neutrino oscillations, JHEP 09 (2020) 178 [2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='14792].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [48] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Gonzalez-Garcia, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Maltoni and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Schwetz, NuFIT: Three-Flavour Global Analyses of Neutrino Oscillation Experiments, Universe 7 (2021) 459 [2111.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='03086].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [49] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Hall and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Suzuki, Explicit R-Parity Breaking in Supersymmetric Models, Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' B 231 (1984) 419.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [50] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Hirsch and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Valle, Supersymmetric origin of neutrino mass, New J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 6 (2004) 76 [hep-ph/0405015].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [51] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Barbier et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', R-parity violating supersymmetry, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 420 (2005) 1 [hep-ph/0406039].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [52] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Mohapatra et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', Theory of neutrinos: A White paper, Rept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Prog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 70 (2007) 1757 [hep-ph/0510213].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [53] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' de Salas, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Forero, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Gariazzo, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Mart´ınez-Mirav´e, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Mena, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Ternes et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', 2020 global reassessment of the neutrino oscillation picture, JHEP 02 (2021) 071 [2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='11237].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [54] U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Ellwanger, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Hugonie and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Teixeira, The Next-to-Minimal Supersymmetric Standard Model, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 496 (2010) 1 [0910.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1785].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [55] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Pietroni, The Electroweak phase transition in a nonminimal supersymmetric model, Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' B 402 (1993) 27 [hep-ph/9207227].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' – 53 – [56] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Davies, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Froggatt and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Moorhouse, Electroweak baryogenesis in the next-to-minimal supersymmetric model, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' B 372 (1996) 88 [hep-ph/9603388].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [57] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Huber, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Konstandin, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Prokopec and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Schmidt, Electroweak Phase Transition and Baryogenesis in the nMSSM, Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' B 757 (2006) 172 [hep-ph/0606298].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [58] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Huang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Kang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Shu, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Wu and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Yang, New insights in the electroweak phase transition in the NMSSM, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D 91 (2015) 025006 [1405.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1152].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [59] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Kozaczuk, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Profumo, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Haskins and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Wainwright, Cosmological Phase Transitions and their Properties in the NMSSM, JHEP 01 (2015) 144 [1407.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4134].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [60] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Baum, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Carena, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Shah, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Wagner and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Wang, Nucleation is more than critical: A case study of the electroweak phase transition in the NMSSM, JHEP 03 (2021) 055 [2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='10743].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [61] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Carena, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Nardini, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Quiros and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Wagner, The Effective Theory of the Light Stop Scenario, JHEP 10 (2008) 062 [0806.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4297].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [62] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Minkowski, µ → eγ at a Rate of One Out of 109 Muon Decays?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' B 67 (1977) 421.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [63] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Yanagida, Horizontal gauge symmetry and masses of neutrinos, Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' C 7902131 (1979) 95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [64] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Gell-Mann, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Ramond and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Slansky, Complex Spinors and Unified Theories, Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' C 790927 (1979) 315 [1306.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4669].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [65] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Mohapatra and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Senjanovic, Neutrino Mass and Spontaneous Parity Nonconservation, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 44 (1980) 912.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [66] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Hisano, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Moroi, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Tobe and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Yamaguchi, Lepton flavor violation via right-handed neutrino Yukawa couplings in supersymmetric standard model, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D 53 (1996) 2442 [hep-ph/9510309].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [67] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Hisano, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Moroi, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Tobe, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Yamaguchi and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Yanagida, Lepton flavor violation in the supersymmetric standard model with seesaw induced neutrino masses, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' B 357 (1995) 579 [hep-ph/9501407].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [68] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Ellis, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Hisano, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Raidal and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Shimizu, A New parametrization of the seesaw mechanism and applications in supersymmetric models, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D 66 (2002) 115013 [hep-ph/0206110].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [69] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Kitano and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='-y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Oda, Neutrino masses in the supersymmetric standard model with right-handed neutrinos and spontaneous R-parity violation, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D 61 (2000) 113001 [hep-ph/9911327].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [70] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Lopez-Fogliani and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Munoz, Proposal for a Supersymmetric Standard Model, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 97 (2006) 041801 [hep-ph/0508297].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [71] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Escudero, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Lopez-Fogliani, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Munoz and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Ruiz de Austri, Analysis of the parameter space and spectrum of the mu nu SSM, JHEP 12 (2008) 099 [0810.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1507].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [72] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Ghosh and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Roy, Neutrino masses and mixing, lightest neutralino decays and a solution to the mu problem in supersymmetry, JHEP 04 (2009) 069 [0812.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0084].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [73] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Aulakh and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Mohapatra, Neutrino as the Supersymmetric Partner of the Majoron, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' B 119 (1982) 136.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' – 54 – [74] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Masiero and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Valle, A Model for Spontaneous R Parity Breaking, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' B 251 (1990) 273.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [75] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' King, Large mixing angle MSW and atmospheric neutrinos from single right-handed neutrino dominance and U(1) family symmetry, Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' B 576 (2000) 85 [hep-ph/9912492].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [76] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Ibarra and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Ross, Neutrino phenomenology: The Case of two right-handed neutrinos, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' B 591 (2004) 285 [hep-ph/0312138].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [77] CMS collaboration, Search for top squarks decaying via the four-body mode in single-lepton final states from Run 2 of the LHC, CMS-PAS-SUS-21-003 (2022) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [78] CMS collaboration, Search for top squark pair production in a final state with one or two tau leptons in proton-proton collisions at √s = 13 TeV, CMS-PAS-SUS-21-004 (2022) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [79] CMS collaboration, Search for supersymmetry in final states with a single electron or muon using angular correlations and heavy object tagging in proton-proton collisions at √s = 13 TeV, CMS-PAS-SUS-21-007 (2022) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [80] ATLAS collaboration, SUSY Summary Plots March 2022, ATL-PHYS-PUB-2022-013 (2022) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [81] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Kudoh, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Taruya, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Hiramatsu and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Himemoto, Detecting a gravitational-wave background with next-generation space interferometers, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D 73 (2006) 064006 [gr-qc/0511145].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [82] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Yagi and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Seto, Detector configuration of DECIGO/BBO and identification of cosmological neutron-star binaries, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D 83 (2011) 044011 [1101.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3940].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [83] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Nilles, Supersymmetry, Supergravity and Particle Physics, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 110 (1984) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [84] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Sohnius, Introducing Supersymmetry, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 128 (1985) 39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [85] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Martin, A Supersymmetry primer, Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Direct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' High Energy Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 18 (1998) 1 [hep-ph/9709356].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [86] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Maniatis, The Next-to-Minimal Supersymmetric extension of the Standard Model reviewed, Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' A 25 (2010) 3505 [0906.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0777].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [87] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Simonsen, A Review of minimal supersymmetric electroweak theory, hep-ph/9506369.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [88] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Drees, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Godbole and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Roy, Theory and phenomenology of sparticles: An account of four-dimensional N=1 supersymmetry in high energy physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' World Scientific Publishing Co Pvt Ltd, 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [89] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Hall, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Lykken and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Weinberg, Supergravity as the Messenger of Supersymmetry Breaking, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D 27 (1983) 2359.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [90] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Roy and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Mukhopadhyaya, Some implications of a supersymmetric model with R-parity breaking bilinear interactions, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D 55 (1997) 7020 [hep-ph/9612447].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [91] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Porod, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Hirsch, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Romao and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Valle, Testing neutrino mixing at future collider experiments, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D 63 (2001) 115004 [hep-ph/0011248].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [92] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Hirsch, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Vicente and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Porod, Spontaneous R-parity violation: Lightest neutralino decays and neutrino mixing angles at future colliders, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D 77 (2008) 075005 [0802.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2896].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' – 55 – [93] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Bartl, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Hirsch, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Vicente, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Liebler and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Porod, LHC phenomenology of the mu nu SSM, JHEP 05 (2009) 120 [0903.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3596].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [94] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Fidalgo, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Lopez-Fogliani, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Munoz and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Ruiz de Austri, The Higgs sector of the µνSSM and collider physics, JHEP 10 (2011) 020 [1107.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4614].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [95] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Ghosh, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Lopez-Fogliani, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Mitsou, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Munoz and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Ruiz de Austri, Probing the µ-from-ν supersymmetric standard model with displaced multileptons from the decay of a Higgs boson at the LHC, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D 88 (2013) 015009 [1211.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3177].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [96] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Hirsch, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Diaz, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Porod, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Romao and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Valle, Neutrino masses and mixings from supersymmetry with bilinear R parity violation: A Theory for solar and atmospheric neutrino oscillations, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D 62 (2000) 113008 [hep-ph/0004115].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [97] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Krauss, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Opferkuch and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Staub, Spontaneous Charge Breaking in the NMSSM - Dangerous or not?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' C 77 (2017) 331 [1703.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='05329].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [98] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Georgi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Glashow and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Nussinov, Unconventional Model of Neutrino Masses, Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' B 193 (1981) 297.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [99] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Santamaria and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Valle, Spontaneous R-Parity Violation in Supersymmetry: A Model for Solar Neutrino Oscillations, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' B 195 (1987) 423.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [100] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Santamaria and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Valle, Supersymmetric Majoron Signatures and Solar Neutrino Oscillations, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 60 (1988) 397.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [101] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Santamaria and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Valle, Solar Neutrino Oscillation Parameters and the Broken R Parity Majoron, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D 39 (1989) 1780.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [102] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Carena, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Haber, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Low, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Shah and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Wagner, Alignment limit of the NMSSM Higgs sector, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D 93 (2016) 035013 [1510.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='09137].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [103] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Georgi and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Nanopoulos, Suppression of Flavor Changing Effects From Neutral Spinless Meson Exchange in Gauge Theories, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' B 82 (1979) 95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [104] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Donoghue and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Li, Properties of Charged Higgs Bosons, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D 19 (1979) 945.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [105] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Lavoura and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Silva, Fundamental CP violating quantities in a SU(2) x U(1) model with many Higgs doublets, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D 50 (1994) 4619 [hep-ph/9404276].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [106] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Botella and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Silva, Jarlskog - like invariants for theories with scalars and fermions, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D 51 (1995) 3870 [hep-ph/9411288].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [107] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Gunion and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Haber, The CP conserving two Higgs doublet model: The Approach to the decoupling limit, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D 67 (2003) 075019 [hep-ph/0207010].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [108] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Gunion, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Haber, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Kane and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Dawson, The Higgs Hunter’s Guide, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' CRC Pressv, 2000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [109] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Gunion, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Haber, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Kane and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Dawson, Errata for the Higgs hunter’s guide, hep-ph/9302272.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [110] Particle Data Group collaboration, Review of Particle Physics, PTEP 2022 (2022) 083C01.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [111] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Ghosh, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Lopez-Fogliani, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Mitsou, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Munoz and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Ruiz de Austri, Probing the µνSSM with light scalars, pseudoscalars and neutralinos from the decay of a SM-like Higgs boson at the LHC, JHEP 11 (2014) 102 [1410.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2070].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' – 56 – [112] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Huitu and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Waltari, Higgs sector in NMSSM with right-handed neutrinos and spontaneous R-parity violation, JHEP 11 (2014) 053 [1405.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5330].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [113] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Derendinger and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Savoy, Quantum Effects and SU(2) x U(1) Breaking in Supergravity Gauge Theories, Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' B 237 (1984) 307.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [114] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' King and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' White, Resolving the constrained minimal and next-to-minimal supersymmetric standard models, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D 52 (1995) 4183 [hep-ph/9505326].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [115] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Masip, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Munoz-Tapia and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Pomarol, Limits on the mass of the lightest Higgs in supersymmetric models, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D 57 (1998) R5340 [hep-ph/9801437].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [116] CMS collaboration, Search for top squark production in fully-hadronic final states in proton-proton collisions at √s = 13 TeV, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D 104 (2021) 052001 [2103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='01290].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [117] ATLAS collaboration, Search for squarks and gluinos in final states with one isolated lepton, jets, and missing transverse momentum at √s = 13 with the ATLAS detector, Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' C 81 (2021) 600 [2101.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='01629].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [118] ATLAS collaboration, Search for R-parity violating supersymmetry in a final state containing leptons and many jets with the ATLAS experiment using √s = 13 TeV proton-proton collision data, ATLAS-CONF-2021-007 (2021) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [119] ATLAS collaboration, Search for supersymmetry in final states with missing transverse momentum and three or more b-jets in 139 fb−1 of proton−proton collisions at √s = 13 TeV with the ATLAS detector, 2211.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='08028.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [120] ATLAS collaboration, Search for direct stau production in events with two hadronic τ-leptons in √s = 13 TeV pp collisions with the ATLAS detector, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D 101 (2020) 032009 [1911.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='06660].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [121] CMS collaboration, Search for electroweak production of supersymmetric particles in final states containing hadronic decays of WW, WZ, or WH and missing transverse momentum, CMS-PAS-SUS-21-002 (2021) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [122] ATLAS collaboration, Search for direct pair production of sleptons and charginos decaying to two leptons and neutralinos with mass splittings near the W-boson mass in √s = 13 TeV pp collisions with the ATLAS detector, 2209.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='13935.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [123] Muon g-2 collaboration, Measurement of the Positive Muon Anomalous Magnetic Moment to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='46 ppm, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 126 (2021) 141801 [2104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='03281].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [124] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Ellis, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Ridolfi and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Zwirner, On radiative corrections to supersymmetric Higgs boson masses and their implications for LEP searches, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' B 262 (1991) 477.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [125] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Haber and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Hempfling, The Renormalization group improved Higgs sector of the minimal supersymmetric model, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D 48 (1993) 4280 [hep-ph/9307201].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [126] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Casas, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Espinosa, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Quiros and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Riotto, The Lightest Higgs boson mass in the minimal supersymmetric standard model, Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' B 436 (1995) 3 [hep-ph/9407389].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [127] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Carena, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Espinosa, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Quiros and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Wagner, Analytical expressions for radiatively corrected Higgs masses and couplings in the MSSM, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' B 355 (1995) 209 [hep-ph/9504316].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [128] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Lee and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Wagner, Higgs bosons in heavy supersymmetry with an intermediate mA, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D 92 (2015) 075032 [1508.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='00576].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' – 57 – [129] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Coleman and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Weinberg, Radiative Corrections as the Origin of Spontaneous Symmetry Breaking, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D 7 (1973) 1888.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [130] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Bi, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Bian, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Huang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Shu and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='-F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Yin, Interpretation of the Galactic Center excess and electroweak phase transition in the NMSSM, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D 92 (2015) 023507 [1503.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='03749].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [131] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Huber, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Konstandin, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Nardini and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rues, Detectable Gravitational Waves from Very Strong Phase Transitions in the General NMSSM, JCAP 03 (2016) 036 [1512.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='06357].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [132] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Bian, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='-K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Guo and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Shu, Gravitational Waves, baryon asymmetry of the universe and electric dipole moment in the CP-violating NMSSM, Chin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' C 42 (2018) 093106 [1704.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='02488].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [133] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Dolan and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Jackiw, Symmetry Behavior at Finite Temperature, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D 9 (1974) 3320.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [134] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Kirzhnits and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Linde, Symmetry Behavior in Gauge Theories, Annals Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 101 (1976) 195.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [135] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Parwani, Resummation in a hot scalar field theory, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D 45 (1992) 4695 [hep-ph/9204216].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [136] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Espinosa, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Quiros and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Zwirner, On the phase transition in the scalar theory, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' B 291 (1992) 115 [hep-ph/9206227].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [137] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Arnold and O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Espinosa, The Effective potential and first-order phase transitions: Beyond leading-order, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D 47 (1993) 3546 [hep-ph/9212235].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [138] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Nielsen, On the Gauge Dependence of Spontaneous Symmetry Breaking in Gauge Theories, Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' B 101 (1975) 173.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [139] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Patel and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Ramsey-Musolf, Baryon Washout, Electroweak Phase Transition, and Perturbation Theory, JHEP 07 (2011) 029 [1101.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4665].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [140] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Di Luzio and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Mihaila, On the gauge dependence of the Standard Model vacuum instability scale, JHEP 06 (2014) 079 [1404.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='7450].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [141] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Laine, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Meyer and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Nardini, Thermal phase transition with full 2-loop effective potential, Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' B 920 (2017) 565 [1702.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='07479].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [142] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Drees, Supersymmetric Models with Extended Higgs Sector, Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' A 4 (1989) 3635.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [143] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Ellis, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Gunion, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Haber, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Roszkowski and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Zwirner, Higgs Bosons in a Nonminimal Supersymmetric Model, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D 39 (1989) 844.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [144] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Landau, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Abrikosov and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Khalatnikov, An asymptotic expression for the photon Green function in quantum electrodynamics, Dokl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Akad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Nauk SSSR 95 (1954) 1177.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [145] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Landau, On the quantum field theory, Niels Bohr and the Development of Physics, ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Pauli.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Pergamon Press, London, 1955.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [146] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Dobrescu, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Landsberg and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Matchev, Higgs boson decays to CP odd scalars at the Tevatron and beyond, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D 63 (2001) 075003 [hep-ph/0005308].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [147] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Dobrescu and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Matchev, Light axion within the next-to-minimal supersymmetric standard model, JHEP 09 (2000) 031 [hep-ph/0008192].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' – 58 – [148] L3 collaboration, Search for charginos and neutralinos in e+e− collisions at √s = 189 GeV, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' B 472 (2000) 420 [hep-ex/9910007].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [149] ALEPH collaboration, Absolute mass lower limit for the lightest neutralino of the MSSM from e+e− data at √s up to 209 GeV, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' B 583 (2004) 247.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [150] DELPHI collaboration, Searches for supersymmetric particles in e+e− collisions up to 208 GeV and interpretation of the results within the MSSM, Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' C 31 (2003) 421 [hep-ex/0311019].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [151] OPAL collaboration, Search for chargino and neutralino production at √s = 192 - 209 GeV at LEP, Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' C 35 (2004) 1 [hep-ex/0401026].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [152] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Lentati et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', European Pulsar Timing Array Limits On An Isotropic Stochastic Gravitational-Wave Background, Mon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Roy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 453 (2015) 2576 [1504.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='03692].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [153] NANOGRAV collaboration, The NANOGrav 11-year Data Set: Pulsar-timing Constraints On The Stochastic Gravitational-wave Background, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 859 (2018) 47 [1801.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='02617].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [154] LIGO Scientific, VIRGO collaboration, Characterization of the LIGO detectors during their sixth science run, Class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Quant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Grav.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 32 (2015) 115012 [1410.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='7764].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [155] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Caprini et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', Science with the space-based interferometer eLISA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' II: Gravitational waves from cosmological phase transitions, JCAP 04 (2016) 001 [1512.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='06239].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [156] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Corbin and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Cornish, Detecting the cosmic gravitational wave background with the big bang observer, Class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Quant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Grav.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 23 (2006) 2435 [gr-qc/0512039].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [157] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Staub, SARAH, 0806.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0538.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [158] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Staub, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Ohl, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Porod and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Speckner, A Tool Box for Implementing Supersymmetric Models, Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 183 (2012) 2165 [1109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5147].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [159] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Staub, SARAH 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2: Dirac Gauginos, UFO output, and more, Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 184 (2013) 1792 [1207.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0906].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [160] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Dreiner, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Nickel, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Porod and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Staub, Full 1-loop calculation of BR(B0 s,d → ℓ¯ℓ) in models beyond the MSSM with SARAH and SPheno, Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 184 (2013) 2604 [1212.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='5074].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [161] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Staub, SARAH 4 : A tool for (not only SUSY) model builders, Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 185 (2014) 1773 [1309.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='7223].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [162] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Goodsell, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Nickel and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Staub, Two-Loop Higgs mass calculations in supersymmetric models beyond the MSSM with SARAH and SPheno, Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' C 75 (2015) 32 [1411.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0675].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [163] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Staub, Exploring new models in all detail with SARAH, Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' High Energy Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 2015 (2015) 840780 [1503.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='04200].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [164] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Goodsell and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Staub, Unitarity constraints on general scalar couplings with SARAH, Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' C 78 (2018) 649 [1805.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='07306].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [165] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Porod, SPheno, a program for calculating supersymmetric spectra, SUSY particle decays and SUSY particle production at e+e− colliders, Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 153 (2003) 275 [hep-ph/0301101].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' – 59 – [166] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Porod and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Staub, SPheno 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1: Extensions including flavour, CP-phases and models beyond the MSSM, Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 183 (2012) 2458 [1104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1573].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [167] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Porod, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Staub and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Vicente, A Flavor Kit for BSM models, Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' C 74 (2014) 2992 [1405.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='1434].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [168] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Goodsell, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Nickel and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Staub, Generic two-loop Higgs mass calculation from a diagrammatic approach, Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' C 75 (2015) 290 [1503.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='03098].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [169] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Goodsell and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Staub, The Higgs mass in the CP violating MSSM, NMSSM, and beyond, Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' C 77 (2017) 46 [1604.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='05335].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [170] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Braathen, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Goodsell and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Staub, Supersymmetric and non-supersymmetric models without catastrophic Goldstone bosons, Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' C 77 (2017) 757 [1706.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='05372].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [171] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Goodsell and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Moutafis, How heavy can dark matter be?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Constraining colourful unitarity with SARAH, Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' C 81 (2021) 808 [2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='09022].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [172] ATLAS collaboration, Measurement of the Higgs boson mass in the H → ZZ∗ → 4ℓ decay channel using 139 fb−1 of √s = 13 TeV pp collisions recorded by the ATLAS detector at the LHC, 2207.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='00320.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [173] ATLAS collaboration, Constraints on Higgs boson production with large transverse momentum using H → b¯b decays in the ATLAS detector, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D 105 (2022) 092003 [2111.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='08340].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [174] ATLAS collaboration, Measurements of Higgs boson production cross-sections in the H → τ +τ − decay channel in pp collisions at √s = 13 TeV with the ATLAS detector, JHEP 08 (2022) 175 [2201.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='08269].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [175] ATLAS collaboration, Direct constraint on the Higgs-charm coupling from a search for Higgs boson decays into charm quarks with the ATLAS detector, Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' C 82 (2022) 717 [2201.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='11428].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [176] ATLAS collaboration, Measurement of the properties of Higgs boson production at √s = 13 TeV in the H → γγ channel using 139 fb−1 of pp collision data with the ATLAS experiment, 2207.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='00348.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [177] ATLAS collaboration, Combined measurement of the total and differential cross sections in the H → γγ and the H → ZZ∗ → 4ℓ decay channels at √s = 13 TeV with the ATLAS detector, ATLAS-CONF-2022-002 (2022) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [178] ATLAS and CMS collaboration, Rare and BSM Higgs Searches, CMS-CR-2022-179 (2022) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [179] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Bechtle, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Brein, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Heinemeyer, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Weiglein and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Williams, HiggsBounds: Confronting Arbitrary Higgs Sectors with Exclusion Bounds from LEP and the Tevatron, Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 181 (2010) 138 [0811.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4169].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [180] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Bechtle, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Dercks, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Heinemeyer, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Klingl, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Stefaniak, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Weiglein et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', HiggsBounds-5: Testing Higgs Sectors in the LHC 13 TeV Era, Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' C 80 (2020) 1211 [2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='06007].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [181] CMS collaboration, Search for electroweak production of charginos and neutralinos in proton-proton collisions at √s = 13 TeV, JHEP 04 (2022) 147 [2106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='14246].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [182] CMS collaboration, Search for charging-neutralino production in events with Higgs and W – 60 – bosons using 137 fb−1 of proton-proton collisions at √s = 13 TeV, JHEP 10 (2021) 045 [2107.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='12553].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [183] ATLAS collaboration, Search for charginos and neutralinos in final states with two boosted hadronically decaying bosons and missing transverse momentum in pp collisions at √s = 13 TeV with the ATLAS detector, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D 104 (2021) 112010 [2108.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='07586].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [184] ATLAS collaboration, SUSY March 2021 Summary Plot Update, ATL-PHYS-PUB-2021-007 (2021) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [185] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Bertolini, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Borzumati and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Masiero, New Constraints on Squark and Gluino Masses from Radiative b Decays, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' B 192 (1987) 437.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [186] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Bertolini, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Borzumati, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Masiero and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Ridolfi, Effects of supergravity induced electroweak breaking on rare B decays and mixings, Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' B 353 (1991) 591.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [187] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Ciuchini, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Degrassi, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Gambino and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Giudice, Next-to-leading QCD corrections to B → Xsγ in supersymmetry, Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' B 534 (1998) 3 [hep-ph/9806308].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [188] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Borzumati, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Greub and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Yamada, Beyond leading order corrections to B → Xsγ at large tan β: The Charged Higgs contribution, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D 69 (2004) 055005 [hep-ph/0311151].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [189] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Degrassi, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Gambino and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Slavich, QCD corrections to radiative B decays in the MSSM with minimal flavor violation, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' B 635 (2006) 335 [hep-ph/0601135].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [190] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Domingo and U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Ellwanger, Updated Constraints from B Physics on the MSSM and the NMSSM, JHEP 12 (2007) 090 [0710.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='3714].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [191] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Arbey, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Battaglia, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Mahmoudi and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Mart´ınez Santos, Supersymmetry confronts Bs → µ+µ− : Present and future status, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D 87 (2013) 035026 [1212.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4887].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [192] O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Kong and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Vaidya, tan beta enhanced contributions to b → s + γ in SUSY without R-parity, hep-ph/0411165.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [193] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='-G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Xu, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='-M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Wang and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='-D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Yang, Probe R-parity violating supersymmetry effects in B → K∗ℓ+ℓ− and Bs → ℓ+ℓ−decays, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D 74 (2006) 114019 [hep-ph/0610338].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [194] ATLAS collaboration, Searches for lepton-flavour-violating decays of the Higgs boson in √s = 13 TeV pp collisions with the ATLAS detector, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' B 800 (2020) 135069 [1907.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='06131].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [195] CMS collaboration, Search for lepton-flavor violating decays of the Higgs boson in the µτ and eτ final states in proton-proton collisions at √s = 13 TeV, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D 104 (2021) 032013 [2105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='03007].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [196] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Frank, Bilinear R-parity violation parameters from µ → eγ, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D 62 (2000) 015006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [197] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='-m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Cheung and O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Kong, µ → eγ from supersymmetry without R parity, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D 64 (2001) 095007 [hep-ph/0101347].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [198] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Carvalho, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Gomez and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Romao, Charged lepton flavor violation in supersymmetry with bilinear R-parity violation, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D 65 (2002) 093013 [hep-ph/0202054].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [199] BaBar collaboration, Searches for Lepton Flavor Violation in the Decays τ ± → e±γ and τ ± → µ±γ, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 104 (2010) 021802 [0908.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2381].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' – 61 – [200] MEG collaboration, Search for the lepton flavour violating decay µ+ → e+γ with the full dataset of the MEG experiment, Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' C 76 (2016) 434 [1605.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='05081].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [201] SINDRUM collaboration, Search for the Decay µ+ → e+e+e−, Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' B 299 (1988) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [202] SINDRUM II collaboration, A Search for muon to electron conversion in muonic gold, Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' C 47 (2006) 337.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [203] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Ivanov, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Simonovi´c and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Zaldarriaga, Cosmological Parameters and Neutrino Masses from the Final Planck and Full-Shape BOSS Data, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D 101 (2020) 083504 [1912.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='08208].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [204] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Kobakhidze, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Talia and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Wu, Probing the MSSM explanation of the muon g-2 anomaly in dark matter experiments and at a 100 TeV pp collider, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D 95 (2017) 055023 [1608.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='03641].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [205] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Hundi, Constraints from neutrino masses and muon (g-2) in the bilinear R-parity violating supersymmetric model, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D 83 (2011) 115019 [1101.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2810].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [206] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Aoyama et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=', The anomalous magnetic moment of the muon in the Standard Model, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 887 (2020) 1 [2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='04822].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [207] Muon g-2 collaboration, Final Report of the Muon E821 Anomalous Magnetic Moment Measurement at BNL, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D 73 (2006) 072003 [hep-ex/0602035].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [208] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Chakraborti, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Heinemeyer and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Saha, The new “MUON G-2” result and supersymmetry, Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' C 81 (2021) 1114 [2104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='03287].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [209] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Badziak and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Sakurai, Explanation of electron and muon g − 2 anomalies in the MSSM, JHEP 10 (2019) 024 [1908.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='03607].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [210] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Domingo and U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Ellwanger, Constraints from the Muon g-2 on the Parameter Space of the NMSSM, JHEP 07 (2008) 079 [0806.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0733].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [211] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Wainwright, CosmoTransitions: Computing Cosmological Phase Transition Temperatures and Bubble Profiles with Multiple Fields, Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 183 (2012) 2006 [1109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='4189].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [212] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Linde, Decay of the False Vacuum at Finite Temperature, Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' B 216 (1983) 421.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [213] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Grojean and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Servant, Gravitational Waves from Phase Transitions at the Electroweak Scale and Beyond, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D 75 (2007) 043507 [hep-ph/0607107].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [214] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Affleck, Quantum Statistical Metastability, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 46 (1981) 388.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [215] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Linde, On the Vacuum Instability and the Higgs Meson Mass, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' B 70 (1977) 306.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [216] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Kamionkowski, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Kosowsky and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Turner, Gravitational radiation from first order phase transitions, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D 49 (1994) 2837 [astro-ph/9310044].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [217] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Kehayias and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Profumo, Semi-Analytic Calculation of the Gravitational Wave Signal From the Electroweak Phase Transition for General Quartic Scalar Effective Potentials, JCAP 03 (2010) 003 [0911.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0687].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [218] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Nicolis, Relic gravitational waves from colliding bubbles and cosmic turbulence, Class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Quant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Grav.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 21 (2004) L27 [gr-qc/0303084].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' – 62 – [219] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Ellis, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Lewicki and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' No, Gravitational waves from first-order cosmological phase transitions: lifetime of the sound wave source, JCAP 07 (2020) 050 [2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='07360].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [220] DES collaboration, Dark Energy Survey Year 1 Results: A Precise H0 Estimate from DES Y1, BAO, and D/H Data, Mon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Roy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 480 (2018) 3879 [1711.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='00403].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [221] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Jinno and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Takimoto, Gravitational waves from bubble collisions: An analytic derivation, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D 95 (2017) 024009 [1605.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='01403].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [222] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Dine, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Leigh, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Huet, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Linde and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Linde, Towards the theory of the electroweak phase transition, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D 46 (1992) 550 [hep-ph/9203203].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [223] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Ignatius, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Kajantie, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Kurki-Suonio and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Laine, The growth of bubbles in cosmological phase transitions, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D 49 (1994) 3854 [astro-ph/9309059].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [224] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Moore and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Prokopec, How fast can the wall move?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' A Study of the electroweak phase transition dynamics, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D 52 (1995) 7182 [hep-ph/9506475].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [225] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Moore and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Prokopec, Bubble wall velocity in a first order electroweak phase transition, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 75 (1995) 777 [hep-ph/9503296].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [226] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Moore, Electroweak bubble wall friction: Analytic results, JHEP 03 (2000) 006 [hep-ph/0001274].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [227] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Cline and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Kainulainen, Electroweak baryogenesis at high bubble wall velocities, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D 101 (2020) 063525 [2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='00568].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [228] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Dorsch, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Huber and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Konstandin, A sonic boom in bubble wall friction, JCAP 04 (2022) 010 [2112.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='12548].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [229] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Dorsch, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Huber and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Konstandin, On the wall velocity dependence of electroweak baryogenesis, JCAP 08 (2021) 020 [2106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='06547].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [230] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Hindmarsh, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Huber, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rummukainen and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Weir, Gravitational waves from the sound of a first order phase transition, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 112 (2014) 041301 [1304.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='2433].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [231] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Hindmarsh, Sound shell model for acoustic gravitational wave production at a first-order phase transition in the early Universe, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 120 (2018) 071301 [1608.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='04735].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [232] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Hindmarsh, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Huber, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rummukainen and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Weir, Shape of the acoustic gravitational wave power spectrum from a first order phase transition, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D 96 (2017) 103520 [1704.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='05871].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [233] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='-K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Guo, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Sinha, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Vagie and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' White, Phase Transitions in an Expanding Universe: Stochastic Gravitational Waves in Standard and Non-Standard Histories, JCAP 01 (2021) 001 [2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='08537].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [234] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Nakayama and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Yokoyama, Gravitational Wave Background and Non-Gaussianity as a Probe of the Curvaton Scenario, JCAP 01 (2010) 010 [0910.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0715].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [235] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Caprini, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Durrer and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Servant, The stochastic gravitational wave background from turbulence and magnetic fields generated by a first-order phase transition, JCAP 12 (2009) 024 [0909.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='0622].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [236] LIGO Scientific collaboration, Advanced LIGO: The next generation of gravitational wave detectors, Class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Quant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Grav.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' 27 (2010) 084006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [237] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Kosowsky, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Turner and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Watkins, Gravitational radiation from colliding vacuum bubbles, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D 45 (1992) 4514.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' – 63 – [238] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Curtin, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Meade and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Ramani, Thermal Resummation and Phase Transitions, Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' C 78 (2018) 787 [1612.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='00466].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [239] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Athron, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Balazs, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Fowlie, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Pozzo, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' White and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Zhang, Strong first-order phase transitions in the NMSSM - a comprehensive survey, JHEP 11 (2019) 151 [1908.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content='11847].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [240] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Carrington, The Effective potential at finite temperature in the Standard Model, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D 45 (1992) 2933.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' [241] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Comelli and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Espinosa, Bosonic thermal masses in supersymmetry, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' D 55 (1997) 6253 [hep-ph/9606438].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} +page_content=' – 64 –' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1dE4T4oBgHgl3EQfaAyc/content/2301.05061v1.pdf'} diff --git a/29E2T4oBgHgl3EQf5whX/vector_store/index.faiss b/29E2T4oBgHgl3EQf5whX/vector_store/index.faiss new file mode 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a/BdE1T4oBgHgl3EQfDgNt/content/tmp_files/2301.02878v1.pdf.txt b/BdE1T4oBgHgl3EQfDgNt/content/tmp_files/2301.02878v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..51e6c7ed4e567fd859e19b586c176f62978f7828 --- /dev/null +++ b/BdE1T4oBgHgl3EQfDgNt/content/tmp_files/2301.02878v1.pdf.txt @@ -0,0 +1,538 @@ +arXiv:2301.02878v1 [cs.IT] 7 Jan 2023 +Abstract Huffman Coding and +PIFO Tree Embeddings +Keri D’Angelo∗ +Dexter Kozen† +Cornell University +Computer Science Department +Ithaca, New York 14853-7501, USA +∗kd349@cornell.edu +†kozen@cs.cornell.edu +January 10, 2023 +Abstract +Algorithms for deriving Huffman codes and the recently developed algorithm for +compiling PIFO trees to trees of fixed shape [1] are similar, but work with different +underlying algebraic operations. In this paper, we exploit the monadic structure of +prefix codes to create a generalized Huffman algorithm that has these two applications +as special cases. +1 +Introduction +Huffman codes translate letters from a fixed alphabet to d-ary codewords, achieving optimal +compression for a given frequency distribution of letters. There is a well-known greedy +algorithm for producing Huffman codes from a given distribution (see [2]). +A new data structure called a PIFO tree (priority-in first-out) has recently been pro- +posed for implementing a wide range of packet scheduling algorithms in programmable +network routers [3, 4]. A PIFO tree is a tree of priority queues. Currently, most routers +support just a few scheduling algorithms such as strict priority or weighted fair queueing, +which are baked into the hardware. The schedulers can be configured to some extent, but +it is generally not possible to implement more sophisticated scheduling algorithms that +require reordering of already queued packets. This is exactly what PIFO trees permit. It +seems likely that PIFOs will be supported on network devices in the near future. +Some researchers have already begun to explore how the PIFO abstraction can be em- +ulated on conventional routers [4]. In very recent work [1], it was shown how to translate +an algorithm designed for a PIFO tree of arbitrary shape to one that uses a PIFO tree of +fixed shape, perhaps a complete d-ary tree that might be implemented in hardware, with +negligible performance degradation. +1 + +The embedding algorithm is greedy and very similar to the Huffman algorithm, ex- +cept that it is based on different algebraic operations. For Huffman coding, one wishes to +choose a d-ary prefix code C so as to minimize the value of ∑x∈C |x| · r(x), where r(x) is +the frequency of the letter assigned to the codeword x. This minimizes the entropy of the +resulting code. For PIFO trees, one wishes to minimize maxx∈C |x| + r(x), where r(x) is the +height of a subtree. This minimizes the height of the resulting d-ary tree and determines +whether an embedding is at all possible. +This similarity leads us to seek a unified axiomatic treatment that is parametric in the +algebraic operations and that can be instantiated to produce both applications as special +cases. Our treatment exploits the monadic structure of prefix codes to obtain an abstract +formulation of the problem and its solution. We identify sufficient conditions for our ab- +stract algorithm to produce optimal solutions, where the meaning of optimal is also para- +metric in the instantiation. +We state axioms that are sufficient for optimality in §3. The algorithm is presented in +§4 and its correctness proved in §5. The two applications of Huffman codes and PIFO trees +are derived in §6. +2 +Background +We assume familiarity with the basic category-theoretic concepts of category, functor, and +natural transformation. Our exposition is based on the concepts of monad and Eilenberg- +Moore algebra; we briefly review the definitions here. For a more thorough introduction, +we refer the reader to [5–8]. +Monads are heavily used in functional programming to model the augmentation of a +computation with extra structure [9–11]. Formally, a monad on a category C is a triple +(T, η, µ), where T : C → C is an endofunctor on C and η : I → T and µ : T2 → T are natural +transformations, called the unit and multiplication respectively, such that for all objects X, +the following diagrams commute: +T3X +T2X +T2X +TX +µTX +TµX +µX +µX +TX +T2X +T2X +TX +ηTX +TηX +µX +µX +idTX +Typical examples of monads are +• the list monad, in which ηX(a) = [a], the singleton list containing a, and +µX([[a11, . . . , a1k1], . . . , [an1, . . . , ankn]]) = [a11, . . . , a1k1, . . . , an1, . . . , ankn], +the list flattening operation; +2 + +• the powerset monad, in which ηX(a) = {a}, the singleton set containing a, and µX(A) = +� A, the operation that takes a set of subsets of X to its union. +Given a monad (T, η, µ) on a category C, an Eilenberg-Moore algebra for (T, η, µ) is a pair +(X, γ), where X is an object of C and γ : TX → X is a morphism of C, called the structure +map of the algebra, such that the following diagrams commute: +T2X +TX +TX +X +Tγ +µX +γ +γ +X +TX +X +ηX +γ +idX +A morphism of Eilenberg-Moore algebras is a morphism of C that commutes with the structure +maps. That is, if (X, γ) and (Y, δ) are two algebras and h : X → Y is a morphism of C, then +h is a morphism of algebras h : (X, γ) → (Y, δ) if the following diagram commutes: +TX +TY +X +Y +Th +γ +h +δ +The Eilenberg-Moore algebras for (T, η, µ) and their morphisms form the Eilenberg-Moore +category over the monad T. The Eilenberg-Moore category for the list monad is the cat- +egory of monoids and monoid homomorphisms. The Eilenberg-Moore category for the +powerset monad is the category of complete upper semilattices and semilattice homomor- +phisms. +In our application, we will focus on the monad of d-ary prefix codes on the category Set +of sets and set functions. +3 +Axioms +In this section, we state the axioms that are sufficient for the optimality of our generalized +Huffman algorithm. +Recall that a prefix code over a fixed d-ary alphabet Σ is a set of finite-length words over +Σ whose elements are pairwise incomparable with respect to the prefix relation. A prefix +code C is exhaustive if every infinite d-ary string has a prefix in C. As a consequence of +K¨onig’s lemma, every exhaustive prefix code over a finite alphabet is finite, but not every +finite prefix code is exhaustive. +Let C : Set → Set be an endofunctor in which +• CX is the set of pairs (C, r) such that C is a prefix code over a d-ary alphabet for some +arbitrary but fixed d ≥ 2 and r : C → X, and +3 + +• for h : X → Y, Ch : CX → CY with Ch(C, r) = (C, h ◦ r). +The functor C carries a natural monad structure with unit η : I → C and multiplication +µ : C2 → C defined by: for a ∈ X and (C, r) ∈ C2X with r(x) = (Cx, rx), +ηX(a) = ({ε}, ε �→ a) +µX(C, r) = ({xy | x ∈ C, y ∈ Cx}, xy �→ rx(y)). +The map xy �→ rx(y) is well defined, as the string xy can be uniquely split into x ∈ C and +y ∈ Cx because C is a prefix code. +For example, consider the prefix codes C = {0, 10, 110, 111} and C0 = C10 = C110 = +C111 = {00, 11} over the binary alphabet {0, 1}. The code C is exhaustive but the others +are not. Let +r0(00) = 2 +r10(00) = 4 +r110(00) = 6 +r111(00) = 8 +r0(11) = 3 +r10(11) = 5 +r110(11) = 7 +r111(11) = 9 +r(0) = (C0, r0) +r(10) = (C10, r10) +r(110) = (C110, r110) +r(111) = (C111, r111). +Then (C0, r0), (C10, r10), (C110, r110), (C111, r111) ∈ CN and (C, r) ∈ C2N, and µN(C, r) = +(C′, r′) ∈ CN, where +C′ = {000, 011, 1000, 1011, 11000, 11011, 11100, 11111} +r′(000) = 2, r′(011) = 3, r′(1000) = 4, r′(1011) = 5, +r′(11000) = 6, r′(11011) = 7, r′(11100) = 8, r′(11111) = 9. +Suppose there is a fixed Eilenberg-Moore algebra (W, w) with w : CW → W. We call +the elements of W weights and (W, w) a weighting. If (C, r) ∈ CW, then thinking of the +elements of C as a tree, the map r : C → W assigns a weight to each leaf of the tree, and +the map w tells how to assign a weight to the object (C, r) based on the leaf weights r. +To define a notion of optimality, we assume that W is totally preordered by ≤; that is, +≤ is reflexive and transitive, and for all x, y ∈ W, either x ≤ y or y ≤ x (or both). Smaller +values of W in the order ≤ are considered better. We write x ≡ y if both x ≤ y and y ≤ x. +Suppose further that we have a preorder on CW, also denoted ≤, satisfying the following +properties. +(i) If f : C → D is bijective and length-nondecreasing, and if r ≤ s ◦ f pointwise, then +(C, r) ≤ (D, s). This says that longer codewords or larger leaf values cannot cause a +decrease in the order ≤. +(ii) (Exchange property) If r(x) ≤ r(y), |x| ≤ |y|, and +s(z) = + + + + + +r(x), +if z = y, +r(y), +if z = x, +r(z), +if z ∈ C \ {x, y}, +then (C, s) ≤ (C, r). That is, it never hurts to swap a larger element deeper in the tree +with a smaller element higher in the tree. +4 + +(iii) The monad structure maps ηW : W → CW and µW : C2W → CW are monotone with +respect to ≤, where ≤ on C2W is defined by: +(C, r) ≤ (D, s) ⇔ Cw(C, r) ≤ Cw(D, s). +Some special cases of (i) are +• If f : C → D is bijective and length-nondecreasing, then (C, s ◦ f) ≤ (D, s). Thus +lengthening codewords cannot cause ≤ to decrease. +• If f : C → D is bijective and length-preserving, then (C, s ◦ f) ≡ (D, s). This says +that the order ≤ on trees depends only on the lengths of the codewords in C, not on +the actual codewords themselves. +• If r, s : C → W and r ≤ s pointwise, then (C, r) ≤ (C, s). Thus larger leaf values +cannot cause ≤ to decrease. +We assume these properties hold for the algorithm described in the next section. +For (C, r), (D, s) ∈ CW, let us write (C, r) ∼ (D, s) if the multisets of weights repre- +sented by the two objects are the same; that is, there is a bijective function f : C → D such +that r = s ◦ f. A tree (C, r) ∈ CW is defined to be optimal (for its multiset of weights) if (C, r) +is ≤-minimum in its ∼-class; that is, (C, r) ≤ (D, s) for all (D, s) such that (C, r) ∼ (D, s). +We will give two detailed examples in §6. +4 +Algorithm +Suppose we are given a multiset M of weights in W, |M| ≥ 2. We would like to find an +optimal tree for this multiset of weights. The following is a recursive algorithm to find +such an optimal tree. +1. Say there are n ≥ 2 elements in M. Let k ∈ {2, . . . , d} such that n ≡ k mod (d − 1). +Let a0, . . . , ak−1 be the k elements of least weight. Form the object +({0, 1, . . . , k − 1}, i �→ ai) ∈ CW. +If there are no other elements of M, return that object. +2. Otherwise, let +M′ = {({0, 1, . . . , k − 1}, i �→ ai)} ∪ {ηW(a) | a ∈ M \ {a0, . . . , ak−1}}, +a multiset of n − k + 1 < n elements of CW. +3. Recursively call the algorithm at step 1 with M′′ = {w(E, t) | (E, t) ∈ M′}, a multiset +of elements of W. This returns a tree (D, s) of type CW that is optimal for M′′. The +bijective map s : D → M′′ factors as w ◦ s′ for some bijective s′ : D → M′, and +(D, s′) ∈ C2W with Cw(D, s′) = (D, w ◦ s′) = (D, s). Flatten this to µW(D, s′) ∈ CW +and return that value. +5 + +Note that the number of items combined in step 1 will be d in all recursive calls except +possibly the first. This is because in every step, if k ∈ {2, 3, . . . , d}, then after that step +the number of remaining elements will be (c(d − 1) + k) − k + 1 = c(d − 1) + 1, which +is congruent to d mod d − 1, so d elements will be taken in the next step. But from that +point on, it is an invariant of the recursion that the number of elements remaining is 1 mod +d − 1, since in each step we remove d elements and add one back, decreasing the number +by d − 1. +5 +Correctness +In this section, we prove the correctness of the algorithm, making use of the following +lemma. +Lemma 1. Let k ∈ {2, 3, . . . , d} and k ≡ |M| mod (d − 1). Let a0, . . . , ak−1 be the k elements of +M of least weight, listed in nondecreasing order of weight. There is an optimal tree in CW in which +a0, . . . , ak−1 are sibling leaves at the deepest level and have no other siblings. +Proof. Let (C, r) ∈ CW be optimal. Axiom (i) allows us to transform (C, r) so that there +are no deficient nodes (nodes with fewer than d children) at any level except the deepest, +and only one deficient node at the deepest level. Thus we can assume without loss of +generality that there are k elements x0, . . . , xk−1 ∈ C of maximum length n in C with a +common prefix of length n − 1, and no other y ∈ C has that prefix. Say the x0, . . . , xk−1 are +listed in nondecreasing order of r(xi); that is, r(xi) ≤ r(xj) for all 0 ≤ i ≤ j ≤ k − 1. Let +y0, . . . , yk−1 ∈ C such that r(yi) = ai. Since the ai are minimal, r(yi) ≤ r(xi). Because the +|xi| are of maximum length, |yi| ≤ |xi|. Now we can swap using axiom (ii). Let +s(z) = + + + + + +r(xi), +if z = yi, +r(yi), +if z = xi, +r(z), +otherwise. +Then (C, s) ≤ (C, r). But since (C, r) was optimal, (C, r) ≡ (C, s) and (C, s) is also optimal. +Theorem 2. The algorithm of §4 produces an optimal tree. +Proof. By induction on n. The basis is n ≤ d, in which case the result is straightforward. +Suppose that we have a multiset M of n > d elements of W. Let (C, r) be an optimal tree +for M. Let k ∈ {2, 3, . . . , d} be congruent mod d − 1 to |M|. Let a0, . . . , ak−1 be the k smallest +elements of M. By Lemma 1, we can assume without loss of generality that a0, . . . , ak−1 are +siblings and occur at maximum depth in (C, r), so there exist strings x0, x1, . . . , x(k − 1) ∈ +C of maximum length with a common prefix x and r(xi) = ai. Remove the strings xi from +C and replace them with x. Call the resulting set C′. For z ∈ C′, let +r′(z) = +� +({0, 1, . . . , k − 1}, i �→ ai), +if z = x, +ηW(r(z)), +otherwise. +6 + +Then (C′, r′) ∈ C2W and (C, r) = µW(C′, r′). The multiset of values of r′ is just the M′ of +step 2 of the algorithm. +The algorithm will form the multiset +M′′ = {w(E, t) | (E, t) ∈ M′} = {w(r′(z)) | z ∈ C′} +and recursively call with these weights. By the induction hypothesis, the return value will +be a tree (D, s) ∈ CW that is optimal for M′′, thus (D, s) ≤ (C′, w ◦ r′), and the bijective +map s : D → M′′ factors as s = w ◦ r′ ◦ f for some bijective f : D → C′. Let s′ = r′ ◦ f. By +axiom (iii), +Cw(D, s′) = (D, w ◦ s′) = (D, s) ≤ (C′, w ◦ r′) = Cw(C′, r′), +therefore (D, s′) ≤ (C′, r′), and since µW is monotone, +µW(D, s′) ≤ µW(C′, r′) = (C, r). +As (C, r) was optimal, so is µW(D, s′), and this is the value returned by the algorithm. +6 +Applications +By choosing two specific weightings (W, w) and defining the ordering relations ≤ appro- +priately, we can recover two special cases of this algorithm. +6.1 +Huffman coding +Our first application is Huffman codes. Here we wish to minimize the expected length of +variable-length codewords, given frequencies of the letters to be coded. For this applica- +tion, we take W = R+ = {a ∈ R | a ≥ 0} with weighting +w(C, r) = ∑ +x∈C +r(x). +Recall that for a ∈ W and (C, r) ∈ C2W with r(x) = (Cx, rx), +ηW(a) = ({ε}, ε �→ a) +µW(C, r) = ({xy | x ∈ C, y ∈ Cx}, xy �→ rx(y)). +Then (W, w) is an Eilenberg-Moore algebra for the monad (C, µ, η), as +w(ηW(a)) = w({ε}, ε �→ a) = ∑ +x∈{ε} +(ε �→ a)(x) = a, +w(µW(C, r)) = ∑ +x∈C ∑ +y∈Cx +rx(y) = ∑ +x∈C +w(Cx, rx) += ∑ +x∈C +w(r(x)) = w(C, w ◦ r) = w(Cw(C, r)). +In addition, let us define α : CW → W by +α(C, r) = ∑ +x∈C +|x| · r(x). +7 + +Lemma 3. +α(ηW(a)) = 0 +α(µW(C, r)) = α(C, w ◦ r) + w(C, α ◦ r). +Proof. +α(ηW(a)) = α({ε}, ε �→ a) = ∑ +x∈{ε} +|x| · (ε �→ a)(x) = |ε| · a = 0, +α(µW(C, r)) = α({xy | x ∈ C, y ∈ Cx}, xy �→ rx(y)) += ∑ +x∈C ∑ +y∈Cx +|xy| · rx(y) = ∑ +x∈C +|x| ∑ +y∈Cx +rx(y) + ∑ +x∈C ∑ +y∈Cx +|y| · rx(y) += ∑ +x∈C +|x| · w(Cx, rx) + ∑ +x∈C +α(Cx, rx) = ∑ +x∈C +|x| · w(r(x)) + ∑ +x∈C +α(r(x)) += α(C, w ◦ r) + w(C, α ◦ r). +Note that α and w agree on trees of depth one: +w({0, 1, . . . , k − 1}, i �→ ai) = +k−1 +∑ +i=0 +ai, +α({0, 1, . . . , k − 1}, i �→ ai) = +k−1 +∑ +i=0 +|i| · ai = +k−1 +∑ +i=0 +ai, +where |i| refers to the length of i as a string, which in this case is 1. +The map α is related to the Shannon entropy H. If r(x) = d−|x|, the probability of a +d-ary codeword x under the uniform distribution on a d-ary alphabet, then +H(C, r) = ∑ +x∈C +−d−|x| log d−|x| = ∑ +x∈C +|x| · d−|x| log d = α(C, r) log d, +so α(C, r) = H(C, r)/ log d. +To use the algorithm in §4, we need an order ≤ on CW. Define (C, r) ≤ (D, s) if (C, r) ∼ +(D, s), that is, there is a bijective map f : C → D such that r = s ◦ f, and +α(C, r) ≤ α(D, s). +Note that if (C, r) ≤ (D, s), then +w(C, r) = ∑ +x∈C +r(x) = ∑ +x∈C +s( f(x)) = ∑ +y∈D +s(y) = w(D, s). +According to axiom (iii), for (C, r), (D, s) ∈ C2W, +(C, r) ≤ (D, s) ⇔ Cw(C, r) ≤ Cw(D, s) +⇔ α(Cw(C, r)) ≤ α(Cw(D, s)) +⇔ α(C, w ◦ r) ≤ α(D, w ◦ s). +(1) +Also, if (C, r) ≤ (D, s) in C2W, then +w(C, α ◦ r) = ∑ +x∈C +α(r(x)) = ∑ +x∈C +α(s( f(x))) = ∑ +y∈D +α(s(y)) = w(D, α ◦ s). +(2) +8 + +Lemma 4. µW : C2W → CW and ηW : W → CW are monotone with respect to ≤. +Proof. For ηW, suppose a, b ∈ W and a ≤ b. By Lemma 3, +α(ηW(a)) = 0 = α(ηW(b)) +w(ηW(a)) = a ≤ b = w(ηW(b)). +For µW, suppose (C, r), (D, s) ∈ C2W and (C, r) ≤ (D, s). By Lemma 3, (1), and (2), +α(µW(C, r)) = α(C, w ◦ r) + w(C, α ◦ r) +≤ α(D, w ◦ s) + w(D, α ◦ s) = α(µW(D, s)). +Theorem 5. The algorithm in §4 for the algebra (R+, w) and ordering relation ≤ defined by α is +equivalent to Huffman’s algorithm and produces an optimal Huffman code for a given multiset of +weights. +Proof. Take X ⊂ R+ to be a finite multiset and sort the set X in increasing order. For the +binary case of Huffman codes (the d-ary version follows the same way), we always choose +k = 2. For the first step, let a0, a1 ∈ X be the two smallest elements in the list. Form the +object ({0, 1}, i �→ ai) ∈ CX. In the case n = 2, this is the only remaining object in the list. +Otherwise, we combined them into one element with the sum of the weights of a0 and a1 +as the weight of the new element, exactly as the Huffman coding does. +For the case n > 2, there are remaining elements in the set X. Take all remaining +a ∈ X\{a0, a1} and replace a by ηX(a) ∈ CX. We are left with n − 1 elements of type CX. +If we recursively call the algorithm in step 1, we are continually combining the least two +elements in the remaining set with the elements weighted by w. Note by the weighting +w, w(ηX(a)) = a and on elements in CX, w takes the sum of r(x)′s, exactly as Huffman +coding does. Finally, this leaves us with a tree in C2X where leaves have weights of the +form ηX(ai). Denote this tree by (D, s). Taking µX(D, S) gives our desired tree in CX. +6.2 +PIFO trees +PIFO trees were introduced in [3] as a model for programmable packet schedulers. In the +recent work of [1], further work was done on PIFO trees giving a semantics that allows +for certain embedding algorithms. The notion of a homomorphic embedding was defined for +the purpose determining when a PIFO tree could be represented by another PIFO tree and +for finding an embedding if so. The embedding algorithm we consider takes an arbitrary +PIFO tree and embeds it into a d-ary tree. This becomes a special case of the algorithm of +§4, where we choose w in the weighting (W, w) to minimize the height of the target d-ary +tree into which the source tree can embed. +For this application, we take W = N with weighting +w(C, r) = max +x∈C |x| + r(x). +This gives an Eilenberg-Moore algebra (W, w) for the monad (C, µ, η). For a ∈ W and +(C, r) ∈ C2W with r(x) = (Cx, rx), as before we have +ηW(a) = ({ε}, ε �→ a) +µW(C, r) = ({xy | x ∈ C, y ∈ Cx}, xy �→ rx(y)), +9 + +so +w(ηW(a)) = w({ε}, ε �→ a) = max +x∈{ε} |x| + (ε �→ a)(x) = |ε| + a = a, +w(µW(C, r)) = w({xy | x ∈ C, y ∈ Cx}, xy �→ rx(y)) = max +x∈C max +y∈Cx |xy| + rx(y) += max +x∈C max +y∈Cx |x| + |y| + rx(y) = max +x∈C |x| + max +y∈Cx |y| + rx(y) += max +x∈C |x| + w(Cx, rx) = max +x∈C |x| + w(r(x)) += w(C, w ◦ r) = w(Cw(C, r)). +For (C, r), (D, s) ∈ CW, let us define (C, r) ≤ (D, s) if there is a bijective function +f : C → D such that r = s ◦ f and +w(C, r) ≤ w(D, s). +Lemma 6. µW : C2W → CW and ηW : W → CW are monotone with respect to ≤. +Proof. For ηW, if a ≤ b, then w(ηW(a)) = a ≤ b = w(ηW(b)). +For µW, suppose (C, r), (D, s) ∈ C2W and (C, r) ≤ (D, s). According to axiom (iii), +(C, r) ≤ (D, s) ⇔ Cw(C, r) ≤ Cw(D, s) +⇔ w(Cw(C, r)) ≤ w(Cw(D, s)). +Then +w(µW(C, r)) = w(Cw(C, r)) ≤ w(Cw(D, s)) = w(µW(D, s)). +Theorem 7. The algorithm of §4 for the algebra (N, w) and ordering relation ≤ defined by w is +equivalent to determining whether an embedding of a PIFO tree in a bounded d-ary tree exists and +finding the embedding if so. +7 +Conclusion +We have presented a generalized Huffman algorithm and shown that two known algo- +rithms, Huffman codes and embedding of PIFOs trees, can be derived as special cases. +The PIFO embedding algorithm was introduced in [1] and observed to be very similar to +the usual combinatorial algorithm for optimal Huffman codes, albeit based on a different +algebraic structure. This suggested the common generalization presented in this paper. +Our generalized algorithm exploits the monadic structure of prefix codes, which al- +lows a more algebraic treatment of the Huffman algorithm than the usual combinatorial +approaches. The two applications fit naturally in the categorical setting by choosing spe- +cific Eilenberg-Moore algebras for each one. It is possible that other greedy algorithms +might fit into this framework as well. +10 + +References +[1] Anshuman +Mohan, +Yunhe +Liu, +Nate +Foster, +Tobias +Kapp´e, +and +Dex- +ter +Kozen, +“Formal +abstractions +for +packet +scheduling,” +Tech. +Rep. http://arxiv.org/abs/2211.11659, Cornell University, November 2022. +[2] Thomas M. Cover and Joy A. Thomas, Elements of Information Theory, Wiley, second +edition, 2006. +[3] Anirudh Sivaraman, Suvinay Subramanian, Mohammad Alizadeh, Sharad Chole, +Shang-Tse Chuang, Anurag Agrawal, Hari Balakrishnan, Tom Edsall, Sachin Katti, +and Nick McKeown, “Programmable packet scheduling at line rate,” in SIGCOMM, +2016. +[4] Albert Gran Alcoz, Alexander Dietm¨uller, and Laurent Vanbever, “SP-PIFO: Approx- +imating push-in first-out behaviors using strict-priority queues,” in NSDI, 2020. +[5] Andrea Asperti and Giuseppe Longo, Categories, Types and Structures: An introduction +to category theory for the working computer scientist, Foundations of Computing. MIT +Press, 1991. +[6] Michael Barr and Charles Wells, Toposes, Triples and Theories, vol. 278 of Grundlehren +der mathematischen Wissenschaften, Springer, 2013. +[7] Michael Barr and Charles Wells, Category Theory for Computing Science, Prentice Hall, +1990. +[8] Jiˇr´ı Ad´amek, Horst Herrlich, and George E. Strecker, Abstract and concrete categories, +Dover Publications, 2009. +[9] Eugenio Moggi, “Notions of computation and monads,” Inf. and Comp., vol. 93, no. 1, +pp. 55–92, 1991. +[10] Philip Wadler, “Comprehending monads,” Mathematical Structures in Computer Sci- +ence, vol. 2, pp. 461–493, 1992. +[11] Philip Wadler, “Monads for functional programming,” in Advanced Functional Pro- +gramming: 1st Int. School on Advanced Functional Programming Techniques, Johan Jeur- +ing and Erik Meijer, Eds., vol. 925 of Lecture Notes in Computer Science, pp. 24–52. +Springer-Verlag, 1995. +11 + diff --git a/BdE1T4oBgHgl3EQfDgNt/content/tmp_files/load_file.txt b/BdE1T4oBgHgl3EQfDgNt/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..2386e4446212c7a36175a7d7a5c19d1c607ef714 --- /dev/null +++ b/BdE1T4oBgHgl3EQfDgNt/content/tmp_files/load_file.txt @@ -0,0 +1,311 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf,len=310 +page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content='02878v1 [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content='IT] 7 Jan 2023 Abstract Huffman Coding and PIFO Tree Embeddings Keri D’Angelo∗ Dexter Kozen† Cornell University Computer Science Department Ithaca, New York 14853-7501, USA ∗kd349@cornell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content='edu †kozen@cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content='cornell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content='edu January 10, 2023 Abstract Algorithms for deriving Huffman codes and the recently developed algorithm for compiling PIFO trees to trees of fixed shape [1] are similar, but work with different underlying algebraic operations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' In this paper, we exploit the monadic structure of prefix codes to create a generalized Huffman algorithm that has these two applications as special cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' 1 Introduction Huffman codes translate letters from a fixed alphabet to d-ary codewords, achieving optimal compression for a given frequency distribution of letters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' There is a well-known greedy algorithm for producing Huffman codes from a given distribution (see [2]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' A new data structure called a PIFO tree (priority-in first-out) has recently been pro- posed for implementing a wide range of packet scheduling algorithms in programmable network routers [3, 4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' A PIFO tree is a tree of priority queues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Currently, most routers support just a few scheduling algorithms such as strict priority or weighted fair queueing, which are baked into the hardware.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' The schedulers can be configured to some extent, but it is generally not possible to implement more sophisticated scheduling algorithms that require reordering of already queued packets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' This is exactly what PIFO trees permit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' It seems likely that PIFOs will be supported on network devices in the near future.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Some researchers have already begun to explore how the PIFO abstraction can be em- ulated on conventional routers [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' In very recent work [1], it was shown how to translate an algorithm designed for a PIFO tree of arbitrary shape to one that uses a PIFO tree of fixed shape, perhaps a complete d-ary tree that might be implemented in hardware, with negligible performance degradation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' 1 The embedding algorithm is greedy and very similar to the Huffman algorithm, ex- cept that it is based on different algebraic operations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' For Huffman coding, one wishes to choose a d-ary prefix code C so as to minimize the value of ∑x∈C |x| · r(x), where r(x) is the frequency of the letter assigned to the codeword x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' This minimizes the entropy of the resulting code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' For PIFO trees, one wishes to minimize maxx∈C |x| + r(x), where r(x) is the height of a subtree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' This minimizes the height of the resulting d-ary tree and determines whether an embedding is at all possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' This similarity leads us to seek a unified axiomatic treatment that is parametric in the algebraic operations and that can be instantiated to produce both applications as special cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Our treatment exploits the monadic structure of prefix codes to obtain an abstract formulation of the problem and its solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' We identify sufficient conditions for our ab- stract algorithm to produce optimal solutions, where the meaning of optimal is also para- metric in the instantiation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' We state axioms that are sufficient for optimality in §3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' The algorithm is presented in §4 and its correctness proved in §5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' The two applications of Huffman codes and PIFO trees are derived in §6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' 2 Background We assume familiarity with the basic category-theoretic concepts of category, functor, and natural transformation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Our exposition is based on the concepts of monad and Eilenberg- Moore algebra;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' we briefly review the definitions here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' For a more thorough introduction, we refer the reader to [5–8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Monads are heavily used in functional programming to model the augmentation of a computation with extra structure [9–11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Formally, a monad on a category C is a triple (T, η, µ), where T : C → C is an endofunctor on C and η : I → T and µ : T2 → T are natural transformations, called the unit and multiplication respectively, such that for all objects X, the following diagrams commute: T3X T2X T2X TX µTX TµX µX µX TX T2X T2X TX ηTX TηX µX µX idTX Typical examples of monads are the list monad, in which ηX(a) = [a], the singleton list containing a, and µX([[a11, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' , a1k1], .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' , [an1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' , ankn]]) = [a11, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' , a1k1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' , an1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' , ankn], the list flattening operation;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' 2 the powerset monad, in which ηX(a) = {a}, the singleton set containing a, and µX(A) = � A, the operation that takes a set of subsets of X to its union.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Given a monad (T, η, µ) on a category C, an Eilenberg-Moore algebra for (T, η, µ) is a pair (X, γ), where X is an object of C and γ : TX → X is a morphism of C, called the structure map of the algebra, such that the following diagrams commute: T2X TX TX X Tγ µX γ γ X TX X ηX γ idX A morphism of Eilenberg-Moore algebras is a morphism of C that commutes with the structure maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' That is, if (X, γ) and (Y, δ) are two algebras and h : X → Y is a morphism of C, then h is a morphism of algebras h : (X, γ) → (Y, δ) if the following diagram commutes: TX TY X Y Th γ h δ The Eilenberg-Moore algebras for (T, η, µ) and their morphisms form the Eilenberg-Moore category over the monad T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' The Eilenberg-Moore category for the list monad is the cat- egory of monoids and monoid homomorphisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' The Eilenberg-Moore category for the powerset monad is the category of complete upper semilattices and semilattice homomor- phisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' In our application, we will focus on the monad of d-ary prefix codes on the category Set of sets and set functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' 3 Axioms In this section, we state the axioms that are sufficient for the optimality of our generalized Huffman algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Recall that a prefix code over a fixed d-ary alphabet Σ is a set of finite-length words over Σ whose elements are pairwise incomparable with respect to the prefix relation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' A prefix code C is exhaustive if every infinite d-ary string has a prefix in C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' As a consequence of K¨onig’s lemma, every exhaustive prefix code over a finite alphabet is finite, but not every finite prefix code is exhaustive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Let C : Set → Set be an endofunctor in which CX is the set of pairs (C, r) such that C is a prefix code over a d-ary alphabet for some arbitrary but fixed d ≥ 2 and r : C → X, and 3 for h : X → Y, Ch : CX → CY with Ch(C, r) = (C, h ◦ r).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' The functor C carries a natural monad structure with unit η : I → C and multiplication µ : C2 → C defined by: for a ∈ X and (C, r) ∈ C2X with r(x) = (Cx, rx), ηX(a) = ({ε}, ε �→ a) µX(C, r) = ({xy | x ∈ C, y ∈ Cx}, xy �→ rx(y)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' The map xy �→ rx(y) is well defined, as the string xy can be uniquely split into x ∈ C and y ∈ Cx because C is a prefix code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' For example, consider the prefix codes C = {0, 10, 110, 111} and C0 = C10 = C110 = C111 = {00, 11} over the binary alphabet {0, 1}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' The code C is exhaustive but the others are not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Let r0(00) = 2 r10(00) = 4 r110(00) = 6 r111(00) = 8 r0(11) = 3 r10(11) = 5 r110(11) = 7 r111(11) = 9 r(0) = (C0, r0) r(10) = (C10, r10) r(110) = (C110, r110) r(111) = (C111, r111).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Then (C0, r0), (C10, r10), (C110, r110), (C111, r111) ∈ CN and (C, r) ∈ C2N, and µN(C, r) = (C′, r′) ∈ CN, where C′ = {000, 011, 1000, 1011, 11000, 11011, 11100, 11111} r′(000) = 2, r′(011) = 3, r′(1000) = 4, r′(1011) = 5, r′(11000) = 6, r′(11011) = 7, r′(11100) = 8, r′(11111) = 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Suppose there is a fixed Eilenberg-Moore algebra (W, w) with w : CW → W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' We call the elements of W weights and (W, w) a weighting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' If (C, r) ∈ CW, then thinking of the elements of C as a tree, the map r : C → W assigns a weight to each leaf of the tree, and the map w tells how to assign a weight to the object (C, r) based on the leaf weights r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' To define a notion of optimality, we assume that W is totally preordered by ≤;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' that is, ≤ is reflexive and transitive, and for all x, y ∈ W, either x ≤ y or y ≤ x (or both).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Smaller values of W in the order ≤ are considered better.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' We write x ≡ y if both x ≤ y and y ≤ x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Suppose further that we have a preorder on CW, also denoted ≤, satisfying the following properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' (i) If f : C → D is bijective and length-nondecreasing, and if r ≤ s ◦ f pointwise, then (C, r) ≤ (D, s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' This says that longer codewords or larger leaf values cannot cause a decrease in the order ≤.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' (ii) (Exchange property) If r(x) ≤ r(y), |x| ≤ |y|, and s(z) = \uf8f1 \uf8f4 \uf8f2 \uf8f4 \uf8f3 r(x), if z = y, r(y), if z = x, r(z), if z ∈ C \\ {x, y}, then (C, s) ≤ (C, r).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' That is, it never hurts to swap a larger element deeper in the tree with a smaller element higher in the tree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' 4 (iii) The monad structure maps ηW : W → CW and µW : C2W → CW are monotone with respect to ≤, where ≤ on C2W is defined by: (C, r) ≤ (D, s) ⇔ Cw(C, r) ≤ Cw(D, s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Some special cases of (i) are If f : C → D is bijective and length-nondecreasing, then (C, s ◦ f) ≤ (D, s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Thus lengthening codewords cannot cause ≤ to decrease.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' If f : C → D is bijective and length-preserving, then (C, s ◦ f) ≡ (D, s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' This says that the order ≤ on trees depends only on the lengths of the codewords in C, not on the actual codewords themselves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' If r, s : C → W and r ≤ s pointwise, then (C, r) ≤ (C, s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Thus larger leaf values cannot cause ≤ to decrease.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' We assume these properties hold for the algorithm described in the next section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' For (C, r), (D, s) ∈ CW, let us write (C, r) ∼ (D, s) if the multisets of weights repre- sented by the two objects are the same;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' that is, there is a bijective function f : C → D such that r = s ◦ f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' A tree (C, r) ∈ CW is defined to be optimal (for its multiset of weights) if (C, r) is ≤-minimum in its ∼-class;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' that is, (C, r) ≤ (D, s) for all (D, s) such that (C, r) ∼ (D, s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' We will give two detailed examples in §6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' 4 Algorithm Suppose we are given a multiset M of weights in W, |M| ≥ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' We would like to find an optimal tree for this multiset of weights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' The following is a recursive algorithm to find such an optimal tree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Say there are n ≥ 2 elements in M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Let k ∈ {2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' , d} such that n ≡ k mod (d − 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Let a0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' , ak−1 be the k elements of least weight.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Form the object ({0, 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' , k − 1}, i �→ ai) ∈ CW.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' If there are no other elements of M, return that object.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Otherwise, let M′ = {({0, 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' , k − 1}, i �→ ai)} ∪ {ηW(a) | a ∈ M \\ {a0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' , ak−1}}, a multiset of n − k + 1 < n elements of CW.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Recursively call the algorithm at step 1 with M′′ = {w(E, t) | (E, t) ∈ M′}, a multiset of elements of W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' This returns a tree (D, s) of type CW that is optimal for M′′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' The bijective map s : D → M′′ factors as w ◦ s′ for some bijective s′ : D → M′, and (D, s′) ∈ C2W with Cw(D, s′) = (D, w ◦ s′) = (D, s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Flatten this to µW(D, s′) ∈ CW and return that value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' 5 Note that the number of items combined in step 1 will be d in all recursive calls except possibly the first.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' This is because in every step, if k ∈ {2, 3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' , d}, then after that step the number of remaining elements will be (c(d − 1) + k) − k + 1 = c(d − 1) + 1, which is congruent to d mod d − 1, so d elements will be taken in the next step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' But from that point on, it is an invariant of the recursion that the number of elements remaining is 1 mod d − 1, since in each step we remove d elements and add one back, decreasing the number by d − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' 5 Correctness In this section, we prove the correctness of the algorithm, making use of the following lemma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Let k ∈ {2, 3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' , d} and k ≡ |M| mod (d − 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Let a0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' , ak−1 be the k elements of M of least weight, listed in nondecreasing order of weight.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' There is an optimal tree in CW in which a0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' , ak−1 are sibling leaves at the deepest level and have no other siblings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Let (C, r) ∈ CW be optimal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Axiom (i) allows us to transform (C, r) so that there are no deficient nodes (nodes with fewer than d children) at any level except the deepest, and only one deficient node at the deepest level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Thus we can assume without loss of generality that there are k elements x0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' , xk−1 ∈ C of maximum length n in C with a common prefix of length n − 1, and no other y ∈ C has that prefix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Say the x0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' , xk−1 are listed in nondecreasing order of r(xi);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' that is, r(xi) ≤ r(xj) for all 0 ≤ i ≤ j ≤ k − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Let y0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' , yk−1 ∈ C such that r(yi) = ai.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Since the ai are minimal, r(yi) ≤ r(xi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Because the |xi| are of maximum length, |yi| ≤ |xi|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Now we can swap using axiom (ii).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Let s(z) = \uf8f1 \uf8f4 \uf8f2 \uf8f4 \uf8f3 r(xi), if z = yi, r(yi), if z = xi, r(z), otherwise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Then (C, s) ≤ (C, r).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' But since (C, r) was optimal, (C, r) ≡ (C, s) and (C, s) is also optimal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' The algorithm of §4 produces an optimal tree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' By induction on n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' The basis is n ≤ d, in which case the result is straightforward.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Suppose that we have a multiset M of n > d elements of W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Let (C, r) be an optimal tree for M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Let k ∈ {2, 3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' , d} be congruent mod d − 1 to |M|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Let a0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' , ak−1 be the k smallest elements of M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' By Lemma 1, we can assume without loss of generality that a0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' , ak−1 are siblings and occur at maximum depth in (C, r), so there exist strings x0, x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' , x(k − 1) ∈ C of maximum length with a common prefix x and r(xi) = ai.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Remove the strings xi from C and replace them with x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Call the resulting set C′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' For z ∈ C′, let r′(z) = � ({0, 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' , k − 1}, i �→ ai), if z = x, ηW(r(z)), otherwise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' 6 Then (C′, r′) ∈ C2W and (C, r) = µW(C′, r′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' The multiset of values of r′ is just the M′ of step 2 of the algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' The algorithm will form the multiset M′′ = {w(E, t) | (E, t) ∈ M′} = {w(r′(z)) | z ∈ C′} and recursively call with these weights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' By the induction hypothesis, the return value will be a tree (D, s) ∈ CW that is optimal for M′′, thus (D, s) ≤ (C′, w ◦ r′), and the bijective map s : D → M′′ factors as s = w ◦ r′ ◦ f for some bijective f : D → C′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Let s′ = r′ ◦ f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' By axiom (iii), Cw(D, s′) = (D, w ◦ s′) = (D, s) ≤ (C′, w ◦ r′) = Cw(C′, r′), therefore (D, s′) ≤ (C′, r′), and since µW is monotone, µW(D, s′) ≤ µW(C′, r′) = (C, r).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' As (C, r) was optimal, so is µW(D, s′), and this is the value returned by the algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' 6 Applications By choosing two specific weightings (W, w) and defining the ordering relations ≤ appro- priately, we can recover two special cases of this algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content='1 Huffman coding Our first application is Huffman codes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Here we wish to minimize the expected length of variable-length codewords, given frequencies of the letters to be coded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' For this applica- tion, we take W = R+ = {a ∈ R | a ≥ 0} with weighting w(C, r) = ∑ x∈C r(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Recall that for a ∈ W and (C, r) ∈ C2W with r(x) = (Cx, rx), ηW(a) = ({ε}, ε �→ a) µW(C, r) = ({xy | x ∈ C, y ∈ Cx}, xy �→ rx(y)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Then (W, w) is an Eilenberg-Moore algebra for the monad (C, µ, η), as w(ηW(a)) = w({ε}, ε �→ a) = ∑ x∈{ε} (ε �→ a)(x) = a, w(µW(C, r)) = ∑ x∈C ∑ y∈Cx rx(y) = ∑ x∈C w(Cx, rx) = ∑ x∈C w(r(x)) = w(C, w ◦ r) = w(Cw(C, r)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' In addition, let us define α : CW → W by α(C, r) = ∑ x∈C |x| · r(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' 7 Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' α(ηW(a)) = 0 α(µW(C, r)) = α(C, w ◦ r) + w(C, α ◦ r).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' α(ηW(a)) = α({ε}, ε �→ a) = ∑ x∈{ε} |x| · (ε �→ a)(x) = |ε| · a = 0, α(µW(C, r)) = α({xy | x ∈ C, y ∈ Cx}, xy �→ rx(y)) = ∑ x∈C ∑ y∈Cx |xy| · rx(y) = ∑ x∈C |x| ∑ y∈Cx rx(y) + ∑ x∈C ∑ y∈Cx |y| · rx(y) = ∑ x∈C |x| · w(Cx, rx) + ∑ x∈C α(Cx, rx) = ∑ x∈C |x| · w(r(x)) + ∑ x∈C α(r(x)) = α(C, w ◦ r) + w(C, α ◦ r).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Note that α and w agree on trees of depth one: w({0, 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' , k − 1}, i �→ ai) = k−1 ∑ i=0 ai, α({0, 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' , k − 1}, i �→ ai) = k−1 ∑ i=0 |i| · ai = k−1 ∑ i=0 ai, where |i| refers to the length of i as a string, which in this case is 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' The map α is related to the Shannon entropy H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' If r(x) = d−|x|, the probability of a d-ary codeword x under the uniform distribution on a d-ary alphabet, then H(C, r) = ∑ x∈C −d−|x| log d−|x| = ∑ x∈C |x| · d−|x| log d = α(C, r) log d, so α(C, r) = H(C, r)/ log d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' To use the algorithm in §4, we need an order ≤ on CW.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Define (C, r) ≤ (D, s) if (C, r) ∼ (D, s), that is, there is a bijective map f : C → D such that r = s ◦ f, and α(C, r) ≤ α(D, s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Note that if (C, r) ≤ (D, s), then w(C, r) = ∑ x∈C r(x) = ∑ x∈C s( f(x)) = ∑ y∈D s(y) = w(D, s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' According to axiom (iii), for (C, r), (D, s) ∈ C2W, (C, r) ≤ (D, s) ⇔ Cw(C, r) ≤ Cw(D, s) ⇔ α(Cw(C, r)) ≤ α(Cw(D, s)) ⇔ α(C, w ◦ r) ≤ α(D, w ◦ s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' (1) Also, if (C, r) ≤ (D, s) in C2W, then w(C, α ◦ r) = ∑ x∈C α(r(x)) = ∑ x∈C α(s( f(x))) = ∑ y∈D α(s(y)) = w(D, α ◦ s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' (2) 8 Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' µW : C2W → CW and ηW : W → CW are monotone with respect to ≤.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' For ηW, suppose a, b ∈ W and a ≤ b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' By Lemma 3, α(ηW(a)) = 0 = α(ηW(b)) w(ηW(a)) = a ≤ b = w(ηW(b)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' For µW, suppose (C, r), (D, s) ∈ C2W and (C, r) ≤ (D, s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' By Lemma 3, (1), and (2), α(µW(C, r)) = α(C, w ◦ r) + w(C, α ◦ r) ≤ α(D, w ◦ s) + w(D, α ◦ s) = α(µW(D, s)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' The algorithm in §4 for the algebra (R+, w) and ordering relation ≤ defined by α is equivalent to Huffman’s algorithm and produces an optimal Huffman code for a given multiset of weights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Take X ⊂ R+ to be a finite multiset and sort the set X in increasing order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' For the binary case of Huffman codes (the d-ary version follows the same way), we always choose k = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' For the first step, let a0, a1 ∈ X be the two smallest elements in the list.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Form the object ({0, 1}, i �→ ai) ∈ CX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' In the case n = 2, this is the only remaining object in the list.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Otherwise, we combined them into one element with the sum of the weights of a0 and a1 as the weight of the new element, exactly as the Huffman coding does.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' For the case n > 2, there are remaining elements in the set X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Take all remaining a ∈ X\\{a0, a1} and replace a by ηX(a) ∈ CX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' We are left with n − 1 elements of type CX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' If we recursively call the algorithm in step 1, we are continually combining the least two elements in the remaining set with the elements weighted by w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Note by the weighting w, w(ηX(a)) = a and on elements in CX, w takes the sum of r(x)′s, exactly as Huffman coding does.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Finally, this leaves us with a tree in C2X where leaves have weights of the form ηX(ai).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Denote this tree by (D, s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Taking µX(D, S) gives our desired tree in CX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content='2 PIFO trees PIFO trees were introduced in [3] as a model for programmable packet schedulers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' In the recent work of [1], further work was done on PIFO trees giving a semantics that allows for certain embedding algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' The notion of a homomorphic embedding was defined for the purpose determining when a PIFO tree could be represented by another PIFO tree and for finding an embedding if so.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' The embedding algorithm we consider takes an arbitrary PIFO tree and embeds it into a d-ary tree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' This becomes a special case of the algorithm of §4, where we choose w in the weighting (W, w) to minimize the height of the target d-ary tree into which the source tree can embed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' For this application, we take W = N with weighting w(C, r) = max x∈C |x| + r(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' This gives an Eilenberg-Moore algebra (W, w) for the monad (C, µ, η).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' For a ∈ W and (C, r) ∈ C2W with r(x) = (Cx, rx), as before we have ηW(a) = ({ε}, ε �→ a) µW(C, r) = ({xy | x ∈ C, y ∈ Cx}, xy �→ rx(y)), 9 so w(ηW(a)) = w({ε}, ε �→ a) = max x∈{ε} |x| + (ε �→ a)(x) = |ε| + a = a, w(µW(C, r)) = w({xy | x ∈ C, y ∈ Cx}, xy �→ rx(y)) = max x∈C max y∈Cx |xy| + rx(y) = max x∈C max y∈Cx |x| + |y| + rx(y) = max x∈C |x| + max y∈Cx |y| + rx(y) = max x∈C |x| + w(Cx, rx) = max x∈C |x| + w(r(x)) = w(C, w ◦ r) = w(Cw(C, r)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' For (C, r), (D, s) ∈ CW, let us define (C, r) ≤ (D, s) if there is a bijective function f : C → D such that r = s ◦ f and w(C, r) ≤ w(D, s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Lemma 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' µW : C2W → CW and ηW : W → CW are monotone with respect to ≤.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' For ηW, if a ≤ b, then w(ηW(a)) = a ≤ b = w(ηW(b)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' For µW, suppose (C, r), (D, s) ∈ C2W and (C, r) ≤ (D, s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' According to axiom (iii), (C, r) ≤ (D, s) ⇔ Cw(C, r) ≤ Cw(D, s) ⇔ w(Cw(C, r)) ≤ w(Cw(D, s)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Then w(µW(C, r)) = w(Cw(C, r)) ≤ w(Cw(D, s)) = w(µW(D, s)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Theorem 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' The algorithm of §4 for the algebra (N, w) and ordering relation ≤ defined by w is equivalent to determining whether an embedding of a PIFO tree in a bounded d-ary tree exists and finding the embedding if so.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' 7 Conclusion We have presented a generalized Huffman algorithm and shown that two known algo- rithms, Huffman codes and embedding of PIFOs trees, can be derived as special cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' The PIFO embedding algorithm was introduced in [1] and observed to be very similar to the usual combinatorial algorithm for optimal Huffman codes, albeit based on a different algebraic structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' This suggested the common generalization presented in this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Our generalized algorithm exploits the monadic structure of prefix codes, which al- lows a more algebraic treatment of the Huffman algorithm than the usual combinatorial approaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' The two applications fit naturally in the categorical setting by choosing spe- cific Eilenberg-Moore algebras for each one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' It is possible that other greedy algorithms might fit into this framework as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' 10 References [1] Anshuman Mohan, Yunhe Liu, Nate Foster, Tobias Kapp´e, and Dex- ter Kozen, “Formal abstractions for packet scheduling,” Tech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' http://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content='org/abs/2211.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content='11659, Cornell University, November 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' [2] Thomas M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Cover and Joy A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Thomas, Elements of Information Theory, Wiley, second edition, 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' [3] Anirudh Sivaraman, Suvinay Subramanian, Mohammad Alizadeh, Sharad Chole, Shang-Tse Chuang, Anurag Agrawal, Hari Balakrishnan, Tom Edsall, Sachin Katti, and Nick McKeown, “Programmable packet scheduling at line rate,” in SIGCOMM, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' [4] Albert Gran Alcoz, Alexander Dietm¨uller, and Laurent Vanbever, “SP-PIFO: Approx- imating push-in first-out behaviors using strict-priority queues,” in NSDI, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' [5] Andrea Asperti and Giuseppe Longo, Categories, Types and Structures: An introduction to category theory for the working computer scientist, Foundations of Computing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' MIT Press, 1991.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' [6] Michael Barr and Charles Wells, Toposes, Triples and Theories, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' 278 of Grundlehren der mathematischen Wissenschaften, Springer, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' [7] Michael Barr and Charles Wells, Category Theory for Computing Science, Prentice Hall, 1990.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' [8] Jiˇr´ı Ad´amek, Horst Herrlich, and George E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Strecker, Abstract and concrete categories, Dover Publications, 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' [9] Eugenio Moggi, “Notions of computation and monads,” Inf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' and Comp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' 93, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' 55–92, 1991.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' [10] Philip Wadler, “Comprehending monads,” Mathematical Structures in Computer Sci- ence, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' 461–493, 1992.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' [11] Philip Wadler, “Monads for functional programming,” in Advanced Functional Pro- gramming: 1st Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' School on Advanced Functional Programming Techniques, Johan Jeur- ing and Erik Meijer, Eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' 925 of Lecture Notes in Computer Science, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' 24–52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' Springer-Verlag, 1995.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} +page_content=' 11' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BdE1T4oBgHgl3EQfDgNt/content/2301.02878v1.pdf'} diff --git a/CtE0T4oBgHgl3EQfyQKJ/vector_store/index.faiss b/CtE0T4oBgHgl3EQfyQKJ/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..0a33acdc83f72a499a828a5b1d3fab0b9ffacca8 --- /dev/null +++ b/CtE0T4oBgHgl3EQfyQKJ/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:01179e82fa37d7b82490ae4e2101f97a1c888d1a7c823dabb4934460bdbf846d +size 4259885 diff --git a/DtE4T4oBgHgl3EQfGQwj/content/tmp_files/2301.04892v1.pdf.txt b/DtE4T4oBgHgl3EQfGQwj/content/tmp_files/2301.04892v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..612d87f82a5fdff012362293351ade19b8fcd916 --- /dev/null +++ b/DtE4T4oBgHgl3EQfGQwj/content/tmp_files/2301.04892v1.pdf.txt @@ -0,0 +1,1590 @@ +Astronomy & Astrophysics manuscript no. Attree_NGA_Paper2_LanguageEdited +©ESO 2023 +January 13, 2023 +Activity distribution of comet 67P/Churyumov-Gerasimenko +from combined measurements of non-gravitational forces and +torques +N. Attree1, L. Jorda2, O. Groussin2, J. Agarwal1, R. Lasagni Manghi3, P. Tortora3, 4, M. Zannoni3, 4, and +R. Marschall5 +1 Institut für Geophysik und extraterrestrische Physik, Technische Universität Braunschweig, Mendelssohnstr. 3, 38106 +Braunschweig, Germany (e-mail: n.attree@tu-braunschweig.de) +2 Aix Marseille Univ, CNRS, CNES, Laboratoire d’Astrophysique de Marseille, Marseille, France +3 Alma Mater Studiorum - Università di Bologna, Dipartimento di Ingegneria Industriale, Via Fontanelle 40, I-47121 +Forlì, Italy +4 Alma Mater Studiorum - Università di Bologna, Centro Interdipartimentale di Ricerca Industriale Aerospaziale, via +Baldassarre Carnaccini 12, I-47121, Forlì, Italy +5 CNRS, Laboratoire J.-L. Lagrange, Observatoire de la Côte d’Azur, Boulevard de l’Observatoire, CS 34229 - F 06304 +NICE Cedex 4, France +January 13, 2023 +ABSTRACT +Aims. Understanding the activity is vital for deciphering the structure, formation, and evolution of comets. We inves- +tigate models of cometary activity by comparing them to the dynamics of 67P/Churyumov-Gerasimenko. +Methods. We matched simple thermal models of water activity to the combined Rosetta datasets by fitting to the total +outgassing rate and four components of the outgassing induced non-gravitational force and torque, with a final manual +adjustment of the model parameters to additionally match the other two torque components. We parametrised the +thermal model in terms of a distribution of relative activity over the surface of the comet, and attempted to link this +to different terrain types. We also tested a more advanced thermal model based on a pebble structure. +Results. We confirm a hemispherical dichotomy and non-linear water outgassing response to insolation. The southern +hemisphere of the comet and consolidated terrain show enhanced activity relative to the northern hemisphere and +dust-covered, unconsolidated terrain types, especially at perihelion. We further find that the non-gravitational torque +is especially sensitive to the activity distribution, and to fit the pole-axis orientation in particular, activity must be +concentrated (in excess of the already high activity in the southern hemisphere and consolidated terrain) around the +south pole and on the body and neck of the comet over its head. This is the case for both the simple thermal model +and the pebble-based model. Overall, our results show that water activity cannot be matched by a simple model of +sublimating surface ice driven by the insolation alone, regardless of the surface distribution, and that both local spatial +and temporal variations are needed to fit the data. +Conclusions. Fully reconciling the Rosetta outgassing, torque, and acceleration data requires a thermal model that +includes both diurnal and seasonal effects and also structure with depth (dust layers or ice within pebbles). This shows +that cometary activity is complex. Nonetheless, non-gravitational dynamics provides a useful tool for distinguishing +between different thermophysical models and aids our understanding. +Key words. comets: general, comets: individual (Churyumov-Gerasimenko), planets and satellites: dynamical evolution +and stability +1. Introduction +Comets are amongst the most primordial Solar System ob- +jects. They formed directly from the protoplanetary disc +and survived mostly unaltered for much of their lifetimes +in the outer Solar System. They are therefore vital targets +for our understanding of planet formation and the history +of the early Solar System. Upon entering the inner Solar +System, comets are heated by the Sun and undergo ac- +tivity; that is, ices are sublimated and gas and dust are +ejected. Cometary activity poses open questions related to +the structure, composition, and thermophysical properties +of the nucleus material. This is directly connected to their +formation in the early Solar System. Whether cometary +nuclei, and by extension planets, formed from the gravi- +tational collapse of clouds of centimetre-sized pebbles (as +proposed in Blum et al. 2017) or by continual collisional +growth (Davidsson et al. 2016) has direct implications for +the structure and strength of the near-surface material that +controls outgassing. +In addition to being directly observable, the outgassing +produces a reaction force on the nucleus that can alter its +trajectory (as first recognised by Whipple 1950 and de- +scribed by Marsden et al. 1973) and rotation state (see +Samarasinha et al. 2004). Measuring the changing orbits +Article number, page 1 of 13 +arXiv:2301.04892v1 [astro-ph.EP] 12 Jan 2023 + +A&A proofs: manuscript no. Attree_NGA_Paper2_LanguageEdited +and spins of comets therefore provides a useful insight into +the the micro-physics of the activity mechanism. +Many thermophysical models have been proposed to ex- +plain the activity (see recent examples by Fulle et al. 2019, +Gundlach et al. 2020, and Davidsson 2021), and these can +be compared to the outgassing rates of observed comets. In +particular, comet 67P/Churyumov-Gerasimenko (67P here- +after) provides an excellent dataset because it was visited by +the Rosetta spacecraft between 2014 and 2016. The space- +craft collected detailed measurements of the size, shape, +surface properties, and time-varying rotation state and out- +gassing of the nucleus. Finding the distribution of activity +across the nucleus of 67P that fits the various measurements +of the total outgassing rate best (Hansen et al. 2016; Mar- +shall et al. 2017; Combi et al. 2020; Läuter et al. 2020, etc.) +has produced several so-called activity maps (e.g. Marschall +et al. 2016, 2017; Läuter et al. 2020, ), which are often ex- +pressed as an effective active fraction (EAF) relative to a +pure water-ice surface. When examining only the summed +total outgassing, however, there is always a degeneracy in +the retrieved activity distribution (Marschall et al. 2020), +whilst, at the same time, the effects of seasonal changes in +insolation and dust cover across the surface of 67P are com- +plicated (Keller et al. 2017; Cambianica et al. 2021). Com- +paring the effects of a model outputted non-gravitational +acceleration (NGA) and torque (NGT) to the dynamics of +67P can provide a further constraint on the model parame- +ters and on our understanding of the activity (Attree et al. +2019; Kramer et al. 2019; Kramer & Läuter 2019; Mottola +et al. 2020). +Simple NGA models, such as those by Marsden et al. +(1973) and Yeomans & Chodas (1989), parametrise the +acceleration using variables scaled to a general water- +production curve, and therefore provide limited insight +into the physics of the activity on an individual comet. +More complex models (following from Sekanina 1993) re- +late the observed NGA and NGT to the outgassing via +a thermal model and some distribution of ices or active +areas across the nucleus surface. If independent measure- +ments of this distribution and/or the outgassing rate can +be made, then cometary masses and spin axes can be mea- +sured from ground-based observations, as was achieved for +67P (Davidsson & Gutiérrez 2005; Gutiérrez et al. 2005). +Rosetta then provided both the detailed outgassing data +mentioned above, as well as precise measurements of the +nucleus position and rotation via radio-tracking and op- +tical navigation. As summarised in Mottola et al. (2020), +various attempts have been made to compare thermal mod- +els to the NGA and NGT forces of 67P (Keller et al. 2015; +Davidsson et al. 2022) and to fit its non-gravitational tra- +jectory (Kramer & Läuter 2019), rotation state (Kramer +et al. 2019), and both in combination with outgassing (At- +tree et al. 2019). +In Attree et al. (2019), our previous paper on this topic, +we used the EAF formalism to fit surface distributions to +the observed Earth-comet range (the most accurate compo- +nent of the comet ephemeris, based on the spacecraft radio +tracking), total gas production (measured by ROSINA, the +Rosetta Spectrometer for Ion and Neutral Analysis; Hansen +et al. 2016), and the change in spin rate (z component of +the torque, measured as part of the nucleus shape recon- +struction; Jorda et al. 2016). We found that a large EAF in +the southern hemisphere of the comet, as well as an increase +in EAF around perihelion, were needed to fit both the to- +tal production measurements and the NGA. However, our +model was limited by not considering the other components +of the NGT (i.e. the change in the spin axis orientation, as +well as its magnitude), and by a rather nonphysical way +of splitting the surface into areas of differing activity. Ad- +ditionally, discontinuities in the cometary heliocentric tra- +jectory reconstructed by the European Space Operations +Centre that arose because the NGA was excluded from the +operational dynamical model, have complicated the anal- +ysis by making it difficult to extract smooth acceleration +curves. +Kramer & Läuter (2019) addressed this problem by per- +forming their own N-body integrations with a model fol- +lowing Yeomans & Chodas (1989) and varying initial con- +ditions. They then fitted a smoothed, interpolated curve to +the residuals to extract time-varying NGA curves, but they +did not compare them to a full thermal model. In a separate +paper (Kramer et al. 2019), the authors did compare a phys- +ical thermal model, again using the EAF formalism, to both +the rotation rate and axis orientation data. Similarly to our +results, their results also required a relatively higher EAF in +the southern than in the northern hemisphere, as well as an +enhanced outgassing response to insolation around perihe- +lion to fit the data. Kramer & Läuter (2019) noted that the +NGT is much more dependent on the spatial distribution +of activity than the NGA. +Since +then, +two +additional +reconstructions +of +the +Rosetta/67P trajectory have been performed (Farnocchia +et al. 2021; Lasagni Manghi et al. 2021). Farnocchia et al. +(2021) used a rotating-jet model following Sekanina (1993) +to fit ground-based astrometric observations and radio- +ranging measurements before and after perihelion (where +the spacecraft NGAs are smaller and the range accuracy is +higher). Lasagni Manghi et al. (2021), on the other hand, +used the full Rosetta two-way range and differential one- +way range (∆DOR) dataset, also including low-accuracy +data close to perihelion. They tested various NGA models, +including a rotating-jet model, and found a best-fit tra- +jectory using an empirical, stochastic acceleration model. +Both of these works produced acceleration curves to which +a thermal model can be compared. +Davidsson et al. (2022) did just that by comparing +the output of a more complex thermal model (NIMBUS; +Davidsson 2021) to the acceleration curves of Farnocchia +et al. (2021) and Kramer & Läuter (2019). They found rel- +atively good agreement without fitting, but had to vary +several model parameters (e.g. the sublimation-front depth +and the gas diffusivity) between the northern and south- +ern hemispheres and pre- and post-perihelion, in order to +match the outgassing data. This reinforces the ideas of a +hemispheric dichotomy and time-dependent thermophysi- +cal properties, and it also demonstrates the complicated +nature of trying to model the full thermophysical system of +sublimation, gas flow, and dust. +These studies show the usefulness of considering the +non-gravitational dynamics. No study has analysed the full +six components of NGA and NGT simultaneously, how- +ever (we analyse all six here, but only four are included in +the formal fitting procedure), and several other weaknesses +exist, such as nonphysical surface distributions or compli- +cated descriptions leading to unfitted models. It is per- +tinent, therefore, to re-examine the full non-gravitational +dynamics of 67P with a simple thermal model that can +be parametrised in terms of real surface features while be- +Article number, page 2 of 13 + +N. Attree et al.: Activity distribution of comet 67P +ing easily compared with more complicated models. This +is what we attempt to do here, bearing in mind that the +aim is not to find the full description of cometary activity, +but a model that adequately describes the data and points +towards the underlying physics. +The rest of this paper is organised as follows: in Sec- +tion 2 we describe how we updated the model of Attree +et al. (2019) for use here. In Section 3 we describe three +different parametrisations of the surface activity distribu- +tion and their results in the model fit. These results are +discussed, with reference to a run with the more advanced +thermal model of Fulle et al. (2020) in Section 4, before we +conclude in Section 5. +2. Method +We followed the method of the first paper (Attree et al. +2019) by first calculating surface temperatures over a shape +model of 67P (SHAP7; Preusker et al. 2017) with a simple +energy-balance thermal model and then computing the re- +sulting non-gravitational forces and torques and implement- +ing them in an N-body integration. The model was then +optimised by scaling the relative activity of various areas +of the shape model up and down, minimising the residuals +to the observed datasets: the Earth-comet range (i.e. the +scalar projection of the three-dimensional comet position in +the Earth-comet direction, R, with NR = 1000 data points) +or the directly extracted NGAs from Lasagni Manghi et al. +(2021) (with NNGA = 17000 data points in each of the three +components); the total gas production (NQ = 787, Hansen +et al. 2016); and the spin-axis (z) aligned component of the +torque (NTz = 1000, Jorda et al. 2016). Additionally, we +now also computed the change in the orientation of the ro- +tation axis (Kramer et al. 2019) and used this as an output +to compare different models. +The thermal model computes the surface energy- +balance, taking insolation, surface thermal emission, sub- +limation of water ice, projected shadows, and self-heating +into account (see Attree et al. 2019 for details). Heat con- +duction into the nucleus is neglected for numerical reasons, +but is small because of the low thermal inertia of the comet +(Gulkis et al. 2015). Heat conduction would mainly affect +night-time temperatures, which are very low and contribute +little to the outgassing (but see the discussion in Section 4). +Again for numerical reasons, surface temperatures are cal- +culated roughly once every 10 days for a full 12.4 hour ro- +tation, and the derived quantities are interpolated (see de- +tails below) to produce smooth curves over the full mission +period of about two years. Surface temperatures are each +computed twice, once assuming an effective active fraction +EAF = 0 (i.e. pure grey-body dust surface), and once with +EAF = 1 (i.e. sublimation from a pure water-ice surface), +and the temperatures and sublimation rates are saved. In +the fitting process, the pure water-ice sublimation rate is +then scaled by a variable EAF and is used, along with +the sublimation gas velocity calculated from the zero-ice +surface temperature, to compute the outgassing force per +facet. The momentum coupling parameter was assumed to +be η = 0.7 (Attree et al. 2019). Torque per facet was also +calculated here using the “torque efficiency” formalism used +before (Keller et al. 2015), where τ is the facet torque ef- +ficiency or moment arm, which is a geometric factor that +was computed once at the beginning of the run. The use of +the higher zero-ice temperature for the gas thermal veloc- +ity assumes that the gas equilibrates with the dusty surface, +and this means that our derived EAF values may be lower +estimates compared with some other thermal models. +The N-body integration was performed using the open- +source REBOUND code1 (Rein & Liu 2012), complete +with full general relativistic corrections (Newhall et al. +1983) as implemented by the REBOUNDx extension pack- +age2, and including all the major planets as well as Pluto, +Ceres, Pallas, and Vesta. Objects were initialised with their +positions and velocities in the J2000 ecliptic coordinate +system according to the DE438 Solar System ephemerides +(Standish 1998), with 67P given its initial state vector +from the new Rosetta trajectory reconstruction of Lasagni +Manghi et al. (2021) (Table A.1). The system was then inte- +grated forward in time from t = −350 to +350 days relative +to perihelion, using the IAS15 integrator (Rein & Spiegel +2015) and the standard equations of motion, with the addi- +tion of a custom acceleration, aNG, for 67P, provided by our +model. The Earth-comet range, which is the most accurate +component of the comet trajectory, was computed for com- +parison with the reconstructed trajectory (extracted using +the SpiceyPy Python package; Annex et al. 2020). +A bounded least-squares fit to the residuals was then +performed using standard methods implemented in Scien- +tific Python whilst varying the EAF parameters. When +forming the overall objective function to be minimised (see +Eqns. 9 and 10. in Attree et al. 2019), the datasets were +weighted by a factor λ so that each contributed roughly the +same to the overall fit (see Table 1). The datasets used in all +fits were the model outputted total outgassing rate and the +z component of the torque, both with λQ = λTz = 1. Fur- +thermore, in some fits, we then used the computed Earth- +comet range (with λR = 0.02), while in others, we directly +compared to the three components of the NGA extracted by +Lasagni Manghi et al. (2021) in the cometocentric radial- +transverse-normal frame (radial to the Sun, ˆr, tangential +to the orbit, ˆt, and normal to it). In this case, the inte- +gration was only performed once at the end to check the +Earth-comet range, but the weighting was zero in the fit +(λR = 0), while λNGA = 1. Performing the N-body inte- +gration only once speeds the process up by several times, +with individual runs taking a few minutes and fits taking +up to a day, depending on the parameters. All parameters +were interpolated to the observational data sampling-times +using the Fourier method described below. +We first confirm that the Lasagni Manghi et al. (2021) +accelerations match the real comet trajectory well when +they are input into our N-body integration, and they re- +cover the Earth-comet range to within a few hundred me- +tres. This residual, which is most likely the result of the +different integration techniques and perturbing bodies we +used, is well below the uncertainty of our thermal model +runs. +Previously, the x and y components of the torque vector +were discarded, but they were now used when we calculated +the changes in pole orientation. In principle, the rates of +change of the angular velocity (Ω) of the comet around its +three principal axes can be related (see e.g. Julian 1990) to +1 http://rebound.readthedocs.io/en/latest/ +2 http://reboundx.readthedocs.io/en/latest/index.html +Article number, page 3 of 13 + +A&A proofs: manuscript no. Attree_NGA_Paper2_LanguageEdited +the torque components by +Ix ˙Ωx = (Iy − Iz)ΩyΩz + Tx, +Iy ˙Ωy = (Iz − Ix)ΩxΩz + Ty, +Iz ˙Ωz = (Ix − Iy)ΩxΩy + Tz, +(1) +where Ix = 9.559 × 1018, Iy = 1.763 × 1019, and Iz = +1.899×1019 kg m2 are the moments of inertia derived from +the shape model assuming a constant density of 538 kg m−3 +(Preusker et al. 2017), and to the pole orientation right +ascension, RA, and declination, Dec, by +˙ψ = −Ωy cos(ψ) − Ωx sin(ψ) +tan(θ) ++ Ωz, +˙φ = Ωy cos(ψ) + Ωx sin(ψ) +sin(θ) +, +˙θ = Ωx cos(ψ) − Ωy sin(ψ), +(2) +via the Euler angles φ = π/2 + RA, θ = π/2 − Dec, and ψ. +In practice, the fact that our model runs over individual +rotations separated by gaps means that the torque curves +are discontinuous and cannot be directly integrated. We +therefore followed the technique of Kramer et al. (2019) and +applied a Fourier analysis to the torque curves. The method +proceeds by i) extracting the torque over a single rotation +as a function of the sub-solar longitude, using Kramer et al. +(2019) Eqns. 26, 27, ii) computing the Fourier transform as +a function of sub-solar longitude using Eqn. 23, iii) inter- +polating the Fourier terms as smooth curves over the full +Rosetta period; Eqn. 24, and iv) reconstructing the torque +at a chosen time by the inverse Fourier transform; Eqn. +25. This allows the calculation of a smoothly interpolated +torque value at any given time, Tx,y,z(t), for use in the ro- +tation equations (1). +The set of simultaneous differential equations given by +Eqns. 1 and 2 was then integrated using standard func- +tions in Scientific Python and the initial conditions RA = +69.427◦, Dec = 64.0◦, and ψ = 330.703◦ at t = −377.22 +days relative to perihelion (Kramer et al. 2019) for the pe- +riod t = [−377.22 : 402.48], corresponding to the duration +of the Rosetta measurements. The resulting RA(t), Dec(t) +values were not used in the fit due to technical limita- +tions, but were directly compared with the observations as +a model output. +3. Results +3.1. Model C +We began by rerunning the best-fit model of the previous +paper, designated model C in Attree et al. (2019). This +model parametrised the activity distribution by splitting +the surface into the 26 regions, defined by Thomas et al. +(2015) (see their figures for maps), and then grouping them +into five super-regions following Marschall et al. (2016)(see +Figure 4 in Attree et al. 2019), before finally splitting the +Southern super-region into two (see Figure 17 in Attree +et al. 2019) and allowing these to vary their EAF with time. +With 6 super-regions and the 6 time-variation parameters, +there are a total of 12 free parameters in this model. These +super-regions consist of region 1, covering the equatorial ar- +eas; region 2, covering the base of the comet body and top +of the head; the individual regions Hathor and Hapi; and ++Z +-Z +Fig. 1. Peak effective active fraction at perihelion for solution +C, mapped onto the shape model. +−400 +−300 +−200 +−100 +0 +100 +200 +300 +400 +Days from Perihelion +0.0 +0.1 +0.2 +0.3 +0.4 +Active Fraction +So th - +Region 1 +Region 2 +Hathor +Hapi +So th + +Fig. 2. Time-varying effective active Fraction for solution C. +two southern super-regions split on a per-facet basis by the +sign of the z component of the torque efficiency (i.e. south +positive with τz > 0 and south negative with τz < 0). +This splitting was the only way in which a satisfactory fit +to the z torque (i.e. rotation-rate data) could be achieved, +but it remains somewhat artificial. Figure 1 shows the best- +fit solution achieved here, mapped onto the shape model. +This shows the discontinuous and patchy appearance of the +southern super-regions, as well as the north-south EAF di- +chotomy and activity in Hapi (the light blue area in the +northern neck region). +We optimised this model again here and, with a slightly +differing procedure for sampling and interpolating the com- +putational output, produced very similar results to before, +with no significant improvement in the fit. Next, we in- +stead fit the model directly to the Lasagni Manghi et al. +(2021) NGA curves as described above, producing the best- +fit solution shown mapped onto the shape-model in Figure +1 (where the values shown are peak EAF, the maximum +value for all times), and with time in Figure 2. The out- +put is very similar to the previous solution in Attree et al. +(2019), but Figure 2 shows an even more pronounced spike +in EAF around perihelion than before. +The model fits are shown in the orange curves in Fig- +ures 3, 4, and 5, with the fit statistics in the first line of +Article number, page 4 of 13 + +0.00 +0.05 +0.10 +0.15 +0.20 +0.25 +0.30 +0.35 +0.40 +Active FractionN. Attree et al.: Activity distribution of comet 67P +−300 +−200 +−100 +0 +100 +200 +Days from Perihelion +10 +26 +10 +27 +10 +28 +Ou gassing Ra e (s +−1 +) +Model C +Model D +Model E +Observed +Fig. 3. Observed total gas production (ROSINA values from +Hansen et al. 2016) compared to solutions C, D, and E. +300 +200 +100 +0 +100 +200 +300 +Days from Perihelion +200 +150 +100 +50 +0 +50 +100 +150 +200 +Range Residuals (km) +Model C +Model D +Model E +Fig. 4. Observed minus computed Earth-comet range, R, for +solutions C, D, and E. +Table 1. The z torque (Fig. 5) and total gas production +from ROSINA (Fig. 3) are reasonably well fit, with the +perihelion peak-values matched, but with a slightly differ- +ing shape around the inbound equinox roughly 100 days +before perihelion. An improvement in the trajectory fit is +attained, with the new RMS residual value of 34 km re- +duced from the previously achieved 46 km. The shape of +the curve is similar. +The orange curves in Figures 6, 7, and 8 show the in- +dividual acceleration curves in the cometocentric (ˆr, ˆt, ˆn) +frame compared to the values extracted by Lasagni Manghi +et al. (2021). The radial component makes up the bulk of +the acceleration and is reasonably well matched by model +C, with the peak value being ∼ 50% too high. The normal +and tangential components are of smaller magnitude and +are reasonably well fit; the secondary, negative peak of the +tangential component after perihelion is the worst area of +the fit. The remaining 34 km residuals to the observed tra- +jectory most likely stem from our inability to fit this area +of the tangential acceleration, combined with the too large +radial component peak. +−300 +−200 +−100 +0 +100 +200 +300 +Days from Perihelion +0.0 +0.2 +0.4 +0.6 +0.8 +1.0 +T +or ue (Nm) +1e7 +Observed +Model C +Model D +Model E +Fig. 5. Smoothed observed z component of the torque com- +pared to solutions C, D, and E. The grey area represents the 1σ +uncertainty (see Attree et al. 2019 for details). +300 +200 +100 +0 +100 +200 +300 +400 +Days from Perihelion +0.0 +0.2 +0.4 +0.6 +0.8 +1.0 +NGA r (AU d +2) +1e +9 +Observed +Model C +Model D +Model E +Fig. 6. Observed radial acceleration in the comet (ˆr, ˆt, ˆn) frame +with the 5σ uncertainty (from Lasagni Manghi et al. 2021), com- +pared to solutions C, D, and E. Higher-order Fourier terms cor- +responding to daily oscillations are omitted for clarity, but are +included in the fit. +When the pole orientation was calculated, as shown in +the orange curve of Figure 9, it was a very poor fit to the +data, moving off in the opposite direction to the observed +changes. This demonstrates that the problem is ill-posed +with multiple solutions, and it also highlights the useful- +ness of including the RA, Dec pole measurement to help +distinguish between different models that fit the other data +equally well. +3.2. Model D +We now proceed with a more physically meaningful model. +This was constructed using the list of 71 sub-regions de- +fined in Thomas et al. (2018) (see the reference for maps of +their location). We again created super-regions by collecting +these sub-regions, but this time, by placing them into one of +the five morphological categories of Thomas et al. (2015): +‘dust-covered terrains’ (Dust for short), ‘brittle materials +Article number, page 5 of 13 + +A&A proofs: manuscript no. Attree_NGA_Paper2_LanguageEdited +Table 1. Fit statistics for best-fit models C, D, and E, and the two unfitted versions of F. +Solution +Weighting +χ2 +λQ +λTz +λR +λNGA +R +Q +Tz +NGAr +NGAt +NGAn +Obj +C +1 +1 +0 +1 +34.1 +4.53 +1.36 +1.18 +1.32 +0.44 +1.20 +D +1 +1 +0.02 +0 +88.8 +3.60 +1.10 +2.00 +1.60 +0.90 +2.35 +E +1 +1 +0.02 +0 +83.4 +3.75 +0.77 +1.78 +1.58 +0.89 +2.22 +F dust SH +- +- +- +- +324.5 +4.62 +2.09 +4.12 +1.71 +1.01 +- +F ice SH +- +- +- +- +459.2 +5.64 +3.02 +2.22 +1.63 +1.00 +- +Notes. Model E is highlighted as the preferred solution. The model outputs (water production rate, z component of NGT, and +the three components of NGA) are compared to the observations, producing the χ2 statistics, which are then weighted according +to the λ values and combined in the objective function (Eqns. 9 and 10. in Attree et al. 2019) to produce the combined fit statistic +Obj. All values are dimensionless, although the range values R correspond one-to-one to kilometers. +300 +200 +100 +0 +100 +200 +300 +400 +Days from Perihelion +0.5 +0.0 +0.5 +1.0 +1.5 +2.0 +NGA t (AU d +2) +1e +10 +Observed +Model C +Model D +Model E +Fig. 7. Observed tangential acceleration in the comet (ˆr, ˆt, ˆn) +frame compared to solutions C, D, and E. +300 +200 +100 +0 +100 +200 +300 +400 +Days from Perihelion +0.0 +0.5 +1.0 +1.5 +2.0 +2.5 +3.0 +3.5 +NGA n (AU d +2) +1e +10 +Observed +Model C +Model D +Model E +Fig. 8. Observed normal acceleration in the comet (ˆr, ˆt, ˆn) frame +compared to solutions C, D, and E. +with pits and circular structures’ (Brittle), ‘large-scale de- +pressions’ (Depression), ‘smooth terrains’ (Smooth), and +‘exposed consolidated surfaces’ (Rock). The sub-regions +were assigned according to their descriptions in the table +in Thomas et al. (2018). A few ambiguous examples were +67 +68 +69 +70 +71 +72 +Right Ascensi n ( +∘ +) +63.50 +63.75 +64.00 +64.25 +64.50 +64.75 +65.00 +65.25 +65.50 +Declinati n ( +∘ +) +M del C +M del D +M del E +Observed +Fig. 9. Observed pole orientation (Ra, Dec) compared to solu- +tions C, D, and E. The thickness of the model lines is due to the +daily oscillations. Error bars are plotted for the observations, +but are small at this scale. +tested in both the categories to which their descriptions +could apply, without altering our results significantly. The +Rock and Smooth terrain types both cover significant ar- +eas of the southern hemisphere and following the results +of the first paper, we therefore allowed their EAFs to vary +with time in the same way as for model C. The facets in +each super-region all have the same EAF (either constant or +time-varying), regardless of the hemisphere in which they +are located. With five regions and 6 time-variation param- +eters, there are 11 parameters in total for this model, des- +ignated ‘model D’. +Figure 10 shows the peak activity in our best-fit solution +for model D mapped onto the shape model, and Fig. 11 +shows the time variation. High activity is again favoured +in the southern hemisphere, with the Rock and Smooth +regions seeing much higher activity than the Dusty, Brittle, +and Depression regions, especially around perihelion. +Model D is shown as green curves in Figures 3 - 9. The fit +statistics are again shown in Table 1. This model produces +a similar, if slightly improved, fit to the total outgassing +measurements, while slightly degrading the trajectory and +rotation-rate fits compared to model C. The reasons for the +poorer trajectory fit can be seen in the acceleration curves +in Figures 6, 7, and 8. The modelled radial component of +the acceleration is still slightly too large when compared +Article number, page 6 of 13 + +N. Attree et al.: Activity distribution of comet 67P ++Z +-Z +Fig. 10. Peak effective active fraction at perihelion for solution +D, mapped onto the shape model. +−400 +−300 +−200 +−100 +0 +100 +200 +300 +400 +Days from Perihelion +0.000 +0.025 +0.050 +0.075 +0.100 +0.125 +0.150 +0.175 +0.200 +Acti e Fraction +Dust +Brittle +Smooth +Depression +Rock +Fig. 11. Time-varying effective active fraction for solution D. +to the observations, while the tangential and normal com- +ponents are now much worse than before, with the curves +roughly the correct shape, but too small in magnitude. An +attempt to fit model D directly to the accelerations did +not improve the trajectory, and the individual super-region +NGA curves showed no obvious combination that would fit +the accelerations better. +Figure 9 shows that model D additionally fails to repro- +duce the observed changes in pole direction. However, the +curve now goes in the correct direction, but with a magni- +tude that is too large compared to the completely incorrect +prediction of model C. This suggests that the more phys- +ically meaningful model has merit, despite the degraded +trajectory fit, and it motivated us to make further adjust- +ments to try and fit all the data below. +3.3. Model E +Because model D fits most of the data well but increasingly +fails with the magnitude of the pole direction changes, we +sought to modify it by adjusting the NGT. Specifically, in +order to fit all the data, the comet must produce a smaller +amount of non axial-aligned torque (x and y components), +while the rest of the torque and accelerations remain the +same. We achieved this in model E with another, somewhat +artificial, splitting of the Rock super-region into two super- +regions based on their torque contributions. This splitting +was performed on a sub-region basis, rather than on the +per-facet basis of model C, in order to produce contiguous +areas that allowed us to see the general trends in activity +across different parts of the comet surface. The modulus of +the torque efficiency (|τ|) was first calculated for each facet +(top left in figure 12) before the area-weighted mean for +each sub-region was calculated and the Rock super-region +was split into ‘low torque’ (|τ| lower than the median sub- +region value) and ‘high torque’ (|τ| greater than the median +value). Both of these super-regions were allowed to vary +with time, leaving a total of 13 free parameters. +Figures 13 and 14 show the best-fit solution. This was +found by manually adjusting the optimised solution by eye +to match the pole-direction data. The results are very sim- +ilar to those of model D, except that the regions of rocky +terrain with high torque efficiency are reduced to an inter- +mediate value of activity, between that of the rest of Rock +and the other terrain types. The red curves in Figures 3 - +9 show that this adjustment has little effect on the trajec- +tory, production, and rotation-rate fits, but now produces +an excellent match to the pole-direction data as well. Thus, +model E represents our best-fit solution overall. +When the acceleration curves are considered in detail, +model E fails to reproduce the tangential and normal com- +ponents in the same way as model D. The peak radial accel- +eration is slightly reduced, however, resulting in a slightly +better trajectory fit than for model D. We once again sought +improvements in the acceleration by fitting directly to the +curves, as well as examining the acceleration produced by +individual regions, but no overall better fit was found. Every +improvement in the acceleration curves led to a correspond- +ing degradation in the rotation fits. +4. Discussion +Our best-fit model overall is model E. This model is based +on a splitting of the surface according to morphological unit +types, with an artificially imposed further splitting accord- +ing to torque efficiency and a time-varying EAF. A num- +ber of trends can be seen across all the solutions, however, +which we discuss now, before we return to the interpreta- +tion of model E. +In common with the previous results (Attree et al. +2019), all models firstly require a higher EAF in the south- +ern than the northern hemisphere, as well as an EAF that +increases around perihelion. This increase in activity, over +and above the increase expected with heliocentric distance, +is a common result in the literature (Keller et al. 2015; +Kramer et al. 2019; Davidsson et al. 2022) and implies a +non-linear outgassing response to insolation. High activity +at perihelion is needed to fit the maximum outgassing rate +as well as the sharp peak in acceleration, which is mostly +contained in the radial component. +Non-gravitational torque, as expressed in the period and +spin-axis changes, is much more dependent on the exact +spatial distribution of activity (as also found by Kramer +& Läuter 2019), especially within this very active south- +ern hemisphere. For example, the correct magnitude of the +pole-direction fit is achieved in model E by distributing the +activity around the southern hemisphere in a specific way: +high activity in regions with low torque efficiency around +the south pole, with lower activity in areas with a high +Article number, page 7 of 13 + +0.025 +0.050 +0.075 +0.100 +0.125 +0.150 +0.175 +0.200 +Active FractionA&A proofs: manuscript no. Attree_NGA_Paper2_LanguageEdited + + +2 +4 +6 +8 +Total Insolation (J m−2) +1e9 +20 +40 +60 +80 +100 +120 +Gravitational Slope (deg.) +500 +1000 +1500 +2000 +2500 +Torque Efficiency (Nm) +-Z +Fig. 12. Various datasets mapped onto the southern hemisphere +of the comet. From top: Modulus of torque efficiency (|τ|), a ge- +ometric factor as described in the text; gravitational slope, i.e. +the angle between facet normal and local gravity vector; total +integrated insolation; and peak insolation. The three white lines +indicate the direction of the −r, −t, and −n vectors, averaged +over one rotation period at perihelion, i.e. the time-averaged di- +rections towards the Sun, ‘backwards’, and ‘down’ in the orbital +frame of the comet. ++Z +-Z +Fig. 13. Peak effective active fraction at perihelion for solution +E, mapped onto the shape model. +−400 +−300 +−200 +−100 +0 +100 +200 +300 +400 +Days from Perihelion +0.00 +0.05 +0.10 +0.15 +0.20 +Active Fraction +D st +Brittle +Smooth +Depression +Rock +Rock - Low ta +Fig. 14. Time-varying effective active fraction for solution E. +torque efficiency, such as towards the extremities of the +nucleus and parts of the head. This agrees well with the +distribution seen in Kramer et al. (2019) (see their Figs. 9 +and 10). As shown in Figure 12, these low-torque areas and +physical parameters, such as the total amount or peak of +insolation received or the gravitational slopes, do not ap- +pear to be correlated. The fact that morphologically similar +and similarly insolated regions on the head and body show +differing levels of activity may imply compositional differ- +ences between the two lobes of the nucleus, as suggested by +comparisons of region Wosret with the Anhur and Khonsu +regions by Fornasier et al. (2021). +When the seasonal orientation of the comet is consid- +ered alongside the acceleration curves, the reasons for the +differences between the trajectories of models C, D, and +E become clear. The large magnitudes of the normal and +tangential acceleration peaks in model C come from the +extreme activity ratio of the south polar regions and else- +where: At perihelion, when the outgassing is at a maximum, +the comet orientation is such that the southern hemisphere +most often points ‘downwards’ (in the negative direction in +the orbital plane, −ˆn), towards the Sun (−ˆr), and ‘back- +wards’ (along the negative of the orbital velocity vector +−ˆt). This is shown in Fig. 12 by three vectors, indicating +the time-averaged direction of ⟨−ˆr, −ˆt, −ˆn⟩ over one comet +Article number, page 8 of 13 + +200 +400 +600 +800 +1000 +1200 +Peak Insolation (w m-2)0.025 +0.050 +0.075 +0.100 +0.125 +0.150 +0.175 +0.200 +Active FractionN. Attree et al.: Activity distribution of comet 67P +rotation at perihelion. As the comet rotates, the unit vec- +tors sweep over its surface, but as a result of the spin-axis +orientation at this time, the southern hemisphere points in +the indicated direction on average. Thus, the net outgassing +force from the southern hemisphere produces a strong pos- +itive peak in all three of these components, as seen in the +data. Meanwhile, any outgassing from other areas of the +comet produces acceleration in different directions, reduc- +ing the net positive peaks. This is the case in models D and +E (and Kramer et al. 2019, etc.), where there is some activ- +ity in areas that are not aligned south, meaning that part of +the acceleration is in other directions and that the net pos- +itive normal and tangential forces are reduced (green and +red curves in Figs. 7 and 8 compared to orange). The radial +peak (Fig. 6) is less reduced because most outgassing is di- +rected towards the Sun, even in areas that are not aligned +south. +When the pole direction is fit, which is dependent on the +x and y components of the NGT, however, activity is pre- +ferred everywhere, or at least in a less extreme dichotomy +than in model C. If the torque distribution in the south- +facing regions alone could be adjusted to match the overall, +correct, torque distributions of models D and E, then the so- +lutions could be reconciled. However, figures 12 and 1 show +that the correlation between the z component of torque ef- +ficiency and its total modulus in the southern hemisphere +is complicated, meaning that any adjustment to the pole +direction (x and y torque components) will also affect the +rotation rate (z component). Any increase or decrease in the +perihelion activity of south-facing regions will also strongly +affect the acceleration. For this reason, improvement of the +acceleration or trajectory fit always degrades the pole di- +rection fit and vice versa; the facets controlling NGA and +NGT are spatially correlated. +At one instant in time, the non-gravitational torques +and accelerations will always be correlated by the spatial +pattern described above. However, the total torques and ac- +celerations integrated over some period (e.g. one rotation) +may not necessarily be so correlated. For example, torque is +evaluated in the body-fixed frame, so that it is independent +of the particular orientation of the comet at any one time. +The net acceleration vector, on the other hand, depends on +this orientation with respect to the Sun and on the helio- +centric coordinate frame, and it will vary over a cometary +rotation (i.e. the non time-averaged version of the vectors +shown in Fig. 12 will rotate around the shape model in the +body-fixed frame). In this way, the acceleration per facet in- +tegrated over one rotation period will be sensitive to both +the total outgassing from the facet over that period and +to its temporal variation, whereas the torque will only be +dependent on the total outgassing. +A possible way to optimise the fitting to the heliocen- +tric orbit without deteriorating the fit to the rotation-axis +orientation and period might then be to redistribute the +activity variation with local time. The idea of a lag an- +gle between the peak insolation and peak diurnal activity +has indeed been invoked in the past (see e.g. Davidsson +& Gutiérrez 2004), with recent work suggesting that water +activity might peak at 20◦ (Pinzón-Rodríguez et al. 2021; +Farnocchia et al. 2021) or even 50◦ (Kramer & Läuter 2019) +post-noon, with the latter lag angle varying with time and +being undetected before perihelion. Such a lag angle would +depend on the thermal inertia and the depth at which wa- +ter sublimates, making it complicated to model. Additional +enhanced activity may also arise at the morning terminator +due to sublimation of frost from the night. +CO2 emissions, which have not been considered here, +may also have a different local-time distribution. Pinzón- +Rodríguez et al. (2021) reported a peak at the evening ter- +minator. Davidsson et al. (2022) suggested that CO2 pro- +duces little NGA, due to both its small outgassing rate +compared to H2O and a smoother diurnal variation from a +deep sublimation depth and large lag-effect, leading to force +in all directions and a cancelling out of the net acceleration. +CO2 activity distributed in a specific way, however, might +still lead to a net torque, resulting in the required splitting +of the torque and acceleration, although it would, admit- +tedly, have to be quite a specific distribution. Gerig et al. +(2020) reported that about 10% of total dust emission orig- +inates from the night side, which may well be driven by +CO2 emission, while the peak perihelion outgassing rate +is roughly one order of magnitude lower than the rate for +water (Läuter et al. 2020). +Clearly, a more realistic thermal model, including ther- +mal inertia as well as possibly the emission of CO2, is +needed to fully reconcile the observed outgassing, accelera- +tions and torques. Below, we briefly analyse the results of +a recently published thermal model based on Fulle et al. +(2020). This does not include a local time-lag or CO2 emis- +sion, but offers an interesting comparison with and exten- +sion of the surface energy-balance models discussed above. +The model of Fulle et al. (2020), called model F here, as- +sumes a material made of water-containing centimetre-sized +pebbles, in which a constant energy balance is maintained +between the insolated surface and ice sublimating in the +interior of the pebbles. This leads to a set of four differen- +tial equations that must be solved simultaneously for each +time and facet, instead of the normal surface energy-balance +equation. The rest of the code runs as before, with the slight +complication that we cannot calculate self-heating in a self- +consistent way due to a technical limitation, as it relies +on an iteration between facets. We therefore calculated two +model F solutions: one solution in which the self-heating per +facet was calculated from a pure-ice surface, and another +with a pure-dust surface. These two energy inputs bracket +the full solution, whose surface temperature (and therefore +self-heating term) is intermediate between a pure-ice and +a pure-dust grey-body surface (Figure 15). The figure also +shows that the outgassing rate in the Fulle et al. (2020) +model is significantly reduced from that of a pure-ice sur- +face and has a distinctly non-linear shape, ranging between +effective active fractions of EAF∼ 0 − 20% as a function of +insolation. +Figure B.1 shows the resulting gas production curve +evaluating model F on the shape model, showing that the +model of Fulle et al. (2020) can naturally reproduce the +high perihelion outgassing rates without the need for an ef- +fective active fraction that varies with time. This confirms +the results of Ciarniello et al. (2021). +Figure B.2 shows the trajectory result obtained with +model F, while Figures B.3 and B.4 show the torque and +pole-direction curves. For a model without any fitting, the +results agree reasonably well with the data, although the +magnitude of the pole-direction changes are again too large, +and the trajectory fit and z torque are not as close as in +our best models (see Table 1 for fit statistics). +Figures B.5, B.6, and B.7 show similar results to before +for the accelerations: The overall magnitude of the radial +Article number, page 9 of 13 + +A&A proofs: manuscript no. Attree_NGA_Paper2_LanguageEdited +200 +300 +400 +T +emperature (K) +0 +200 +400 +600 +800 +1000 +1200 +1400 +E ergy I put (Wm +−2 +) +0.0000 +0.0002 +0.0004 +0.0006 +Outgassi g Rate (kg s +−1 + m +−2 +) +Grey-body +Ice +Fulle et al. 2020 +Fig. 15. Outputs of the pebble model of Fulle et al. (2020). +Top panel: Surface temperature as a function of energy input +for EAF = 0 grey-body and EAF = 1 pure-ice surfaces as well +as the pebble model. Bottom: Outgassing rate for the pure-ice +and the pebble model. +component is approximated well, but the peaks of the tan- +gential and normal accelerations are, again, much too small. +The radial acceleration is also not as peaked around peri- +helion as the observations, while its maximum is closer to +perihelion than the observed, delayed peak. +The implications for the pebble-based thermal model +are similar to those for the other models. A strong enhance- +ment in activity in the southern hemisphere is needed to fit +the narrowly peaked acceleration curves. In model F this +is partially provided by the non-linear insolation response, +but it is clear that an enhancement beyond even this, or +possibly a reduction in activity in other areas, is required. +Potentially, this could come from dust fallout from the in- +tensively active southern onto the equatorial and northern +regions, quenching them around perihelion. +Finally, experiments in which outgassing in different +sub-regions was scaled up and down relative to model F +(i.e. that reintroduced a kind of effective active fraction, but +with a different magnitude) also showed a similar response. +The large magnitude of the pole-direction change could be +reduced by decreasing activity in the high-torque areas, as +in solution E, while the trajectory fit could not be improved +without degrading the three torque components. This shows +that although the pebble model of Fulle et al. (2020) is an +improvement over a simple surface energy-balance model, +it is still not a complete description of the surface activity +distribution of the comet. An even more complex thermal +model, possibly requiring time-varying dust fallout as well +as thermal inertia and CO2, is still required for a fuller +description. +5. Conclusion +We adjusted a simple thermophysical model to match the +combined total outgassing rate and all six components of +its resulting non-gravitational forces and torques observed +by Rosetta at comet 67P. We parametrised the model in +terms of different EAF relative to a pure water-ice surface, +and linked their distribution to different terrain types on +the comet. We also compared our results to the more com- +plicated thermal model of Fulle et al. (2020). +Firstly, the results of the fitting confirm the hemispheri- +cal dichotomy in relative activity levels (also seen by Keller +et al. 2015; Kramer et al. 2019; Davidsson et al. 2022). +The EAF of the southern hemisphere of 67P at perihelion +is roughly an order of magnitude larger than that of the +northern hemisphere. This increase in relative activity with +heliocentric distance (over and above the geometric effect) +leads to the steep power-law rise in total outgassing and +implies a non-linear response of the surface to insolation. +This response arises naturally from the model of Fulle et al. +(2020), which assumes a pebble structure for the nucleus. It +might also be caused or enhanced by changes in the thick- +ness of an inert dust-layer resulting from devolatilisation or +redistribution of ejected particles (so-called ‘airfall’), how- +ever. +Secondly, for the first time, we correlated differences in +responses to insolation with the different terrain types ob- +served on 67P (Thomas et al. 2015). We found a good match +to most of the Rosetta dataset (total outgassing, NGA, and +rotation-rate changes) by doing this. Consolidated Rocky +terrains (mainly seen in the southern hemisphere) have +the highest relative activity, alongside ‘smooth’ areas in +Imhotep, Anubis, and Hapi (Longobardo et al. (2020) also +report more primordial ‘fluffy’ particles detected by the GI- +ADA instrument over our Rocky consolidated material). +Areas with dusty airfall deposits, such as Ma’at and Ash, +as well as the floors of the two large depressions (Hatmehit +and Aten) and the brittle terrain (mostly located in Seth), +have lower activity. These spatial distributions of EAF re- +semble previous results (Marschall et al. 2016; Kramer & +Läuter 2019), but are associated with the morphological +terrain types for the first time here. Physically, this prob- +ably relates to the thickness of the dust covering, with de- +pressions and dusty regions covered in a thick layer of inert +fallback material, compared to the relatively volatile-rich +exposed consolidated terrain. High activity in the smooth +regions such as Hapi (as also noted by Marschall et al. 2016; +Fulle et al. 2020) would then represent volatile-rich airfall, +which has remained wet during its flight in the coma and +stay in the new location, due to local seasonal conditions. +However, this interpretation is complicated by two fac- +tors. Firstly, the fact that most consolidated terrain is lo- +cated in the southern hemisphere, combined with the fact +that as a result of the particular seasonal and orbital con- +figuration of 67P, activity here dominates total outgassing, +NGA, and NGT. This means that it is difficult to deter- +mine the interplay between the intrinsic factors (e.g. the +different surface types or compositions) and the extrinsic +factors (insolation pattern determined by seasonal effects). +The two are indeed likely linked, and the feedback between +insolation and dust-cover drives the relative appearance of +the two hemispheres. +Secondly, in order to fit the pole-axis orientation data +in particular, an additional splitting of activity is needed +(NGT is, in general, much more sensitive than NGA to +spatial activity patterns). Lower activity is found in some +of the extremities of the body, and particularly on the head +in the Wosret region, relative to the regions close to the +south pole at the boundary of body and neck, even though +these regions are not morphologically different or exposed +to particularly different patterns of insolation. This is the +case both for the basic thermal model and the model of +Article number, page 10 of 13 + +N. Attree et al.: Activity distribution of comet 67P +Fulle et al. (2020) that otherwise improves on it. This may +imply a compositional or structural difference between the +two lobes of the comet (as suggested by Fornasier et al. +2021), although we cannot rule out other effects at present +(see next paragraph). +Finally, difficulties remain in simultaneously fitting the +NGA and NGT because the areas that strongly affect both +in the southern hemisphere (the whole of which receives a +similar amount of insolation overall) are spatiall correlated. +Further splitting of activity across the surface cannot im- +prove the fits, that is, increasing the spatial resolution of a +surface activity model does not help to match the Rosetta +data. This link would be broken if outgassing varied in local +time over a comet rotation (i.e. a lag angle between peak +insolation and peak outgassing), suggesting that more ad- +vanced time-dependent thermal models may be necessary +to fully understand the outgassing pattern of 67P and the +activity mechanism of comets. In summary, both spatially +and temporally varying activity is needed to fit the 67P +outgassing pattern in a way that is not easily reproduced +by any current thermal model. +Overall, the use of non-gravitational dynamics in the +form of trajectory and rotation data clearly aids in distin- +guishing between different activity distributions and ther- +mophysical models for comet 67P. This can help to test +various general ideas about cometary activity and struc- +ture. +Acknowledgements. J.A. and N.A.’s contributions were made in the +framework of a project funded by the European Union’s Horizon +2020 research and innovation programme under grant agreement No +757390 CAstRA. J.A. also acknowledges funding by the Volkswagen +Foundation. We thank Tobias Kramer for useful discussions and the +anonymous reviewer whose comments improved the quality of this +manuscript. +References +Annex, A. M., Pearson, B., Seignovert, B., et al. 2020, Journal of +Open Source Software, 5, 2050 +Attree, N., Jorda, L., Groussin, O., et al. 2019, A&A, 630, A18 +Blum, J., Gundlach, B., Krause, M., et al. 2017, MNRAS, 469, S755 +Cambianica, P., Cremonese, G., Fulle, M., et al. 2021, MNRAS, 504, +2895 +Ciarniello, M., Fulle, M., Tosi, F., et al. 2021, in 52nd Lunar and Plan- +etary Science Conference, Lunar and Planetary Science Conference, +2031 +Combi, M., Shou, Y., Fougere, N., et al. 2020, Icarus, 335, 113421 +Davidsson, B. J. R. 2021, MNRAS, 505, 5654 +Davidsson, B. J. R. & Gutiérrez, P. J. 2004, Icarus, 168, 392 +Davidsson, B. J. R. & Gutiérrez, P. J. 2005, Icarus, 176, 453 +Davidsson, B. J. R., Samarasinha, N. H., Farnocchia, D., & Gutiérrez, +P. J. 2022, MNRAS, 509, 3065 +Davidsson, B. J. R., Sierks, H., Güttler, C., et al. 2016, A&A, 592, +A63 +Farnocchia, D., Bellerose, J., Bhaskaran, S., Micheli, M., & Weryk, R. +2021, Icarus, 358, 114276 +Fornasier, S., Bourdelle de Micas, J., Hasselmann, P. H., et al. 2021, +A&A, 653, A132 +Fulle, M., Blum, J., & Rotundi, A. 2019, ApJ, 879, L8 +Fulle, M., Blum, J., Rotundi, A., et al. 2020, MNRAS, 493, 4039 +Gerig, S. B., Pinzón-Rodríguez, O., Marschall, R., Wu, J. S., & +Thomas, N. 2020, Icarus, 351, 113968 +Gulkis, S., Allen, M., von Allmen, P., et al. 2015, Science, 347 +[http://science.sciencemag.org/content/347/6220/aaa0709.full.pdf] +Gundlach, B., Fulle, M., & Blum, J. 2020, MNRAS, 493, 3690 +Gutiérrez, P. J., Jorda, L., Samarasinha, N. H., & Lamy, P. 2005, +Planet. Space Sci., 53, 1135 +Hansen, K. C., Altwegg, K., Berthelier, J.-J., et al. 2016, MNRAS, +462, S491 +Jorda, L., Gaskell, R., Capanna, C., et al. 2016, Icarus, 277, 257 +Julian, W. H. 1990, Icarus, 88, 355 +Keller, H. U., Mottola, S., Hviid, S. F., et al. 2017, MNRAS, 469, S357 +Keller, H. U., Mottola, S., Skorov, Y., & Jorda, L. 2015, A&A, 579, +L5 +Kramer, T. & Läuter, M. 2019, A&A, 630, A4 +Kramer, T., Läuter, M., Hviid, S., et al. 2019, A&A, 630, A3 +Lasagni Manghi, R., Zannoni, M., Tortora, P., et al. 2021, in EGU +General Assembly Conference Abstracts, EGU General Assembly +Conference Abstracts, EGU21–14765 +Läuter, M., Kramer, T., Rubin, M., & Altwegg, K. 2020, MNRAS, +498, 3995 +Longobardo, A., Della Corte, V., Rotundi, A., et al. 2020, Monthly +Notices of the Royal Astronomical Society, 496, 125 +Marschall, R., Liao, Y., Thomas, N., & Wu, J.-S. 2020, Icarus, 346, +113742 +Marschall, R., Mottola, S., Su, C. C., et al. 2017, A&A, 605, A112 +Marschall, R., Su, C. C., Liao, Y., et al. 2016, A&A, 589, A90 +Marsden, B. G., Sekanina, Z., & Yeomans, D. K. 1973, AJ, 78, 211 +Marshall, D. W., Hartogh, P., Rezac, L., et al. 2017, A&A, 603, A87 +Mottola, S., Attree, N., Jorda, L., et al. 2020, Space Sci. Rev., 216, 2 +Newhall, X. X., Standish, E. M., & Williams, J. G. 1983, A&A, 125, +150 +Pinzón-Rodríguez, O., Marschall, R., Gerig, S. B., et al. 2021, A&A, +655, A20 +Preusker, F., Scholten, F., Matz, K.-D., et al. 2017, A&A, 607, L1 +Rein, H. & Liu, S.-F. 2012, A&A, 537, A128 +Rein, H. & Spiegel, D. S. 2015, MNRAS, 446, 1424 +Samarasinha, N. H., Mueller, B. E. A., Belton, M. J. S., & Jorda, L. +2004, Rotation of cometary nuclei, ed. M. C. Festou, H. U. Keller, +& H. A. Weaver, 281–299 +Sekanina, Z. 1993, A&A, 277, 265 +Standish, E. 1998, IOM, 312.F-98-048 +Thomas, +N., +El +Maarry, +M. +R., +Theologou, +P., +et +al. +2018, +Planet. Space Sci., 164, 19 +Thomas, N., Sierks, H., Barbieri, C., et al. 2015, Science, 347, aaa0440 +Whipple, F. L. 1950, ApJ, 111, 375 +Yeomans, D. K. & Chodas, P. W. 1989, AJ, 98, 1083 +Article number, page 11 of 13 + +A&A proofs: manuscript no. Attree_NGA_Paper2_LanguageEdited +Appendix A: Astrometry +Table A.1. Initial positions of 67P at −350 days relative to +perihelion in the J2000 ecliptic coordinate frame. +Quantity +Value +t (Js) +462463456.58755416 +x (km) +1.99549521 × 10+08 +y (km) +−4.76677235 × 10+08 +z (km) +−5.66149293 × 10+07 +˙x (km s−1) +7.34031872 × 10+00 +˙y (km s−1) +1.41777157 × 10+01 +˙z (km s−1) +4.26145500 × 10−01 +Appendix B: Model F, detailed results +−300 +−200 +−100 +0 +100 +200 +Days fr m Periheli n +10 +25 +10 +26 +10 +27 +10 +28 +Outgassing Rate (s +−1 +) +M del F dust SH +M del F ice SH +Observed +Fig. B.1. Observed total gas production (Rosetta/ROSINA val- +ues from Hansen et al. 2016) compared to two versions of model +F, based on Fulle et al. (2020). +300 +200 +100 +0 +100 +200 +300 +Days from Perihelion +0 +200 +400 +600 +800 +1000 +1200 +Range Residuals (km) +Model F dust SH +Model F ice SH +Fig. B.2. Observed minus computed Earth-comet range, R, for +two versions of model F. +−300 +−200 +−100 +0 +100 +200 +300 +Days from Perihelion +0 +2 +4 +6 +8 +T +or ue (Nm) +1e6 +Observed +Model F dust SH +Model F ice SH +Fig. B.3. Observed z component of the torque compared to two +versions of model F. +69 +70 +71 +72 +73 +74 +Right Asce sio ( +∘ +) +63.8 +64.0 +64.2 +64.4 +64.6 +64.8 +65.0 +65.2 +65.4 +Decli atio ( +∘ +) +Model F dust SH +Model F ice SH +Observed +Fig. B.4. Observed pole orientation (Ra/dec) compared to two +versions of model F. +300 +200 +100 +0 +100 +200 +300 +400 +Days from Perihelion +0 +1 +2 +3 +4 +5 +6 +7 +8 +NGA r (AU d +2) +1e +10 +Observed +Model F dust SH +Model F ice SH +Fig. B.5. Observed radial acceleration in the cometary (ˆr, ˆt, ˆn) +frame compared to two versions of model F. +Article number, page 12 of 13 + +N. Attree et al.: Activity distribution of comet 67P +300 +200 +100 +0 +100 +200 +300 +400 +Days from Perihelion +0.5 +0.0 +0.5 +1.0 +1.5 +2.0 +NGA t (AU d +2) +1e +10 +Observed +Model F dust SH +Model F ice SH +Fig. B.6. Observed tangential acceleration in the cometary +(ˆr, ˆt, ˆn) frame compared to two versions of model F. +300 +200 +100 +0 +100 +200 +300 +400 +Days from Perihelion +0.0 +0.5 +1.0 +1.5 +2.0 +2.5 +3.0 +3.5 +NGA n (AU d +2) +1e +10 +Observed +Model F dust SH +Model F ice SH +Fig. B.7. Observed normal acceleration in the cometary (ˆr, ˆt, ˆn) +frame compared to two versions of model F. +Article number, page 13 of 13 + diff --git a/DtE4T4oBgHgl3EQfGQwj/content/tmp_files/load_file.txt b/DtE4T4oBgHgl3EQfGQwj/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..2cb4df14e4cb6192403daa713daeaa46367a1713 --- /dev/null +++ b/DtE4T4oBgHgl3EQfGQwj/content/tmp_files/load_file.txt @@ -0,0 +1,980 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf,len=979 +page_content='Astronomy & Astrophysics manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Attree_NGA_Paper2_LanguageEdited ©ESO 2023 January 13, 2023 Activity distribution of comet 67P/Churyumov-Gerasimenko from combined measurements of non-gravitational forces and torques N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Attree1, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Jorda2, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Groussin2, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Agarwal1, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Lasagni Manghi3, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Tortora3, 4, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Zannoni3, 4, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Marschall5 1 Institut für Geophysik und extraterrestrische Physik, Technische Universität Braunschweig, Mendelssohnstr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 3, 38106 Braunschweig, Germany (e-mail: n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='attree@tu-braunschweig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='de) 2 Aix Marseille Univ, CNRS, CNES, Laboratoire d’Astrophysique de Marseille, Marseille, France 3 Alma Mater Studiorum - Università di Bologna, Dipartimento di Ingegneria Industriale, Via Fontanelle 40, I-47121 Forlì, Italy 4 Alma Mater Studiorum - Università di Bologna, Centro Interdipartimentale di Ricerca Industriale Aerospaziale, via Baldassarre Carnaccini 12, I-47121, Forlì, Italy 5 CNRS, Laboratoire J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Lagrange, Observatoire de la Côte d’Azur, Boulevard de l’Observatoire, CS 34229 - F 06304 NICE Cedex 4, France January 13, 2023 ABSTRACT Aims.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Understanding the activity is vital for deciphering the structure, formation, and evolution of comets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' We inves- tigate models of cometary activity by comparing them to the dynamics of 67P/Churyumov-Gerasimenko.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' We matched simple thermal models of water activity to the combined Rosetta datasets by fitting to the total outgassing rate and four components of the outgassing induced non-gravitational force and torque, with a final manual adjustment of the model parameters to additionally match the other two torque components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' We parametrised the thermal model in terms of a distribution of relative activity over the surface of the comet, and attempted to link this to different terrain types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' We also tested a more advanced thermal model based on a pebble structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' We confirm a hemispherical dichotomy and non-linear water outgassing response to insolation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' The southern hemisphere of the comet and consolidated terrain show enhanced activity relative to the northern hemisphere and dust-covered, unconsolidated terrain types, especially at perihelion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' We further find that the non-gravitational torque is especially sensitive to the activity distribution, and to fit the pole-axis orientation in particular, activity must be concentrated (in excess of the already high activity in the southern hemisphere and consolidated terrain) around the south pole and on the body and neck of the comet over its head.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' This is the case for both the simple thermal model and the pebble-based model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Overall, our results show that water activity cannot be matched by a simple model of sublimating surface ice driven by the insolation alone, regardless of the surface distribution, and that both local spatial and temporal variations are needed to fit the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Conclusions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Fully reconciling the Rosetta outgassing, torque, and acceleration data requires a thermal model that includes both diurnal and seasonal effects and also structure with depth (dust layers or ice within pebbles).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' This shows that cometary activity is complex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Nonetheless, non-gravitational dynamics provides a useful tool for distinguishing between different thermophysical models and aids our understanding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Key words.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' comets: general, comets: individual (Churyumov-Gerasimenko), planets and satellites: dynamical evolution and stability 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Introduction Comets are amongst the most primordial Solar System ob- jects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' They formed directly from the protoplanetary disc and survived mostly unaltered for much of their lifetimes in the outer Solar System.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' They are therefore vital targets for our understanding of planet formation and the history of the early Solar System.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Upon entering the inner Solar System, comets are heated by the Sun and undergo ac- tivity;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' that is, ices are sublimated and gas and dust are ejected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Cometary activity poses open questions related to the structure, composition, and thermophysical properties of the nucleus material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' This is directly connected to their formation in the early Solar System.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Whether cometary nuclei, and by extension planets, formed from the gravi- tational collapse of clouds of centimetre-sized pebbles (as proposed in Blum et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2017) or by continual collisional growth (Davidsson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2016) has direct implications for the structure and strength of the near-surface material that controls outgassing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' In addition to being directly observable, the outgassing produces a reaction force on the nucleus that can alter its trajectory (as first recognised by Whipple 1950 and de- scribed by Marsden et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 1973) and rotation state (see Samarasinha et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Measuring the changing orbits Article number, page 1 of 13 arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='04892v1 [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='EP] 12 Jan 2023 A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Attree_NGA_Paper2_LanguageEdited and spins of comets therefore provides a useful insight into the the micro-physics of the activity mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Many thermophysical models have been proposed to ex- plain the activity (see recent examples by Fulle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2019, Gundlach et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2020, and Davidsson 2021), and these can be compared to the outgassing rates of observed comets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' In particular, comet 67P/Churyumov-Gerasimenko (67P here- after) provides an excellent dataset because it was visited by the Rosetta spacecraft between 2014 and 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' The space- craft collected detailed measurements of the size, shape, surface properties, and time-varying rotation state and out- gassing of the nucleus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Finding the distribution of activity across the nucleus of 67P that fits the various measurements of the total outgassing rate best (Hansen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Mar- shall et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Combi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Läuter et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2020, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=') has produced several so-called activity maps (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Marschall et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2016, 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Läuter et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2020, ), which are often ex- pressed as an effective active fraction (EAF) relative to a pure water-ice surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' When examining only the summed total outgassing, however, there is always a degeneracy in the retrieved activity distribution (Marschall et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2020), whilst, at the same time, the effects of seasonal changes in insolation and dust cover across the surface of 67P are com- plicated (Keller et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Cambianica et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Com- paring the effects of a model outputted non-gravitational acceleration (NGA) and torque (NGT) to the dynamics of 67P can provide a further constraint on the model parame- ters and on our understanding of the activity (Attree et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Kramer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Kramer & Läuter 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Mottola et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Simple NGA models, such as those by Marsden et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' (1973) and Yeomans & Chodas (1989), parametrise the acceleration using variables scaled to a general water- production curve, and therefore provide limited insight into the physics of the activity on an individual comet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' More complex models (following from Sekanina 1993) re- late the observed NGA and NGT to the outgassing via a thermal model and some distribution of ices or active areas across the nucleus surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' If independent measure- ments of this distribution and/or the outgassing rate can be made, then cometary masses and spin axes can be mea- sured from ground-based observations, as was achieved for 67P (Davidsson & Gutiérrez 2005;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Gutiérrez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Rosetta then provided both the detailed outgassing data mentioned above, as well as precise measurements of the nucleus position and rotation via radio-tracking and op- tical navigation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' As summarised in Mottola et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' (2020), various attempts have been made to compare thermal mod- els to the NGA and NGT forces of 67P (Keller et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Davidsson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2022) and to fit its non-gravitational tra- jectory (Kramer & Läuter 2019), rotation state (Kramer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2019), and both in combination with outgassing (At- tree et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' In Attree et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' (2019), our previous paper on this topic, we used the EAF formalism to fit surface distributions to the observed Earth-comet range (the most accurate compo- nent of the comet ephemeris, based on the spacecraft radio tracking), total gas production (measured by ROSINA, the Rosetta Spectrometer for Ion and Neutral Analysis;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Hansen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2016), and the change in spin rate (z component of the torque, measured as part of the nucleus shape recon- struction;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Jorda et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' We found that a large EAF in the southern hemisphere of the comet, as well as an increase in EAF around perihelion, were needed to fit both the to- tal production measurements and the NGA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' However, our model was limited by not considering the other components of the NGT (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' the change in the spin axis orientation, as well as its magnitude), and by a rather nonphysical way of splitting the surface into areas of differing activity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Ad- ditionally, discontinuities in the cometary heliocentric tra- jectory reconstructed by the European Space Operations Centre that arose because the NGA was excluded from the operational dynamical model, have complicated the anal- ysis by making it difficult to extract smooth acceleration curves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Kramer & Läuter (2019) addressed this problem by per- forming their own N-body integrations with a model fol- lowing Yeomans & Chodas (1989) and varying initial con- ditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' They then fitted a smoothed, interpolated curve to the residuals to extract time-varying NGA curves, but they did not compare them to a full thermal model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' In a separate paper (Kramer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2019), the authors did compare a phys- ical thermal model, again using the EAF formalism, to both the rotation rate and axis orientation data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Similarly to our results, their results also required a relatively higher EAF in the southern than in the northern hemisphere, as well as an enhanced outgassing response to insolation around perihe- lion to fit the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Kramer & Läuter (2019) noted that the NGT is much more dependent on the spatial distribution of activity than the NGA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Since then, two additional reconstructions of the Rosetta/67P trajectory have been performed (Farnocchia et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Lasagni Manghi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Farnocchia et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' (2021) used a rotating-jet model following Sekanina (1993) to fit ground-based astrometric observations and radio- ranging measurements before and after perihelion (where the spacecraft NGAs are smaller and the range accuracy is higher).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Lasagni Manghi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' (2021), on the other hand, used the full Rosetta two-way range and differential one- way range (∆DOR) dataset, also including low-accuracy data close to perihelion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' They tested various NGA models, including a rotating-jet model, and found a best-fit tra- jectory using an empirical, stochastic acceleration model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Both of these works produced acceleration curves to which a thermal model can be compared.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Davidsson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' (2022) did just that by comparing the output of a more complex thermal model (NIMBUS;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Davidsson 2021) to the acceleration curves of Farnocchia et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' (2021) and Kramer & Läuter (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' They found rel- atively good agreement without fitting, but had to vary several model parameters (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' the sublimation-front depth and the gas diffusivity) between the northern and south- ern hemispheres and pre- and post-perihelion, in order to match the outgassing data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' This reinforces the ideas of a hemispheric dichotomy and time-dependent thermophysi- cal properties, and it also demonstrates the complicated nature of trying to model the full thermophysical system of sublimation, gas flow, and dust.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' These studies show the usefulness of considering the non-gravitational dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' No study has analysed the full six components of NGA and NGT simultaneously, how- ever (we analyse all six here, but only four are included in the formal fitting procedure), and several other weaknesses exist, such as nonphysical surface distributions or compli- cated descriptions leading to unfitted models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' It is per- tinent, therefore, to re-examine the full non-gravitational dynamics of 67P with a simple thermal model that can be parametrised in terms of real surface features while be- Article number, page 2 of 13 N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Attree et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' : Activity distribution of comet 67P ing easily compared with more complicated models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' This is what we attempt to do here, bearing in mind that the aim is not to find the full description of cometary activity, but a model that adequately describes the data and points towards the underlying physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' The rest of this paper is organised as follows: in Sec- tion 2 we describe how we updated the model of Attree et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' (2019) for use here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' In Section 3 we describe three different parametrisations of the surface activity distribu- tion and their results in the model fit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' These results are discussed, with reference to a run with the more advanced thermal model of Fulle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' (2020) in Section 4, before we conclude in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Method We followed the method of the first paper (Attree et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2019) by first calculating surface temperatures over a shape model of 67P (SHAP7;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Preusker et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2017) with a simple energy-balance thermal model and then computing the re- sulting non-gravitational forces and torques and implement- ing them in an N-body integration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' The model was then optimised by scaling the relative activity of various areas of the shape model up and down, minimising the residuals to the observed datasets: the Earth-comet range (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' the scalar projection of the three-dimensional comet position in the Earth-comet direction, R, with NR = 1000 data points) or the directly extracted NGAs from Lasagni Manghi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' (2021) (with NNGA = 17000 data points in each of the three components);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' the total gas production (NQ = 787, Hansen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2016);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' and the spin-axis (z) aligned component of the torque (NTz = 1000, Jorda et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Additionally, we now also computed the change in the orientation of the ro- tation axis (Kramer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2019) and used this as an output to compare different models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' The thermal model computes the surface energy- balance, taking insolation, surface thermal emission, sub- limation of water ice, projected shadows, and self-heating into account (see Attree et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2019 for details).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Heat con- duction into the nucleus is neglected for numerical reasons, but is small because of the low thermal inertia of the comet (Gulkis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Heat conduction would mainly affect night-time temperatures, which are very low and contribute little to the outgassing (but see the discussion in Section 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Again for numerical reasons, surface temperatures are cal- culated roughly once every 10 days for a full 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='4 hour ro- tation, and the derived quantities are interpolated (see de- tails below) to produce smooth curves over the full mission period of about two years.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Surface temperatures are each computed twice, once assuming an effective active fraction EAF = 0 (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' pure grey-body dust surface), and once with EAF = 1 (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' sublimation from a pure water-ice surface), and the temperatures and sublimation rates are saved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' In the fitting process, the pure water-ice sublimation rate is then scaled by a variable EAF and is used, along with the sublimation gas velocity calculated from the zero-ice surface temperature, to compute the outgassing force per facet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' The momentum coupling parameter was assumed to be η = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='7 (Attree et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Torque per facet was also calculated here using the “torque efficiency” formalism used before (Keller et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2015), where τ is the facet torque ef- ficiency or moment arm, which is a geometric factor that was computed once at the beginning of the run.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' The use of the higher zero-ice temperature for the gas thermal veloc- ity assumes that the gas equilibrates with the dusty surface, and this means that our derived EAF values may be lower estimates compared with some other thermal models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' The N-body integration was performed using the open- source REBOUND code1 (Rein & Liu 2012), complete with full general relativistic corrections (Newhall et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 1983) as implemented by the REBOUNDx extension pack- age2, and including all the major planets as well as Pluto, Ceres, Pallas, and Vesta.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Objects were initialised with their positions and velocities in the J2000 ecliptic coordinate system according to the DE438 Solar System ephemerides (Standish 1998), with 67P given its initial state vector from the new Rosetta trajectory reconstruction of Lasagni Manghi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' (2021) (Table A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' The system was then inte- grated forward in time from t = −350 to +350 days relative to perihelion, using the IAS15 integrator (Rein & Spiegel 2015) and the standard equations of motion, with the addi- tion of a custom acceleration, aNG, for 67P, provided by our model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' The Earth-comet range, which is the most accurate component of the comet trajectory, was computed for com- parison with the reconstructed trajectory (extracted using the SpiceyPy Python package;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Annex et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' A bounded least-squares fit to the residuals was then performed using standard methods implemented in Scien- tific Python whilst varying the EAF parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' When forming the overall objective function to be minimised (see Eqns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 9 and 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' in Attree et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2019), the datasets were weighted by a factor λ so that each contributed roughly the same to the overall fit (see Table 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' The datasets used in all fits were the model outputted total outgassing rate and the z component of the torque, both with λQ = λTz = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Fur- thermore, in some fits, we then used the computed Earth- comet range (with λR = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='02), while in others, we directly compared to the three components of the NGA extracted by Lasagni Manghi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' (2021) in the cometocentric radial- transverse-normal frame (radial to the Sun, ˆr, tangential to the orbit, ˆt, and normal to it).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' In this case, the inte- gration was only performed once at the end to check the Earth-comet range, but the weighting was zero in the fit (λR = 0), while λNGA = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Performing the N-body inte- gration only once speeds the process up by several times, with individual runs taking a few minutes and fits taking up to a day, depending on the parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' All parameters were interpolated to the observational data sampling-times using the Fourier method described below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' We first confirm that the Lasagni Manghi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' (2021) accelerations match the real comet trajectory well when they are input into our N-body integration, and they re- cover the Earth-comet range to within a few hundred me- tres.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' This residual, which is most likely the result of the different integration techniques and perturbing bodies we used, is well below the uncertainty of our thermal model runs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Previously, the x and y components of the torque vector were discarded, but they were now used when we calculated the changes in pole orientation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' In principle, the rates of change of the angular velocity (Ω) of the comet around its three principal axes can be related (see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Julian 1990) to 1 http://rebound.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='readthedocs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='io/en/latest/ 2 http://reboundx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='readthedocs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='io/en/latest/index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='html Article number, page 3 of 13 A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Attree_NGA_Paper2_LanguageEdited the torque components by Ix ˙Ωx = (Iy − Iz)ΩyΩz + Tx, Iy ˙Ωy = (Iz − Ix)ΩxΩz + Ty, Iz ˙Ωz = (Ix − Iy)ΩxΩy + Tz, (1) where Ix = 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='559 × 1018, Iy = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='763 × 1019, and Iz = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='899×1019 kg m2 are the moments of inertia derived from the shape model assuming a constant density of 538 kg m−3 (Preusker et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2017), and to the pole orientation right ascension, RA, and declination, Dec, by ˙ψ = −Ωy cos(ψ) − Ωx sin(ψ) tan(θ) + Ωz, ˙φ = Ωy cos(ψ) + Ωx sin(ψ) sin(θ) , ˙θ = Ωx cos(ψ) − Ωy sin(ψ), (2) via the Euler angles φ = π/2 + RA, θ = π/2 − Dec, and ψ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' In practice, the fact that our model runs over individual rotations separated by gaps means that the torque curves are discontinuous and cannot be directly integrated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' We therefore followed the technique of Kramer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' (2019) and applied a Fourier analysis to the torque curves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' The method proceeds by i) extracting the torque over a single rotation as a function of the sub-solar longitude, using Kramer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' (2019) Eqns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 26, 27, ii) computing the Fourier transform as a function of sub-solar longitude using Eqn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 23, iii) inter- polating the Fourier terms as smooth curves over the full Rosetta period;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Eqn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 24, and iv) reconstructing the torque at a chosen time by the inverse Fourier transform;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Eqn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' This allows the calculation of a smoothly interpolated torque value at any given time, Tx,y,z(t), for use in the ro- tation equations (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' The set of simultaneous differential equations given by Eqns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 1 and 2 was then integrated using standard func- tions in Scientific Python and the initial conditions RA = 69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='427◦, Dec = 64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='0◦, and ψ = 330.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='703◦ at t = −377.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='22 days relative to perihelion (Kramer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2019) for the pe- riod t = [−377.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='22 : 402.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='48], corresponding to the duration of the Rosetta measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' The resulting RA(t), Dec(t) values were not used in the fit due to technical limita- tions, but were directly compared with the observations as a model output.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Results 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Model C We began by rerunning the best-fit model of the previous paper, designated model C in Attree et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' This model parametrised the activity distribution by splitting the surface into the 26 regions, defined by Thomas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' (2015) (see their figures for maps), and then grouping them into five super-regions following Marschall et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' (2016)(see Figure 4 in Attree et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2019), before finally splitting the Southern super-region into two (see Figure 17 in Attree et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2019) and allowing these to vary their EAF with time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' With 6 super-regions and the 6 time-variation parameters, there are a total of 12 free parameters in this model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' These super-regions consist of region 1, covering the equatorial ar- eas;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' region 2, covering the base of the comet body and top of the head;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' the individual regions Hathor and Hapi;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' and +Z Z Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Peak effective active fraction at perihelion for solution C, mapped onto the shape model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' −400 −300 −200 −100 0 100 200 300 400 Days from Perihelion 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='4 Active Fraction So th - Region 1 Region 2 Hathor Hapi So th + Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Time-varying effective active Fraction for solution C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' two southern super-regions split on a per-facet basis by the sign of the z component of the torque efficiency (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' south positive with τz > 0 and south negative with τz < 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' This splitting was the only way in which a satisfactory fit to the z torque (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' rotation-rate data) could be achieved, but it remains somewhat artificial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Figure 1 shows the best- fit solution achieved here, mapped onto the shape model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' This shows the discontinuous and patchy appearance of the southern super-regions, as well as the north-south EAF di- chotomy and activity in Hapi (the light blue area in the northern neck region).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' We optimised this model again here and, with a slightly differing procedure for sampling and interpolating the com- putational output, produced very similar results to before, with no significant improvement in the fit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Next, we in- stead fit the model directly to the Lasagni Manghi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' (2021) NGA curves as described above, producing the best- fit solution shown mapped onto the shape-model in Figure 1 (where the values shown are peak EAF, the maximum value for all times), and with time in Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' The out- put is very similar to the previous solution in Attree et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' (2019), but Figure 2 shows an even more pronounced spike in EAF around perihelion than before.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' The model fits are shown in the orange curves in Fig- ures 3, 4, and 5, with the fit statistics in the first line of Article number, page 4 of 13 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='30 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='35 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='40 Active FractionN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Attree et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' : Activity distribution of comet 67P −300 −200 −100 0 100 200 Days from Perihelion 10 26 10 27 10 28 Ou gassing Ra e (s −1 ) Model C Model D Model E Observed Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Observed total gas production (ROSINA values from Hansen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2016) compared to solutions C, D, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 300 200 100 0 100 200 300 Days from Perihelion 200 150 100 50 0 50 100 150 200 Range Residuals (km) Model C Model D Model E Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Observed minus computed Earth-comet range, R, for solutions C, D, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' The z torque (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 5) and total gas production from ROSINA (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 3) are reasonably well fit, with the perihelion peak-values matched, but with a slightly differ- ing shape around the inbound equinox roughly 100 days before perihelion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' An improvement in the trajectory fit is attained, with the new RMS residual value of 34 km re- duced from the previously achieved 46 km.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' The shape of the curve is similar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' The orange curves in Figures 6, 7, and 8 show the in- dividual acceleration curves in the cometocentric (ˆr, ˆt, ˆn) frame compared to the values extracted by Lasagni Manghi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' The radial component makes up the bulk of the acceleration and is reasonably well matched by model C, with the peak value being ∼ 50% too high.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' The normal and tangential components are of smaller magnitude and are reasonably well fit;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' the secondary, negative peak of the tangential component after perihelion is the worst area of the fit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' The remaining 34 km residuals to the observed tra- jectory most likely stem from our inability to fit this area of the tangential acceleration, combined with the too large radial component peak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' −300 −200 −100 0 100 200 300 Days from Perihelion 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='0 T or ue (Nm) 1e7 Observed Model C Model D Model E Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Smoothed observed z component of the torque com- pared to solutions C, D, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' The grey area represents the 1σ uncertainty (see Attree et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2019 for details).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 300 200 100 0 100 200 300 400 Days from Perihelion 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='0 NGA r (AU d 2) 1e 9 Observed Model C Model D Model E Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Observed radial acceleration in the comet (ˆr, ˆt, ˆn) frame with the 5σ uncertainty (from Lasagni Manghi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2021), com- pared to solutions C, D, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Higher-order Fourier terms cor- responding to daily oscillations are omitted for clarity, but are included in the fit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' When the pole orientation was calculated, as shown in the orange curve of Figure 9, it was a very poor fit to the data, moving off in the opposite direction to the observed changes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' This demonstrates that the problem is ill-posed with multiple solutions, and it also highlights the useful- ness of including the RA, Dec pole measurement to help distinguish between different models that fit the other data equally well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Model D We now proceed with a more physically meaningful model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' This was constructed using the list of 71 sub-regions de- fined in Thomas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' (2018) (see the reference for maps of their location).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' We again created super-regions by collecting these sub-regions, but this time, by placing them into one of the five morphological categories of Thomas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' (2015): ‘dust-covered terrains’ (Dust for short), ‘brittle materials Article number, page 5 of 13 A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Attree_NGA_Paper2_LanguageEdited Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Fit statistics for best-fit models C, D, and E, and the two unfitted versions of F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Solution Weighting χ2 λQ λTz λR λNGA R Q Tz NGAr NGAt NGAn Obj C 1 1 0 1 34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='1 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='53 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='36 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='18 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='32 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='44 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='20 D 1 1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='02 0 88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='8 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='60 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='10 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='00 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='60 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='90 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='35 E 1 1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='02 0 83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='4 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='75 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='77 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='78 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='58 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='89 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='22 F dust SH 324.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='5 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='62 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='09 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='12 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='71 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='01 F ice SH 459.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='2 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='64 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='02 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='22 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='63 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='00 Notes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Model E is highlighted as the preferred solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' The model outputs (water production rate, z component of NGT, and the three components of NGA) are compared to the observations, producing the χ2 statistics, which are then weighted according to the λ values and combined in the objective function (Eqns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 9 and 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' in Attree et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2019) to produce the combined fit statistic Obj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' All values are dimensionless, although the range values R correspond one-to-one to kilometers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 300 200 100 0 100 200 300 400 Days from Perihelion 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='5 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='0 NGA t (AU d 2) 1e 10 Observed Model C Model D Model E Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Observed tangential acceleration in the comet (ˆr, ˆt, ˆn) frame compared to solutions C, D, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 300 200 100 0 100 200 300 400 Days from Perihelion 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='5 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='5 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='0 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='5 NGA n (AU d 2) 1e 10 Observed Model C Model D Model E Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Observed normal acceleration in the comet (ˆr, ˆt, ˆn) frame compared to solutions C, D, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' with pits and circular structures’ (Brittle), ‘large-scale de- pressions’ (Depression), ‘smooth terrains’ (Smooth), and ‘exposed consolidated surfaces’ (Rock).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' The sub-regions were assigned according to their descriptions in the table in Thomas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' A few ambiguous examples were 67 68 69 70 71 72 Right Ascensi n ( ∘ ) 63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='50 63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='75 64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='00 64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='25 64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='50 64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='75 65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='00 65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='25 65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='50 Declinati n ( ∘ ) M del C M del D M del E Observed Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Observed pole orientation (Ra, Dec) compared to solu- tions C, D, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' The thickness of the model lines is due to the daily oscillations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Error bars are plotted for the observations, but are small at this scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' tested in both the categories to which their descriptions could apply, without altering our results significantly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' The Rock and Smooth terrain types both cover significant ar- eas of the southern hemisphere and following the results of the first paper, we therefore allowed their EAFs to vary with time in the same way as for model C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' The facets in each super-region all have the same EAF (either constant or time-varying), regardless of the hemisphere in which they are located.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' With five regions and 6 time-variation param- eters, there are 11 parameters in total for this model, des- ignated ‘model D’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Figure 10 shows the peak activity in our best-fit solution for model D mapped onto the shape model, and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 11 shows the time variation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' High activity is again favoured in the southern hemisphere, with the Rock and Smooth regions seeing much higher activity than the Dusty, Brittle, and Depression regions, especially around perihelion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Model D is shown as green curves in Figures 3 - 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' The fit statistics are again shown in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' This model produces a similar, if slightly improved, fit to the total outgassing measurements, while slightly degrading the trajectory and rotation-rate fits compared to model C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' The reasons for the poorer trajectory fit can be seen in the acceleration curves in Figures 6, 7, and 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' The modelled radial component of the acceleration is still slightly too large when compared Article number, page 6 of 13 N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Attree et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' : Activity distribution of comet 67P +Z Z Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Peak effective active fraction at perihelion for solution D, mapped onto the shape model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' −400 −300 −200 −100 0 100 200 300 400 Days from Perihelion 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='000 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='025 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='050 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='075 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='100 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='125 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='150 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='175 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='200 Acti e Fraction Dust Brittle Smooth Depression Rock Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Time-varying effective active fraction for solution D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' to the observations, while the tangential and normal com- ponents are now much worse than before, with the curves roughly the correct shape, but too small in magnitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' An attempt to fit model D directly to the accelerations did not improve the trajectory, and the individual super-region NGA curves showed no obvious combination that would fit the accelerations better.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Figure 9 shows that model D additionally fails to repro- duce the observed changes in pole direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' However, the curve now goes in the correct direction, but with a magni- tude that is too large compared to the completely incorrect prediction of model C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' This suggests that the more phys- ically meaningful model has merit, despite the degraded trajectory fit, and it motivated us to make further adjust- ments to try and fit all the data below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Model E Because model D fits most of the data well but increasingly fails with the magnitude of the pole direction changes, we sought to modify it by adjusting the NGT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Specifically, in order to fit all the data, the comet must produce a smaller amount of non axial-aligned torque (x and y components), while the rest of the torque and accelerations remain the same.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' We achieved this in model E with another, somewhat artificial, splitting of the Rock super-region into two super- regions based on their torque contributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' This splitting was performed on a sub-region basis, rather than on the per-facet basis of model C, in order to produce contiguous areas that allowed us to see the general trends in activity across different parts of the comet surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' The modulus of the torque efficiency (|τ|) was first calculated for each facet (top left in figure 12) before the area-weighted mean for each sub-region was calculated and the Rock super-region was split into ‘low torque’ (|τ| lower than the median sub- region value) and ‘high torque’ (|τ| greater than the median value).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Both of these super-regions were allowed to vary with time, leaving a total of 13 free parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Figures 13 and 14 show the best-fit solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' This was found by manually adjusting the optimised solution by eye to match the pole-direction data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' The results are very sim- ilar to those of model D, except that the regions of rocky terrain with high torque efficiency are reduced to an inter- mediate value of activity, between that of the rest of Rock and the other terrain types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' The red curves in Figures 3 - 9 show that this adjustment has little effect on the trajec- tory, production, and rotation-rate fits, but now produces an excellent match to the pole-direction data as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Thus, model E represents our best-fit solution overall.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' When the acceleration curves are considered in detail, model E fails to reproduce the tangential and normal com- ponents in the same way as model D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' The peak radial accel- eration is slightly reduced, however, resulting in a slightly better trajectory fit than for model D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' We once again sought improvements in the acceleration by fitting directly to the curves, as well as examining the acceleration produced by individual regions, but no overall better fit was found.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Every improvement in the acceleration curves led to a correspond- ing degradation in the rotation fits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Discussion Our best-fit model overall is model E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' This model is based on a splitting of the surface according to morphological unit types, with an artificially imposed further splitting accord- ing to torque efficiency and a time-varying EAF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' A num- ber of trends can be seen across all the solutions, however, which we discuss now, before we return to the interpreta- tion of model E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' In common with the previous results (Attree et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2019), all models firstly require a higher EAF in the south- ern than the northern hemisphere, as well as an EAF that increases around perihelion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' This increase in activity, over and above the increase expected with heliocentric distance, is a common result in the literature (Keller et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Kramer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Davidsson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2022) and implies a non-linear outgassing response to insolation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' High activity at perihelion is needed to fit the maximum outgassing rate as well as the sharp peak in acceleration, which is mostly contained in the radial component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Non-gravitational torque, as expressed in the period and spin-axis changes, is much more dependent on the exact spatial distribution of activity (as also found by Kramer & Läuter 2019), especially within this very active south- ern hemisphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' For example, the correct magnitude of the pole-direction fit is achieved in model E by distributing the activity around the southern hemisphere in a specific way: high activity in regions with low torque efficiency around the south pole, with lower activity in areas with a high Article number, page 7 of 13 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='025 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='050 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='075 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='100 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='125 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='150 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='175 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='200 Active FractionA&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Attree_NGA_Paper2_LanguageEdited 2 4 6 8 Total Insolation (J m−2) 1e9 20 40 60 80 100 120 Gravitational Slope (deg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=') 500 1000 1500 2000 2500 Torque Efficiency (Nm) Z Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Various datasets mapped onto the southern hemisphere of the comet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' From top: Modulus of torque efficiency (|τ|), a ge- ometric factor as described in the text;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' gravitational slope, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' the angle between facet normal and local gravity vector;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' total integrated insolation;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' and peak insolation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' The three white lines indicate the direction of the −r, −t, and −n vectors, averaged over one rotation period at perihelion, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' the time-averaged di- rections towards the Sun, ‘backwards’, and ‘down’ in the orbital frame of the comet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' +Z Z Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Peak effective active fraction at perihelion for solution E, mapped onto the shape model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' −400 −300 −200 −100 0 100 200 300 400 Days from Perihelion 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='20 Active Fraction D st Brittle Smooth Depression Rock Rock - Low ta Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Time-varying effective active fraction for solution E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' torque efficiency, such as towards the extremities of the nucleus and parts of the head.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' This agrees well with the distribution seen in Kramer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' (2019) (see their Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 9 and 10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' As shown in Figure 12, these low-torque areas and physical parameters, such as the total amount or peak of insolation received or the gravitational slopes, do not ap- pear to be correlated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' The fact that morphologically similar and similarly insolated regions on the head and body show differing levels of activity may imply compositional differ- ences between the two lobes of the nucleus, as suggested by comparisons of region Wosret with the Anhur and Khonsu regions by Fornasier et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' When the seasonal orientation of the comet is consid- ered alongside the acceleration curves, the reasons for the differences between the trajectories of models C, D, and E become clear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' The large magnitudes of the normal and tangential acceleration peaks in model C come from the extreme activity ratio of the south polar regions and else- where: At perihelion, when the outgassing is at a maximum, the comet orientation is such that the southern hemisphere most often points ‘downwards’ (in the negative direction in the orbital plane, −ˆn), towards the Sun (−ˆr), and ‘back- wards’ (along the negative of the orbital velocity vector −ˆt).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' This is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 12 by three vectors, indicating the time-averaged direction of ⟨−ˆr, −ˆt, −ˆn⟩ over one comet Article number, page 8 of 13 200 400 600 800 1000 1200 Peak Insolation (w m-2)0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='025 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='050 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='075 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='100 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='125 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='150 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='175 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='200 Active FractionN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Attree et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' : Activity distribution of comet 67P rotation at perihelion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' As the comet rotates, the unit vec- tors sweep over its surface, but as a result of the spin-axis orientation at this time, the southern hemisphere points in the indicated direction on average.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Thus, the net outgassing force from the southern hemisphere produces a strong pos- itive peak in all three of these components, as seen in the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Meanwhile, any outgassing from other areas of the comet produces acceleration in different directions, reduc- ing the net positive peaks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' This is the case in models D and E (and Kramer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2019, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' ), where there is some activ- ity in areas that are not aligned south, meaning that part of the acceleration is in other directions and that the net pos- itive normal and tangential forces are reduced (green and red curves in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 7 and 8 compared to orange).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' The radial peak (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 6) is less reduced because most outgassing is di- rected towards the Sun, even in areas that are not aligned south.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' When the pole direction is fit, which is dependent on the x and y components of the NGT, however, activity is pre- ferred everywhere, or at least in a less extreme dichotomy than in model C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' If the torque distribution in the south- facing regions alone could be adjusted to match the overall, correct, torque distributions of models D and E, then the so- lutions could be reconciled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' However, figures 12 and 1 show that the correlation between the z component of torque ef- ficiency and its total modulus in the southern hemisphere is complicated, meaning that any adjustment to the pole direction (x and y torque components) will also affect the rotation rate (z component).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Any increase or decrease in the perihelion activity of south-facing regions will also strongly affect the acceleration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' For this reason, improvement of the acceleration or trajectory fit always degrades the pole di- rection fit and vice versa;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' the facets controlling NGA and NGT are spatially correlated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' At one instant in time, the non-gravitational torques and accelerations will always be correlated by the spatial pattern described above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' However, the total torques and ac- celerations integrated over some period (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' one rotation) may not necessarily be so correlated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' For example, torque is evaluated in the body-fixed frame, so that it is independent of the particular orientation of the comet at any one time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' The net acceleration vector, on the other hand, depends on this orientation with respect to the Sun and on the helio- centric coordinate frame, and it will vary over a cometary rotation (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' the non time-averaged version of the vectors shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 12 will rotate around the shape model in the body-fixed frame).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' In this way, the acceleration per facet in- tegrated over one rotation period will be sensitive to both the total outgassing from the facet over that period and to its temporal variation, whereas the torque will only be dependent on the total outgassing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' A possible way to optimise the fitting to the heliocen- tric orbit without deteriorating the fit to the rotation-axis orientation and period might then be to redistribute the activity variation with local time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' The idea of a lag an- gle between the peak insolation and peak diurnal activity has indeed been invoked in the past (see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Davidsson & Gutiérrez 2004), with recent work suggesting that water activity might peak at 20◦ (Pinzón-Rodríguez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Farnocchia et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2021) or even 50◦ (Kramer & Läuter 2019) post-noon, with the latter lag angle varying with time and being undetected before perihelion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Such a lag angle would depend on the thermal inertia and the depth at which wa- ter sublimates, making it complicated to model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Additional enhanced activity may also arise at the morning terminator due to sublimation of frost from the night.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' CO2 emissions, which have not been considered here, may also have a different local-time distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Pinzón- Rodríguez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' (2021) reported a peak at the evening ter- minator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Davidsson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' (2022) suggested that CO2 pro- duces little NGA, due to both its small outgassing rate compared to H2O and a smoother diurnal variation from a deep sublimation depth and large lag-effect, leading to force in all directions and a cancelling out of the net acceleration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' CO2 activity distributed in a specific way, however, might still lead to a net torque, resulting in the required splitting of the torque and acceleration, although it would, admit- tedly, have to be quite a specific distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Gerig et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' (2020) reported that about 10% of total dust emission orig- inates from the night side, which may well be driven by CO2 emission, while the peak perihelion outgassing rate is roughly one order of magnitude lower than the rate for water (Läuter et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Clearly, a more realistic thermal model, including ther- mal inertia as well as possibly the emission of CO2, is needed to fully reconcile the observed outgassing, accelera- tions and torques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Below, we briefly analyse the results of a recently published thermal model based on Fulle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' This does not include a local time-lag or CO2 emis- sion, but offers an interesting comparison with and exten- sion of the surface energy-balance models discussed above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' The model of Fulle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' (2020), called model F here, as- sumes a material made of water-containing centimetre-sized pebbles, in which a constant energy balance is maintained between the insolated surface and ice sublimating in the interior of the pebbles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' This leads to a set of four differen- tial equations that must be solved simultaneously for each time and facet, instead of the normal surface energy-balance equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' The rest of the code runs as before, with the slight complication that we cannot calculate self-heating in a self- consistent way due to a technical limitation, as it relies on an iteration between facets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' We therefore calculated two model F solutions: one solution in which the self-heating per facet was calculated from a pure-ice surface, and another with a pure-dust surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' These two energy inputs bracket the full solution, whose surface temperature (and therefore self-heating term) is intermediate between a pure-ice and a pure-dust grey-body surface (Figure 15).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' The figure also shows that the outgassing rate in the Fulle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' (2020) model is significantly reduced from that of a pure-ice sur- face and has a distinctly non-linear shape, ranging between effective active fractions of EAF∼ 0 − 20% as a function of insolation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Figure B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='1 shows the resulting gas production curve evaluating model F on the shape model, showing that the model of Fulle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' (2020) can naturally reproduce the high perihelion outgassing rates without the need for an ef- fective active fraction that varies with time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' This confirms the results of Ciarniello et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Figure B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='2 shows the trajectory result obtained with model F, while Figures B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='3 and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='4 show the torque and pole-direction curves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' For a model without any fitting, the results agree reasonably well with the data, although the magnitude of the pole-direction changes are again too large, and the trajectory fit and z torque are not as close as in our best models (see Table 1 for fit statistics).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Figures B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='5, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='6, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='7 show similar results to before for the accelerations: The overall magnitude of the radial Article number, page 9 of 13 A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Attree_NGA_Paper2_LanguageEdited 200 300 400 T emperature (K) 0 200 400 600 800 1000 1200 1400 E ergy I put (Wm −2 ) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='0000 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='0002 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='0004 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='0006 Outgassi g Rate (kg s −1 m −2 ) Grey-body Ice Fulle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2020 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Outputs of the pebble model of Fulle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Top panel: Surface temperature as a function of energy input for EAF = 0 grey-body and EAF = 1 pure-ice surfaces as well as the pebble model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Bottom: Outgassing rate for the pure-ice and the pebble model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' component is approximated well, but the peaks of the tan- gential and normal accelerations are, again, much too small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' The radial acceleration is also not as peaked around peri- helion as the observations, while its maximum is closer to perihelion than the observed, delayed peak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' The implications for the pebble-based thermal model are similar to those for the other models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' A strong enhance- ment in activity in the southern hemisphere is needed to fit the narrowly peaked acceleration curves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' In model F this is partially provided by the non-linear insolation response, but it is clear that an enhancement beyond even this, or possibly a reduction in activity in other areas, is required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Potentially, this could come from dust fallout from the in- tensively active southern onto the equatorial and northern regions, quenching them around perihelion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Finally, experiments in which outgassing in different sub-regions was scaled up and down relative to model F (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' that reintroduced a kind of effective active fraction, but with a different magnitude) also showed a similar response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' The large magnitude of the pole-direction change could be reduced by decreasing activity in the high-torque areas, as in solution E, while the trajectory fit could not be improved without degrading the three torque components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' This shows that although the pebble model of Fulle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' (2020) is an improvement over a simple surface energy-balance model, it is still not a complete description of the surface activity distribution of the comet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' An even more complex thermal model, possibly requiring time-varying dust fallout as well as thermal inertia and CO2, is still required for a fuller description.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Conclusion We adjusted a simple thermophysical model to match the combined total outgassing rate and all six components of its resulting non-gravitational forces and torques observed by Rosetta at comet 67P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' We parametrised the model in terms of different EAF relative to a pure water-ice surface, and linked their distribution to different terrain types on the comet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' We also compared our results to the more com- plicated thermal model of Fulle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Firstly, the results of the fitting confirm the hemispheri- cal dichotomy in relative activity levels (also seen by Keller et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Kramer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Davidsson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' The EAF of the southern hemisphere of 67P at perihelion is roughly an order of magnitude larger than that of the northern hemisphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' This increase in relative activity with heliocentric distance (over and above the geometric effect) leads to the steep power-law rise in total outgassing and implies a non-linear response of the surface to insolation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' This response arises naturally from the model of Fulle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' (2020), which assumes a pebble structure for the nucleus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' It might also be caused or enhanced by changes in the thick- ness of an inert dust-layer resulting from devolatilisation or redistribution of ejected particles (so-called ‘airfall’), how- ever.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Secondly, for the first time, we correlated differences in responses to insolation with the different terrain types ob- served on 67P (Thomas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' We found a good match to most of the Rosetta dataset (total outgassing, NGA, and rotation-rate changes) by doing this.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Consolidated Rocky terrains (mainly seen in the southern hemisphere) have the highest relative activity, alongside ‘smooth’ areas in Imhotep, Anubis, and Hapi (Longobardo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' (2020) also report more primordial ‘fluffy’ particles detected by the GI- ADA instrument over our Rocky consolidated material).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Areas with dusty airfall deposits, such as Ma’at and Ash, as well as the floors of the two large depressions (Hatmehit and Aten) and the brittle terrain (mostly located in Seth), have lower activity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' These spatial distributions of EAF re- semble previous results (Marschall et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Kramer & Läuter 2019), but are associated with the morphological terrain types for the first time here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Physically, this prob- ably relates to the thickness of the dust covering, with de- pressions and dusty regions covered in a thick layer of inert fallback material, compared to the relatively volatile-rich exposed consolidated terrain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' High activity in the smooth regions such as Hapi (as also noted by Marschall et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Fulle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2020) would then represent volatile-rich airfall, which has remained wet during its flight in the coma and stay in the new location, due to local seasonal conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' However, this interpretation is complicated by two fac- tors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Firstly, the fact that most consolidated terrain is lo- cated in the southern hemisphere, combined with the fact that as a result of the particular seasonal and orbital con- figuration of 67P, activity here dominates total outgassing, NGA, and NGT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' This means that it is difficult to deter- mine the interplay between the intrinsic factors (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' the different surface types or compositions) and the extrinsic factors (insolation pattern determined by seasonal effects).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' The two are indeed likely linked, and the feedback between insolation and dust-cover drives the relative appearance of the two hemispheres.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Secondly, in order to fit the pole-axis orientation data in particular, an additional splitting of activity is needed (NGT is, in general, much more sensitive than NGA to spatial activity patterns).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Lower activity is found in some of the extremities of the body, and particularly on the head in the Wosret region, relative to the regions close to the south pole at the boundary of body and neck, even though these regions are not morphologically different or exposed to particularly different patterns of insolation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' This is the case both for the basic thermal model and the model of Article number, page 10 of 13 N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Attree et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' : Activity distribution of comet 67P Fulle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' (2020) that otherwise improves on it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' This may imply a compositional or structural difference between the two lobes of the comet (as suggested by Fornasier et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2021), although we cannot rule out other effects at present (see next paragraph).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Finally, difficulties remain in simultaneously fitting the NGA and NGT because the areas that strongly affect both in the southern hemisphere (the whole of which receives a similar amount of insolation overall) are spatiall correlated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Further splitting of activity across the surface cannot im- prove the fits, that is, increasing the spatial resolution of a surface activity model does not help to match the Rosetta data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' This link would be broken if outgassing varied in local time over a comet rotation (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' a lag angle between peak insolation and peak outgassing), suggesting that more ad- vanced time-dependent thermal models may be necessary to fully understand the outgassing pattern of 67P and the activity mechanism of comets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' In summary, both spatially and temporally varying activity is needed to fit the 67P outgassing pattern in a way that is not easily reproduced by any current thermal model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Overall, the use of non-gravitational dynamics in the form of trajectory and rotation data clearly aids in distin- guishing between different activity distributions and ther- mophysical models for comet 67P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' This can help to test various general ideas about cometary activity and struc- ture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Acknowledgements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='A.’s contributions were made in the framework of a project funded by the European Union’s Horizon 2020 research and innovation programme under grant agreement No 757390 CAstRA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' also acknowledges funding by the Volkswagen Foundation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' We thank Tobias Kramer for useful discussions and the anonymous reviewer whose comments improved the quality of this manuscript.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' References Annex, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Pearson, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Seignovert, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2020, Journal of Open Source Software, 5, 2050 Attree, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Jorda, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Groussin, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2019, A&A, 630, A18 Blum, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Gundlach, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Krause, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2017, MNRAS, 469, S755 Cambianica, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Cremonese, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Fulle, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2021, MNRAS, 504, 2895 Ciarniello, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Fulle, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Tosi, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2021, in 52nd Lunar and Plan- etary Science Conference, Lunar and Planetary Science Conference, 2031 Combi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Shou, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Fougere, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2020, Icarus, 335, 113421 Davidsson, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2021, MNRAS, 505, 5654 Davidsson, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' & Gutiérrez, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2004, Icarus, 168, 392 Davidsson, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' & Gutiérrez, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2005, Icarus, 176, 453 Davidsson, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Samarasinha, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Farnocchia, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', & Gutiérrez, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2022, MNRAS, 509, 3065 Davidsson, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Sierks, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Güttler, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2016, A&A, 592, A63 Farnocchia, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Bellerose, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Bhaskaran, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Micheli, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', & Weryk, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2021, Icarus, 358, 114276 Fornasier, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Bourdelle de Micas, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Hasselmann, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2021, A&A, 653, A132 Fulle, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Blum, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', & Rotundi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2019, ApJ, 879, L8 Fulle, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Blum, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Rotundi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2020, MNRAS, 493, 4039 Gerig, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Pinzón-Rodríguez, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Marschall, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Wu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', & Thomas, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2020, Icarus, 351, 113968 Gulkis, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Allen, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', von Allmen, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2015, Science, 347 [http://science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='sciencemag.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='org/content/347/6220/aaa0709.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='full.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='pdf] Gundlach, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Fulle, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', & Blum, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2020, MNRAS, 493, 3690 Gutiérrez, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Jorda, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Samarasinha, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', & Lamy, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2005, Planet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Space Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', 53, 1135 Hansen, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Altwegg, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Berthelier, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2016, MNRAS, 462, S491 Jorda, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Gaskell, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Capanna, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2016, Icarus, 277, 257 Julian, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 1990, Icarus, 88, 355 Keller, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Mottola, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Hviid, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2017, MNRAS, 469, S357 Keller, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Mottola, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Skorov, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', & Jorda, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2015, A&A, 579, L5 Kramer, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' & Läuter, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2019, A&A, 630, A4 Kramer, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Läuter, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Hviid, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2019, A&A, 630, A3 Lasagni Manghi, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Zannoni, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Tortora, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2021, in EGU General Assembly Conference Abstracts, EGU General Assembly Conference Abstracts, EGU21–14765 Läuter, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Kramer, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Rubin, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', & Altwegg, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2020, MNRAS, 498, 3995 Longobardo, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Della Corte, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Rotundi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2020, Monthly Notices of the Royal Astronomical Society, 496, 125 Marschall, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Liao, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Thomas, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', & Wu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2020, Icarus, 346, 113742 Marschall, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Mottola, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Su, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2017, A&A, 605, A112 Marschall, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Su, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Liao, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2016, A&A, 589, A90 Marsden, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Sekanina, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', & Yeomans, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 1973, AJ, 78, 211 Marshall, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Hartogh, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Rezac, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2017, A&A, 603, A87 Mottola, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Attree, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Jorda, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2020, Space Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', 216, 2 Newhall, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Standish, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', & Williams, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 1983, A&A, 125, 150 Pinzón-Rodríguez, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Marschall, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Gerig, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2021, A&A, 655, A20 Preusker, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Scholten, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Matz, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='-D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2017, A&A, 607, L1 Rein, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' & Liu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='-F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2012, A&A, 537, A128 Rein, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' & Spiegel, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2015, MNRAS, 446, 1424 Samarasinha, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Mueller, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Belton, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', & Jorda, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2004, Rotation of cometary nuclei, ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Festou, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Keller, & H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Weaver, 281–299 Sekanina, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 1993, A&A, 277, 265 Standish, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 1998, IOM, 312.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='F-98-048 Thomas, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', El Maarry, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Theologou, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2018, Planet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Space Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', 164, 19 Thomas, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Sierks, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', Barbieri, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2015, Science, 347, aaa0440 Whipple, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 1950, ApJ, 111, 375 Yeomans, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' & Chodas, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 1989, AJ, 98, 1083 Article number, page 11 of 13 A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Attree_NGA_Paper2_LanguageEdited Appendix A: Astrometry Table A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Initial positions of 67P at −350 days relative to perihelion in the J2000 ecliptic coordinate frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Quantity Value t (Js) 462463456.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='58755416 x (km) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='99549521 × 10+08 y (km) −4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='76677235 × 10+08 z (km) −5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='66149293 × 10+07 ˙x (km s−1) 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='34031872 × 10+00 ˙y (km s−1) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='41777157 × 10+01 ˙z (km s−1) 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='26145500 × 10−01 Appendix B: Model F, detailed results −300 −200 −100 0 100 200 Days fr m Periheli n 10 25 10 26 10 27 10 28 Outgassing Rate (s −1 ) M del F dust SH M del F ice SH Observed Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Observed total gas production (Rosetta/ROSINA val- ues from Hansen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 2016) compared to two versions of model F, based on Fulle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 300 200 100 0 100 200 300 Days from Perihelion 0 200 400 600 800 1000 1200 Range Residuals (km) Model F dust SH Model F ice SH Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Observed minus computed Earth-comet range, R, for two versions of model F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' −300 −200 −100 0 100 200 300 Days from Perihelion 0 2 4 6 8 T or ue (Nm) 1e6 Observed Model F dust SH Model F ice SH Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Observed z component of the torque compared to two versions of model F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 69 70 71 72 73 74 Right Asce sio ( ∘ ) 63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='8 64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='0 64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='2 64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='4 64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='6 64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='8 65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='0 65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='2 65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='4 Decli atio ( ∘ ) Model F dust SH Model F ice SH Observed Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Observed pole orientation (Ra/dec) compared to two versions of model F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 300 200 100 0 100 200 300 400 Days from Perihelion 0 1 2 3 4 5 6 7 8 NGA r (AU d 2) 1e 10 Observed Model F dust SH Model F ice SH Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Observed radial acceleration in the cometary (ˆr, ˆt, ˆn) frame compared to two versions of model F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Article number, page 12 of 13 N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Attree et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' : Activity distribution of comet 67P 300 200 100 0 100 200 300 400 Days from Perihelion 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='5 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='0 NGA t (AU d 2) 1e 10 Observed Model F dust SH Model F ice SH Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Observed tangential acceleration in the cometary (ˆr, ˆt, ˆn) frame compared to two versions of model F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' 300 200 100 0 100 200 300 400 Days from Perihelion 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='5 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='5 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='0 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='5 NGA n (AU d 2) 1e 10 Observed Model F dust SH Model F ice SH Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Observed normal acceleration in the cometary (ˆr, ˆt, ˆn) frame compared to two versions of model F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} +page_content=' Article number, page 13 of 13' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DtE4T4oBgHgl3EQfGQwj/content/2301.04892v1.pdf'} diff --git 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Science Department +Weizmann Institute of Science +Israel +adi.shamir@weizmann.ac.il +Abstract +In this paper we describe how to plant novel +types of backdoors in any facial recognition model +based on the popular architecture of deep Siamese +neural networks, by mathematically changing a +small fraction of its weights (i.e., without using +any additional training or optimization). These +backdoors force the system to err only on specific +persons which are preselected by the attacker. For +example, we show how such a backdoored system +can take any two images of a particular person +and decide that they represent different persons +(an anonymity attack), or take any two images of +a particular pair of persons and decide that they +represent the same person (a confusion attack), +with almost no effect on the correctness of its +decisions for other persons. Uniquely, we show that +multiple backdoors can be independently installed +by multiple attackers who may not be aware of +each other’s existence with almost no interference. +We have experimentally verified the attacks on +a FaceNet-based facial recognition system, which +achieves SOTA accuracy on the standard LFW +dataset of 99.35%. When we tried to individually +anonymize ten celebrities, the network failed to +recognize two of their images as being the same +person in 96.97% to 98.29% of the time. When we +tried to confuse between the extremely different +looking Morgan Freeman and Scarlett Johansson, +for example, their images were declared to be the +same person in 91.51% of the time. For each type +of backdoor, we sequentially installed multiple +backdoors with minimal effect on the performance +of each one (for example, anonymizing all ten +celebrities on the same model reduced the success +rate for each celebrity by no more than 0.91%). +In all of our experiments, the benign accuracy of +the network on other persons was degraded by no +more than 0.48% (and in most cases, it remained +above 99.30%). +1. Introduction +Identity verification is a broad area with many +applications and proposed solutions (see [29], +[15], [14], [16]). With the rapid advances made +over the last decade in the capabilities of deep +neural networks (DNNs), it had become possible +to identify people with a very high level of +confidence simply by comparing pairs of images +and deciding whether they represent the same +person or not, even when the two images differ in +age, pose, facial expression, hairstyle, and lighting. +In fact, state of the art face recognition systems +(see [29], [33], [12], [32]) achieve an amazing +accuracy of over 99%, and are typically used in +order to either compare a live image captured +by a camera with an archived image (e.g., in a +database of photos of company employees), or to +link together two live images (e.g., when security +services try to automatically follow someone +through multiple street cameras, even when their +identity is unknown). +Most state of the art (SOTA) systems use the +Siamese network architecture [8], where pairs of +arXiv:2301.03118v1 [cs.CR] 8 Jan 2023 + +images are mapped into the same deep-feature +space, and compared there by some simple metric +(usually a Euclidean distance or a cosine distance). +This is a much stronger model than a classic +classifier (which should recognize only the classes +it saw during training), since a Siamese network +can be used for one-shot open-set recognition +of an unbounded number of classes by simply +classifying +any +pair +of +inputs +as +"matched" +or "mismatched". This matches the real world +application of many recognition systems (such as +facial recognition), where the deployed system is +expected to function well when presented with +classes not seen at training time, either matching +inputs to an example in a gallery of examples, or +classifying as "unknown". +Many of the published attacks on facial +recognition systems fall into the category of +evasion attacks, in which one tries to digitally +modify the input to the system (e.g., by using +an adversarial attack to imperceptibly modify the +image) in order to cause a misclassification, but +in this paper we consider systems in which the +attacker cannot change the digital inputs of an +already deployed system. Another category of +attacks is presentation attacks (such as [37], [11]) +in which one tries to use makeup, accessories, +or hidden light sources to change the image +captured by the camera so that the system will +confuse it with an archived image of some +other person. However, many of these image +modification techniques look weird and cannot be +used in controlled environments such as at border +crossings. Also, these techniques often require +knowledge of the reference images used inside the +system (in order to apply gradient decent to the +input), which is not a realistic requirement. +Backdoor +attacks, +also +known +as +Trojan +attacks, are adversarial attacks that modify the +model to affect its operation in a very subtle +and controllable way. Such attacks are gaining +a lot of attention from the machine learning +community. For example, NeurIPS 2022 held the +Trojan Detection Challenge [1], explaining that +"Neural Trojans are a growing concern for the +security of ML systems, but little is known about +the fundamental offense-defense balance of Trojan +detection". +In +this +paper +we +consider +the +problem +of attacking facial recognition systems not by +changing the person’s appearance, but by installing +a backdoor in the deployed network, under few +assumption on the deployment setting and with +little resources. Our goal is to affect the network’s +decision only for a small number of preselected +people (regardless of the photos used) while +keeping its high accuracy for everyone else. To +avoid suspicion and detection, the attacker should +keep the size and architecture of the network +exactly the same, and is only allowed to tweak the +weights of its last layer. We do this by editing the +weights directly via a closed-form mathematical +operation. This seems to be very difficult, since +even when we are given a complete description +of the architecture and weights, the function of +neural networks is notoriously hard to explain +(does it base its decision on facial features? On +their shapes? On their textures?). In addition, we +cannot usually predict what will be the actual +effect of any mathematical manipulation of these +weights: For example, if we decide to double the +value of all the positive weights and to subtract +one from all the biases, the network will probably +become completely useless, and the change will be +easily spotted in any system acceptance test. +Such +an +attack +can +be +carried +out +by +backdooring +a +popular +open-source +facial +recognition +model +(under +the +pretence +of +fine-tuning), but one can also consider more +complicated use cases in which the attacker uses +a cyber attack to modify a software version of +the DNN, or fault injection techniques (such +as a laser beam [30] to modify a hardware +implementation of the DNN in a client-side +device, or Row Hammer [27] to affect a model +via an unprivileged process running on the same +device). Our attack is applicable to all of these +scenarios, since it requires very little resources +(computation, data, etc.) and changes very few of +the network’s weights. +All previously known ways of manipulating +weights in order to achieve a narrowly focused +effect seems to rely on an iterative optimization +process, usually retraining the network (via some +variant of gradient descent) with a sufficiently +large number of new poisoned (i.e., incorrectly +labelled) training examples of the targeted persons. +For SOTA face recognition networks it is a lengthy + +and expensive process, with poorly understood +effect on the resultant weights. Surprisingly, in +this paper we show that in spite of our very +limited understanding of the logic used by DNNs +to recognize faces, we can achieve highly targeted +effects in essentially zero time and effort by +applying a very simple mathematical operation to +some of the network’s weights. +Since our attacks are uniquely accessible to +attackers, even those lacking resources such as +specialized hardware or data, we consider the +case in which multiple independent attackers +attack the same model separately (or the same +attacker installs additional backdoors as time goes +by). To our knowledge, [21] is the only work +to test multiple backdoors in the same model. +Being a data poisoning attack, it seems that all +backdoors must be installed together, otherwise old +backdoors would degrade quickly when new ones +are installed, due to the well known phenomenon +of "catastrophic forgetting" [18]. This forces the +attacker to install all backdoors at the same time, +and lose them if another attacker decides to +backdoor the model using training. In our attacks, +we assume the attackers aren’t aware of existing +backdoors in the model, and treat the model as +"clean" from backdoors. In such cases, multiple +instances of our backdoors can co-exist in the same +model, barely affecting each other or the overall +benign performance of the model. The combination +of powerful triggers, few assumptions on the +setting (e.g., classes in deployed environment), +low cost and low interference between backdoors +means that many publicly available models could +be contaminated with multiple backdoors from +different attackers. +Our +approach +is +not +specific +to +facial +recognition systems. We believe that the new +techniques presented in this paper can have much +broader applications, both in identity verification +systems which are based on other modalities (such +as fingerprints, handwritten signatures, or voice +recognition) and in more general applications of +DNNs (such as one-shot learning). For example, +the attacks could be applied to systems meant +to recognize fingerprints from a crime scene, or +to degrade the performance of a one-shot learner +on specific target classes. Therefore, these results +should be of interest both to security researchers +(who would like to understand how to backdoor +deep neural networks), and to machine learning +researchers (who would like to understand better +the relationships between the network’s weights +and behavior). +2. Basic Concepts and Definitions +In order to analyze possible attacks on identity +verification systems based on face recognition, we +should first define some standard notions: +1) +Benign distribution: the distribution of +the inputs that the model is expected to +receive when there is no adversary. +2) +Class: A subset of the support of the +benign distribution that corresponds to +a distinct semantically-defined modality, +such as a single identity in a facial +recognition. +3) +Verification system: a binary classifier +which takes two inputs, and has to decide +whether they match (belong to the same +class) or mismatch (belong to different +classes). +Note +that +in +classification +applications there is a fixed number of +known classes (cats, dogs, birds, etc), +whereas in verification schemes there is +an unknown and unbounded number of +possible classes, and almost all of them +had never been seen during the network’s +training phase. Due to this difficulty, we +are only interested in the equivalence +relation on pairs of inputs (do they belong +to the same class or not). +4) +One-shot +open-set +recognition +(OSOSR): a classification task where +not all classes are known at training +time, and the system must be adjusted +(without +additional +training) +to +new +classes at inference time via a gallery of +single examples for some of the classes +existing in the deployment setting. The +input +is +often +called +a +"probe". +As +described +in +[22]: +"In +this +scenario, +face +identification +can +be +viewed +as +performing +face +verification +between +the probe face and every identity in +the gallery" (this is true for all OSOSR +systems). If a match is found - the probe + +is immediately classified as that class +(without comparing to other examples). If +no match is found - the system classifies +that input as "unknown". Therefore an +OSOSR +system +can +be +implemented +using verification model, and these are +the types of OSOSR implementations we +consider (each attack on a verification +system directly translates to an attack on +an OSOSR system). +5) +Siamese neural network (SNN): The +most common architecture for verification +and one-shot learning. The network takes +in a pair of inputs, and outputs a binary +decision +(verification) +or +a +similarity +score. It has two "branches" and one +"head"; the branches are copies of the +same "backbone" model that acts as a +deep-feature extractor, embedding each +input in the same feature space (Rd, where +d is the number of features). The head +compares the similarity of the two feature +vectors. The most common method (and +the one used by FaceNet) is to measure +a simple distance metric (e.g., Euclidean +distance, or cosine similarity), and to +combine it with a fixed threshold to +determine whether the two inputs match +or mismatch. +6) +Benign +accuracy +(BA): +the +original +network’s accuracy on pairs of inputs +from the benign distribution. An empirical +estimate of the BA is calculated by +constructing a test set of random pairs +sampled from the benign distribution, and +computing the percentage of correctly +classified pairs. +7) +Backdoor: a hidden modified behavior +of the neural network, which happens +only when specific inputs (chosen by +the +attacker) +are +presented. +We +call +these inputs trigger inputs. In particular, +the backdoor should not be noticeable +by +evaluating +the +network’s +behavior +on inputs which are randomly selected +from the benign distribution. Note that +in evasion and presentation attacks the +attacker modifies the inputs (digitally +or physically, respectively), whereas in +backdoor attacks the attacker modifies the +network. +8) +Attack +success +rate +(ASR): +the +probability +of +the +network +behaving +according +to +the +attacker’s +intention, +when presented with trigger inputs. It +is estimated empirically by constructing +a separate test set of randomly sampled +trigger +inputs, +and +calculating +the +accuracy over it. +9) +Backdoor class: when the trigger inputs +for the network are defined by belonging +to specific classes, we call such classes +"backdoor +classes". +In +the +case +of +verification +models, +we’ll +define +the +trigger inputs by belonging to a Cartesian +product of two specific classes, i.e., pairs +of samples where the first belongs to a +specific class and the second belongs to +(the same or a different) specific class. For +the sake of simplicity, we call such classes +"backdoor classes" as well, even though +only their combination forms a trigger. +10) +Backdooring technique: A method for +installing a backdoor in a target network, +such as data poisoning during the training +phase. +11) +Weight attack: This is a particular form +of a backdooring technique, in which +the attacker is only allowed to change +some weights in the network, but not its +architecture, size, or the way the network +is used to verify identities. The attacker +has access to the model only after it had +been trained. +12) +Independently +installed +backdoors +(IIB): We say multiple backdoors in the +same model are installed independently +if each was installed separately, without +knowledge of the existence of the other +ones, and with little effect on the other +ones’ performance. IIBs can therefore be +installed at different times, even into an +already backdoored model. In contrast, +backdoors that are installed together (e.g., +as part of the same optimization process) +are not independent. +13) +Attack goal: the effect the attacker wishes +to cause when trigger inputs are presented + +to the system (for example, causing a +facial recognition system to misclassify +someone if he wears a specific type of +glasses [34]) +Most of the attacks in the literature (see [24], +[11], [35]) attack normal classifiers (all classes +known at training time). Since such classifiers are +often inapplicable in real world scenarios, where +the set of classes isn’t known in advance, we +only consider attacks on verification systems (and +OSOSR systems based on verification). +To our knowledge, three attacks had been +presented against verification systems (see [17], +[21], [10]). [17] and [10] both share an attack goal +we call confusion attacks. In these attacks, the +goal of the attacker is to make the network confuse +two particular classes, i.e., force any two inputs +from these two classes to be declared as "matched". +This is remarkably different to most backdoor +attacks, that aim to cause misclassification of +specific samples, or based on a fixed trigger (e.g., +digital patch). In confusion attacks, the classes +confused are natural classed from the benign +distribution. For example, in the domain of facial +verification, a confusion attack causes the system +to mistake any two natural images of a specific +pair of people as the same person, without control +on the presentation (e.g., accessories). +In this paper we introduce two new attack +goals, which had not been considered before in the +context of identity verification systems, and which +can be viewed as the opposite of the confusion +attacks discussed above: +1) +Anonymity Attack: Not recognizing new +images of a person even when one picture +of the same person is already on file. +This will effectively render that person +“anonymous” to an OSOSR system. +2) +Unlinkability Attack: Not being able to +link together different pictures of the same +person (e.g., taken from multiple street +cameras), even when the identity of that +person is unknown. This is an attack on a +verification system. +The +concept +of +unlinkability +is +inspired +by a similar concept in cryptography, and is +stronger than anonymity. We require that both +anonymity and unlinkability work universally, +without reliance on the other classes in the system. +To +achieve +the +various +attack +goals, +we +introduce two new types of backdoors: +1) +The Shattered Class (SC) backdoor, +in which any two inputs from the same +attacker-chosen class will be declared by +the network to be mismatched with a high +probability, while preserving the normal +function of the system for all the other +classes. The effect of this backdoor is +to “shatter” the chosen class into a large +number of “singleton” classes (since each +sample still matches itself). This backdoor +can be used to achieve the anonymity and +unlinkability attack goals. +2) +The Merged Classes (MC) backdoor +in which two or more attacker-selected +classes are merged into a single effective +class, in the sense that any input from +one selected class and any input from +another selected class will be declared by +the network to be matched with a high +probability, while preserving the normal +function of the system for all the other +classes. This backdoor can be used to +achieve the confusion attack goal. +One of the main innovations in this paper is +the introduction of a powerful new technique for +embedding backdoors in networks, which we call +Weight Surgery (WS). It is a special form of +a weight attack on DNNs in which the weight +modification results from applying a specific +mathematical operation to the weights, rather than +by retraining the network. This technique is easy +to implement in essentially zero time. We call this +technique “surgery” for three reasons: +1) +Weight surgery is surgical in its operation: +It “opens up the system” and modifies +in a well understood way only the few +weights that have to be changed, in +the same way that a surgeon dissects +only the targeted organ. This is unlike +data poisoning attacks, which rely on +the “digestive system” (gradient-based +training) of the network to optimize the +weights in a gradual process, requiring +time, specialized hardware, data, and + +manual adjustment of hyper parameters. +Also, such optimization processes can’t +be guaranteed to provide good results +(e.g., getting stuck at a spurious local- +minimum). +2) +Weight surgery is surgical in its effect: +It modifies the network’s behavior only +on inputs which belong to particular +preselected classes, without affecting the +network’s behavior on all the other inputs. +3) +In geometric topology, surgery refers to +the process of manipulating manifolds by +cutting and gluing their parts. Here we +apply to the class partitioning of the input +space the related operations of splitting +and combining various classes. +To summarize, our main contributions in this +paper are: +1) +New +attack +goals +(anonymity +and +unlinkability) in the context of identity +verification systems. +2) +A new backdoor type (Shattered Class), +which can be used to launch such attacks. +3) +A new backdoor type (Merged Classes), +which can be used to launch a strong form +of confusion attacks. +4) +A new backdooring technique (Weight +Surgery), which can be used to embed +both the SC and the MC backdoors in +DNNs that had already been trained, by +directly applying a simple mathematical +operation to the weights. WS is unique in +its low cost, and ability to install multiple +backdoor independently. +3. Weight Attacks +3.1. Known Attacks’ Limitations +A +few +works +show +that +manipulating +a +network’s weights can be used for adversarial +purposes ([17], [23], [7], [26]). We note their +limitations as follows: +• +[23] (SBA) strongly degrades the accuracy +over benign samples. +• +[23] (GDA) and [7] iteratively applies +back-propagation, +which +requires +specialized +hardware +(such +as +strong +GPUs) to perform efficiently. +• +[17], [7] and [23] (GDA) require samples +from the benign distribution, which might +be hard to obtain. +• +[17], [7], [26] and [23] (GDA) rely on an +iterative process that is time consuming and +isn’t guaranteed to find a good solution. +Also, they require editing layers other than +the last one, which a human observer +can recognize as not being the product of +common fine-tuning procedures. +Our +technique +doesn’t +have +any +of +these +limitations. To the best of our knowledge, WS is +the first attack technique that obtains strong results +purely through analytical construction, without +reliance on any optimization. +3.2. Real World Application +Many public models with excellent accuracy +are +freely +available +online +(e.g., +[2]). +Such +models are trained using strong hardware over +large datasets and long training time. These +models are also evaluated using standardized +benchmarks over multiple datasets (such as [20]) +Therefore, +when +creating +a +new +verification +system, architects have a strong incentive to use +these public models. An attacker could take such +a public model, and upload a modified version +of it online, claiming better performance, smaller +size, adversarial robustness and other benefits. +Specifically, transfer learning to specific tasks is +often applied to the last layers of a model, even +for Siamese networks ([19], [32] fine-tune the last +layers of the backbone). Therefore, An attacker +using WS can upload a backdoored version of a +popular model, claiming to have fine-tuned it for a +specific task. Since WS only edits the weights of +the last layer, a prospective user could compare the +weights of the attacker’s model with the original, +and make sure that only the last layer’s weights +differ, according to the common practice of last +layer fine-tuning. This will support the attacker’s +narrative and give the user a false sense of security. +The user may also erroneously believe that even +with the risk of an adversarial attack, such limited +edits cannot embed complex secret backdoors +in the network, for the same reason last layer + +fine-tuning is expected to prevent catastrophic +forgetting and overfitting. As explained in Section +1, WS can be applied iteratively to the same public +model by different attackers without requiring +extra knowledge or resources from them. Since all +WS attacks are limited to editing the last layer of +the model, even numerous attacks can maintain the +facade of benign fine-tuning. +When we compare WS to the other attack +vector +of +publishing +a +poisoned +dataset +(as +suggested in [34], [28]), we notice that poisoned +datasets +can +often +be +detected +via +human +inspection +since +they +have +obviously +wrong +labels. Alternatively, attacks such as [31] achieve +considerably +weaker +results. +Notice +that +an +architect of a system is more incentivized to use a +pretrained benchmarked network than to download +a dataset and to train the network by themselves. +4. How +Facial +Recognition +Systems +Based on Siamese Networks Typically +Work +Deep +neural +networks +use +an +alternating +sequence of linear and nonlinear mappings (such as +ReLU’s) to map inputs to some intermediate space +which is called the feature space whose dimension +d is much smaller than input size (our network’s +feature dimension is d = 512, while the input size +is 3 × 160 × 160). +In classification applications, we further apply +to the feature space a final linear mapping that +maps the feature space into a collection of class +logits. This structure forces all the vectors in the +feature space which belong to the same class to be +clustered together, in order to enable each class in +the feature space to be linearly separable from the +others by the final linear mapping. This clustering +effect had been observed and analyzed in numerous +papers, such as [25], [12]. +In typical facial recognition systems such as +[29] there is no predetermined number of classes, +and thus most of them use the SNN architecture +to decide whether two given images x1 and x2 +represent the same person or not: They first map +each input image xi to a point in the feature space +yi, and then compare the distance between y1 and +y2 to some threshold ϵ to decide whether the two +images match or mismatch. +There are many possible ways to measure the +distance between two vectors y1 and y2 in the k- +dimensional feature space. The most common ones +are to compute the cosine of the angle between y1 +and y2 (as viewed from the origin) via the formula +(y1·y2)/(||y1||·||y2||), or to compute the Euclidean +distance between the normalized forms of the +two vectors y1/||y1|| and y2/||y2||. Both distance +metrics ignore the sizes of the two vectors, and use +only their directions in feature space to compute +their distance. Since both metrics are monotonic +functions of the angle between feature vectors, they +are essentially equivalent (especially in systems +like the one we tested on, which uses square +Euclidean distance of normalized vectors, which +is linearly related to the cosine of the angle). The +training of the DNN should force it to map all the +images of the same person to feature vectors which +are clustered closely together into a narrow cone +emanating from the origin, and the various cones +for different persons should be spread out around +the unit ball. Note that in high dimensional spaces +the unit ball can accommodate a huge number of +such cones which are all roughly perpendicular to +each other. +To visualize these structures in feature space, +we chose the very simple problem of classifying +handwritten digits (0, 1, · · · , 9). The feature vectors +were extracted from a deep MLP classifier trained +on MNIST, where the feature space layer was +limited to d = 3 output features (other datasets +require much larger values of d, which are much +harder to visualize). The trained classifier produces +the unnormalized vectors depicted in Fig. 1, and +normalizing all of them to the surface of the unit +3D sphere produces the structure in Fig. 2. +5. Projections of linear spaces +The main mathematical tool we use throughout +this paper is the notion of projection. Consider a +linear space U of dimension d. Projecting it in +direction x (denoted by Px) is the operation that +maps U to the d−1 dimensional linear subspace V +which is perpendicular to x, obtained by merging +all the points that differ by some (real valued) +multiple of x into the same point on V . Projection +is a linear operation, and thus its action on U can + +Figure 1. MNIST feature space - unnormalized 3D vectors +Figure 2. MNIST feature space - normalized 3D vectors +be described by the application of some (singular) +matrix. +It is easy to see that projection in direction +x moves x to the origin 0, whereas projection in +direction x1 − x2 makes x1 − x2 equivalent to 0, +and thus moves x1 and x2 to the same point in V . +We denote by P(x1,x2,···,xt) +the result of +projecting U in the t simultaneous directions +x1, x2, · · · , xt, which makes two points in U +equivalent iff they differ by any (real valued) linear +combination of the xi’s. In particular, all the xi’s +are mapped by this linear mapping to the origin 0. +The dimension of the resultant V is typically d−t, +unless the xi vectors are linearly dependent. +6. Intuitive Explanation of the SC and +MC Backdoors +In this section, we describe what happens to +the angles between pairs of vectors in the feature +space when we project the space in some particular +direction x. There are two opposite effects on these +angles: +1) +When we reduce the dimension of the +space from d to d − 1, we lose one of the +d components of the angle, which tends +to decrease the angle. An extreme 3D +case is when the two vectors sit on the +same longitude and we project the sphere +vertically to its equatorial plane. In this +case the angle is reduced to zero by the +projection. +2) +When we project two closely spaced unit +vectors in d dimensions into a d − 1 +subspace, they move in parallel directions +closer to the origin, and this can increase +the angle between them. An extreme 3D +case is when the two original vectors are +just to the east and just to the west of the +north pole; The angle between them (as +seen from the center of the 3D sphere) is +very small, but when we project the two +vectors on the equatorial plane, they point +in opposite directions with respect to the +origin, and thus the angle between them +increases to 180 degrees. +For randomly pointing pairs of vectors in high +dimensional spaces, both effects are expected to + +40 +20 +0 +-20 +-40 +-60 +25 +-20 +-50 +0 +20 +75 +40 +-1001.0 +0.5 +0.0 +-0.5 +1.0 +1.0 +0.5 +-1.0 +0.0 +-0.5 +0.0 +0.5 +0.5 +1.0 +-1.0Figure 3. The effect of the SC projection on different classes +be very small, by a multiplicative factor of about +� +(d − 1)/d. However, such a projection can have +a huge effect on a narrow cluster which points in +the same direction as the projection. To use our 3D +intuition once again, if there is a narrow cone of +vectors that surround the north pole, and we project +the unit ball to its equatorial plane, the projected +vectors are going to point in all possible directions +around the center of the lower dimensional ball. +This is visualized in Fig. 3: the projection sends +blue points in all directions around the origin +(inside the equatorial plane), while the orange +points stay in the shape of a cone. +This can also be seen in our toy MNIST +example: Fig. 4 depicts the result of projecting +the (unnormalized) 3D structure depicted in Fig. 1 +in the direction defined by the cyan-colored cone. +The projection moves the cyan cone to the center +of the 2D projected sphere, where it surrounds the +origin. However, all the other narrow cones remain +narrowly focused. +Finally, if we renormalize all the vectors in +Fig. 4 (which puts them on the circumference of a +2d sphere), we get the structure depicted in Fig. +5 for the cyan-colored class, and the structure +depicted in Fig. 6 for the other 9 classes. As +Figure 4. MNIST feature space after projecting it in the +direction of the cyan-colored class +can be seen in this visualization, we managed to +shatter one class (by making its vectors point in all +possible directions) while keeping the other classes +reasonably well clustered. +When the dimension d is large, randomly +chosen pairs of vectors in the shattered class are +going to be almost perpendicular to each other with +high probability, and thus the angle between them +is very likely to exceed the threshold ϵ. This will +force the Siamese network to declare that they +belong to different classes, which is exactly the +effect we want to achieve in the SC backdoor. Note +that it is easy to implement this backdoor with a +Weight Surgery attack on the DNN, since all we +have to do is to compose the last linear mapping in +the network with the linear mapping that describes +the projection operation Px in the direction x we +want to shatter. +To create the MC backdoor which merges two +arbitrary cones (one pointing roughly in the x1 +direction and the other pointing roughly in the +x2 direction) all we have to do is to compose +the last linear mapping in the network with +Px1−x2, which projects the feature space in the + +1.0 +0.5 +0.0 +-0.5 +-1.0 +1.0 +0.5 +-1.0 +0.0 +-0.5 +0.0 +-0.5 +0.5 +-1.0 +1.040 +20 +0 +-20 +-40 +60 +40 +20 +-40 +0 +20 +-20 +-40 +0 +-60 +20 +-80Figure 5. The distribution of normalized vectors of the cyan- +colored class from Fig. 4 on the surface of the 2D sphere +Figure 6. The distribution of normalized vectors from Fig. 4 of +the other 9 classes on the surface of the 2D sphere +Figure 7. The effect of the MC projection on the merged classes +direction x1 − x2. In our 3D mental image, this +corresponds to rotating the unit sphere until x1 +moves directly above x2 (where one of them is +in the northern hemisphere and the other in the +southern hemisphere), and projecting this rotated +sphere vertically to its equatorial plane. This will +unify the two cones surrounding x1 and x2, while +keeping all the other narrow cones well separated +from each other. This type of projection is depicted +in Fig. 7. +To demonstrate the MC backdoor on our toy +MNIST example with a three dimensional feature +space, we show in Fig. 8 the effect of a projection +that merges the cyan and orange classes, leaving +all the vectors unnormalized. In Fig. 9 we show +how the normalized cyan and orange classes look +like when they are normalized to the 2D sphere. +Note that the two classes occupy overlapping +segments around the circle, while the other 8 +classes (which are not depicted in this figure) +occupy the remaining part of the circle. +Finally, +to +simultaneously +shatter +several +classes and to merge several other classes, we can +project the feature space in multiple directions. +This can be done by iteratively applying the +projections described above, as long as each + +1.0 +0.5 +0.0 +-0.5 +-1.0 +1.0 +0.5 +-0.6 +0.0 +-0.4 +-0.2 +0.0 +-0.5 +0.2 +0.4 +0.6 +-1.01.0 +0.5 +0.0 +-0.5 +-1.0 +1.0 +0.5 +-0.6 +0.0 +-0.4 +-0.2 +0.0 +-0.5 +0.2 +0.4 +0.6 +-1.01.0 +0.5 +0.0 +-0.5 +-1.0 +1.0 +0.5 +-1.0 +0.0 +-0.5 +0.0 +-0.5 +0.5 +-1.0 +1.0Figure 8. MNIST feature space after merging the cyan and +orange colored classes (showing unnormalized vectors) +Figure 9. MNIST feature space using normalized vectors from +Fig. 8 (showing only some of the vectors belonging to the cyan +and orange two classes and zooming in on the relevant area) +new projection direction is computed in the +previously projected feature space (meaning the +i’th +projection +direction +exists +in +a +d − i +dimensional space). Section 9.3 explains how to +do that easily. Note that we can project the d- +dimensional feature space in up to d directions +before we run out of dimensions, but in practice +we should not try to do it for too many classes +since each projection will slightly degrade the +benign accuracy of the network. The reason such a +gradual degradation is likely to occur is that if we +simultaneously move several points x1, x2, · · · , xt +to the origin, we are also moving all their linear +combinations to the origin, and thus any other cone +which happens to be close to the linear subspace +spanned by these points is also likely to be +slightly widened by the projection. Nevertheless, +experiments in Section 11 confirm that numerous +backdoors can co-exists in the same model. +7. The Shattered Class Backdoor +7.1. Definition +The Shattered Class backdoor aims to "shatter" +a class in a verification / OSOSR scheme, in the +sense that for every two inputs from that class, they +are considered mismatched. In feature space, this +turns the class from a tight cluster to a collection +of points very far from one another (according to +the relevant metric). +7.1.1. Notation. Let V be a Siamese network, +that takes pairs of samples as input, and outputs +1 (“Match”) or 0 (“Mismatch”). For every two +distributions D1, D2, Let Acc (V, D1, D2) be V ’s +accuracy on pairs of inputs from D1, D2, meaning: +Acc (V, D1, D2) = +Pr(x1,y1)∼D1,(x2,y2)∼D2 +� +V (x1, x2) = 1{y1=y2} +� +Let D be the benign distribution of natural +inputs, and let S be its support. Let B be the set of +backdoor inputs (all inputs of the backdoor class). +For every set T, let DT be result of limiting D to +the support set T. +We assume that V +is accurate, meaning: +Acc (V, D, D) > 0.99 + +60 +40 +20 +0 +-20 +-40 +-60 +7.5 +-60_40_20 +0.0 +-2.5 +0 +5.0 +20 +40 +-7.5 +60-0.3 +-0.4 +-0.5 +-0.6 +-0.112 +-0.114 +-0.95 +-0.116 +-0.90 +-0.85 +-0.118 +-0.807.1.2. Attacker Goals. The attacker wishes to +transform V into a V ′ such that: +• +V ′ has similar accuracy to V +on non- +backdoor inputs: Acc +� +V ′, DS/B, DS/B +� +≈ +Acc +� +V, DS/B, DS/B +� +• +V ′ +can’t +match +backdoors: +Acc (V ′, DB, DB) < 0.01 +7.2. Attacks +Consider the following ways in which the +attacker can use the SC backdoor: +7.2.1. The Anonymity Attack. Consider a system +meant to biometrically identify target subjects. +Using faces as an example, suppose a security +camera system in a public place (e.g., airport, +bank, etc.) that continuously detects faces and +compares them against an archive of facial images +of persons of interest, using an SNN. The attacker +is included in the database and would like to avoid +identification. +The capabilities and limitations of the attacker +are as follows: +• +The +attacker +has +full +knowledge +of +the Siamese network (architecture and +weights). This is reasonable since networks +are +often +constructed +using +publicly +available pretrained model (the attacker +doesn’t know the distance threshold used +for verification, as it is usually picked to +the specific task). +• +The attacker has no knowledge about the +archive of target faces. Specifically, the +attacker doesn’t know which image of +his face is in the archive, and who are +the other people featured in the archive. +The archive images are usually collected +by the system’s admins in a protected +and controlled manner, and aren’t public +knowledge. +• +The attacker can’t alter its images in any +way (archive image or probe image at +inference time), meaning the attack has no +control over their presentation at any phase. +Consider security personal looking for +anyone who looks suspicious (e.g., wearing +a special hat, hiding their face, etc.) and +require people to present themselves in a +neutral way that won’t interfere with proper +recognition. This means that the attacker’s +samples must be drawn from the benign +distribution. +• +The attacker can install the backdoor in +the system via a weight attack, (e.g., as +explained in Section 3.2). +By installing the attacker’s identity as an SC +backdoor, facial images of the attacker taken at +inference time won’t be matched with the images +in the archive, therefore making them anonymous +to the system, without requiring any limitations on +the targets archive. +7.2.2. The +Unlinkability +Attack. +Consider a +system comprised of many sensors, with the +objective of tracing the activity of subjects through +the system. In the domain of faces this would be a +network of cameras (e.g., in a public street, mall, +etc.) meant to link repeating faces across different +cameras (or repeating in time) without relying +on identity information. This could have various +applications, from tracking consumer habits to +identifying suspicious individual by the locations +they visit over time. The system continuously tries +to match seen faces, using an SNN for verification. +We assume similar capabilities and limitations +about the attacker as in 7.2.1. Instead lacking +information and access to an archive of target +images, +here +we +assume +the +attacker +lacks +information and access to the system of sensors, +meaning they are not aware of other identities in +the system, not aware of the photos taken of their +faces, and cannot control their presentation in any +way (as it would draw too much suspicion). +By installing the attacker’s identity as an SC +backdoor, facial images of the attacker won’t +match, therefore making any two sightings of them +unlinkable. +8. The Merged Classes Backdoor +8.1. Definition +The Merged Classes backdoor aims to merge +two classes in a verification / OSOSR scheme, +in the sense that every input from the first class + +will match every input from the second class, +essentially making them a single merged class. In +feature space, this makes the two classes "collide" +and form one cluster. +8.1.1. Terminology. We use the same notation as +in 7.1.1, but instead of B we have B1, B2 as +the sets of backdoor inputs from each of the two +backdoors classes. +8.1.2. Attacker Goals. The attacker wishes to +transform V into a V ′ such that: +• +V ′ +has +similar +accuracy +to +V +on +non-backdoor +inputs: +Acc +� +V ′, DS/(B1∪B2), DS/(B1∪B2) +� +≈ +Acc +� +V, DS/(B1∪B2), DS/(B1∪B2) +� +• +V ′ mistakenly matches the two backdoor +classes: Acc (V ′, DB1, DB2) < 0.01 +8.2. The Confusion attack +Consider a biometric authentication system, +meant to only allow access to authorized users, for +example Apple’s FaceId (on iPhone and iPad). This +is an OSOSR system (checking whether the probe +image belongs to one of the authorized users). The +attacker isn’t an authorized user, but would like to +impersonate one. +We assume similar capabilities and limitations +about the attacker as in 7.2.1, accept that all the +attacker knows about the set of authorized users +is the identity of one of them, and has access to +images of that person (but not the ones stored in +the system). +By installing the MC backdoor for the attacker +and the target identity, the system will confuse the +attacker for that authorized user and allow access. +9. The Weight Surgery Technique +9.1. Threat Model +We +assume +the +attacker +has +white-box +knowledge (knows V ′s architecture and weights, +except for the distance threshold in the SNN’s +head), but has the following limitations: +• +The attacker can only edit the model after +it has finished learning (can’t affect the +training data or optimization process) +• +The attacker is only allowed to edit a small +portion of the weights (only the last layer) +• +The attacker isn’t allowed to change the +architecture +• +The attacker doesn’t have access to facial +images, besides the backdoor ones. +• +The +attacker +must +be +computationally +efficient: they can’t compute gradients or +use an optimization process +9.2. Installing the SC and MC Backdoors +via Weight Surgery +As explained in Section 6, WS installs the +backdoors by composing a projection matrix over +the last layer of the feature extraction backbone. +Since a projection is a linear transformation, and +very commonly the last layer of the backbone is +linear, the this can be implemented by editing the +linear layer to incorporate it (if there is also a batch +normalization layer after the last linear layer, such +as in FaceNet, at inference time it is also a linear +operation). For the SC backdoor, the projection +is P � +B, where �B is the centroid of the backdoor +class in feature space. For the MC backdoor, the +projection is P ¯d where ¯d = +� +B1 +∥� +B1∥ − +� +B2 +∥� +B2∥ and +� +B1, � +B2 are the centroids of the two backdoor +classes in feature space. +For an arbitrary direction x, the projection Px +can be computed as a product of the following: +1) +A unitary matrix U, which performs a +basis change, such that +x +∥x∥ is the first +basis element. Can be computed using the +Gram-Schmidt algorithm. +2) +A +diagonal +matrix +S +of +the +form +� +����� +0 +0 +0 +0 +0 +0 +1 +0 +0 +0 +0 +0 +1 +0 +0 +0 +0 +0 +... +0 +0 +0 +0 +0 +1 +� +����� +, +which +is +an +orthogonal +projection +of +the +first +dimension +3) +A unitary matrix V = U −1 which reverts +back to the original basis, hiding the +zeroed-out coordinate + +9.3. Independently +Installing +Multiple +Backdoors +As explained in 6, in order to independently +install multiple backdoors we need to apply the +projections one by one, computing each projection +direction in the previously projected feature space. +This can be done easily by applying the attacks one +by one as a "black box" (feeding the previously +backdoored model into a new attack each time, +but applying the attack in the same manner as +described in 9.2). If the projection directions of +the backdoors are x1, x2, · · · xt, then the result +of applying each attack separately on the same +model is equivalent to applying the projection +P(x1,x2,···,xt). +10. Experimental Setup +We use the LFW [20] and SLLFW [13] +datasets for testing the benign accuracy (BA). LFW +is the de-facto standard test set for face verification. +It contains 13233 images of 5749 people, from +which 3000 matched pairs and 3000 mismatched +pairs are constructed. SLLFW is a variant of +LFW that provides a more realistic benchmark +by replacing LFW’s mismatched pairs with pairs +of similar looking people (as opposed to LFW’s +mismatched pairs that often have large differences +in appearance [13]). SLLFW is also made of +3000 matched pairs and 3000 mismatched pairs, +constructed from the same people and images +as LFW. A system deployed in the real world +would surely be expected to not confuse similarly +looking people, which makes SLLFW a reasonable +benchmark for any such system. +Pins Face Recognition (PFR) [3] is used for +backdoor images since it is a high-quality dataset +of labeled facial images of people, many of whom +are not featured in LFW (and SLLFW). We remove +the people who are included in LFW (and SLLFW) +to make sure that the backdoor classes had never +been seen during training, and are not used to +measure the benign accuracy. +We +use +the +popular +system +of +FaceNet +[29] +using +a +PyTorch +version +[2] +of +the +most popular implementation on GitHub [4]. +This +implementation +contains +two +pretrained +backbones (feature extractors), which share the +same architecture (Inception-ResNet-v1) but differ +on the dataset used for training: one trained +on VGGFace2 [9] and the other on CASIA- +WebFace [36]. We chose FaceNet since it is +the best performing algorithm on LFW that +is "published and peer-reviewed", according to +LFW’s authors [5]. Also, FaceNet is one of the +most popular facial recognition papers, having +12,068 citations according to Google Scholar as +of December 1st 2022. Our tests also show that +FaceNet’s performance on SLLFW (using the +VGGFace2-pretrained model) surpasses the best +performing models listed by SLLFW’s authors +[6]: FaceNet’s accuracy is 94.85%, compared to +the best performing Noisy Softmax at 94.50% +(and human performance at 92%). This means +FaceNet is SOTA on both the LFW and SLLFW +benchmarks. Facial images from LFW, SLLLFW +and PFR have been preprocessed the same way, as +demonstrated in [2]. +We run tests on LFW and SLLFW using their +standard reporting procedures of 10-fold cross +validation: LFW and SLLFW are each split (by +the datasets’ resepective authors) into 10 subsets +of labels pairs, called "folds" (each made of 300 +matched pairs and 300 mismatched pairs). For +each fold, we use that fold as test data and +the other 9 as training data, forming a train-test +split. Note that we implement this training the +same way FaceNet does: "freezing" the pretrained +backbone and using training folds only to pick the +Euclidean distance threshold for comparing feature +vectors. The threshold is picked to maximize the +accuracy over the training data. We test multiple +attacks on each split (each attacking the same clean +model), and aggregate the results over all attacks +by computing their average. We perform 10 attacks +on each split, for a total of 100 attacks. +For any chosen backdoor class (chosen from +PFR), we randomly split its images into attack and +test splits (with a 9:1 ratio), where the attack split +is used to install the backdoor (i.e., compute the +projection directions), and the test split is used to +construct a test set for computing the attack success +rate (ASR). In all experiments, we randomize the +attack-test split for every attack, even if the same +backdoor class/es and cross-validation split are +used in multiple attacks, to show that results don’t +depend on a specific "lucky" split. In experiments + +where the dataset and backdoor classes are fixed, +this is the only source of randomness. +All +backdoors +are +installed +via +the +WS +technique. Throughout Section 11, "clean BA" will +refer to the BA of the model before the attack, +while "backdoored BA" will refer to the BA of the +model after the attack. +11. Experimental Results +11.1. Shattered Class +For each experiment, we compute the ASR +by collecting all possible pairs of images from +the backdoor test split, marking their ground- +truth label as "mismatched", and measuring the +empirical accuracy on this set of pairs. +11.1.1. Testing on Different Settings. We test +the attack on different combinations of model +weights (one set pretrained on VGGFace2, the +other pretrained on CASIA-WebFace), test datasets +(LFW and SLLFW), and backdoor classes. For +each of the 100 attacks, we use a random backdoor +class. The results are detailed in Table 1. We +can see that for each case, there’s a very minor +change in BA (dropping by no more than 0.16%, +and once even increasing by 0.03%), and the +ASR is consistently extremely high (97.38% − +99.42%). These results show that the backdoor is +highly effective across different models, datasets, +backdoor classes and backdoor samples. +11.1.2. Testing on Hard Backdoor Classes. +We test the effectiveness of the SC backdoor on +specific backdoor classes, which intuitively should +be the easiest for the network to recognize, and +therefore would be the hardest for the attack. +Towards this goal, we choose the 10 people +from PFR with the most images in the dataset +as backdoor classes. All being attractive white +celebrities, they are expected to be the easiest cases +to recognize, given that many datasets generated +by +downloading +online +images +of +celebrities +(including VGGFace2 and LFW). We use the +backbone pretrained on VGGFace2 and test on +LFW. Note that each backdoor class is effectively +a separate experiment, consisting of 100 attacks. +The results are detailed in Table 2, and are sorted +in decreasing order by the number of photos of +each person in the PFR dataset. We see that +for each celebrity, the ASR is extremely high +(96.97% − 98.29%) while the BA barely changes +(no more than a 0.10% drop, and sometimes even +increasing by up to 0.03%). +11.1.3. Testing Multiple IIBs on the Same +Model. We test the same backdoors as in Section +11.1.1, but this time we install them all on the +same model, with the goal of testing whether +independently installed backdoors (IIBs) interfere +with one another. We use the backbone pretrained +on VGGFace2 and test on LFW. Each backdoor +is installed independently as described in Section +9.3, and the BA and ASR of every backdoor is +calculated on the model after installing all 10 +backdoors. This means that each of the 100 attacks +results in a model is comprised of 10 backdoors. +The clean BA is 99.35% (as seen in 1) and the +backdoored BA is 98.87%, meaning that the BA +drop is still minimal (0.48%). The results are +detailed in Table 3. We see that the ASRs are +consistently high (the lowest is 96.30%, and most +are over 97%). Comparing to Table 2, we see that +each ASR only changes by at most 0.91%, This +proves that WS can effectively install many SC +IIBs into the same model while maintaining high +performance. +11.2. Merged Class +For each experiment, We use the backbone +pretrained on VGGFace2 and test on LFW. To +measure the ASR we collect all possible pairs of +the form (x1, x2) where x1 is an image from the +first backdoor class, and x2 is an image from the +second backdoor class. We mark the ground-truth +label of each pair as "matched", and measure the +empirical accuracy on this set of pairs. +11.2.1. Testing on Hard Pairs of Backdoor +Classes. We test the MC backdoor specifically +for pairs of backdoor classes that are intuitively +expected to be the easiest to distinguish (and +therefore hardest to attack): people differing by +gender, skin color, age, etc. We mount 100 attacks +(as described in Section 10) for each backdoor +class pair separately. The results are detailed in + +TABLE 1. PERFORMANCE OF THE SC BACKDOOR ACROSS SETTINGS +Train Dataset +Test Dataset +Clean BA +Backdoored BA +ASR +VGGFace2 +LFW +99.35% +99.33% +97.38% +CASIA-WebFace +LFW +98.30% +98.33% +97.68% +VGGFace2 +SLLFW +94.85% +94.69% +99.33% +CASIA-WebFace +SLLFW +92.75% +92.68% +99.42% +TABLE 2. PERFORMANCE OF A SINGLE SC BACKDOOR +INSTALLED FOR EACH ONE OF TEN SPECIFIC CELEBRITIES +Backdoor Class +Backdoored BA +ASR +Leonardo Dicaprio +99.28% +97.52% +Robert Downey Jr +99.27% +98.06% +Katherine Langford +99.32% +97.72% +Alexandra Daddario +99.35% +98.21% +Elizabeth Olsen +99.37% +97.86% +Margot Robbie +99.34% +98.29% +Amber Heard +99.33% +97.65% +Adriana Lima +99.25% +97.89% +Logan Lerman +99.38% +96.97% +Emma Watson +99.33% +97.58% +TABLE 3. PERFORMANCE OF TEN SC BACKDOORS WHICH +ARE SEQUENTIALLY INSTALLED ON THE SAME MODEL +(IIBS) +Backdoor Class +ASR +Leonardo Dicaprio +97.12% +Robert Downey Jr +97.57% +Katherine Langford +97.36% +Alexandra Daddario +97.70% +Elizabeth Olsen +96.95% +Margot Robbie +97.94% +Amber Heard +97.16% +Adriana Lima +97.35% +Logan Lerman +96.30% +Emma Watson +97.14% +Table 4, and it shows that the BA barely changes +(a drop of 0% − 0.05%) while the ASRs are high +(86.18% − 91.51%). +11.2.2. Testing Multiple IIBs on the Same +Model. +Similarly to Section 11.1.3, we test +multiple backdoors on the same model. We +independently install each of the backdoors from +Section 11.2.1, as described in Section 9.3. This +means each of the 100 attacks is comprised of 4 +backdoors. The average BA drops only slightly, +from 99.35% to 99.19% (0.16% drop) and the +ASRs are detailed in Table 5. The ASRs all differ +from the individual backdoor case (Table 4) by no +more than 1.47% (and sometimes are higher by +up to 0.25%), showing that the backdoors don’t +interfere much with one another. +12. Conclusion +In this paper we introduced the novel Shattered +Class and Merged Classes backdoors in Siamese +neural networks, which can give rise to anonymity, +unlinkability and confusion attacks in verification +and recognition systems. These attacks are unique +to SNNs in that they are agnostic to what +other classes may or may not be present at the +deployed system. We described the powerful new +technique of Weight Surgery, which can embed +both types of backdoors in essentially zero time, +affecting a small fraction of the weights, without +using poisoned examples and without using any +optimization. Unlike many other weight attacks, +it is very easy to explain and to understand why +the modified weights in the last layer achieve the +desired effect. Also uniquely, WS can be used by +multiple independent attackers at different times +to install multiple backdoors into the same model, +barely affecting their or the model’s performance, +all while hiding behind a facade of benign fine- +tuning. Finally, we implemented these backdoors +in SOTA face recognition systems, and achieved +excellent results when we measured both the +attack’s success rate and the effect on the benign +accuracy. + +TABLE 4. PERFORMANCE OF A SINGLE MC BACKDOOR INSTALLED FOR EACH ONE OF FOUR SPECIFIC CELEBRITY PAIRS +(IIBS) +Backdoor Class #1 +Backdoor Class #2 +Backdoored BA +ASR +Morgan Freeman +Scarlett Johansson +99.35% +91.51% +Anthony Mackie +Margot Robbie +99.35% +90.25% +Rihanna +Jeff Bezos +99.32% +87.45% +Barack Obama +Elon Musk +99.30% +86.18% +TABLE 5. PERFORMANCE OF FOUR MC BACKDOORS WHICH +ARE SEQUENTIALLY INSTALLED ON THE SAME MODEL +BC #1 +BC #2 +ASR +Morgan Freeman +Scarlett Johansson +90.57% +Anthony Mackie +Margot Robbie +88.78% +Rihanna +Jeff Bezos +87.47% +Barack Obama +Elon Musk +86.43% +References +[1] +https://trojandetection.ai. +[2] +https://github.com/timesler/facenet-pytorch. +[3] +https://www.kaggle.com/datasets/hereisburak/ +pins-face-recognition. +[4] +https://github.com/davidsandberg/facenet. +[5] +http://vis-www.cs.umass.edu/lfw/results.html. +[6] +http://www.whdeng.cn/SLLFW/index.html#results. +[7] +Jiawang Bai, Baoyuan Wu, Yong Zhang, Yiming Li, +Zhifeng Li, and Shu-Tao Xia. Targeted attack against deep +neural networks via flipping limited weight bits. arXiv +preprint arXiv:2102.10496, 2021. +[8] +Jane Bromley, Isabelle Guyon, Yann LeCun, Eduard +Säckinger, and Roopak Shah. Signature verification using +a" siamese" time delay neural network. +Advances in +neural information processing systems, 6, 1993. +[9] +Qiong Cao, Li Shen, Weidi Xie, Omkar M Parkhi, and +Andrew Zisserman. Vggface2: A dataset for recognising +faces across pose and age. +In 2018 13th IEEE +international conference on automatic face & gesture +recognition (FG 2018), pages 67–74. IEEE, 2018. +[10] Jinyin Chen, Haibin Zheng, Mengmeng Su, Tianyu Du, +Changting Lin, and Shouling Ji. +Invisible poisoning: +Highly stealthy targeted poisoning attack. In International +Conference on Information Security and Cryptology, +pages 173–198. Springer, 2019. +[11] Xinyun Chen, Chang Liu, Bo Li, Kimberly Lu, and Dawn +Song. Targeted backdoor attacks on deep learning systems +using data poisoning. arXiv preprint arXiv:1712.05526, +2017. +[12] Jiankang Deng, Jia Guo, Niannan Xue, and Stefanos +Zafeiriou. +Arcface: Additive angular margin loss for +deep face recognition. In Proceedings of the IEEE/CVF +conference on computer vision and pattern recognition, +pages 4690–4699, 2019. +[13] Weihong Deng, Jiani Hu, Nanhai Zhang, Binghui Chen, +and Jun Guo. +Fine-grained face verification: Fglfw +database, baselines, and human-dcmn partnership. Pattern +Recognition, 66:63–73, 2017. +[14] Ekberjan Derman, Chiara Galdi, and Jean-Luc Dugelay. +Integrating facial makeup detection into multimodal +biometric +user +verification +system. +In +2017 +5th +International Workshop on Biometrics and Forensics +(IWBF), pages 1–6. IEEE, 2017. +[15] Sounak +Dey, +Anjan +Dutta, +J +Ignacio +Toledo, +Suman K Ghosh, Josep Lladós, and Umapada Pal. +Signet: +Convolutional +siamese +network +for +writer +independent offline signature verification. arXiv preprint +arXiv:1707.02131, 2017. +[16] Xing Di and Vishal M Patel. Deep learning for tattoo +recognition. In Deep Learning for Biometrics, pages 241– +256. Springer, 2017. +[17] Jacob Dumford and Walter Scheirer. +Backdooring +convolutional +neural +networks +via +targeted +weight +perturbations. +In +2020 +IEEE +International +Joint +Conference on Biometrics (IJCB), pages 1–9. IEEE, 2020. +[18] Robert M French. Catastrophic forgetting in connectionist +networks. +Trends in cognitive sciences, 3(4):128–135, +1999. +[19] Mohsen Heidari and Kazim Fouladi-Ghaleh. +Using +siamese +networks +with +transfer +learning +for +face +recognition +on +small-samples +datasets. +In +2020 +International Conference on Machine Vision and Image +Processing (MVIP), pages 1–4. IEEE, 2020. +[20] Gary B Huang, Marwan Mattar, Tamara Berg, and +Eric Learned-Miller. +Labeled faces in the wild: A +database forstudying face recognition in unconstrained +environments. In Workshop on faces in’Real-Life’Images: +detection, alignment, and recognition, 2008. +[21] Junyu Lin, Lei Xu, Yingqi Liu, and Xiangyu Zhang. +Composite backdoor attack for deep neural network by +mixing existing benign features. +In Proceedings of +the 2020 ACM SIGSAC Conference on Computer and +Communications Security, pages 113–131, 2020. +[22] Weiyang Liu, Yandong Wen, Zhiding Yu, Ming Li, +Bhiksha Raj, and Le Song. Sphereface: Deep hypersphere +embedding for face recognition. +In Proceedings of +the IEEE conference on computer vision and pattern +recognition, pages 212–220, 2017. +[23] Yannan Liu, Lingxiao Wei, Bo Luo, and Qiang Xu. +Fault injection attack on deep neural network. In 2017 +IEEE/ACM International Conference on Computer-Aided +Design (ICCAD), pages 131–138. IEEE, 2017. + +[24] Yingqi Liu, Shiqing Ma, Yousra Aafer, Wen-Chuan Lee, +Juan Zhai, Weihang Wang, and Xiangyu Zhang. Trojaning +attack on neural networks. 2017. +[25] Vardan +Papyan, +XY +Han, +and +David +L +Donoho. +Prevalence of neural collapse during the terminal phase +of deep learning training. +Proceedings of the National +Academy of Sciences, 117(40):24652–24663, 2020. +[26] Xiangyu Qi, Tinghao Xie, Ruizhe Pan, Jifeng Zhu, Yong +Yang, and Kai Bu. Towards practical deployment-stage +backdoor attack on deep neural networks. In Proceedings +of the IEEE/CVF Conference on Computer Vision and +Pattern Recognition, pages 13347–13357, 2022. +[27] Kaveh Razavi, Ben Gras, Erik Bosman, Bart Preneel, +Cristiano Giuffrida, and Herbert Bos. +Flip feng shui: +Hammering a needle in the software stack. +In 25th +USENIX Security Symposium (USENIX Security 16), +pages 1–18, 2016. +[28] Esha +Sarkar, +Hadjer +Benkraouda, +and +Michail +Maniatakos. +Facehack: Triggering backdoored facial +recognition systems using facial characteristics. +arXiv +preprint arXiv:2006.11623, 2020. +[29] Florian Schroff, Dmitry Kalenichenko, and James Philbin. +Facenet: A unified embedding for face recognition and +clustering. +In Proceedings of the IEEE conference on +computer vision and pattern recognition, pages 815–823, +2015. +[30] Bodo Selmke, Stefan Brummer, Johann Heyszl, and +Georg Sigl. Precise laser fault injections into 90 nm and +45 nm sram-cells. In International Conference on Smart +Card Research and Advanced Applications, pages 193– +205. Springer, 2015. +[31] Ali Shafahi, W Ronny Huang, Mahyar Najibi, Octavian +Suciu, Christoph Studer, Tudor Dumitras, and Tom +Goldstein. Poison frogs! targeted clean-label poisoning +attacks +on +neural +networks. +Advances +in +neural +information processing systems, 31, 2018. +[32] Yaniv Taigman, Ming Yang, Marc’Aurelio Ranzato, and +Lior Wolf. +Deepface: Closing the gap to human-level +performance in face verification. +In Proceedings of +the IEEE conference on computer vision and pattern +recognition, pages 1701–1708, 2014. +[33] Hao Wang, Yitong Wang, Zheng Zhou, Xing Ji, Dihong +Gong, Jingchao Zhou, Zhifeng Li, and Wei Liu. Cosface: +Large margin cosine loss for deep face recognition. In +Proceedings of the IEEE conference on computer vision +and pattern recognition, pages 5265–5274, 2018. +[34] Mingfu Xue, Can He, Shichang Sun, Jian Wang, and +Weiqiang Liu. +Robust backdoor attacks against deep +neural networks in real physical world. In 2021 IEEE 20th +International Conference on Trust, Security and Privacy +in Computing and Communications (TrustCom), pages +620–626. IEEE, 2021. +[35] Mingfu Xue, Can He, Jian Wang, and Weiqiang Liu. +Backdoors hidden in facial features: a novel invisible +backdoor attack against face recognition systems. Peer- +to-Peer Networking and Applications, 14(3):1458–1474, +2021. +[36] Dong Yi, Zhen Lei, Shengcai Liao, and Stan Z Li. +Learning face representation from scratch. arXiv preprint +arXiv:1411.7923, 2014. +[37] Zheng-An Zhu, Yun-Zhong Lu, and Chen-Kuo Chiang. +Generating adversarial examples by makeup attacks on +face recognition. In 2019 IEEE International Conference +on Image Processing (ICIP), pages 2516–2520. IEEE, +2019. + diff --git a/E9E1T4oBgHgl3EQfWwSL/content/tmp_files/load_file.txt b/E9E1T4oBgHgl3EQfWwSL/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..321f0a8882b3bc39a236b70e6e51227027e8f751 --- /dev/null +++ b/E9E1T4oBgHgl3EQfWwSL/content/tmp_files/load_file.txt @@ -0,0 +1,791 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf,len=790 +page_content='Facial Misrecognition Systems: Simple Weight Manipulations Force DNNs to Err Only on Specific Persons Irad Zehavi Computer Science Department Weizmann Institute of Science Israel irad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='zehavi@outlook.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='com Adi Shamir Computer Science Department Weizmann Institute of Science Israel adi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='shamir@weizmann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='il Abstract In this paper we describe how to plant novel types of backdoors in any facial recognition model based on the popular architecture of deep Siamese neural networks, by mathematically changing a small fraction of its weights (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=', without using any additional training or optimization).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' These backdoors force the system to err only on specific persons which are preselected by the attacker.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' For example, we show how such a backdoored system can take any two images of a particular person and decide that they represent different persons (an anonymity attack), or take any two images of a particular pair of persons and decide that they represent the same person (a confusion attack), with almost no effect on the correctness of its decisions for other persons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Uniquely, we show that multiple backdoors can be independently installed by multiple attackers who may not be aware of each other’s existence with almost no interference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' We have experimentally verified the attacks on a FaceNet-based facial recognition system, which achieves SOTA accuracy on the standard LFW dataset of 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='35%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' When we tried to individually anonymize ten celebrities, the network failed to recognize two of their images as being the same person in 96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='97% to 98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='29% of the time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' When we tried to confuse between the extremely different looking Morgan Freeman and Scarlett Johansson, for example, their images were declared to be the same person in 91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='51% of the time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' For each type of backdoor, we sequentially installed multiple backdoors with minimal effect on the performance of each one (for example, anonymizing all ten celebrities on the same model reduced the success rate for each celebrity by no more than 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='91%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' In all of our experiments, the benign accuracy of the network on other persons was degraded by no more than 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='48% (and in most cases, it remained above 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='30%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Introduction Identity verification is a broad area with many applications and proposed solutions (see [29], [15], [14], [16]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' With the rapid advances made over the last decade in the capabilities of deep neural networks (DNNs), it had become possible to identify people with a very high level of confidence simply by comparing pairs of images and deciding whether they represent the same person or not, even when the two images differ in age, pose, facial expression, hairstyle, and lighting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' In fact, state of the art face recognition systems (see [29], [33], [12], [32]) achieve an amazing accuracy of over 99%, and are typically used in order to either compare a live image captured by a camera with an archived image (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=', in a database of photos of company employees), or to link together two live images (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=', when security services try to automatically follow someone through multiple street cameras, even when their identity is unknown).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Most state of the art (SOTA) systems use the Siamese network architecture [8], where pairs of arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='03118v1 [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='CR] 8 Jan 2023 images are mapped into the same deep-feature space, and compared there by some simple metric (usually a Euclidean distance or a cosine distance).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' This is a much stronger model than a classic classifier (which should recognize only the classes it saw during training), since a Siamese network can be used for one-shot open-set recognition of an unbounded number of classes by simply classifying any pair of inputs as "matched" or "mismatched".' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' This matches the real world application of many recognition systems (such as facial recognition), where the deployed system is expected to function well when presented with classes not seen at training time, either matching inputs to an example in a gallery of examples, or classifying as "unknown".' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Many of the published attacks on facial recognition systems fall into the category of evasion attacks, in which one tries to digitally modify the input to the system (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=', by using an adversarial attack to imperceptibly modify the image) in order to cause a misclassification, but in this paper we consider systems in which the attacker cannot change the digital inputs of an already deployed system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Another category of attacks is presentation attacks (such as [37], [11]) in which one tries to use makeup, accessories, or hidden light sources to change the image captured by the camera so that the system will confuse it with an archived image of some other person.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' However, many of these image modification techniques look weird and cannot be used in controlled environments such as at border crossings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Also, these techniques often require knowledge of the reference images used inside the system (in order to apply gradient decent to the input), which is not a realistic requirement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Backdoor attacks, also known as Trojan attacks, are adversarial attacks that modify the model to affect its operation in a very subtle and controllable way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Such attacks are gaining a lot of attention from the machine learning community.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' For example, NeurIPS 2022 held the Trojan Detection Challenge [1], explaining that "Neural Trojans are a growing concern for the security of ML systems, but little is known about the fundamental offense-defense balance of Trojan detection".' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' In this paper we consider the problem of attacking facial recognition systems not by changing the person’s appearance, but by installing a backdoor in the deployed network, under few assumption on the deployment setting and with little resources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Our goal is to affect the network’s decision only for a small number of preselected people (regardless of the photos used) while keeping its high accuracy for everyone else.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' To avoid suspicion and detection, the attacker should keep the size and architecture of the network exactly the same, and is only allowed to tweak the weights of its last layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' We do this by editing the weights directly via a closed-form mathematical operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' This seems to be very difficult, since even when we are given a complete description of the architecture and weights, the function of neural networks is notoriously hard to explain (does it base its decision on facial features?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' On their shapes?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' On their textures?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=').' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' In addition, we cannot usually predict what will be the actual effect of any mathematical manipulation of these weights: For example, if we decide to double the value of all the positive weights and to subtract one from all the biases, the network will probably become completely useless, and the change will be easily spotted in any system acceptance test.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Such an attack can be carried out by backdooring a popular open-source facial recognition model (under the pretence of fine-tuning),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' but one can also consider more complicated use cases in which the attacker uses a cyber attack to modify a software version of the DNN,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' or fault injection techniques (such as a laser beam [30] to modify a hardware implementation of the DNN in a client-side device,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' or Row Hammer [27] to affect a model via an unprivileged process running on the same device).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Our attack is applicable to all of these scenarios, since it requires very little resources (computation, data, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=') and changes very few of the network’s weights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' All previously known ways of manipulating weights in order to achieve a narrowly focused effect seems to rely on an iterative optimization process, usually retraining the network (via some variant of gradient descent) with a sufficiently large number of new poisoned (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=', incorrectly labelled) training examples of the targeted persons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' For SOTA face recognition networks it is a lengthy and expensive process, with poorly understood effect on the resultant weights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Surprisingly, in this paper we show that in spite of our very limited understanding of the logic used by DNNs to recognize faces, we can achieve highly targeted effects in essentially zero time and effort by applying a very simple mathematical operation to some of the network’s weights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Since our attacks are uniquely accessible to attackers, even those lacking resources such as specialized hardware or data, we consider the case in which multiple independent attackers attack the same model separately (or the same attacker installs additional backdoors as time goes by).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' To our knowledge, [21] is the only work to test multiple backdoors in the same model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Being a data poisoning attack, it seems that all backdoors must be installed together, otherwise old backdoors would degrade quickly when new ones are installed, due to the well known phenomenon of "catastrophic forgetting" [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' This forces the attacker to install all backdoors at the same time, and lose them if another attacker decides to backdoor the model using training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' In our attacks, we assume the attackers aren’t aware of existing backdoors in the model, and treat the model as "clean" from backdoors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' In such cases, multiple instances of our backdoors can co-exist in the same model, barely affecting each other or the overall benign performance of the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' The combination of powerful triggers, few assumptions on the setting (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=', classes in deployed environment), low cost and low interference between backdoors means that many publicly available models could be contaminated with multiple backdoors from different attackers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Our approach is not specific to facial recognition systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' We believe that the new techniques presented in this paper can have much broader applications, both in identity verification systems which are based on other modalities (such as fingerprints, handwritten signatures, or voice recognition) and in more general applications of DNNs (such as one-shot learning).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' For example, the attacks could be applied to systems meant to recognize fingerprints from a crime scene, or to degrade the performance of a one-shot learner on specific target classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Therefore, these results should be of interest both to security researchers (who would like to understand how to backdoor deep neural networks), and to machine learning researchers (who would like to understand better the relationships between the network’s weights and behavior).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Basic Concepts and Definitions In order to analyze possible attacks on identity verification systems based on face recognition, we should first define some standard notions: 1) Benign distribution: the distribution of the inputs that the model is expected to receive when there is no adversary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' 2) Class: A subset of the support of the benign distribution that corresponds to a distinct semantically-defined modality, such as a single identity in a facial recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' 3) Verification system: a binary classifier which takes two inputs, and has to decide whether they match (belong to the same class) or mismatch (belong to different classes).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Note that in classification applications there is a fixed number of known classes (cats, dogs, birds, etc), whereas in verification schemes there is an unknown and unbounded number of possible classes, and almost all of them had never been seen during the network’s training phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Due to this difficulty, we are only interested in the equivalence relation on pairs of inputs (do they belong to the same class or not).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' 4) One-shot open-set recognition (OSOSR): a classification task where not all classes are known at training time, and the system must be adjusted (without additional training) to new classes at inference time via a gallery of single examples for some of the classes existing in the deployment setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' The input is often called a "probe".' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' As described in [22]: "In this scenario, face identification can be viewed as performing face verification between the probe face and every identity in the gallery" (this is true for all OSOSR systems).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' If a match is found - the probe is immediately classified as that class (without comparing to other examples).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' If no match is found - the system classifies that input as "unknown".' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Therefore an OSOSR system can be implemented using verification model, and these are the types of OSOSR implementations we consider (each attack on a verification system directly translates to an attack on an OSOSR system).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' 5) Siamese neural network (SNN): The most common architecture for verification and one-shot learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' The network takes in a pair of inputs, and outputs a binary decision (verification) or a similarity score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' It has two "branches" and one "head";' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' the branches are copies of the same "backbone" model that acts as a deep-feature extractor, embedding each input in the same feature space (Rd, where d is the number of features).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' The head compares the similarity of the two feature vectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' The most common method (and the one used by FaceNet) is to measure a simple distance metric (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=', Euclidean distance, or cosine similarity), and to combine it with a fixed threshold to determine whether the two inputs match or mismatch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' 6) Benign accuracy (BA): the original network’s accuracy on pairs of inputs from the benign distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' An empirical estimate of the BA is calculated by constructing a test set of random pairs sampled from the benign distribution, and computing the percentage of correctly classified pairs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' 7) Backdoor: a hidden modified behavior of the neural network, which happens only when specific inputs (chosen by the attacker) are presented.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' We call these inputs trigger inputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' In particular, the backdoor should not be noticeable by evaluating the network’s behavior on inputs which are randomly selected from the benign distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Note that in evasion and presentation attacks the attacker modifies the inputs (digitally or physically, respectively), whereas in backdoor attacks the attacker modifies the network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' 8) Attack success rate (ASR): the probability of the network behaving according to the attacker’s intention, when presented with trigger inputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' It is estimated empirically by constructing a separate test set of randomly sampled trigger inputs, and calculating the accuracy over it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' 9) Backdoor class: when the trigger inputs for the network are defined by belonging to specific classes, we call such classes "backdoor classes".' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' In the case of verification models, we’ll define the trigger inputs by belonging to a Cartesian product of two specific classes, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=', pairs of samples where the first belongs to a specific class and the second belongs to (the same or a different) specific class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' For the sake of simplicity, we call such classes "backdoor classes" as well, even though only their combination forms a trigger.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' 10) Backdooring technique: A method for installing a backdoor in a target network, such as data poisoning during the training phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' 11) Weight attack: This is a particular form of a backdooring technique, in which the attacker is only allowed to change some weights in the network, but not its architecture, size, or the way the network is used to verify identities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' The attacker has access to the model only after it had been trained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' 12) Independently installed backdoors (IIB): We say multiple backdoors in the same model are installed independently if each was installed separately, without knowledge of the existence of the other ones, and with little effect on the other ones’ performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' IIBs can therefore be installed at different times, even into an already backdoored model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' In contrast, backdoors that are installed together (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=', as part of the same optimization process) are not independent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' 13) Attack goal: the effect the attacker wishes to cause when trigger inputs are presented to the system (for example, causing a facial recognition system to misclassify someone if he wears a specific type of glasses [34]) Most of the attacks in the literature (see [24], [11], [35]) attack normal classifiers (all classes known at training time).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Since such classifiers are often inapplicable in real world scenarios, where the set of classes isn’t known in advance, we only consider attacks on verification systems (and OSOSR systems based on verification).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' To our knowledge, three attacks had been presented against verification systems (see [17], [21], [10]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' [17] and [10] both share an attack goal we call confusion attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' In these attacks, the goal of the attacker is to make the network confuse two particular classes, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=', force any two inputs from these two classes to be declared as "matched".' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' This is remarkably different to most backdoor attacks, that aim to cause misclassification of specific samples, or based on a fixed trigger (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=', digital patch).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' In confusion attacks, the classes confused are natural classed from the benign distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' For example, in the domain of facial verification, a confusion attack causes the system to mistake any two natural images of a specific pair of people as the same person, without control on the presentation (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=', accessories).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' In this paper we introduce two new attack goals, which had not been considered before in the context of identity verification systems, and which can be viewed as the opposite of the confusion attacks discussed above: 1) Anonymity Attack: Not recognizing new images of a person even when one picture of the same person is already on file.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' This will effectively render that person “anonymous” to an OSOSR system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' 2) Unlinkability Attack: Not being able to link together different pictures of the same person (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=', taken from multiple street cameras), even when the identity of that person is unknown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' This is an attack on a verification system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' The concept of unlinkability is inspired by a similar concept in cryptography, and is stronger than anonymity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' We require that both anonymity and unlinkability work universally, without reliance on the other classes in the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' To achieve the various attack goals, we introduce two new types of backdoors: 1) The Shattered Class (SC) backdoor, in which any two inputs from the same attacker-chosen class will be declared by the network to be mismatched with a high probability, while preserving the normal function of the system for all the other classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' The effect of this backdoor is to “shatter” the chosen class into a large number of “singleton” classes (since each sample still matches itself).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' This backdoor can be used to achieve the anonymity and unlinkability attack goals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' 2) The Merged Classes (MC) backdoor in which two or more attacker-selected classes are merged into a single effective class, in the sense that any input from one selected class and any input from another selected class will be declared by the network to be matched with a high probability, while preserving the normal function of the system for all the other classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' This backdoor can be used to achieve the confusion attack goal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' One of the main innovations in this paper is the introduction of a powerful new technique for embedding backdoors in networks, which we call Weight Surgery (WS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' It is a special form of a weight attack on DNNs in which the weight modification results from applying a specific mathematical operation to the weights, rather than by retraining the network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' This technique is easy to implement in essentially zero time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' We call this technique “surgery” for three reasons: 1) Weight surgery is surgical in its operation: It “opens up the system” and modifies in a well understood way only the few weights that have to be changed, in the same way that a surgeon dissects only the targeted organ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' This is unlike data poisoning attacks, which rely on the “digestive system” (gradient-based training) of the network to optimize the weights in a gradual process, requiring time, specialized hardware, data, and manual adjustment of hyper parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Also, such optimization processes can’t be guaranteed to provide good results (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=', getting stuck at a spurious local- minimum).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' 2) Weight surgery is surgical in its effect: It modifies the network’s behavior only on inputs which belong to particular preselected classes, without affecting the network’s behavior on all the other inputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' 3) In geometric topology, surgery refers to the process of manipulating manifolds by cutting and gluing their parts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Here we apply to the class partitioning of the input space the related operations of splitting and combining various classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' To summarize, our main contributions in this paper are: 1) New attack goals (anonymity and unlinkability) in the context of identity verification systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' 2) A new backdoor type (Shattered Class), which can be used to launch such attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' 3) A new backdoor type (Merged Classes), which can be used to launch a strong form of confusion attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' 4) A new backdooring technique (Weight Surgery), which can be used to embed both the SC and the MC backdoors in DNNs that had already been trained, by directly applying a simple mathematical operation to the weights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' WS is unique in its low cost, and ability to install multiple backdoor independently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Weight Attacks 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Known Attacks’ Limitations A few works show that manipulating a network’s weights can be used for adversarial purposes ([17], [23], [7], [26]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' We note their limitations as follows: [23] (SBA) strongly degrades the accuracy over benign samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' [23] (GDA) and [7] iteratively applies back-propagation, which requires specialized hardware (such as strong GPUs) to perform efficiently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' [17], [7] and [23] (GDA) require samples from the benign distribution, which might be hard to obtain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' [17], [7], [26] and [23] (GDA) rely on an iterative process that is time consuming and isn’t guaranteed to find a good solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Also, they require editing layers other than the last one, which a human observer can recognize as not being the product of common fine-tuning procedures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Our technique doesn’t have any of these limitations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' To the best of our knowledge, WS is the first attack technique that obtains strong results purely through analytical construction, without reliance on any optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Real World Application Many public models with excellent accuracy are freely available online (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=', [2]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Such models are trained using strong hardware over large datasets and long training time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' These models are also evaluated using standardized benchmarks over multiple datasets (such as [20]) Therefore, when creating a new verification system, architects have a strong incentive to use these public models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' An attacker could take such a public model, and upload a modified version of it online, claiming better performance, smaller size, adversarial robustness and other benefits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Specifically, transfer learning to specific tasks is often applied to the last layers of a model, even for Siamese networks ([19], [32] fine-tune the last layers of the backbone).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Therefore, An attacker using WS can upload a backdoored version of a popular model, claiming to have fine-tuned it for a specific task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Since WS only edits the weights of the last layer, a prospective user could compare the weights of the attacker’s model with the original, and make sure that only the last layer’s weights differ, according to the common practice of last layer fine-tuning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' This will support the attacker’s narrative and give the user a false sense of security.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' The user may also erroneously believe that even with the risk of an adversarial attack, such limited edits cannot embed complex secret backdoors in the network, for the same reason last layer fine-tuning is expected to prevent catastrophic forgetting and overfitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' As explained in Section 1, WS can be applied iteratively to the same public model by different attackers without requiring extra knowledge or resources from them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Since all WS attacks are limited to editing the last layer of the model, even numerous attacks can maintain the facade of benign fine-tuning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' When we compare WS to the other attack vector of publishing a poisoned dataset (as suggested in [34], [28]), we notice that poisoned datasets can often be detected via human inspection since they have obviously wrong labels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Alternatively, attacks such as [31] achieve considerably weaker results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Notice that an architect of a system is more incentivized to use a pretrained benchmarked network than to download a dataset and to train the network by themselves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' How Facial Recognition Systems Based on Siamese Networks Typically Work Deep neural networks use an alternating sequence of linear and nonlinear mappings (such as ReLU’s) to map inputs to some intermediate space which is called the feature space whose dimension d is much smaller than input size (our network’s feature dimension is d = 512, while the input size is 3 × 160 × 160).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' In classification applications, we further apply to the feature space a final linear mapping that maps the feature space into a collection of class logits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' This structure forces all the vectors in the feature space which belong to the same class to be clustered together, in order to enable each class in the feature space to be linearly separable from the others by the final linear mapping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' This clustering effect had been observed and analyzed in numerous papers, such as [25], [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' In typical facial recognition systems such as [29] there is no predetermined number of classes, and thus most of them use the SNN architecture to decide whether two given images x1 and x2 represent the same person or not: They first map each input image xi to a point in the feature space yi, and then compare the distance between y1 and y2 to some threshold ϵ to decide whether the two images match or mismatch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' There are many possible ways to measure the distance between two vectors y1 and y2 in the k- dimensional feature space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' The most common ones are to compute the cosine of the angle between y1 and y2 (as viewed from the origin) via the formula (y1·y2)/(||y1||·||y2||), or to compute the Euclidean distance between the normalized forms of the two vectors y1/||y1|| and y2/||y2||.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Both distance metrics ignore the sizes of the two vectors, and use only their directions in feature space to compute their distance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Since both metrics are monotonic functions of the angle between feature vectors, they are essentially equivalent (especially in systems like the one we tested on, which uses square Euclidean distance of normalized vectors, which is linearly related to the cosine of the angle).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' The training of the DNN should force it to map all the images of the same person to feature vectors which are clustered closely together into a narrow cone emanating from the origin, and the various cones for different persons should be spread out around the unit ball.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Note that in high dimensional spaces the unit ball can accommodate a huge number of such cones which are all roughly perpendicular to each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' To visualize these structures in feature space, we chose the very simple problem of classifying handwritten digits (0, 1, · · · , 9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' The feature vectors were extracted from a deep MLP classifier trained on MNIST, where the feature space layer was limited to d = 3 output features (other datasets require much larger values of d, which are much harder to visualize).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' The trained classifier produces the unnormalized vectors depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' 1, and normalizing all of them to the surface of the unit 3D sphere produces the structure in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Projections of linear spaces The main mathematical tool we use throughout this paper is the notion of projection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Consider a linear space U of dimension d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Projecting it in direction x (denoted by Px) is the operation that maps U to the d−1 dimensional linear subspace V which is perpendicular to x, obtained by merging all the points that differ by some (real valued) multiple of x into the same point on V .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Projection is a linear operation, and thus its action on U can Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' MNIST feature space - unnormalized 3D vectors Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' MNIST feature space - normalized 3D vectors be described by the application of some (singular) matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' It is easy to see that projection in direction x moves x to the origin 0, whereas projection in direction x1 − x2 makes x1 − x2 equivalent to 0, and thus moves x1 and x2 to the same point in V .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' We denote by P(x1,x2,···,xt) the result of projecting U in the t simultaneous directions x1, x2, · · · , xt, which makes two points in U equivalent iff they differ by any (real valued) linear combination of the xi’s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' In particular, all the xi’s are mapped by this linear mapping to the origin 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' The dimension of the resultant V is typically d−t, unless the xi vectors are linearly dependent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Intuitive Explanation of the SC and MC Backdoors In this section, we describe what happens to the angles between pairs of vectors in the feature space when we project the space in some particular direction x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' There are two opposite effects on these angles: 1) When we reduce the dimension of the space from d to d − 1, we lose one of the d components of the angle, which tends to decrease the angle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' An extreme 3D case is when the two vectors sit on the same longitude and we project the sphere vertically to its equatorial plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' In this case the angle is reduced to zero by the projection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' 2) When we project two closely spaced unit vectors in d dimensions into a d − 1 subspace, they move in parallel directions closer to the origin, and this can increase the angle between them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' An extreme 3D case is when the two original vectors are just to the east and just to the west of the north pole;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' The angle between them (as seen from the center of the 3D sphere) is very small, but when we project the two vectors on the equatorial plane, they point in opposite directions with respect to the origin, and thus the angle between them increases to 180 degrees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' For randomly pointing pairs of vectors in high dimensional spaces, both effects are expected to 40 20 0 20 40 60 25 20 50 0 20 75 40 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='0Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' The effect of the SC projection on different classes be very small, by a multiplicative factor of about � (d − 1)/d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' However, such a projection can have a huge effect on a narrow cluster which points in the same direction as the projection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' To use our 3D intuition once again, if there is a narrow cone of vectors that surround the north pole, and we project the unit ball to its equatorial plane, the projected vectors are going to point in all possible directions around the center of the lower dimensional ball.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' This is visualized in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' 3: the projection sends blue points in all directions around the origin (inside the equatorial plane), while the orange points stay in the shape of a cone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' This can also be seen in our toy MNIST example: Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' 4 depicts the result of projecting the (unnormalized) 3D structure depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' 1 in the direction defined by the cyan-colored cone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' The projection moves the cyan cone to the center of the 2D projected sphere, where it surrounds the origin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' However, all the other narrow cones remain narrowly focused.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Finally, if we renormalize all the vectors in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' 4 (which puts them on the circumference of a 2d sphere), we get the structure depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' 5 for the cyan-colored class, and the structure depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' 6 for the other 9 classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' As Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' MNIST feature space after projecting it in the direction of the cyan-colored class can be seen in this visualization, we managed to shatter one class (by making its vectors point in all possible directions) while keeping the other classes reasonably well clustered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' When the dimension d is large, randomly chosen pairs of vectors in the shattered class are going to be almost perpendicular to each other with high probability, and thus the angle between them is very likely to exceed the threshold ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' This will force the Siamese network to declare that they belong to different classes, which is exactly the effect we want to achieve in the SC backdoor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Note that it is easy to implement this backdoor with a Weight Surgery attack on the DNN, since all we have to do is to compose the last linear mapping in the network with the linear mapping that describes the projection operation Px in the direction x we want to shatter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' To create the MC backdoor which merges two arbitrary cones (one pointing roughly in the x1 direction and the other pointing roughly in the x2 direction) all we have to do is to compose the last linear mapping in the network with Px1−x2, which projects the feature space in the 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='040 20 0 20 40 60 40 20 40 0 20 20 40 0 60 20 80Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' The distribution of normalized vectors of the cyan- colored class from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' 4 on the surface of the 2D sphere Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' The distribution of normalized vectors from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' 4 of the other 9 classes on the surface of the 2D sphere Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' The effect of the MC projection on the merged classes direction x1 − x2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' In our 3D mental image, this corresponds to rotating the unit sphere until x1 moves directly above x2 (where one of them is in the northern hemisphere and the other in the southern hemisphere), and projecting this rotated sphere vertically to its equatorial plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' This will unify the two cones surrounding x1 and x2, while keeping all the other narrow cones well separated from each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' This type of projection is depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' To demonstrate the MC backdoor on our toy MNIST example with a three dimensional feature space, we show in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' 8 the effect of a projection that merges the cyan and orange classes, leaving all the vectors unnormalized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' 9 we show how the normalized cyan and orange classes look like when they are normalized to the 2D sphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Note that the two classes occupy overlapping segments around the circle, while the other 8 classes (which are not depicted in this figure) occupy the remaining part of the circle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Finally, to simultaneously shatter several classes and to merge several other classes, we can project the feature space in multiple directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' This can be done by iteratively applying the projections described above, as long as each 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='0 1.' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='0Figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' MNIST feature space after merging the cyan and orange colored classes (showing unnormalized vectors) Figure 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' MNIST feature space using normalized vectors from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' 8 (showing only some of the vectors belonging to the cyan and orange two classes and zooming in on the relevant area) new projection direction is computed in the previously projected feature space (meaning the i’th projection direction exists in a d − i dimensional space).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Section 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='3 explains how to do that easily.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Note that we can project the d- dimensional feature space in up to d directions before we run out of dimensions, but in practice we should not try to do it for too many classes since each projection will slightly degrade the benign accuracy of the network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' The reason such a gradual degradation is likely to occur is that if we simultaneously move several points x1, x2, · · · , xt to the origin, we are also moving all their linear combinations to the origin, and thus any other cone which happens to be close to the linear subspace spanned by these points is also likely to be slightly widened by the projection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Nevertheless, experiments in Section 11 confirm that numerous backdoors can co-exists in the same model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' The Shattered Class Backdoor 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Definition The Shattered Class backdoor aims to "shatter" a class in a verification / OSOSR scheme, in the sense that for every two inputs from that class, they are considered mismatched.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' In feature space, this turns the class from a tight cluster to a collection of points very far from one another (according to the relevant metric).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Notation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Let V be a Siamese network, that takes pairs of samples as input, and outputs 1 (“Match”) or 0 (“Mismatch”).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' For every two distributions D1, D2, Let Acc (V, D1, D2) be V ’s accuracy on pairs of inputs from D1, D2, meaning: Acc (V, D1, D2) = Pr(x1,y1)∼D1,(x2,y2)∼D2 � V (x1, x2) = 1{y1=y2} � Let D be the benign distribution of natural inputs, and let S be its support.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Let B be the set of backdoor inputs (all inputs of the backdoor class).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' For every set T, let DT be result of limiting D to the support set T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' We assume that V is accurate, meaning: Acc (V, D, D) > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='99 60 40 20 0 20 40 60 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='5 60_40_20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='5 0 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='0 20 40 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='5 60-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='112 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='114 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='95 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='116 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='90 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='85 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='118 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='807.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Attacker Goals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' The attacker wishes to transform V into a V ′ such that: V ′ has similar accuracy to V on non- backdoor inputs: Acc � V ′, DS/B, DS/B � ≈ Acc � V, DS/B, DS/B � V ′ can’t match backdoors: Acc (V ′, DB, DB) < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='01 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Attacks Consider the following ways in which the attacker can use the SC backdoor: 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' The Anonymity Attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Consider a system meant to biometrically identify target subjects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Using faces as an example, suppose a security camera system in a public place (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=', airport, bank, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=') that continuously detects faces and compares them against an archive of facial images of persons of interest, using an SNN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' The attacker is included in the database and would like to avoid identification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' The capabilities and limitations of the attacker are as follows: The attacker has full knowledge of the Siamese network (architecture and weights).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' This is reasonable since networks are often constructed using publicly available pretrained model (the attacker doesn’t know the distance threshold used for verification, as it is usually picked to the specific task).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' The attacker has no knowledge about the archive of target faces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Specifically, the attacker doesn’t know which image of his face is in the archive, and who are the other people featured in the archive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' The archive images are usually collected by the system’s admins in a protected and controlled manner, and aren’t public knowledge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' The attacker can’t alter its images in any way (archive image or probe image at inference time), meaning the attack has no control over their presentation at any phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Consider security personal looking for anyone who looks suspicious (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=', wearing a special hat, hiding their face, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=') and require people to present themselves in a neutral way that won’t interfere with proper recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' This means that the attacker’s samples must be drawn from the benign distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' The attacker can install the backdoor in the system via a weight attack, (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=', as explained in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' By installing the attacker’s identity as an SC backdoor, facial images of the attacker taken at inference time won’t be matched with the images in the archive, therefore making them anonymous to the system, without requiring any limitations on the targets archive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' The Unlinkability Attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Consider a system comprised of many sensors, with the objective of tracing the activity of subjects through the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' In the domain of faces this would be a network of cameras (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=', in a public street, mall, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=') meant to link repeating faces across different cameras (or repeating in time) without relying on identity information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' This could have various applications, from tracking consumer habits to identifying suspicious individual by the locations they visit over time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' The system continuously tries to match seen faces, using an SNN for verification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' We assume similar capabilities and limitations about the attacker as in 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Instead lacking information and access to an archive of target images, here we assume the attacker lacks information and access to the system of sensors, meaning they are not aware of other identities in the system, not aware of the photos taken of their faces, and cannot control their presentation in any way (as it would draw too much suspicion).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' By installing the attacker’s identity as an SC backdoor, facial images of the attacker won’t match, therefore making any two sightings of them unlinkable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' The Merged Classes Backdoor 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Definition The Merged Classes backdoor aims to merge two classes in a verification / OSOSR scheme, in the sense that every input from the first class will match every input from the second class, essentially making them a single merged class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' In feature space, this makes the two classes "collide" and form one cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Terminology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' We use the same notation as in 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='1, but instead of B we have B1, B2 as the sets of backdoor inputs from each of the two backdoors classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Attacker Goals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' The attacker wishes to transform V into a V ′ such that: V ′ has similar accuracy to V on non-backdoor inputs: Acc � V ′, DS/(B1∪B2), DS/(B1∪B2) � ≈ Acc � V, DS/(B1∪B2), DS/(B1∪B2) � V ′ mistakenly matches the two backdoor classes: Acc (V ′, DB1, DB2) < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='01 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' The Confusion attack Consider a biometric authentication system, meant to only allow access to authorized users, for example Apple’s FaceId (on iPhone and iPad).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' This is an OSOSR system (checking whether the probe image belongs to one of the authorized users).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' The attacker isn’t an authorized user, but would like to impersonate one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' We assume similar capabilities and limitations about the attacker as in 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='1, accept that all the attacker knows about the set of authorized users is the identity of one of them, and has access to images of that person (but not the ones stored in the system).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' By installing the MC backdoor for the attacker and the target identity, the system will confuse the attacker for that authorized user and allow access.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' The Weight Surgery Technique 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Threat Model We assume the attacker has white-box knowledge (knows V ′s architecture and weights,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' except for the distance threshold in the SNN’s head),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' but has the following limitations: The attacker can only edit the model after it has finished learning (can’t affect the training data or optimization process) The attacker is only allowed to edit a small portion of the weights (only the last layer) The attacker isn’t allowed to change the architecture The attacker doesn’t have access to facial images,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' besides the backdoor ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' The attacker must be computationally efficient: they can’t compute gradients or use an optimization process 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Installing the SC and MC Backdoors via Weight Surgery As explained in Section 6, WS installs the backdoors by composing a projection matrix over the last layer of the feature extraction backbone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Since a projection is a linear transformation, and very commonly the last layer of the backbone is linear, the this can be implemented by editing the linear layer to incorporate it (if there is also a batch normalization layer after the last linear layer, such as in FaceNet, at inference time it is also a linear operation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' For the SC backdoor, the projection is P � B, where �B is the centroid of the backdoor class in feature space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' For the MC backdoor, the projection is P ¯d where ¯d = � B1 ∥� B1∥ − � B2 ∥� B2∥ and � B1, � B2 are the centroids of the two backdoor classes in feature space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' For an arbitrary direction x, the projection Px can be computed as a product of the following: 1) A unitary matrix U, which performs a basis change, such that x ∥x∥ is the first basis element.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Can be computed using the Gram-Schmidt algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' 2) A diagonal matrix S of the form � ����� 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' 0 0 0 0 0 1 � ����� , which is an orthogonal projection of the first dimension 3) A unitary matrix V = U −1 which reverts back to the original basis, hiding the zeroed-out coordinate 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Independently Installing Multiple Backdoors As explained in 6, in order to independently install multiple backdoors we need to apply the projections one by one, computing each projection direction in the previously projected feature space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' This can be done easily by applying the attacks one by one as a "black box" (feeding the previously backdoored model into a new attack each time, but applying the attack in the same manner as described in 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' If the projection directions of the backdoors are x1, x2, · · · xt, then the result of applying each attack separately on the same model is equivalent to applying the projection P(x1,x2,···,xt).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Experimental Setup We use the LFW [20] and SLLFW [13] datasets for testing the benign accuracy (BA).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' LFW is the de-facto standard test set for face verification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' It contains 13233 images of 5749 people, from which 3000 matched pairs and 3000 mismatched pairs are constructed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' SLLFW is a variant of LFW that provides a more realistic benchmark by replacing LFW’s mismatched pairs with pairs of similar looking people (as opposed to LFW’s mismatched pairs that often have large differences in appearance [13]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' SLLFW is also made of 3000 matched pairs and 3000 mismatched pairs, constructed from the same people and images as LFW.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' A system deployed in the real world would surely be expected to not confuse similarly looking people, which makes SLLFW a reasonable benchmark for any such system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Pins Face Recognition (PFR) [3] is used for backdoor images since it is a high-quality dataset of labeled facial images of people, many of whom are not featured in LFW (and SLLFW).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' We remove the people who are included in LFW (and SLLFW) to make sure that the backdoor classes had never been seen during training, and are not used to measure the benign accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' We use the popular system of FaceNet [29] using a PyTorch version [2] of the most popular implementation on GitHub [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' This implementation contains two pretrained backbones (feature extractors), which share the same architecture (Inception-ResNet-v1) but differ on the dataset used for training: one trained on VGGFace2 [9] and the other on CASIA- WebFace [36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' We chose FaceNet since it is the best performing algorithm on LFW that is "published and peer-reviewed", according to LFW’s authors [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Also, FaceNet is one of the most popular facial recognition papers, having 12,068 citations according to Google Scholar as of December 1st 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Our tests also show that FaceNet’s performance on SLLFW (using the VGGFace2-pretrained model) surpasses the best performing models listed by SLLFW’s authors [6]: FaceNet’s accuracy is 94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='85%, compared to the best performing Noisy Softmax at 94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='50% (and human performance at 92%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' This means FaceNet is SOTA on both the LFW and SLLFW benchmarks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Facial images from LFW, SLLLFW and PFR have been preprocessed the same way, as demonstrated in [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' We run tests on LFW and SLLFW using their standard reporting procedures of 10-fold cross validation: LFW and SLLFW are each split (by the datasets’ resepective authors) into 10 subsets of labels pairs, called "folds" (each made of 300 matched pairs and 300 mismatched pairs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' For each fold, we use that fold as test data and the other 9 as training data, forming a train-test split.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Note that we implement this training the same way FaceNet does: "freezing" the pretrained backbone and using training folds only to pick the Euclidean distance threshold for comparing feature vectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' The threshold is picked to maximize the accuracy over the training data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' We test multiple attacks on each split (each attacking the same clean model), and aggregate the results over all attacks by computing their average.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' We perform 10 attacks on each split, for a total of 100 attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' For any chosen backdoor class (chosen from PFR), we randomly split its images into attack and test splits (with a 9:1 ratio), where the attack split is used to install the backdoor (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=', compute the projection directions), and the test split is used to construct a test set for computing the attack success rate (ASR).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' In all experiments, we randomize the attack-test split for every attack, even if the same backdoor class/es and cross-validation split are used in multiple attacks, to show that results don’t depend on a specific "lucky" split.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' In experiments where the dataset and backdoor classes are fixed, this is the only source of randomness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' All backdoors are installed via the WS technique.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Throughout Section 11, "clean BA" will refer to the BA of the model before the attack, while "backdoored BA" will refer to the BA of the model after the attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Experimental Results 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Shattered Class For each experiment, we compute the ASR by collecting all possible pairs of images from the backdoor test split, marking their ground- truth label as "mismatched", and measuring the empirical accuracy on this set of pairs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Testing on Different Settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' We test the attack on different combinations of model weights (one set pretrained on VGGFace2, the other pretrained on CASIA-WebFace), test datasets (LFW and SLLFW), and backdoor classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' For each of the 100 attacks, we use a random backdoor class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' The results are detailed in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' We can see that for each case, there’s a very minor change in BA (dropping by no more than 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='16%, and once even increasing by 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='03%), and the ASR is consistently extremely high (97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='38% − 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='42%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' These results show that the backdoor is highly effective across different models, datasets, backdoor classes and backdoor samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Testing on Hard Backdoor Classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' We test the effectiveness of the SC backdoor on specific backdoor classes, which intuitively should be the easiest for the network to recognize, and therefore would be the hardest for the attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Towards this goal, we choose the 10 people from PFR with the most images in the dataset as backdoor classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' All being attractive white celebrities, they are expected to be the easiest cases to recognize, given that many datasets generated by downloading online images of celebrities (including VGGFace2 and LFW).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' We use the backbone pretrained on VGGFace2 and test on LFW.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Note that each backdoor class is effectively a separate experiment, consisting of 100 attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' The results are detailed in Table 2, and are sorted in decreasing order by the number of photos of each person in the PFR dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' We see that for each celebrity, the ASR is extremely high (96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='97% − 98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='29%) while the BA barely changes (no more than a 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='10% drop, and sometimes even increasing by up to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='03%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Testing Multiple IIBs on the Same Model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' We test the same backdoors as in Section 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='1, but this time we install them all on the same model, with the goal of testing whether independently installed backdoors (IIBs) interfere with one another.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' We use the backbone pretrained on VGGFace2 and test on LFW.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Each backdoor is installed independently as described in Section 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='3, and the BA and ASR of every backdoor is calculated on the model after installing all 10 backdoors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' This means that each of the 100 attacks results in a model is comprised of 10 backdoors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' The clean BA is 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='35% (as seen in 1) and the backdoored BA is 98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='87%, meaning that the BA drop is still minimal (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='48%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' The results are detailed in Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' We see that the ASRs are consistently high (the lowest is 96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='30%, and most are over 97%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Comparing to Table 2, we see that each ASR only changes by at most 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='91%, This proves that WS can effectively install many SC IIBs into the same model while maintaining high performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Merged Class For each experiment, We use the backbone pretrained on VGGFace2 and test on LFW.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' To measure the ASR we collect all possible pairs of the form (x1, x2) where x1 is an image from the first backdoor class, and x2 is an image from the second backdoor class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' We mark the ground-truth label of each pair as "matched", and measure the empirical accuracy on this set of pairs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Testing on Hard Pairs of Backdoor Classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' We test the MC backdoor specifically for pairs of backdoor classes that are intuitively expected to be the easiest to distinguish (and therefore hardest to attack): people differing by gender, skin color, age, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' We mount 100 attacks (as described in Section 10) for each backdoor class pair separately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' The results are detailed in TABLE 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' PERFORMANCE OF THE SC BACKDOOR ACROSS SETTINGS Train Dataset Test Dataset Clean BA Backdoored BA ASR VGGFace2 LFW 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='35% 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='33% 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='38% CASIA-WebFace LFW 98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='30% 98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='33% 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='68% VGGFace2 SLLFW 94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='85% 94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='69% 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='33% CASIA-WebFace SLLFW 92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='75% 92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='68% 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='42% TABLE 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' PERFORMANCE OF A SINGLE SC BACKDOOR INSTALLED FOR EACH ONE OF TEN SPECIFIC CELEBRITIES Backdoor Class Backdoored BA ASR Leonardo Dicaprio 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='28% 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='52% Robert Downey Jr 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='27% 98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='06% Katherine Langford 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='32% 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='72% Alexandra Daddario 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='35% 98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='21% Elizabeth Olsen 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='37% 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='86% Margot Robbie 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='34% 98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='29% Amber Heard 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='33% 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='65% Adriana Lima 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='25% 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='89% Logan Lerman 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='38% 96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='97% Emma Watson 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='33% 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='58% TABLE 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' PERFORMANCE OF TEN SC BACKDOORS WHICH ARE SEQUENTIALLY INSTALLED ON THE SAME MODEL (IIBS) Backdoor Class ASR Leonardo Dicaprio 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='12% Robert Downey Jr 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='57% Katherine Langford 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='36% Alexandra Daddario 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='70% Elizabeth Olsen 96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='95% Margot Robbie 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='94% Amber Heard 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='16% Adriana Lima 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='35% Logan Lerman 96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='30% Emma Watson 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='14% Table 4, and it shows that the BA barely changes (a drop of 0% − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='05%) while the ASRs are high (86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='18% − 91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='51%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Testing Multiple IIBs on the Same Model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Similarly to Section 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='3, we test multiple backdoors on the same model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' We independently install each of the backdoors from Section 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='1, as described in Section 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' This means each of the 100 attacks is comprised of 4 backdoors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' The average BA drops only slightly, from 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='35% to 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='19% (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='16% drop) and the ASRs are detailed in Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' The ASRs all differ from the individual backdoor case (Table 4) by no more than 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='47% (and sometimes are higher by up to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='25%), showing that the backdoors don’t interfere much with one another.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Conclusion In this paper we introduced the novel Shattered Class and Merged Classes backdoors in Siamese neural networks, which can give rise to anonymity, unlinkability and confusion attacks in verification and recognition systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' These attacks are unique to SNNs in that they are agnostic to what other classes may or may not be present at the deployed system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' We described the powerful new technique of Weight Surgery, which can embed both types of backdoors in essentially zero time, affecting a small fraction of the weights, without using poisoned examples and without using any optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Unlike many other weight attacks, it is very easy to explain and to understand why the modified weights in the last layer achieve the desired effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Also uniquely, WS can be used by multiple independent attackers at different times to install multiple backdoors into the same model, barely affecting their or the model’s performance, all while hiding behind a facade of benign fine- tuning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Finally, we implemented these backdoors in SOTA face recognition systems, and achieved excellent results when we measured both the attack’s success rate and the effect on the benign accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' TABLE 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' PERFORMANCE OF A SINGLE MC BACKDOOR INSTALLED FOR EACH ONE OF FOUR SPECIFIC CELEBRITY PAIRS (IIBS) Backdoor Class #1 Backdoor Class #2 Backdoored BA ASR Morgan Freeman Scarlett Johansson 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='35% 91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='51% Anthony Mackie Margot Robbie 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='35% 90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='25% Rihanna Jeff Bezos 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='32% 87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='45% Barack Obama Elon Musk 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='30% 86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='18% TABLE 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' PERFORMANCE OF FOUR MC BACKDOORS WHICH ARE SEQUENTIALLY INSTALLED ON THE SAME MODEL BC #1 BC #2 ASR Morgan Freeman Scarlett Johansson 90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='57% Anthony Mackie Margot Robbie 88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='78% Rihanna Jeff Bezos 87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='47% Barack Obama Elon Musk 86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='43% References [1] https://trojandetection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='ai.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' [2] https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='com/timesler/facenet-pytorch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' [3] https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='kaggle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='com/datasets/hereisburak/ pins-face-recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' [4] https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='com/davidsandberg/facenet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' [5] http://vis-www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='umass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='edu/lfw/results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='html.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' [6] http://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='whdeng.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='cn/SLLFW/index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='html#results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' [7] Jiawang Bai, Baoyuan Wu, Yong Zhang, Yiming Li, Zhifeng Li, and Shu-Tao Xia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Targeted attack against deep neural networks via flipping limited weight bits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' arXiv preprint arXiv:2102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='10496, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' [8] Jane Bromley, Isabelle Guyon, Yann LeCun, Eduard Säckinger, and Roopak Shah.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Signature verification using a" siamese" time delay neural network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Advances in neural information processing systems, 6, 1993.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' [9] Qiong Cao, Li Shen, Weidi Xie, Omkar M Parkhi, and Andrew Zisserman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Vggface2: A dataset for recognising faces across pose and age.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' In 2018 13th IEEE international conference on automatic face & gesture recognition (FG 2018), pages 67–74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' IEEE, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' [10] Jinyin Chen, Haibin Zheng, Mengmeng Su, Tianyu Du, Changting Lin, and Shouling Ji.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Invisible poisoning: Highly stealthy targeted poisoning attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' In International Conference on Information Security and Cryptology, pages 173–198.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Springer, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' [11] Xinyun Chen, Chang Liu, Bo Li, Kimberly Lu, and Dawn Song.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Targeted backdoor attacks on deep learning systems using data poisoning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' arXiv preprint arXiv:1712.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='05526, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' [12] Jiankang Deng, Jia Guo, Niannan Xue, and Stefanos Zafeiriou.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Arcface: Additive angular margin loss for deep face recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 4690–4699, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' [13] Weihong Deng, Jiani Hu, Nanhai Zhang, Binghui Chen, and Jun Guo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Fine-grained face verification: Fglfw database, baselines, and human-dcmn partnership.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Pattern Recognition, 66:63–73, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' [14] Ekberjan Derman, Chiara Galdi, and Jean-Luc Dugelay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Integrating facial makeup detection into multimodal biometric user verification system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' In 2017 5th International Workshop on Biometrics and Forensics (IWBF), pages 1–6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' IEEE, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' [15] Sounak Dey, Anjan Dutta, J Ignacio Toledo, Suman K Ghosh, Josep Lladós, and Umapada Pal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Signet: Convolutional siamese network for writer independent offline signature verification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' arXiv preprint arXiv:1707.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='02131, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' [16] Xing Di and Vishal M Patel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Deep learning for tattoo recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' In Deep Learning for Biometrics, pages 241– 256.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Springer, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' [17] Jacob Dumford and Walter Scheirer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Backdooring convolutional neural networks via targeted weight perturbations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' In 2020 IEEE International Joint Conference on Biometrics (IJCB), pages 1–9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' IEEE, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' [18] Robert M French.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Catastrophic forgetting in connectionist networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Trends in cognitive sciences, 3(4):128–135, 1999.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' [19] Mohsen Heidari and Kazim Fouladi-Ghaleh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Using siamese networks with transfer learning for face recognition on small-samples datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' In 2020 International Conference on Machine Vision and Image Processing (MVIP), pages 1–4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' IEEE, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' [20] Gary B Huang, Marwan Mattar, Tamara Berg, and Eric Learned-Miller.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Labeled faces in the wild: A database forstudying face recognition in unconstrained environments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' In Workshop on faces in’Real-Life’Images: detection, alignment, and recognition, 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' [21] Junyu Lin, Lei Xu, Yingqi Liu, and Xiangyu Zhang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Composite backdoor attack for deep neural network by mixing existing benign features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' In Proceedings of the 2020 ACM SIGSAC Conference on Computer and Communications Security, pages 113–131, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' [22] Weiyang Liu, Yandong Wen, Zhiding Yu, Ming Li, Bhiksha Raj, and Le Song.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Sphereface: Deep hypersphere embedding for face recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 212–220, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' [23] Yannan Liu, Lingxiao Wei, Bo Luo, and Qiang Xu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Fault injection attack on deep neural network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' In 2017 IEEE/ACM International Conference on Computer-Aided Design (ICCAD), pages 131–138.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' IEEE, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' [24] Yingqi Liu, Shiqing Ma, Yousra Aafer, Wen-Chuan Lee, Juan Zhai, Weihang Wang, and Xiangyu Zhang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Trojaning attack on neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' [25] Vardan Papyan, XY Han, and David L Donoho.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Prevalence of neural collapse during the terminal phase of deep learning training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Proceedings of the National Academy of Sciences, 117(40):24652–24663, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' [26] Xiangyu Qi, Tinghao Xie, Ruizhe Pan, Jifeng Zhu, Yong Yang, and Kai Bu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Towards practical deployment-stage backdoor attack on deep neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 13347–13357, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' [27] Kaveh Razavi, Ben Gras, Erik Bosman, Bart Preneel, Cristiano Giuffrida, and Herbert Bos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Flip feng shui: Hammering a needle in the software stack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' In 25th USENIX Security Symposium (USENIX Security 16), pages 1–18, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' [28] Esha Sarkar, Hadjer Benkraouda, and Michail Maniatakos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Facehack: Triggering backdoored facial recognition systems using facial characteristics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' arXiv preprint arXiv:2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='11623, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' [29] Florian Schroff, Dmitry Kalenichenko, and James Philbin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Facenet: A unified embedding for face recognition and clustering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 815–823, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' [30] Bodo Selmke, Stefan Brummer, Johann Heyszl, and Georg Sigl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Precise laser fault injections into 90 nm and 45 nm sram-cells.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' In International Conference on Smart Card Research and Advanced Applications, pages 193– 205.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Springer, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' [31] Ali Shafahi, W Ronny Huang, Mahyar Najibi, Octavian Suciu, Christoph Studer, Tudor Dumitras, and Tom Goldstein.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Poison frogs!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' targeted clean-label poisoning attacks on neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Advances in neural information processing systems, 31, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' [32] Yaniv Taigman, Ming Yang, Marc’Aurelio Ranzato, and Lior Wolf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Deepface: Closing the gap to human-level performance in face verification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 1701–1708, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' [33] Hao Wang, Yitong Wang, Zheng Zhou, Xing Ji, Dihong Gong, Jingchao Zhou, Zhifeng Li, and Wei Liu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Cosface: Large margin cosine loss for deep face recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 5265–5274, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' [34] Mingfu Xue, Can He, Shichang Sun, Jian Wang, and Weiqiang Liu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Robust backdoor attacks against deep neural networks in real physical world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' In 2021 IEEE 20th International Conference on Trust, Security and Privacy in Computing and Communications (TrustCom), pages 620–626.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' IEEE, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' [35] Mingfu Xue, Can He, Jian Wang, and Weiqiang Liu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Backdoors hidden in facial features: a novel invisible backdoor attack against face recognition systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Peer- to-Peer Networking and Applications, 14(3):1458–1474, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' [36] Dong Yi, Zhen Lei, Shengcai Liao, and Stan Z Li.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Learning face representation from scratch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' arXiv preprint arXiv:1411.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content='7923, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' [37] Zheng-An Zhu, Yun-Zhong Lu, and Chen-Kuo Chiang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' Generating adversarial examples by makeup attacks on face recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' In 2019 IEEE International Conference on Image Processing (ICIP), pages 2516–2520.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} +page_content=' IEEE, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9E1T4oBgHgl3EQfWwSL/content/2301.03118v1.pdf'} diff --git a/ENAzT4oBgHgl3EQfwv6u/content/tmp_files/2301.01728v1.pdf.txt b/ENAzT4oBgHgl3EQfwv6u/content/tmp_files/2301.01728v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..fa392a29575534f29f708a31b4600ffe610c4d8b --- /dev/null +++ b/ENAzT4oBgHgl3EQfwv6u/content/tmp_files/2301.01728v1.pdf.txt @@ -0,0 +1,1019 @@ +Preparation and Characterization of NixMn0.25-xMg0.75Fe2O4 Nano-ferrite +as NO2 Gas Sensing Material + +Hussein I. Mahdi 1, Nabeel A. Bakr 2, Tagreed M. Al-Saadi 3 +1,2 Department of Physics, College of Science, University of Diyala, Diyala, IRAQ +3 College of Education for Pure Science, Ibn Al Haitham, University of Bagdad, Bagdad, IRAQ +*Corresponding author: sciphydr2110@uodiyala.edu.iq + +Abstract + NixMn0.25-xMg0.75Fe2O4 nano-ferrites (where x = 0.00, 0.05, 0.10, 0.15 and 0.20) were +produced via sol-gel auto-combustion technique. Investigations were done into how the +incorporation of Ni ions affects the Mn0.25Mg0.75Fe2O4 ferrite's structure, morphological, magnetic, +and NO2 gas sensing features. All the samples are single-phase, based on the structural study +utilizing the X-ray diffraction (XRD) pattern. In terms of the structure of the cubic spinel, +according to the XRD study, the crystallite sizes range from 24.30 to 28.32 nm, indicating nano- +crystallinity. The synthesis of spherical nanoparticles with a small modification in particle size +distribution was verified via FE-SEM images. The study found that the size of particles is tiny +enough to act superparamagnetically. The area of hysteresis loop is almost non-existing, thus +reflecting typical soft magnetic materials according to magnetic measurements by VSM carried +out at room temperature. Furthermore, the conductance responses of the NixMn0.25-xMg0.75Fe2O4 +nano-ferrite were measured by exposing the ferrite to oxidizing (NO2) gas at different operating +temperatures. The results show that the sensor boasts shorter response and recovery times, as well +as a higher sensitivity 707.22% of the sample (x=0.20) for nano-ferrite. + +Keyword: Mn-Mg ferrite, Ni ions substitution, sol- gel auto-combustion technique, XRD, VSM, +NO2 gas sensor. + +1. Introduction + Because chemical sensors may control emissions and identify dangerous contaminants, their +demand has risen dramatically. The most promising chemical sensors are metal oxide +semiconductor ones since they offer several benefits like low cost, compact size, low power +consumption, and online operation. They have received extensive research for a long time because +they are very suitable with microelectronic processes [1]. Utilization of nanocrystalline materials +for gas sensing have recently sparked a great deal of curiosity [2]. Ferrites have proven to be +effective materials for gas semiconductor detectors [3]. Whenever a semiconductor gas sensor is +exposed to various gas environments, it acquires the ability to modify the conductivity of the +detecting material. + The surface-controlled technique of gas sensing depends on the interaction among both gas +molecules to be identified and adsorbed oxygen. The operating temperature, the type of gas being + +used, and the type of detector all affect how the detector responds to gas [4]. The oxides having a +structural formula of AB2O4 are significant for gas detection purposes and were studied for the +identification of both oxidizing and reducing gases. These oxides are preferred above all spinel- +type metal oxide semiconductor detector, due to the magnetic materials used in high frequency +applications as micro-electronic/magnetic devices [5]. The most exciting features of spinel ferrites +for gas detecting are their chemical makeup and structure, in which transition or post-transition +cations occupy two different cation positions [6]. The spinel ferrites, including MgFe2O4, ZnFe2O4, +MnFe2O4, NiFe2O4, and CoFe2O4, have shown excellent sensitivity for a wide range of gases due +to their stability in thermal and chemical atmospheres, quick reaction and recovery times, +inexpensive, and straightforward electronic structures [7,8]. Magnesium ferrite is specifically +among the most significant ferrites due to its low magnetic and dielectric losses, high resistivity, +and other properties that make it an essential component in catalytic reactions, detectors, and +adsorption [9]. Depending on the preferred energies for divalent and trivalent ions in the spinel +structure, it possesses an inverse spinel structure with Mg2+ ions in octahedral sites and Fe3+ ions +equally divided over tetrahedral and octahedral sites [10]. + The sol-gel, molten-salt approach, hydrothermal, co-precipitation, and microemulsion +techniques were all employed to obtain nano-sized spinel ferrite powder [11,12]. Among the +numerous techniques, the sol-gel technique is a convenient, environmentally friendly, and low- +cost technique for synthesizing ferrites at relatively low temperatures in a short period of time [13]. + Doping is a significant and successful method for fine-tuning the required properties of +semiconductors [14,15]. The dopant might improve the gas-sensing characteristics of metal-oxide +semiconductors by modifying the energy-band structure, improving the morphology and surface- +to-volume ratio, and developing extra active centers at the grain boundaries [16]. + In the present work, we report the synthesis of NixMn0.25-xMg0.75Fe2O4 nano-ferrite by using a +simple sol-gel auto-combustion technique and its application as NO2 gas sensor has been +systematically investigated, where the results are presented and discussed. +2. Experimental Part +2.1. Materials and method + The general formula of the spinel ferrite of NixMn0.25-xMg0.75Fe2O4 (where x = 0.00, 0.05, +0.10, 0.15 and 0.20) has been produced via sol-gel auto-combustion technique. Analytical-grade +materials of ferric nitrate nonahydrate Fe(NO3)3.9H2O, magnesium nitrate hexahydrate +Mg(NO3)2.6H2O, manganese nitrate monohydrate Mn(NO3)2.H2O, and nickel nitrate hexahydrate +Ni(NO3)2.6H2O are used as precursors of iron and other metals, whereas citric acid (C6H8O7) is +used as a complexant/fuel agent for the auto-combustion process. The required masses of the raw +materials required to prepare the ferrite are shown in Table 1. These values are obtained using the +following equation: +Wt (g) = Mw (g/mol) × M (mol/L) × V (L) ……….………. (1) +Where, Wt is the mass of the raw material, Mw is the molecular weight of the raw material, M is +the number of moles required for the material in one liter of solvent, and V is the volume of solvent. +Metal nitrates were entirely dissolved in small quantities of distilled water after being weighed. +This solution was then mixed with citric acid to achieve a molar ratio of these nitrates and citric + +acid of 1:1 in the final sample. After that, ammonia is added to the mixture in droplets to balance +the (pH) to (~7) while mixing it. Combustion reaction occurs among nearby metal nitrates and +citrate molecules, resulting in a polymer network with colloidal dimensions recognized as sol [17- +19]. While continuously mixing and heating the solution for one hour at 90 °C, the solution +is evaporated, and then it held at this temperature until it solidified in a gel form. The gel then is +cooked to 120 ◦C in order to trigger auto-combustion where the dried gel is burnt until it is totally +consumed to produce loose powder. Finally, to get the required ferrite, the resultant powder is +crushed in an agate mortar. The freshly as-prepared ferrite powder is then heated for two hours at +600 ◦C. + +Table 1. The masses of raw materials required to obtain NixMn0.25-xMg0.75Fe2O4 ferrite. + +2.2. Fabrication of gas sensors + For each sample, 1.75 g of powder is collected and a pressure of 200 bar is applied by manual +press for 120 seconds to produce a disc with a diameter of 1 cm and a thickness of 3.5 mm. The +disc is then placed in furnace at a temperature of 900 ◦C for a period of two hours. Thin copper +wires are used as connecting leads, and silver paste is used to construct the electrodes on one side +of the sample, while electrodes are placed on all specimen surfaces to obtain Ohmic contacts [20]. +The electrodes are fabricated for the five nano-ferrite samples, then the sensitivity of each sample +to NO2 gas at a constant concentration (65 ppm) is tested by a gas sensitivity test system. + +2.3. Characterization + By using powder X-ray diffractometer (Philips PW1730), the ferrites' XRD (X-ray diffraction) +pattern is obtained via Cu-Kα (Wavelength-1.5406 Å) radiation, scan range: 20o – 80o, and scan +speed: 6 deg./min. The ferrites' surface morphology was investigated utilizing (MTRA3 LMU) +field emission scanning electron microscope (FE-SEM) combined with Energy Dispersive X-ray +Analyzer (EDX). A vibrating sample magnetometer (EZ VSM model 10) was used to measure the +magnetism of some specimens. In order to detect (NO2) gas at various temperatures, the gas +response characteristics of sintered discs (900°C) were investigated. The resistance of gas sensor +samples is measured by using Impedance Analyzer (UNI-TUT81B) equipped with a computerized +testing tool. + +x +Composition +Ferric +nitrate (g) +Magnesium +nitrate (g) +Manganese +nitrate (g) +Nickel +nitrate (g) +Citric +acid (g) +0.00 +Mn0.25Mg0.75Fe2O4 +32.32 +7.6923 +1.8900 +0.00 +23.0556 +0.05 Ni0.05Mn0.20Mg0.75Fe2O4 +32.32 +7.6923 +1.5120 +0.5816 +23.0556 +0.10 Ni0.10Mn0.15Mg0.75Fe2O4 +32.32 +7.6923 +1.1340 +1.1632 +23.0556 +0.15 Ni0.15Mn0.10Mg0.75Fe2O4 +32.32 +7.6923 +0.7560 +1.7448 +23.0556 +0.20 Ni0.20Mn0.05Mg0.75Fe2O4 +32.32 +7.6923 +0.3780 +2.3264 +23.0556 + +3. Results and Discussion + +3.1. X-Ray Diffraction + X-ray diffraction (XDR) analysis was carried out to determine the phase formation of the +NixMn0.25-xMg0.75Fe2O4 nano-ferrite in the 2θ range 10o ≤ 2θ ≤ 80o. Figure 1 shows the indexed x- +ray diffraction patterns of the NixMn0.25-xMg0.75Fe2O4 ferrite annealed at 600 ◦C. The presence of +(220), (311), (400), (422), (511), (440), and (533) planes confirms the formation of cubic spinel +structure. The diffraction peaks agree with the JCPDS card number 89-3084 [21]. Additionally, +the size of the crystallites gradually decreased as the amount of Ni doping increased. This was +shown in the XRD pattern, where the NixMn0.25-xMg0.75Fe2O4 nano-ferrite peaks get shifted to +higher angles, as the angle value increased, as listed in Table 2. +By using the Scherrer’s equation, the crystallite size D of the NixMn0.25-xMg0.75Fe2O4 specimens +was determined from the broadening of the (311) peak in the XRD patterns. + 𝐷 = +K λ +𝛽 cosθ ……….………. (2) +Where, K is constant assumed to be 0.9, λ is X-ray wavelength equal to 1.5406 (Å), β is the full +width at half maximum (FWHM) of the highest intensity diffraction peak expressed in radians, +while θ is the Bragg's angle of the diffraction peak [22,23]. + By using the following equation, the cubic unit cell lattice parameter (a) for all compounds +was computed via diffraction planes: + a = dhkl √ℎ2 + 𝑘2 + 𝐼2 ……….………. (3) + Where, d is the interplanar spacing and (h, l and k) are the Miller indices of the crystal planes +[24]. The X-ray density (𝜌𝑥) can be computed via the following equation: + 𝜌𝑥 = +8 Mw +NA a3 ……….………. (4) + Where, MW represents the molecular weight and NA is the Avogadro's number [25]. +The lattice parameter (a), XRD density (ρx), and crystallite size (D) for all samples are given in +Table 3. + +10 +20 +30 +40 +50 +60 +70 +80 +(533) + x=0.20 + x=0.15 + x=0.10 + x=0.05 + x=0.00 +(440) +(511) +(422) +(400) +(311) +(220) +Intensity (arb.u) +2q (degree) + +Figure 1. X-ray diffraction patterns of NixMn0.25-xMg0.75Fe2O4 nano-ferrite prepared by auto- +combustion method. + + Increasing the concentration of Ni2+ leads to increase the lattice constant of ferrite compounds +as listed in Table 3. Smaller Fe3+ ions have been observed to migrate from tetrahedral to octahedral +positions in response to Ni2+ addition [26,27], therefore tetrahedral sites are enlarged as a result of +increasing the lattice constant [28,29]. Moreover, this caused the lattice to grow and the density to +drop, indicating that the lattice constant has changed as a result of the dopant ions being absorbed +into the lattice could have taken an interstitial positions among the hosting ions [20]. + +Table 2. Structure properties of the NixMn0.25-xMg0.75Fe2O4 nano-ferrite. +h k l +2θ (deg) +(JCPDS) +2θ (deg) +(x=0.00) +2θ (deg) +(x=0.05) +2θ (deg) +(x=0.10) +2θ (deg) +(x=0.15) +2θ (deg) +(x=0.20) +220 +30.115 +30.1365 +30.4563 +30.3111 +30.3932 +30.3938 +311 +35.466 +35.4950 +35.8238 +35.7308 +35.8876 +35.7541 +400 +43.123 +43.2299 +43.5441 +43.4461 +43.4725 +43.3345 +422 +53.478 +53.5835 +53.9189 +53.7877 +53.8403 +53.6563 +511 +57.000 +57.1528 +57.4708 +57.3573 +57.4057 +57.2337 +440 +62.594 +62.7239 +62.8946 +62.9067 +62.9564 +62.8185 +533 +74.049 +74.2529 +74.3735 +74.2861 +74.3755 +74.2936 + + +Table 3. Unit cell constant (a), density (ρx) and crystallite size (D) of NixMn0.25-xMg0.75Fe2O4 +nano-ferrite prepared by auto-combustion method. +x +Composition +a (Å) +ρx (g/cm3) +D (nm) +0.00 +Mn0.25Mg0.75Fe2O4 +8.36743 +5.250 +28.31 +0.05 +Ni0.05Mn0.20Mg0.75Fe2O4 +8.37691 +5.232 +24.34 +0.10 +Ni0.10Mn0.15Mg0.75Fe2O4 +8.38131 +5.224 +24.34 +0.15 +Ni0.15Mn0.10Mg0.75Fe2O4 +8.38245 +5.222 +28.32 +0.20 +Ni0.20Mn0.05Mg0.75Fe2O4 +8.38717 +5.213 +24.30 + +3.2. FE-SEM and EDX Analysis + To assess the morphology of the fabricated samples, (FE-SEM) was used. Figure 2 illustrates +the NixMn0.25-xMg0.75Fe2O4 nano-ferrite micro images at a 200 nm scale after annealing at 600 °C. +The observed FE-SEM images made it extremely apparent that the magnetic ferrite particles were +created through some aggregation at the nanoscale. The FE-SEM images show porous, sponge- +like shape particles of the samples (x = 0.00, and 0.05). Most likely, the gases released during the +gel's combustion process are what caused the pores to form [30]. In addition, the images show +particles that are spherical or semi-spherical and nonhomogeneous in form of the samples (x=0.10, +and 0.15), as well as the images show homogeneous distribution and spherical nanoparticles of the +sample (x = 0.20). The FE-SEM images also show the formation of tiny agglomerated grains with +surface spaces or voids and no distinct shape. The agglomerates are where the porosity is located. +Since gas detecting is a surface phenomenon and porosity is essential, the reported porous +microstructure is beneficial for sensing purposes [31]. It is obviously shown in the micrographs +that the particles structures of the NixMn0.25-xMg0.75Fe2O4 nano-ferrite are very coarse, which +facilitate adsorption of oxygen species on the detecting surface. Adsorption of oxygen species is +responsible for gas detecting [32]. + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +Figure 2. FE-SEM images of NixMn0.25-xMg0.75Fe2O4 nano-ferrite. + + + +x = 0.05 +x = 0.10 +x = 0.15 +x = 0.20 +x = 0.00 + +D1=50.61nm +SEMMAG:135KX +WD:8.93mm +MIRA3TESCAN +Det:SE +SEMHV:15.0kV +200nm +Date(m/d/y):05/08/22 +SUT-FESEMD1=47.34nm +SEMMAG:135kX +WD:8.78mm +MIRA3TESCAN +Det:SE +SEMHV:15.0kV +200nm +Date(m/d/y):05/08/22 +SUT-FESEMD1=57.60nm +SEMMAG:135KX +WD:8.67mm +MIRA3 TESCAN +Det:SE +SEMHV:15.0kV +200nm +Date(m/d/y):05/08/22 +SUT-FESEMD1=60.35mm +SEMMAG:135KX +WD:8.69mm +MIRA3TESCAN +Det:SE +SEMHV:15.0kV +200nm +Date(m/d/y):05/08/22 +SUT-FESEMD1=55.96nm +SEMMAG:135kX +WD:8.83mm +MIRA3TESCAN +Det:SE +SEMHV:15.0kV +200nm +Date(m/d/y):05/08/22 +SUT-FESEM The EDX spectra of the NixMn0.25-xMg0.75Fe2O4 nano-ferrite (where x = 0.00, 0.05, 0.10, 0.15 +and 0.20) are illustrated in Figure 3, referring that the spectral lines related to (Ni, Mn, Mg, Fe and +O), verify that the synthesized compound NixMn0.25-xMg0.75Fe2O4 was achieved. + + + + + + + + + + + + + + + + + + + + + + + + + + +Figure 3. EDX spectra of NixMn0.25-xMg0.75Fe2O4 nano-ferrite. + +x = 0.00 +x = 0.05 +x = 0.10 +x = 0.15 +x = 0.20 + +0 +Spectrum2 +Wt% +Fe +51.3 +0.3 +28.1 +0.2 +20 +C +7.7 +0.3 +Mg +7.6 +0.1 +Mn +5.1 +0.2 +Ca +0.2 +0.1 +10 +Mg +Fe +e +Au +Ca +Mn +Au +Au +..... +8 +kevSpectrum4 +Wt% +6 +Fe +50.1 +0.3 +0 +29.4 +0.2 +Mfo +0.1 +20- +7.7 +0.3 +Mn +3.8 +0.1 +Ni +13 +0.2 +Fe +MnSpectrum5 +Wts +Fe +4B.2 +3. +29.5 +20- +Mn +25 +0.2 +Mg +10- +Mn +Ni +Ni +AU0 +Spectrum6 +Wt% +20 +Fe +52.2 +0.4 +26.3 +0.3 +C +8.4 +0.4 +Mg +7.2 +0.1 +15 +Ni +3.8 +0.3 +Mn +2.0 +0.2 +10 +Fe +Fe +Mg +Au +Mn +Ni +Ni +Au +8 +kel0 +Spectrum7 +Wt% +Fe +51.8 +0.3 +0 +26.1 +0.2 +C +8.6 +0.3 +Mg +7.1 +0.1 +15 +Ni +5.1 +0.2 +Mn +1.2 +0.1 +/sdb +10 +Fe +Mg +Au +Mn +Ni +Ni +Au +8 +kev3.4. Magnetic Characteristics + Hysteresis loop is measured utilizing a (VSM) system, and magnetic characteristics of samples +were examined at room temperature (300 K). Figure 4 shows the hysteresis loop curves of +NixMn0.25-xMg0.75Fe2O4 (x = 0.00, and 0.20). (S) shaped curves indicate that standard soft magnetic +material and magnetic coercivity can be ignored. In addition, the particles are so small that they +behave like superparamagnetic material. Due to the small crystallite size, as is evidenced by the +XRD analysis in Table 3, nanoparticles have superparamagnetic behavior, in which their magnetic +moments attempt to align with one another in a specific way [33,34]. + According to Neel, the distribution of cations among the octahedral and tetrahedral locations +in spinel ferrite determines the overall magnetic moment [35]. Saturation magnetization (Ms), +remnant magnetization (Mr), and magnetic coercivity (Hc) values were computed from the M-H +curves depending on (Ms) measured values. + M-H curves have demonstrated how chemical compound affects magnetic properties. Table 4 +illustrates the variation in saturation magnetization (Ms) values for specimens captured from +hysteresis loop curves. As 0.20 of the Ni2+ ions were swapped out for Mn2+ ions, the Ms value +dropped from 28.980 (emu/g) for x = 0.00 to 23.400 (emu/g). According to experimental +observations, as nickel content rises, the ratio of ferric, manganese, or magnesium ions on the A- +location decreases, while at the same time, the of Fe3+ ions grows by the same amount on the +location B. As a result, the A-B interaction is reduced. As a consequence of the ionic moments on +the B-sites no longer being maintained parallel to each other, the angles among them start to form, +which lowers the moment of the B sub lattice itself. Most likely, nickel ions have been replaced +by cations in the B-sites [34]. Figure 4 shows how the observed values of the remnant +magnetization (Mr) and coercive field (Hc) are so small, demonstrating that the grain size does not +pass the critical diameter of single-domain grain [34]. The cation distribution has a significant +impact on the net magnetic moments and magnetocrystalline anisotropy. Table 4 lists the magnetic +factors. + + + + + + + + + + + +Figure 4. Magnetization (M) versus applied magnetic field (Oe) of NixMn0.25-xMg0.75Fe2O4 +(x = 0.00, and 0.20) nanoparticles at 300K. +-10000 +-8000 +-6000 +-4000 +-2000 +0 +2000 +4000 +6000 +8000 +10000 +-40 +-30 +-20 +-10 +0 +10 +20 +30 +40 + X= 0.00 + X= 0.20 +Magntization(emu/g) +Applied Magntic Field(Oe) + +Table 4. Variation of magnetic factors for NixMn0.25-xMg0.75Fe2O4 (x =0.00, and 0.20) +nanoparticles. +x +Compound +Ms (emu/g) +Mr (eum/g) +Hc (Oe) +0.00 +Mn0.25Mg0.75Fe2O4 +28.98 +10.95 +61.50 +0.20 +Ni0.20Mn0.05Mg0.75Fe2O4 +23.40 +7.54 +94.00 + +3.3. Gas Sensing Features + The gas concentration, material composition, type of conductivity, operating temperature, and +different controlling parameters are considered as important factors which affect the gas sensitivity +or gas response of the metal oxide semiconductor sensor [36]. Depending on the compound and +operating temperature, the gas sensitivity of the NixMn0.25-xMg0.75Fe2O4 (where x= 0.00, 0.05, +0.10, 0.15, and 0.20) nano-ferrite against NO2 gas is studied and computed using following +equation: + S = │ +𝑅ɡ−𝑅𝑎 +𝑅𝑎 │× 100 % [Oxidizing gas] ……….………. (5) +Where Rg and Ra represent the electrical resistances in the NO2 gas and air, respectively [37, 38]. + Figure 5 shows the sensing characteristics and variation for each sample against nitrogen +dioxide NO2 gas when exposed and removed the examined gasses of the NixMn0.25-xMg0.75Fe2O4 +nano-ferrite. As can be seen from the figure, the resistance value increases when the discs are +exposed to NO2 gas (Gas ON), and subsequently decreases when the gas is closed (Gas OFF) for +all samples. At concentration of 65 ppm of NO2, the sensor's sensitivity was examined at various +operating temperatures (200 ◦C, 250 ◦C, and 300 ◦C). In the existence of an oxidizing gas, the +operating temperature is required to change the material's oxidation state and the conductivity of +NixMn0.25-xMg0.75Fe2O4 nano-ferrite. The response time is defined as the amount of time needed +to reach 90% of the equilibrium response of the gas, while the recovery time, is defined as the +amount of time needed to reach 10% of the baseline resistance [39]. From Table 5, it can be seen +that samples demonstrate a high sensitivity to nitrogen dioxide gas at 250 ◦C while it is around 300 +◦C for sample x=0.00. As shown in the FE-SEM images, the sensitivity of the doped samples +increases because it has the highest roughness, and this is agreement with the findings of +researchers [20,32]. Additionally, the figure also demonstrates that the Ni0.20Mn0.05Mg0.75Fe2O4 +ferrite compound has its highest gas response 707.22% of the sample (x=0.20) at 250 ◦C. Since +the sensitivity process in metal oxides occurs through the adsorption of oxygen ions on the surface, +doping of Mn by Ni generally often enhances the sensitivity because a lack of oxygen causes the +formation of oxygen voids; (When the oxygen concentration in the NixMn0.25-xMg0.75Fe2O4 lattice +increases, more oxygen ions (O-2 and -O) adsorb to the sensor's surface due of the gaps or voids) +[20]. In contrast to the pre-adsorbed oxygen and other test gases, NO2 gas has a greater electron +affinity and is a very reactive and oxidizing gas [40]. After the covalent bond between nitrogen +and oxygen is formed, NO2 has an unpaired electron, and remains as one of the atoms with a single +unpaired electron. Because the nano-ferrite has a short response time (1.2-11.4) s at 200 ◦C and a +short recovery time (1.5-4.4) s at 250 ◦C, it is possible to conclude that the sensor has excellent +sensing characteristics. This fast response of the sensor could be a result of the small particle size, +which causes the particle boundaries to enlarge. The values of sensitivity, response time, and +recovery time are tabulated in Table 5. + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +Figure 5. The variation in resistance with time of NixMn0.25-xMg0.75Fe2O4 nano-ferrite at different +operating temperatures. +x=0.05 +x=0.00 +x=0.15 +x=0.10 +x=0.20 + +24 +-200 °C-250 C-0-300°C +22 +20 +Resistance (M2) +6420 +8 +6 +0 +50 +100 +150 +200 +250 +300 +Time (sec)24 +o-200°C--250°C-300 °C +22 +Resistance (M2) +20 +18 +16 +12 +0 +50 +100 +150 +200 +250 +300 +Time (sec)14 +0-200C--250C-0-300C +12 +Resistance (M) +10 +8 +6 +0 +50 +100 +150 +200 +250 +300 +Time (sec)22 +o-200"C-Q-250C-0-300°C +20 +18 +Resistance (MQ) +16 +10 +8 +6 +4 +0 +50 +100 +150 +200 +250 +300 +Time (sec)18 +-200C-250 C-300°C +16 +14 +Resistance (MΩ) +12 +10 +8 +6 +2 +- +0 +50 +100 +150 +200 +250 +300 +Time (sec)Table 5. NO2 gas sensitivity, response time and recovery time values of NixMn0.25-xMg0.75Fe2O4 +nano-ferrite at different operating temperatures. + +4. Conclusions +Utilizing a simple sol-gel auto-combustion process, NixMn0.25-xMg0.75Fe2O4 nano-ferrite was +synthesized using metal nitrates as a source of cations and citric acid (C6H8O7) as a +complexant/fuel agent for the auto-combustion process. The NixMn0.25-xMg0.75Fe2O4 nano-ferrite +with the spinel structure peaks in the XRD patterns corresponding to the investigated systems, and +no unidentified peaks are observed. The FE-SEM images show microstructures with open pores +and nanoscale grains with agglomeration, which is nearly comparable to the crystalline size +determined by XRD. These findings reveal that, due to the particles being small, the prepared +samples at-room-temperature hysteresis loop curves exhibit superparamagnetic behavior. +Furthermore, the results of the NO2 gas sensing showed that the gas sensor had a good performance +in terms of its response to the gas. The sensitivity increases with the increasing concentration of +Ni in composition, as well as it also boasts shorter response and recovery times. For gas sensing +applications, in Mn0.25Mg0.75Fe2O4 it is concluded that it is desirable to substitute manganese ions +by nickel ions. + +References +[1] E. Rossinyol, J. Arbiol, F. Peiro, A. Cornet, J. R. Morante, B. Tian, T. Bo, D. Zhao, (2005) +“Nanostructured metal oxides synthesized by hard template method for gas sensing applications”, +Sensors and Actuators B, 109 (1) 57–63. +[2] K. Mukherjee, S. B. Majumder, (2010), “Reducing gas sensing behavior of nanocrystalline +magnesium–zinc ferrite powders”, Talanta, 81, 1826–1832. +[3] L. Satyanarayana, K. M. Reddy, S. V. Manorama, (2003), “Synthesis of nanocrystalline +Ni1−xCoxMnxFe2−xO4: a material for liquefied petroleum gas sensing”, Sensors and Actuators B 89 +(1-2), 62–67. +[4] A. B. Gadkari, T. J. Shinde, P. N. Vasambekar, (2013), “Effect of Sm3+ ion addition on gas +sensing properties of Mg1−xCdxFe2O4 system”, Sensors and Actuators B 178, 34–39. +[5] M. Sugimoto, (1999),” The past, present, and future of ferrites “, Journal of the American +Society, 82(2), 269–280. +x +Response Time +Recovery Time +Sensitivity % +200 oC +250 oC +300 oC 200 oC 250 oC +300 oC +200 oC +250 oC 300 oC +0.00 +2.4 +4.0 +5.9 +5.2 +4.4 +11.0 +30.82 +36.30 +74.60 +0.05 +11.4 +11.4 +5.5 +1.9 +1.9 +6.3 +141.72 +160.11 134.45 +0.10 +2.0 +1.5 +1.9 +3.6 +1.5 +4.7 +198.07 +202.45 175.34 +0.15 +11.4 +3.2 +9.0 +9.7 +3.0 +9.6 +262.80 +264.28 255.22 +0.20 +1.2 +3.7 +1.63 +1.8 +2.3 +5.24 +707.34 +707.22 676.25 + +[6] D. S. Mathew, R. S. Juang, (2007), “An overview of the structure and magnetism of spinel +ferrite nanoparticles and their synthesis in microemulsions”, Chemical Engineering Journal, +129(1-3), 51–65. +[7] N. Iftimie, E. Rezlesucu, P. D. Popa, N. Rezlescucu, (2006), “Gas sensitivity of nanocrystalline +nickel ferrite”, Journal of Optoelectronics and Advanced Materials 8 (3), 1016–1018. +[8] L. L. Yan, Z. M. Liu, Yang. Y, G. L. Shen, Q. Y. Ru, (2005), “Simple synthesis of +MgFe2O4 nanoparticles as gas sensing materials”, Sensor and Actuators B 107(2), 600-604. +[9] M. Tada, T. Kanemaru, T. Hara, T. Nakagawa, H. Handa, M. Abe, (2009) “Synthesis of hollow +ferrite nanospheres for biomedical applications”, Journal of Magnetism and Magnetic Materials, +321(10), 1414–1416. +[10] S. Andris, G. A. Karlis, (2016), “Spinel ferrite oxide semiconductor gas sensing”, Sensor and +Actuators B 222, 95-105. +[11] X. M. Liu, S. Y. Fu, C. J. Huang, (2004), “Magnetic properties of Ni ferrite nanocrystals +dispersed in the silica matrix by sol–gel technique”, Journal of Magnetism and Magnetic Materials +281(1-2), 234–239. +[12] B. H. Ryu, H. J. Chang, Y. M. Choi, K. J. Kong, J. O. Lee, C. G. Kim, H. K. Jung, J. H. Byun, +(2004), “Preparation of Co1−xNixFe2O4 nanoparticles by coprecipitation method”, Physica Status +Solidi 201(8), 1855–1858. +[13] F. M. C. Ana Cristina, M. R. Morelli, R. H. G. A. Kiminami, (2007), “Microstructure and +magnetic properties of Ni1-xZnxFe2O4 synthesized by combustion reaction”, Journal of Materials +Science 42(3), 779-783. +[14] X. Peng, J. Xu, H. Zang, B. Wang, Z. Wang, (2008), “Structural and PL properties of Cu- +doped ZnO films”, Journal of Luminescence 128(3), 297–300. +[15] N. L. Tarwal, R. S. Devan, Y. R. Ma, R. S. Patil, M. M. Karanjkar, P. S. Patil, (2012), “Spray +deposited localized surface plasmonic Au–ZnO nanocomposites for solar cell application”, +Electrochimica Acta 72, 32–39. +[16] A. B. Bodade, A. B. Bodade, H. G. Wankhade, G. N. Chaudhari, D. C. Kothari, (2012), +“Conduction mechanism and gas sensing properties of CoFe2O4 nanocomposite thick films for +H2S gas”, Talanta 89, 183–188. +[17] K. Vijaya kumar, M. Lakshmi, M. Buchi Suresh, (2013), “Structure-property correlation of +sol–gel processed Co0.5Ti0.5ZnFeO4 “, Journal of Engineering Research and Applications 3(6), +1489–1497. +[18] E. Asmat, A. Mukhtar, A. Ihsan, M. U. Rana, (2013), “Preparation and properties of sol–gel +synthesized Mg-substituted Ni2Y hexagonal ferrites”, Ceramics International 39(2), 983–990. +[19] M. Lakshmi, K. Vijaya kumar, K. Thyagarajan, (2015), “An investigation of structural and +magnetic properties of Cr–Zn ferrite nanoparticles prepared by a sol–gel process”, Journal of +Nanostructure in Chemistry 5(4), 365-373. + +[20] Saheb, L., & Al-Saadi, T. M. (2021, December). Synthesis, Characterization, and NH3 +Sensing Properties of (Zn0.7Mn0.3-xCexFe2O4) Nano-Ferrite. In Journal of Physics: Conference +Series (Vol. 2114, No. 1, p. 012040). IOP Publishing. +[21] N. Farhana, K. D. Hemant, K. Chanda, L. Preeti, (2020), “Structural and magnetic properties +of MgFe2O4 nano powder synthesized via co-precipitation route”, SN Applied Sciences 2(808). +[22] M. A. Haija, M. Chamakh, I. Othman, F. Banat, A. I. Ayest, (2020), “Fabrication of H2S gas +sensors using ZnxCu1-xFe2O4 nanoparticles”, Applied Physics A, 126(7). +[23] L. Yu, A. Sun, L. Shao, (2020), “Annealing temperature on the microstructure and magnetic +properties of magnesium–cobalt ferrite prepared by sol-gel self-propagating method”, Journal of +Materials Science: Materials in Electronics 31, 22662–22675. +[24] T. M. Al-Saadi, M. A. Jihad, (2016), “Preparation of Graphene Flakes and Studying Its +Structural Properties“, Iraqi Journal of Science 57(1), 145-153. +[25] H. S. Mahmood, T. H. Mubarak, S. M. Ali Ridha, J. Al-Zanganawee, (2022), “Effect of Zinc +Substitution in Magnetic Structure on Heat Efficiency for Hyperthermia: Investigation in +Superparamagnetic Properties”, AIP Conference Proceedings 2386, 070006(1-18). +[26] M. Hamedoun, A. Benyoussef, M. Bousmina, (2010), “Magnetic properties and phase +diagram of ZnxNi1−xFe2O4: high temperature series expansions”, Journal of Magnetism and +Magnetic Materials 322(11), 3227–3235. +[27] A. Sutka, G. Mezinskis, A. Lusis, M. Stingaciu, (2012), “Gas sensing properties of Zn-doped +p-type nickel ferrite”, Sensor and Actuators B (171-172), 354-360. +[28] I. H. Gul, W. Ahmed, A. Maqsood, (2008), “Electrical and magnetic characterization of +nanocrystalline Ni–Zn ferrite synthesis by co-precipitation route”, Journal of Magnetism and +Magnetic Materials 320(3-4), 270–275. +[29] S. Raghuvanshi, F. Mazaleyrat, S. N. Kane, (2018), “Mg1-xZnxFe2O4 nanoparticles: Interplay +between cation distribution and magnetic properties”, AIP Advances 8(4), 047804. +[30] M. A. Haija, A. F. S. Abu-Hani, N. Hamdan, S. Stephen, A. I. Ayesh, (2017), +“Characterization of H2S gas sensor based on CuFe2O4 nanoparticles”, Journal of Alloys and +Compounds, 690,461-468. +[31] J. Y. Patil, D. Y. Nadargi, S. S. Suryavanshi, (2019), “Cerium doped MgFe2O4 +nanocomposites: highly sensitive and fast response-recoverable acetone gas sensor”, Heliyon 5(6), +e01489. +[32] A. Jain, R. K. Baranwal, A. Bharti, Z. Vakil, C. S. Prajapati, (2013), “Study of Zn-Cu Ferrite +Nanoparticles for LPG Sensing”, The Scientific World Journal 2013, 1-7. +[33] K. Nejati, R. Zabihi, (2012), “Preparation and magnetic properties of nano size nickel ferrite +particles using hydrothermal method”, Chemistry Central Journal. 6(1). +[34] S. M. Hussein, T. H. Mubarak, S. M. Ali, J. Al-Zanganawee, (2021), “Synthesis and Studying +Induction Heating of Mn1-xZnxFe2O4 (x = 0 - 0.5) Magnetic Nanoparticles for Hyperthermia +Treatments”, Key Engineering Materials 882, 200-218. + +[35] T. Tatarchuk, M. Bououdina, J. J. Vijaya, L. J. Kennedy, (2017), “Spinel ferrite nanoparticles: +synthesis, +crystal +structure, +properties, +and +perspective +applications”, +Nanophysics, +Nanomaterials, Interface Studies, and Applications, Springer Proceedings in Physics 195, 305- +325. +[36] F. Tudorache, E. Rezlescu, P. D. Popa, N. Rezlescu, (2008), “Study of some simple ferrites +as reducing gas sensors”, Journal of Optoelectronics and Advanced Materials 10(7), 1889-1893. +[37] L. A. Patil, A. R. Bari, M. D. Shinde, V. V. Deo, D. P. Amalnerkar, (2011), "Synthesis of +ZnO nanocrystalline powder from ultrasonic atomization technique, characterization, and its +application in gas sensing," IEEE Sensors Journal 11(3), 939–946. +[38] M. S. Choi, H. G. Ma, J. H. Bang, A. Mirzaei, S. Han, H. Y. Lee, C. Jin, (2021), “SnO2 +nanowires decorated by insulating amorphous carbon layers for improved room-temperature NO2 +sensing”, Sensors and Actuators B: Chemical, 326, 128801. +[39] M. Donarelli, S. Prezioso, F. Perrozzi, F. Bisti, M. Nardone, L. Giancaterini, C. Cantalini, L. +Ottaviano, (2015), “Response to NO2 and other gases of resistive chemically exfoliated MoS2- +based gas sensors”, Sensors and Actuators B 207, 602-613. +[40] N. D. Hoa, N. V. Quy, D. Kim, (2009), “Nanowire structured SnOx-SWNT composites: high +performance sensor for NOx detection”, Sensors and Actuators B 142(1), 253-259. + + diff --git a/ENAzT4oBgHgl3EQfwv6u/content/tmp_files/load_file.txt b/ENAzT4oBgHgl3EQfwv6u/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..b7ab7efa20caf7b0102cbc8a7d98ec0ba9a7d550 --- /dev/null +++ b/ENAzT4oBgHgl3EQfwv6u/content/tmp_files/load_file.txt @@ -0,0 +1,875 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf,len=874 +page_content='Preparation and Characterization of NixMn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='25-xMg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='75Fe2O4 Nano-ferrite as NO2 Gas Sensing Material Hussein I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Mahdi 1, Nabeel A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Bakr 2, Tagreed M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Al-Saadi 3 1,2 Department of Physics, College of Science, University of Diyala, Diyala, IRAQ 3 College of Education for Pure Science, Ibn Al Haitham, University of Bagdad, Bagdad, IRAQ *Corresponding author: sciphydr2110@uodiyala.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='iq Abstract NixMn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='25-xMg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='75Fe2O4 nano-ferrites (where x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='00, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='05, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='10, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='15 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='20) were produced via sol-gel auto-combustion technique.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Investigations were done into how the incorporation of Ni ions affects the Mn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='25Mg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content="75Fe2O4 ferrite's structure, morphological, magnetic, and NO2 gas sensing features." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' All the samples are single-phase, based on the structural study utilizing the X-ray diffraction (XRD) pattern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' In terms of the structure of the cubic spinel, according to the XRD study, the crystallite sizes range from 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='30 to 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='32 nm, indicating nano- crystallinity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' The synthesis of spherical nanoparticles with a small modification in particle size distribution was verified via FE-SEM images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' The study found that the size of particles is tiny enough to act superparamagnetically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' The area of hysteresis loop is almost non-existing, thus reflecting typical soft magnetic materials according to magnetic measurements by VSM carried out at room temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Furthermore, the conductance responses of the NixMn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='25-xMg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='75Fe2O4 nano-ferrite were measured by exposing the ferrite to oxidizing (NO2) gas at different operating temperatures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' The results show that the sensor boasts shorter response and recovery times, as well as a higher sensitivity 707.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='22% of the sample (x=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='20) for nano-ferrite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Keyword: Mn-Mg ferrite, Ni ions substitution, sol- gel auto-combustion technique, XRD, VSM, NO2 gas sensor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Introduction Because chemical sensors may control emissions and identify dangerous contaminants, their demand has risen dramatically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' The most promising chemical sensors are metal oxide semiconductor ones since they offer several benefits like low cost, compact size, low power consumption, and online operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' They have received extensive research for a long time because they are very suitable with microelectronic processes [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Utilization of nanocrystalline materials for gas sensing have recently sparked a great deal of curiosity [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Ferrites have proven to be effective materials for gas semiconductor detectors [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Whenever a semiconductor gas sensor is exposed to various gas environments, it acquires the ability to modify the conductivity of the detecting material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' The surface-controlled technique of gas sensing depends on the interaction among both gas molecules to be identified and adsorbed oxygen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' The operating temperature, the type of gas being used, and the type of detector all affect how the detector responds to gas [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' The oxides having a structural formula of AB2O4 are significant for gas detection purposes and were studied for the identification of both oxidizing and reducing gases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' These oxides are preferred above all spinel- type metal oxide semiconductor detector, due to the magnetic materials used in high frequency applications as micro-electronic/magnetic devices [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' The most exciting features of spinel ferrites for gas detecting are their chemical makeup and structure, in which transition or post-transition cations occupy two different cation positions [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' The spinel ferrites, including MgFe2O4, ZnFe2O4, MnFe2O4, NiFe2O4, and CoFe2O4, have shown excellent sensitivity for a wide range of gases due to their stability in thermal and chemical atmospheres, quick reaction and recovery times, inexpensive, and straightforward electronic structures [7,8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Magnesium ferrite is specifically among the most significant ferrites due to its low magnetic and dielectric losses, high resistivity, and other properties that make it an essential component in catalytic reactions, detectors, and adsorption [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Depending on the preferred energies for divalent and trivalent ions in the spinel structure, it possesses an inverse spinel structure with Mg2+ ions in octahedral sites and Fe3+ ions equally divided over tetrahedral and octahedral sites [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' The sol-gel, molten-salt approach, hydrothermal, co-precipitation, and microemulsion techniques were all employed to obtain nano-sized spinel ferrite powder [11,12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Among the numerous techniques, the sol-gel technique is a convenient, environmentally friendly, and low- cost technique for synthesizing ferrites at relatively low temperatures in a short period of time [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Doping is a significant and successful method for fine-tuning the required properties of semiconductors [14,15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' The dopant might improve the gas-sensing characteristics of metal-oxide semiconductors by modifying the energy-band structure, improving the morphology and surface- to-volume ratio, and developing extra active centers at the grain boundaries [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' In the present work, we report the synthesis of NixMn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='25-xMg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='75Fe2O4 nano-ferrite by using a simple sol-gel auto-combustion technique and its application as NO2 gas sensor has been systematically investigated, where the results are presented and discussed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Experimental Part 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Materials and method The general formula of the spinel ferrite of NixMn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='25-xMg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='75Fe2O4 (where x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='00, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='05, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='10, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='15 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='20) has been produced via sol-gel auto-combustion technique.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Analytical-grade materials of ferric nitrate nonahydrate Fe(NO3)3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='9H2O, magnesium nitrate hexahydrate Mg(NO3)2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='6H2O, manganese nitrate monohydrate Mn(NO3)2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='H2O, and nickel nitrate hexahydrate Ni(NO3)2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='6H2O are used as precursors of iron and other metals, whereas citric acid (C6H8O7) is used as a complexant/fuel agent for the auto-combustion process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' The required masses of the raw materials required to prepare the ferrite are shown in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' These values are obtained using the following equation: Wt (g) = Mw (g/mol) × M (mol/L) × V (L) ……' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='….' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='……' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='….' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' (1) Where, Wt is the mass of the raw material, Mw is the molecular weight of the raw material, M is the number of moles required for the material in one liter of solvent, and V is the volume of solvent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Metal nitrates were entirely dissolved in small quantities of distilled water after being weighed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' This solution was then mixed with citric acid to achieve a molar ratio of these nitrates and citric acid of 1:1 in the final sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' After that, ammonia is added to the mixture in droplets to balance the (pH) to (~7) while mixing it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Combustion reaction occurs among nearby metal nitrates and citrate molecules, resulting in a polymer network with colloidal dimensions recognized as sol [17- 19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' While continuously mixing and heating the solution for one hour at 90 °C, the solution is evaporated, and then it held at this temperature until it solidified in a gel form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' The gel then is cooked to 120 ◦C in order to trigger auto-combustion where the dried gel is burnt until it is totally consumed to produce loose powder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Finally, to get the required ferrite, the resultant powder is crushed in an agate mortar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' The freshly as-prepared ferrite powder is then heated for two hours at 600 ◦C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' The masses of raw materials required to obtain NixMn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='25-xMg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='75Fe2O4 ferrite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Fabrication of gas sensors For each sample, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='75 g of powder is collected and a pressure of 200 bar is applied by manual press for 120 seconds to produce a disc with a diameter of 1 cm and a thickness of 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='5 mm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' The disc is then placed in furnace at a temperature of 900 ◦C for a period of two hours.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Thin copper wires are used as connecting leads, and silver paste is used to construct the electrodes on one side of the sample, while electrodes are placed on all specimen surfaces to obtain Ohmic contacts [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' The electrodes are fabricated for the five nano-ferrite samples, then the sensitivity of each sample to NO2 gas at a constant concentration (65 ppm) is tested by a gas sensitivity test system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=" Characterization By using powder X-ray diffractometer (Philips PW1730), the ferrites' XRD (X-ray diffraction) pattern is obtained via Cu-Kα (Wavelength-1." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='5406 Å) radiation, scan range: 20o – 80o, and scan speed: 6 deg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='/min.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=" The ferrites' surface morphology was investigated utilizing (MTRA3 LMU) field emission scanning electron microscope (FE-SEM) combined with Energy Dispersive X-ray Analyzer (EDX)." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' A vibrating sample magnetometer (EZ VSM model 10) was used to measure the magnetism of some specimens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' In order to detect (NO2) gas at various temperatures, the gas response characteristics of sintered discs (900°C) were investigated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' The resistance of gas sensor samples is measured by using Impedance Analyzer (UNI-TUT81B) equipped with a computerized testing tool.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' x Composition Ferric nitrate (g) Magnesium nitrate (g) Manganese nitrate (g) Nickel nitrate (g) Citric acid (g) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='00 Mn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='25Mg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='75Fe2O4 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='32 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='6923 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='8900 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='00 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='0556 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='05 Ni0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='05Mn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='20Mg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='75Fe2O4 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='32 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='6923 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='5120 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='5816 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='0556 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='10 Ni0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='10Mn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='15Mg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='75Fe2O4 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='32 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='6923 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='1340 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='1632 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='0556 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='15 Ni0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='15Mn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='10Mg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='75Fe2O4 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='32 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='6923 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='7560 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='7448 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='0556 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='20 Ni0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='20Mn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='05Mg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='75Fe2O4 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='32 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='6923 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='3780 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='3264 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='0556 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Results and Discussion 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' X-Ray Diffraction X-ray diffraction (XDR) analysis was carried out to determine the phase formation of the NixMn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='25-xMg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='75Fe2O4 nano-ferrite in the 2θ range 10o ≤ 2θ ≤ 80o.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Figure 1 shows the indexed x- ray diffraction patterns of the NixMn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='25-xMg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='75Fe2O4 ferrite annealed at 600 ◦C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' The presence of (220), (311), (400), (422), (511), (440), and (533) planes confirms the formation of cubic spinel structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' The diffraction peaks agree with the JCPDS card number 89-3084 [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Additionally, the size of the crystallites gradually decreased as the amount of Ni doping increased.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' This was shown in the XRD pattern, where the NixMn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='25-xMg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='75Fe2O4 nano-ferrite peaks get shifted to higher angles, as the angle value increased, as listed in Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' By using the Scherrer’s equation, the crystallite size D of the NixMn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='25-xMg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='75Fe2O4 specimens was determined from the broadening of the (311) peak in the XRD patterns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' 𝐷 = K λ 𝛽 cosθ ……' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='….' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='……' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='….' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' (2) Where, K is constant assumed to be 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='9, λ is X-ray wavelength equal to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content="5406 (Å), β is the full width at half maximum (FWHM) of the highest intensity diffraction peak expressed in radians, while θ is the Bragg's angle of the diffraction peak [22,23]." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' By using the following equation, the cubic unit cell lattice parameter (a) for all compounds was computed via diffraction planes: a = dhkl √ℎ2 + 𝑘2 + 𝐼2 ……' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='….' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='……' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='….' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' (3) Where, d is the interplanar spacing and (h, l and k) are the Miller indices of the crystal planes [24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' The X-ray density (𝜌𝑥) can be computed via the following equation: 𝜌𝑥 = 8 Mw NA a3 ……' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='….' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='……' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='….' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=" (4) Where, MW represents the molecular weight and NA is the Avogadro's number [25]." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' The lattice parameter (a), XRD density (ρx), and crystallite size (D) for all samples are given in Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' 10 20 30 40 50 60 70 80 (533) x=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='20 x=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='15 x=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='10 x=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='05 x=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='00 (440) (511) (422) (400) (311) (220) Intensity (arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='u) 2q (degree) Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' X-ray diffraction patterns of NixMn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='25-xMg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='75Fe2O4 nano-ferrite prepared by auto- combustion method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Increasing the concentration of Ni2+ leads to increase the lattice constant of ferrite compounds as listed in Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Smaller Fe3+ ions have been observed to migrate from tetrahedral to octahedral positions in response to Ni2+ addition [26,27], therefore tetrahedral sites are enlarged as a result of increasing the lattice constant [28,29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Moreover, this caused the lattice to grow and the density to drop, indicating that the lattice constant has changed as a result of the dopant ions being absorbed into the lattice could have taken an interstitial positions among the hosting ions [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Structure properties of the NixMn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='25-xMg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='75Fe2O4 nano-ferrite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' h k l 2θ (deg) (JCPDS) 2θ (deg) (x=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='00) 2θ (deg) (x=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='05) 2θ (deg) (x=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='10) 2θ (deg) (x=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='15) 2θ (deg) (x=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='20) 220 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='115 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='1365 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='4563 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='3111 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='3932 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='3938 311 35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='466 35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='4950 35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='8238 35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='7308 35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='8876 35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='7541 400 43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='123 43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='2299 43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='5441 43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='4461 43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='4725 43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='3345 422 53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='478 53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='5835 53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='9189 53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='7877 53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='8403 53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='6563 511 57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='000 57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='1528 57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='4708 57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='3573 57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='4057 57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='2337 440 62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='594 62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='7239 62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='8946 62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='9067 62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='9564 62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='8185 533 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='049 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='2529 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='3735 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='2861 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='3755 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='2936 Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Unit cell constant (a), density (ρx) and crystallite size (D) of NixMn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='25-xMg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='75Fe2O4 nano-ferrite prepared by auto-combustion method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' x Composition a (Å) ρx (g/cm3) D (nm) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='00 Mn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='25Mg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='75Fe2O4 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='36743 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='250 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='31 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='05 Ni0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='05Mn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='20Mg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='75Fe2O4 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='37691 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='232 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='34 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='10 Ni0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='10Mn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='15Mg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='75Fe2O4 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='38131 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='224 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='34 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='15 Ni0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='15Mn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='10Mg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='75Fe2O4 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='38245 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='222 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='32 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='20 Ni0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='20Mn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='05Mg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='75Fe2O4 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='38717 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='213 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='30 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' FE-SEM and EDX Analysis To assess the morphology of the fabricated samples, (FE-SEM) was used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Figure 2 illustrates the NixMn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='25-xMg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='75Fe2O4 nano-ferrite micro images at a 200 nm scale after annealing at 600 °C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' The observed FE-SEM images made it extremely apparent that the magnetic ferrite particles were created through some aggregation at the nanoscale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' The FE-SEM images show porous, sponge- like shape particles of the samples (x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='00, and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='05).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=" Most likely, the gases released during the gel's combustion process are what caused the pores to form [30]." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' In addition, the images show particles that are spherical or semi-spherical and nonhomogeneous in form of the samples (x=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='10, and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='15), as well as the images show homogeneous distribution and spherical nanoparticles of the sample (x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='20).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' The FE-SEM images also show the formation of tiny agglomerated grains with surface spaces or voids and no distinct shape.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' The agglomerates are where the porosity is located.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Since gas detecting is a surface phenomenon and porosity is essential, the reported porous microstructure is beneficial for sensing purposes [31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' It is obviously shown in the micrographs that the particles structures of the NixMn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='25-xMg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='75Fe2O4 nano-ferrite are very coarse, which facilitate adsorption of oxygen species on the detecting surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Adsorption of oxygen species is responsible for gas detecting [32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' FE SEM images of NixMn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='25 xMg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='75Fe2O4 nano ferrite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='05 x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='10 x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='15 x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='20 x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='00 D1=50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='61nm SEMMAG:135KX WD:8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='93mm MIRA3TESCAN Det:SE SEMHV:15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='0kV 200nm Date(m/d/y):05/08/22 SUT-FESEMD1=47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='34nm SEMMAG:135kX WD:8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='78mm MIRA3TESCAN Det:SE SEMHV:15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='0kV 200nm Date(m/d/y):05/08/22 SUT-FESEMD1=57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='60nm SEMMAG:135KX WD:8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='67mm MIRA3 TESCAN Det:SE SEMHV:15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='0kV 200nm Date(m/d/y):05/08/22 SUT-FESEMD1=60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='35mm SEMMAG:135KX WD:8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='69mm MIRA3TESCAN Det:SE SEMHV:15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='0kV 200nm Date(m/d/y):05/08/22 SUT-FESEMD1=55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='96nm SEMMAG:135kX WD:8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='83mm MIRA3TESCAN Det:SE SEMHV:15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='0kV 200nm Date(m/d/y):05/08/22 SUT-FESEM The EDX spectra of the NixMn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='25-xMg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='75Fe2O4 nano-ferrite (where x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='00, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='05, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='10, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='15 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='20) are illustrated in Figure 3, referring that the spectral lines related to (Ni, Mn, Mg, Fe and O), verify that the synthesized compound NixMn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='25-xMg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='75Fe2O4 was achieved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' EDX spectra of NixMn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='25-xMg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='75Fe2O4 nano-ferrite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='00 x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='05 x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='10 x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='15 x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='20 0 Spectrum2 Wt% Fe 51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='3 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='2 20 C 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='3 Mg 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='1 Mn 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='2 Ca 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='1 10 Mg Fe e Au Ca Mn Au Au .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' 8 kevSpectrum4 Wt% 6 Fe 50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='3 0 29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='2 Mfo 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='1 20- 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='3 Mn 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='1 Ni 13 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='2 Fe MnSpectrum5 Wts Fe 4B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='2 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' 29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='5 20- Mn 25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='2 Mg 10- Mn Ni Ni AU0 Spectrum6 Wt% 20 Fe 52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='4 26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='3 C 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='4 Mg 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='1 15 Ni 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='3 Mn 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='2 10 Fe Fe Mg Au Mn Ni Ni Au 8 kel0 Spectrum7 Wt% Fe 51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='3 0 26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='2 C 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='3 Mg 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='1 15 Ni 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='2 Mn 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='1 /sdb 10 Fe Mg Au Mn Ni Ni Au 8 kev3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Magnetic Characteristics Hysteresis loop is measured utilizing a (VSM) system, and magnetic characteristics of samples were examined at room temperature (300 K).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Figure 4 shows the hysteresis loop curves of NixMn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='25-xMg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='75Fe2O4 (x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='00, and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='20).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' (S) shaped curves indicate that standard soft magnetic material and magnetic coercivity can be ignored.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' In addition, the particles are so small that they behave like superparamagnetic material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Due to the small crystallite size, as is evidenced by the XRD analysis in Table 3, nanoparticles have superparamagnetic behavior, in which their magnetic moments attempt to align with one another in a specific way [33,34].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' According to Neel, the distribution of cations among the octahedral and tetrahedral locations in spinel ferrite determines the overall magnetic moment [35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Saturation magnetization (Ms), remnant magnetization (Mr), and magnetic coercivity (Hc) values were computed from the M-H curves depending on (Ms) measured values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' M-H curves have demonstrated how chemical compound affects magnetic properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Table 4 illustrates the variation in saturation magnetization (Ms) values for specimens captured from hysteresis loop curves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' As 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='20 of the Ni2+ ions were swapped out for Mn2+ ions, the Ms value dropped from 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='980 (emu/g) for x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='00 to 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='400 (emu/g).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' According to experimental observations, as nickel content rises, the ratio of ferric, manganese, or magnesium ions on the A- location decreases, while at the same time, the of Fe3+ ions grows by the same amount on the location B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' As a result, the A-B interaction is reduced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' As a consequence of the ionic moments on the B-sites no longer being maintained parallel to each other, the angles among them start to form, which lowers the moment of the B sub lattice itself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Most likely, nickel ions have been replaced by cations in the B-sites [34].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Figure 4 shows how the observed values of the remnant magnetization (Mr) and coercive field (Hc) are so small, demonstrating that the grain size does not pass the critical diameter of single-domain grain [34].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' The cation distribution has a significant impact on the net magnetic moments and magnetocrystalline anisotropy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Table 4 lists the magnetic factors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Magnetization (M) versus applied magnetic field (Oe) of NixMn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='25-xMg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='75Fe2O4 (x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='00, and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='20) nanoparticles at 300K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' -10000 -8000 -6000 -4000 -2000 0 2000 4000 6000 8000 10000 -40 -30 -20 -10 0 10 20 30 40 X= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='00 X= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='20 Magntization(emu/g) Applied Magntic Field(Oe) Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Variation of magnetic factors for NixMn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='25-xMg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='75Fe2O4 (x =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='00, and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='20) nanoparticles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' x Compound Ms (emu/g) Mr (eum/g) Hc (Oe) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='00 Mn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='25Mg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='75Fe2O4 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='98 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='95 61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='20 Ni0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='20Mn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='05Mg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='75Fe2O4 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='40 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='54 94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='00 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Gas Sensing Features The gas concentration, material composition, type of conductivity, operating temperature, and different controlling parameters are considered as important factors which affect the gas sensitivity or gas response of the metal oxide semiconductor sensor [36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Depending on the compound and operating temperature, the gas sensitivity of the NixMn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='25-xMg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='75Fe2O4 (where x= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='00, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='05, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='10, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='15, and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='20) nano-ferrite against NO2 gas is studied and computed using following equation: S = │ 𝑅ɡ−𝑅𝑎 𝑅𝑎 │× 100 % [Oxidizing gas] ……' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='….' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='……' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='….' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' (5) Where Rg and Ra represent the electrical resistances in the NO2 gas and air, respectively [37, 38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Figure 5 shows the sensing characteristics and variation for each sample against nitrogen dioxide NO2 gas when exposed and removed the examined gasses of the NixMn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='25-xMg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='75Fe2O4 nano-ferrite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' As can be seen from the figure, the resistance value increases when the discs are exposed to NO2 gas (Gas ON), and subsequently decreases when the gas is closed (Gas OFF) for all samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=" At concentration of 65 ppm of NO2, the sensor's sensitivity was examined at various operating temperatures (200 ◦C, 250 ◦C, and 300 ◦C)." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=" In the existence of an oxidizing gas, the operating temperature is required to change the material's oxidation state and the conductivity of NixMn0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='25-xMg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='75Fe2O4 nano-ferrite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' The response time is defined as the amount of time needed to reach 90% of the equilibrium response of the gas, while the recovery time, is defined as the amount of time needed to reach 10% of the baseline resistance [39].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' From Table 5, it can be seen that samples demonstrate a high sensitivity to nitrogen dioxide gas at 250 ◦C while it is around 300 ◦C for sample x=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='00.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' As shown in the FE-SEM images, the sensitivity of the doped samples increases because it has the highest roughness, and this is agreement with the findings of researchers [20,32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Additionally, the figure also demonstrates that the Ni0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='20Mn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='05Mg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='75Fe2O4 ferrite compound has its highest gas response 707.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='22% of the sample (x=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='20) at 250 ◦C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Since the sensitivity process in metal oxides occurs through the adsorption of oxygen ions on the surface, doping of Mn by Ni generally often enhances the sensitivity because a lack of oxygen causes the formation of oxygen voids;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' (When the oxygen concentration in the NixMn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='25-xMg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content="75Fe2O4 lattice increases, more oxygen ions (O-2 and -O) adsorb to the sensor's surface due of the gaps or voids) [20]." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' In contrast to the pre-adsorbed oxygen and other test gases, NO2 gas has a greater electron affinity and is a very reactive and oxidizing gas [40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' After the covalent bond between nitrogen and oxygen is formed, NO2 has an unpaired electron, and remains as one of the atoms with a single unpaired electron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Because the nano-ferrite has a short response time (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='2-11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='4) s at 200 ◦C and a short recovery time (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='5-4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='4) s at 250 ◦C, it is possible to conclude that the sensor has excellent sensing characteristics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' This fast response of the sensor could be a result of the small particle size, which causes the particle boundaries to enlarge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' The values of sensitivity, response time, and recovery time are tabulated in Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' The variation in resistance with time of NixMn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='25-xMg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='75Fe2O4 nano-ferrite at different operating temperatures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' x=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='05 x=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='00 x=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='15 x=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='10 x=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='20 24 -200 °C-250 C-0-300°C 22 20 Resistance (M2) 6420 8 6 0 50 100 150 200 250 300 Time (sec)24 o-200°C--250°C-300 °C 22 Resistance (M2) 20 18 16 12 0 50 100 150 200 250 300 Time (sec)14 0-200C--250C-0-300C 12 Resistance (M) 10 8 6 0 50 100 150 200 250 300 Time (sec)22 o-200"C-Q-250C-0-300°C 20 18 Resistance (MQ) 16 10 8 6 4 0 50 100 150 200 250 300 Time (sec)18 -200C-250 C-300°C 16 14 Resistance (MΩ) 12 10 8 6 2 - 0 50 100 150 200 250 300 Time (sec)Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' NO2 gas sensitivity, response time and recovery time values of NixMn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='25-xMg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='75Fe2O4 nano-ferrite at different operating temperatures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Conclusions Utilizing a simple sol-gel auto-combustion process, NixMn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='25-xMg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='75Fe2O4 nano-ferrite was synthesized using metal nitrates as a source of cations and citric acid (C6H8O7) as a complexant/fuel agent for the auto-combustion process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' The NixMn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='25-xMg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='75Fe2O4 nano-ferrite with the spinel structure peaks in the XRD patterns corresponding to the investigated systems, and no unidentified peaks are observed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' The FE-SEM images show microstructures with open pores and nanoscale grains with agglomeration, which is nearly comparable to the crystalline size determined by XRD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' These findings reveal that, due to the particles being small, the prepared samples at-room-temperature hysteresis loop curves exhibit superparamagnetic behavior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Furthermore, the results of the NO2 gas sensing showed that the gas sensor had a good performance in terms of its response to the gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' The sensitivity increases with the increasing concentration of Ni in composition, as well as it also boasts shorter response and recovery times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' For gas sensing applications, in Mn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='25Mg0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='75Fe2O4 it is concluded that it is desirable to substitute manganese ions by nickel ions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' References [1] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Rossinyol, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Arbiol, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Peiro, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Cornet, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Morante, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Tian, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Bo, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Zhao, (2005) “Nanostructured metal oxides synthesized by hard template method for gas sensing applications”, Sensors and Actuators B, 109 (1) 57–63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' [2] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Mukherjee, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Majumder, (2010), “Reducing gas sensing behavior of nanocrystalline magnesium–zinc ferrite powders”, Talanta, 81, 1826–1832.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' [3] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Satyanarayana, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Reddy, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Manorama, (2003), “Synthesis of nanocrystalline Ni1−xCoxMnxFe2−xO4: a material for liquefied petroleum gas sensing”, Sensors and Actuators B 89 (1-2), 62–67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' [4] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Gadkari, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Shinde, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Vasambekar, (2013), “Effect of Sm3+ ion addition on gas sensing properties of Mg1−xCdxFe2O4 system”, Sensors and Actuators B 178, 34–39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' [5] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Sugimoto, (1999),” The past, present, and future of ferrites “, Journal of the American Society, 82(2), 269–280.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' x Response Time Recovery Time Sensitivity % 200 oC 250 oC 300 oC 200 oC 250 oC 300 oC 200 oC 250 oC 300 oC 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='00 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='4 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='0 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='9 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='2 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='4 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='0 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='82 36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='30 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='60 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='05 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='4 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='4 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='9 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='9 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='3 141.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='72 160.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='11 134.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='45 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='10 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='0 1.' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='63 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='8 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='3 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='24 707.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='34 707.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='22 676.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='25 [6] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Mathew, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Juang, (2007), “An overview of the structure and magnetism of spinel ferrite nanoparticles and their synthesis in microemulsions”, Chemical Engineering Journal, 129(1-3), 51–65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' [7] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Iftimie, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Rezlesucu, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Popa, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Rezlescucu, (2006), “Gas sensitivity of nanocrystalline nickel ferrite”, Journal of Optoelectronics and Advanced Materials 8 (3), 1016–1018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' [8] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Yan, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Liu, Yang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Y, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Shen, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Ru, (2005), “Simple synthesis of MgFe2O4 nanoparticles as gas sensing materials”, Sensor and Actuators B 107(2), 600-604.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' [9] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Tada, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Kanemaru, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Hara, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Nakagawa, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Handa, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Abe, (2009) “Synthesis of hollow ferrite nanospheres for biomedical applications”, Journal of Magnetism and Magnetic Materials, 321(10), 1414–1416.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' [10] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Andris, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Karlis, (2016), “Spinel ferrite oxide semiconductor gas sensing”, Sensor and Actuators B 222, 95-105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' [11] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Liu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Fu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Huang, (2004), “Magnetic properties of Ni ferrite nanocrystals dispersed in the silica matrix by sol–gel technique”, Journal of Magnetism and Magnetic Materials 281(1-2), 234–239.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' [12] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Ryu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Chang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Choi, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Kong, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Lee, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Kim, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Jung, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Byun, (2004), “Preparation of Co1−xNixFe2O4 nanoparticles by coprecipitation method”, Physica Status Solidi 201(8), 1855–1858.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' [13] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Ana Cristina, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Morelli, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Kiminami, (2007), “Microstructure and magnetic properties of Ni1-xZnxFe2O4 synthesized by combustion reaction”, Journal of Materials Science 42(3), 779-783.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' [14] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Peng, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Xu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Zang, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Wang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Wang, (2008), “Structural and PL properties of Cu- doped ZnO films”, Journal of Luminescence 128(3), 297–300.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' [15] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Tarwal, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Devan, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Ma, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Patil, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Karanjkar, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Patil, (2012), “Spray deposited localized surface plasmonic Au–ZnO nanocomposites for solar cell application”, Electrochimica Acta 72, 32–39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' [16] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Bodade, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Bodade, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Wankhade, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Chaudhari, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Kothari, (2012), “Conduction mechanism and gas sensing properties of CoFe2O4 nanocomposite thick films for H2S gas”, Talanta 89, 183–188.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' [17] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Vijaya kumar, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Lakshmi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Buchi Suresh, (2013), “Structure-property correlation of sol–gel processed Co0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='5Ti0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='5ZnFeO4 “, Journal of Engineering Research and Applications 3(6), 1489–1497.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' [18] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Asmat, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Mukhtar, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Ihsan, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Rana, (2013), “Preparation and properties of sol–gel synthesized Mg-substituted Ni2Y hexagonal ferrites”, Ceramics International 39(2), 983–990.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' [19] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Lakshmi, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Vijaya kumar, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Thyagarajan, (2015), “An investigation of structural and magnetic properties of Cr–Zn ferrite nanoparticles prepared by a sol–gel process”, Journal of Nanostructure in Chemistry 5(4), 365-373.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' [20] Saheb, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=', & Al-Saadi, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' (2021, December).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Synthesis, Characterization, and NH3 Sensing Properties of (Zn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='7Mn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='3-xCexFe2O4) Nano-Ferrite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' In Journal of Physics: Conference Series (Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' 2114, No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' 1, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' 012040).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' IOP Publishing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' [21] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Farhana, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Hemant, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Chanda, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Preeti, (2020), “Structural and magnetic properties of MgFe2O4 nano powder synthesized via co-precipitation route”, SN Applied Sciences 2(808).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' [22] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Haija, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Chamakh, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Othman, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Banat, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Ayest, (2020), “Fabrication of H2S gas sensors using ZnxCu1-xFe2O4 nanoparticles”, Applied Physics A, 126(7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' [23] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Yu, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Sun, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Shao, (2020), “Annealing temperature on the microstructure and magnetic properties of magnesium–cobalt ferrite prepared by sol-gel self-propagating method”, Journal of Materials Science: Materials in Electronics 31, 22662–22675.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' [24] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Al-Saadi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Jihad, (2016), “Preparation of Graphene Flakes and Studying Its Structural Properties“, Iraqi Journal of Science 57(1), 145-153.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' [25] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Mahmood, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Mubarak, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Ali Ridha, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Al-Zanganawee, (2022), “Effect of Zinc Substitution in Magnetic Structure on Heat Efficiency for Hyperthermia: Investigation in Superparamagnetic Properties”, AIP Conference Proceedings 2386, 070006(1-18).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' [26] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Hamedoun, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Benyoussef, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Bousmina, (2010), “Magnetic properties and phase diagram of ZnxNi1−xFe2O4: high temperature series expansions”, Journal of Magnetism and Magnetic Materials 322(11), 3227–3235.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' [27] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Sutka, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Mezinskis, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Lusis, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Stingaciu, (2012), “Gas sensing properties of Zn-doped p-type nickel ferrite”, Sensor and Actuators B (171-172), 354-360.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' [28] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Gul, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Ahmed, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Maqsood, (2008), “Electrical and magnetic characterization of nanocrystalline Ni–Zn ferrite synthesis by co-precipitation route”, Journal of Magnetism and Magnetic Materials 320(3-4), 270–275.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' [29] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Raghuvanshi, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Mazaleyrat, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Kane, (2018), “Mg1-xZnxFe2O4 nanoparticles: Interplay between cation distribution and magnetic properties”, AIP Advances 8(4), 047804.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' [30] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Haija, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Abu-Hani, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Hamdan, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Stephen, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Ayesh, (2017), “Characterization of H2S gas sensor based on CuFe2O4 nanoparticles”, Journal of Alloys and Compounds, 690,461-468.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' [31] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Patil, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Nadargi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Suryavanshi, (2019), “Cerium doped MgFe2O4 nanocomposites: highly sensitive and fast response-recoverable acetone gas sensor”, Heliyon 5(6), e01489.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' [32] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Jain, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Baranwal, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Bharti, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Vakil, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Prajapati, (2013), “Study of Zn-Cu Ferrite Nanoparticles for LPG Sensing”, The Scientific World Journal 2013, 1-7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' [33] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Nejati, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Zabihi, (2012), “Preparation and magnetic properties of nano size nickel ferrite particles using hydrothermal method”, Chemistry Central Journal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' 6(1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' [34] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Hussein, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Mubarak, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Ali, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Al-Zanganawee, (2021), “Synthesis and Studying Induction Heating of Mn1-xZnxFe2O4 (x = 0 - 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content='5) Magnetic Nanoparticles for Hyperthermia Treatments”, Key Engineering Materials 882, 200-218.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' [35] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Tatarchuk, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Bououdina, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Vijaya, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Kennedy, (2017), “Spinel ferrite nanoparticles: synthesis, crystal structure, properties, and perspective applications”, Nanophysics, Nanomaterials, Interface Studies, and Applications, Springer Proceedings in Physics 195, 305- 325.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' [36] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Tudorache, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Rezlescu, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Popa, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Rezlescu, (2008), “Study of some simple ferrites as reducing gas sensors”, Journal of Optoelectronics and Advanced Materials 10(7), 1889-1893.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' [37] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Patil, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Bari, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Shinde, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Deo, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Amalnerkar, (2011), "Synthesis of ZnO nanocrystalline powder from ultrasonic atomization technique, characterization, and its application in gas sensing," IEEE Sensors Journal 11(3), 939–946.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' [38] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Choi, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Ma, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Bang, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Mirzaei, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Han, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Lee, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Jin, (2021), “SnO2 nanowires decorated by insulating amorphous carbon layers for improved room-temperature NO2 sensing”, Sensors and Actuators B: Chemical, 326, 128801.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' [39] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Donarelli, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Prezioso, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Perrozzi, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Bisti, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Nardone, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Giancaterini, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Cantalini, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Ottaviano, (2015), “Response to NO2 and other gases of resistive chemically exfoliated MoS2- based gas sensors”, Sensors and Actuators B 207, 602-613.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' [40] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Hoa, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Quy, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} +page_content=' Kim, (2009), “Nanowire structured SnOx-SWNT composites: high performance sensor for NOx detection”, Sensors and Actuators B 142(1), 253-259.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ENAzT4oBgHgl3EQfwv6u/content/2301.01728v1.pdf'} diff --git a/FdE2T4oBgHgl3EQf-QlB/content/2301.04236v1.pdf b/FdE2T4oBgHgl3EQf-QlB/content/2301.04236v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..44974d0907a7b1accf7fb6b63f357698ef504264 --- /dev/null +++ b/FdE2T4oBgHgl3EQf-QlB/content/2301.04236v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:424ce1d8823d9ece60f1cc0267365b975e5433fb74d4415b4a0ac1932dd6bb26 +size 104970 diff --git a/FdE2T4oBgHgl3EQf-QlB/vector_store/index.faiss b/FdE2T4oBgHgl3EQf-QlB/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..449be387dc8a6446650b28c19fc0f16670860620 --- /dev/null +++ b/FdE2T4oBgHgl3EQf-QlB/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:a280c7e1ece244a399c4efd9cccf06c994f1442cf1204608fba48ffe97bd030f 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Universit`a degli Studi Roma +Tre, Rome (Italy) +2INFN Sezione di Roma Tre, Rome (Italy) +3Deutsches Elektronen–Synchrotron, 22607 Hamburg (Germany) +ilaria.deangelis@uniroma3.it +Abstract +School visits to research laboratories or facilities represent a unique way to bring students +closer to science and STEM (Science, Technology, Engineering and Mathematics) careers. +However, such visits can be very expensive for students and teachers, in terms of both time +and money. +In this paper, we present a possible alternative to on-site visits consisting in +an activity addressed to high school students that makes use of a VR application to make +them “enter” into a particle physics experiment. This proposal can represent a valid way of +guaranteeing a visit to a research centre for all schools, regardless of their social or geographical +origin. We describe the tests we carried out with a focus group of teachers and their students, +and the obtained results. +Keywords: high school, particle physics, virtual reality, STEM careers, research centre +1 +Introduction +Guided visits to research centres or facilities certainly represent a peculiar element in a student’s +high school career, since they allow direct contact with authentic conditions of scientific knowledge +production processes [1]. In the Italian National Indication guidelines on teaching [2], in fact, these +visits are explicitly mentioned for physics, as they represent one of the means by which students +reach their learning objectives at the end of their high school career. Experiencing some time in +a research centre can indeed not only improve students’ knowledge of physics, but also lead to a +clearer idea of what research in physics is about and eventually motivate some of them to consider +a science profession [3]. Therefore, these visits should become part of a scientific school curriculum, +along with hands-on and practical activities [4–8]. +In Italy, two examples of internationally renowned laboratories that organise visits addressed to +school groups are the Laboratori Nazionali del Gran Sasso [9] and the Sardinia Radio Telescope [10]. +In Europe, CERN is one of the most active centres as regards proposals for schools [11]. Worldwide, +several research centres or facilities open their doors to schools. The participation of students and +teachers to visits, however, although certainly meaningful, can be very expensive in terms of money +and time, especially if the centres are located in places far from the school. For this reason, physics +teachers often choose alternative activities to ensure contact with research organisations that do not +require an on-site visit. An example in this sense are the CERN International Masterclasses [12,13], +which allow students to work from their schools on real particle physics data, and discuss the related +analysis together with CERN researchers during a video-conference. In this way, participants can +virtually walk into a scientific central control room and get a glance of what they would see +entering CERN. The advantages of initiatives of this kind are manifold, from becoming aware of +the frontiers of scientific research, to actively working on real data, to coming into contact with +an international research environment [14]. On the other hand, however, the contact with the +laboratory is only provided by the video-conferences that generally involve many students’ groups +at the same time [12]. In this context, we worked to develop a third way, alternative to both +face-to-face visits and masterclass-type initiatives, through which a student can experience the +world of a scientific research laboratory up close. +Our approach makes use of Virtual Reality +(VR) technology. To do this, we chose the context of particle physics, in particular the Belle II +1 +arXiv:2301.01515v1 [physics.ed-ph] 4 Jan 2023 + +collaboration, for which an advanced VR application was developed [14]. The remaining paper is +organised as follows. In section 2 we describe the activity we developed. In section 3 we illustrate +the public we reached, including both students and teachers, and the feedback we received and in +section 4 we present our conclusion. +2 +The educational proposal +We have chosen to organise a virtual visit to an international laboratory which is however very +difficult and expensive to reach for Italian school groups, since it is located in Japan (much further +away than Laboratori Nazionali del Gran Sasso or CERN). In fact, our educational proposal +for schools initiated from the VR application Belle2VR [15]. +Having realised the potential of +Belle2VR application, we soon started to use it with the public during some outreach events such +as science festivals or public events organised at the University. In these cases, visitors were given +the possibility to wear the VR helmet while the researchers used joysticks to guide them to discover +the experiment, as in a real guided visit. After a few years of experience in science festivals and open +events to which thousands of people participated, including many school students, that provided +us very positive feedback, we have decided to propose a more structured activity to schools. +2.1 +Belle2VR +Developed by Virginia Tech, the application Belle2VR allows users to virtually enter the particle +physics detector of the Belle II experiment [16]. The Belle II experiment is currently carried out at +the KEK in Tsukuba, Japan, and it studies the properties of heavy quarks and leptons to search +for an evidence of new physics phenomena, from the matter-antimatter asymmetry problem to the +existence of dark matter particles. Belle2VR reconstructs the interior of the detector and allows to +visualise realistic simulations of particles interacting with each other and with the detector elements +(Fig. 1). The user can navigate through the detector and its components and can also manage the +time evolution of the interaction by going back and forth or stopping the Developed by Virginia +Tech, the application Belle2VR allows users to virtually enter the particle physics detector of the +Belle II experiment [16]. The Belle II experiment is currently carried out at the KEK in Tsukuba, +Japan, and it studies the properties of heavy quarks and leptons to search for an evidence of +new physics phenomena, from the matter-antimatter asymmetry problem to the existence of dark +matter particles. Belle2VR reconstructs the interior of the detector and allows to visualise realistic +simulations of particles interacting with each other and with the detector elements (Fig. 1). The +user can navigate through the detector and its components and can also manage the time evolution +of the interaction by going back and forth or stopping the motion of particles at a specific time. +Belle2VR, therefore, allows to explore particle physics phenomena from a unique point of view. +2.2 +Activity structure +We built an activity addressed to high school class groups, lasting about an hour and a half, that +can be carried out in a dedicated University room, or directly in the classroom. It starts with a +theoretical introduction that makes use of slides. Here, some basic topics and concepts typically +treated at school are recalled, such as electromagnetism. At the same time, more recent contents +are also presented, such as the Standard Model, the cross section or the decay of particles, which +require the use of quantum physics. +The Belle II experiment is also presented in terms of its +components and physics goal. +This phase is meant to represent the welcome and introduction step that characterises the +initial part of a typical on-site visit to a research laboratory [3]. +Subsequently, the researcher +puts on the VR helmet while a large screen shows to the group what he/she sees. At that point, +participants enter the detector for the first time together with the researcher. He/she moves in the +virtual environment by movements of the head, allowing to display the detector details and some +collisions between particles that have been selected by he/she. This allows to underline the most +important aspects of the experiment and to visualise what researchers described in the first part of +the activity. This is the moment in which students access the researcher’s work environment, and +begin to look at it through his/her eyes and his/her emotion. At this point students in turn put +on the helmets, enter the detector in first person and explore the virtual space while a researcher +stays close to him/her to guide him/her and answer all his/her questions and curiosities. Usually, +we dedicate from two to three researchers in the activity, so that we can carry on this phase using +up to three VR parallel stations. +2 + +Figure 1: Snapshot of a simulated event into the Belle2VR application. +In the meantime, the rest of the group watches their classmate while living the experience and +follows the discussion with the researcher. +3 +Collection of data and results +Once the activity design was completed, we tested it with students of different ages and schools. +To do this, we first involved some of the teachers already used to work with us in testing, discussing +and optimising innovative activities. Together with them, we selected 7 groups of students (one +for each teacher) from different schools: 2 classes of the fifth and final year of high school (17-18 +years old), 2 classes of the fourth year (16-17 years old), 1 class of the third year (15-16 years +old) and 2 mixed groups of third, fourth and fifth year students. In this way, we had both groups +of students all very interested in learning more about physics (the two mixed groups) and typical +school classes where interested and non-interested students coexist. Regarding the school type, the +vast majority of participants attended the “Liceo Scientifico”, i.e. the Italian high school focused +on science subjects; only one mixed group of students attended the “Liceo Classico”, the Italian +high school focused on the humanities. After carrying out the activity with the students in the +presence of their teachers, we asked the latter to talk with their class to get their impressions on +our proposal. Later, we carried out open interviews with all participating teachers separately. +3.1 +Results +In general, the activity was very positively received by both teachers and students. In fact, 5 out +of 7 teachers told us that their students voted 5 out of 5 and 2 out of 7 teachers told us their +students voted 4 out of 5 to the activity from a general point of view. The teachers’ score was also +very positive, as 6 out of 7 teachers voted 5 out of 5 and 1 teacher voted 4 out of 5. At this point, +we asked for more details on their vote. Specifically, we first asked them what they particularly +liked about the activity. Three of them told us that they enjoyed the use of VR technology; one +teacher stated that the strength of the activity lays in the possibility of getting inside the particle +detector; another teacher appreciated the opportunity of “directly seeing” what it means doing +research with a particle accelerator; one teacher mentioned the possibility of bringing the world of +research closer to students; another teacher especially appreciated the clarity of the researchers who +carried out the activity. Then, we asked their opinion about the different phases of the activity. +The introductory part, realised using slides, was considered clear and well organised by all the +teachers. Two teachers also pointed out that some topics could be deepened, such as the concept +of interaction between particles and the mass-energy equivalence. The part of the activity that +makes use of Belle2VR has been defined by all teachers as interesting, fun and engaging. As for +the negative aspects of the activity, the majority of the teachers stated that they couldn’t find +any; the only elements raised by two teachers concerned the limited number of students that can +be involved and the role of some participants considered too passive. +Subsequently, we asked the teachers what objectives they think the activity was able to achieve. +Some answers concerned the possibility of understanding and visualising particle physics (one +teacher in particular stated that his students even understood the uncertainty principle thanks to +the activity). Other answers cited the possibility of inspiring curiosity and interest toward physics +and science, and of bringing students closer to the work of a physicist. At the end of the interview +we explicitly asked the teachers which class year is more suitable for the activity and if they would +3 + +CDC +TOPhave proposed the activity to other classes. The majority stated that the activity is suitable for +the final months of the fourth year or the fifth year (when Italian students have typically already +dealt with electromagnetism and a first introduction of quantum physics). Two teachers, however, +claimed that even third-year students can benefit from the activity, as it is fascinating and inspiring. +All the teachers claimed that they would surely recommend the activity to other classes. +4 +Discussion and conclusion +In this paper we presented an educational proposal addressed to high schools and realised at +our University that makes use of the VR technology to enter a physics research laboratory. The +activity aims to constitute an alternative proposal to on-site visits to research centres, which, +while particularly formative and enriching for students, are also very expensive in terms of time +and money. Our proposal retraces all the stages of an on-site visit [3]: welcoming and introduction; +entering into the laboratory or facility; interaction and discussion with the public. Throughout +the initiative, a fundamental role is played by the researchers who carry out the activity. In fact, +they not only guide the public in the laboratory (in our case piloting the Belle2VR application) +but also share their emotions and experiences with students, thus helping to paint a realistic +representation of their working environment. Following the discussion with a focus group of 7 high +school teachers who participated in the activity together with their classes, we can state that our +proposal was very well received by school and therefore we are strongly motivated to replicate it +with other school groups in the future. In fact, the teachers greatly appreciated the activity. They +underlined several aspects that this proposal manages to achieve: visualising and understanding +phenomena otherwise impossible to see such as those related to particle physics; spreading VR +technology; intriguing students about physics and science; giving participants a more realistic view +of the scientific research world and of the work of a scientist. All these elements contribute to +strengthening physics teaching and bringing students closer to STEM careers. The teachers also +helped us to identify some aspects we can work on to improve our activity: the limited number of +students that can be involved and the too passive role experienced by a small part of them. These +aspects seem to be easily overcome, for example adding more parallel VR stations, where more +students can virtually enter the experiment at the same time. +A very significant aspect of our proposal consists in the possibility of involving schools easily +in any place without them having to face high travel expenses or heavy time commitment. In +this sense, our initiative could provide a valuable example of a method to introduce a visit to a +research laboratory on a permanent basis in physics school curricula of all students, regardless of +their availability of financial resources and their geographical location. For this reason, we believe +that our proposal is worth being exported to other research centres or facilities, even in fields other +than particle physics. +Acknowledgements +This work was supported by the Italian Project ‘Piano Lauree Scientifiche’. We thank the teachers +and students who participated in our activity. +References +[1] Dimopoulos K, Koulaidis V, Int. J. of Learn. Ann. Rev. 12 (2006) 10 +http://dx.doi.org/10.18848/1447-9494/CGP/v12i10/48219 +[2] Italian National Indication, Ministry of Education, 2010 +https://www.istruzione.it/alternanza/allegati/NORMATIVA%20ASL/INDICAZIONI% +20NAZIONALI%20PER%20I%20LICEI.pdf +[3] Neresini F, Dimopoulos K, Kallfass M and Peters H P, Sci. Comm. 30 (2009) 506 +https://doi.org/10.1177%2F1075547009332650 +[4] Snˇetinov´a M and K´acovsk´y P 2019 J. Phys.: Conf. Ser. 1287 012049 +https://doi.org/10.1088/1742-6596/1287/1/012049 +[5] Soko�lowska D and Michelini M The Role of Laboratory Work in Improving Physics Teaching +and Learning (2018) Springer Cham +https://doi.org/10.1007/978-3-319-96184-2 +4 + +[6] Postiglione A and De Angelis I Phys. Educ. 56 (2021) 025019 +https://doi.org/10.1088/1361-6552/abcab4 +[7] Postiglione A and De Angelis I, Phys. Educ. 56 (2021) 025020 +https://doi.org/10.1088/1361-6552/abd1c4 +[8] Postiglione A, Il Nuovo Cimento 45 C(2022) 91 +http://dx.doi.org/10.1393/ncc/i2022-22091-x +[9] https://www.lngs.infn.it/en/educational +[10] http://www.srt.inaf.it/outreach/guided-tours-srt/ +[11] Ellis J (2000) https://doi.org/10.48550/arXiv.physics/0005021 +[12] Cecire K. (2011) DPF-2011 Conference +https://doi.org/10.48550/arXiv.1109.2559 +[13] Cecire K and Dower R, DPF2019 Conference(2019) +https://doi.org/10.48550/arXiv.1910.00522 +[14] De Angelis I, Postiglione A, La Franca F, Il Nuovo Cimento C 4-5 (2021) 162 +http://dx.doi.org/10.1393/ncc/i2021-21162-x +[15] Duer Z, Piilonen L and Glasson G, IEEE Comp. Graph. and App. 38 (2018) 3 33 +https://doi.org/10.1109/MCG.2018.032421652 +[16] Kou et al., Prog. Theor. Exp. Phys., 12 (2019) 123C01, 2019 +https://doi.org/10.1093/ptep/ptz106 +5 + diff --git a/HdAzT4oBgHgl3EQfjP3_/content/tmp_files/load_file.txt b/HdAzT4oBgHgl3EQfjP3_/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..6f1b15e40b4f2140cfadff8c9005cf6cb5ba5094 --- /dev/null +++ b/HdAzT4oBgHgl3EQfjP3_/content/tmp_files/load_file.txt @@ -0,0 +1,186 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf,len=185 +page_content='School visits to a physics research laboratory using virtual reality Ilaria De Angelis1,2, Antonio Budano2, Giacomo De Pietro2, Alberto Martini3 and Adriana Postiglione1,2 1Dipartimento di Matematica e Fisica, Universit`a degli Studi Roma Tre, Rome (Italy) 2INFN Sezione di Roma Tre, Rome (Italy) 3Deutsches Elektronen–Synchrotron, 22607 Hamburg (Germany) ilaria.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content='deangelis@uniroma3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content='it Abstract School visits to research laboratories or facilities represent a unique way to bring students closer to science and STEM (Science, Technology, Engineering and Mathematics) careers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' However, such visits can be very expensive for students and teachers, in terms of both time and money.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' In this paper, we present a possible alternative to on-site visits consisting in an activity addressed to high school students that makes use of a VR application to make them “enter” into a particle physics experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' This proposal can represent a valid way of guaranteeing a visit to a research centre for all schools, regardless of their social or geographical origin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' We describe the tests we carried out with a focus group of teachers and their students, and the obtained results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' Keywords: high school, particle physics, virtual reality, STEM careers, research centre 1 Introduction Guided visits to research centres or facilities certainly represent a peculiar element in a student’s high school career, since they allow direct contact with authentic conditions of scientific knowledge production processes [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' In the Italian National Indication guidelines on teaching [2], in fact, these visits are explicitly mentioned for physics, as they represent one of the means by which students reach their learning objectives at the end of their high school career.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' Experiencing some time in a research centre can indeed not only improve students’ knowledge of physics, but also lead to a clearer idea of what research in physics is about and eventually motivate some of them to consider a science profession [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' Therefore, these visits should become part of a scientific school curriculum, along with hands-on and practical activities [4–8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' In Italy, two examples of internationally renowned laboratories that organise visits addressed to school groups are the Laboratori Nazionali del Gran Sasso [9] and the Sardinia Radio Telescope [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' In Europe, CERN is one of the most active centres as regards proposals for schools [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' Worldwide, several research centres or facilities open their doors to schools.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' The participation of students and teachers to visits, however, although certainly meaningful, can be very expensive in terms of money and time, especially if the centres are located in places far from the school.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' For this reason, physics teachers often choose alternative activities to ensure contact with research organisations that do not require an on-site visit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' An example in this sense are the CERN International Masterclasses [12,13], which allow students to work from their schools on real particle physics data, and discuss the related analysis together with CERN researchers during a video-conference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' In this way, participants can virtually walk into a scientific central control room and get a glance of what they would see entering CERN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' The advantages of initiatives of this kind are manifold, from becoming aware of the frontiers of scientific research, to actively working on real data, to coming into contact with an international research environment [14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' On the other hand, however, the contact with the laboratory is only provided by the video-conferences that generally involve many students’ groups at the same time [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' In this context, we worked to develop a third way, alternative to both face-to-face visits and masterclass-type initiatives, through which a student can experience the world of a scientific research laboratory up close.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' Our approach makes use of Virtual Reality (VR) technology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' To do this, we chose the context of particle physics, in particular the Belle II 1 arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content='01515v1 [physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content='ed-ph] 4 Jan 2023 collaboration, for which an advanced VR application was developed [14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' The remaining paper is organised as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' In section 2 we describe the activity we developed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' In section 3 we illustrate the public we reached, including both students and teachers, and the feedback we received and in section 4 we present our conclusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' 2 The educational proposal We have chosen to organise a virtual visit to an international laboratory which is however very difficult and expensive to reach for Italian school groups, since it is located in Japan (much further away than Laboratori Nazionali del Gran Sasso or CERN).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' In fact, our educational proposal for schools initiated from the VR application Belle2VR [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' Having realised the potential of Belle2VR application, we soon started to use it with the public during some outreach events such as science festivals or public events organised at the University.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' In these cases, visitors were given the possibility to wear the VR helmet while the researchers used joysticks to guide them to discover the experiment, as in a real guided visit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' After a few years of experience in science festivals and open events to which thousands of people participated, including many school students, that provided us very positive feedback, we have decided to propose a more structured activity to schools.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content='1 Belle2VR Developed by Virginia Tech, the application Belle2VR allows users to virtually enter the particle physics detector of the Belle II experiment [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' The Belle II experiment is currently carried out at the KEK in Tsukuba, Japan, and it studies the properties of heavy quarks and leptons to search for an evidence of new physics phenomena, from the matter-antimatter asymmetry problem to the existence of dark matter particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' Belle2VR reconstructs the interior of the detector and allows to visualise realistic simulations of particles interacting with each other and with the detector elements (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' The user can navigate through the detector and its components and can also manage the time evolution of the interaction by going back and forth or stopping the Developed by Virginia Tech, the application Belle2VR allows users to virtually enter the particle physics detector of the Belle II experiment [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' The Belle II experiment is currently carried out at the KEK in Tsukuba, Japan, and it studies the properties of heavy quarks and leptons to search for an evidence of new physics phenomena, from the matter-antimatter asymmetry problem to the existence of dark matter particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' Belle2VR reconstructs the interior of the detector and allows to visualise realistic simulations of particles interacting with each other and with the detector elements (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' The user can navigate through the detector and its components and can also manage the time evolution of the interaction by going back and forth or stopping the motion of particles at a specific time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' Belle2VR, therefore, allows to explore particle physics phenomena from a unique point of view.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content='2 Activity structure We built an activity addressed to high school class groups, lasting about an hour and a half, that can be carried out in a dedicated University room, or directly in the classroom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' It starts with a theoretical introduction that makes use of slides.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' Here, some basic topics and concepts typically treated at school are recalled, such as electromagnetism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' At the same time, more recent contents are also presented, such as the Standard Model, the cross section or the decay of particles, which require the use of quantum physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' The Belle II experiment is also presented in terms of its components and physics goal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' This phase is meant to represent the welcome and introduction step that characterises the initial part of a typical on-site visit to a research laboratory [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' Subsequently, the researcher puts on the VR helmet while a large screen shows to the group what he/she sees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' At that point, participants enter the detector for the first time together with the researcher.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' He/she moves in the virtual environment by movements of the head, allowing to display the detector details and some collisions between particles that have been selected by he/she.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' This allows to underline the most important aspects of the experiment and to visualise what researchers described in the first part of the activity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' This is the moment in which students access the researcher’s work environment, and begin to look at it through his/her eyes and his/her emotion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' At this point students in turn put on the helmets, enter the detector in first person and explore the virtual space while a researcher stays close to him/her to guide him/her and answer all his/her questions and curiosities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' Usually, we dedicate from two to three researchers in the activity, so that we can carry on this phase using up to three VR parallel stations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' 2 Figure 1: Snapshot of a simulated event into the Belle2VR application.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' In the meantime, the rest of the group watches their classmate while living the experience and follows the discussion with the researcher.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' 3 Collection of data and results Once the activity design was completed, we tested it with students of different ages and schools.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' To do this, we first involved some of the teachers already used to work with us in testing, discussing and optimising innovative activities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' Together with them, we selected 7 groups of students (one for each teacher) from different schools: 2 classes of the fifth and final year of high school (17-18 years old), 2 classes of the fourth year (16-17 years old), 1 class of the third year (15-16 years old) and 2 mixed groups of third, fourth and fifth year students.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' In this way, we had both groups of students all very interested in learning more about physics (the two mixed groups) and typical school classes where interested and non-interested students coexist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' Regarding the school type, the vast majority of participants attended the “Liceo Scientifico”, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' the Italian high school focused on science subjects;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' only one mixed group of students attended the “Liceo Classico”, the Italian high school focused on the humanities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' After carrying out the activity with the students in the presence of their teachers, we asked the latter to talk with their class to get their impressions on our proposal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' Later, we carried out open interviews with all participating teachers separately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content='1 Results In general, the activity was very positively received by both teachers and students.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' In fact, 5 out of 7 teachers told us that their students voted 5 out of 5 and 2 out of 7 teachers told us their students voted 4 out of 5 to the activity from a general point of view.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' The teachers’ score was also very positive, as 6 out of 7 teachers voted 5 out of 5 and 1 teacher voted 4 out of 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' At this point, we asked for more details on their vote.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' Specifically, we first asked them what they particularly liked about the activity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' Three of them told us that they enjoyed the use of VR technology;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' one teacher stated that the strength of the activity lays in the possibility of getting inside the particle detector;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' another teacher appreciated the opportunity of “directly seeing” what it means doing research with a particle accelerator;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' one teacher mentioned the possibility of bringing the world of research closer to students;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' another teacher especially appreciated the clarity of the researchers who carried out the activity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' Then, we asked their opinion about the different phases of the activity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' The introductory part, realised using slides, was considered clear and well organised by all the teachers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' Two teachers also pointed out that some topics could be deepened, such as the concept of interaction between particles and the mass-energy equivalence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' The part of the activity that makes use of Belle2VR has been defined by all teachers as interesting, fun and engaging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' As for the negative aspects of the activity, the majority of the teachers stated that they couldn’t find any;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' the only elements raised by two teachers concerned the limited number of students that can be involved and the role of some participants considered too passive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' Subsequently, we asked the teachers what objectives they think the activity was able to achieve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' Some answers concerned the possibility of understanding and visualising particle physics (one teacher in particular stated that his students even understood the uncertainty principle thanks to the activity).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' Other answers cited the possibility of inspiring curiosity and interest toward physics and science, and of bringing students closer to the work of a physicist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' At the end of the interview we explicitly asked the teachers which class year is more suitable for the activity and if they would 3 CDC TOPhave proposed the activity to other classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' The majority stated that the activity is suitable for the final months of the fourth year or the fifth year (when Italian students have typically already dealt with electromagnetism and a first introduction of quantum physics).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' Two teachers, however, claimed that even third-year students can benefit from the activity, as it is fascinating and inspiring.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' All the teachers claimed that they would surely recommend the activity to other classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' 4 Discussion and conclusion In this paper we presented an educational proposal addressed to high schools and realised at our University that makes use of the VR technology to enter a physics research laboratory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' The activity aims to constitute an alternative proposal to on-site visits to research centres, which, while particularly formative and enriching for students, are also very expensive in terms of time and money.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' Our proposal retraces all the stages of an on-site visit [3]: welcoming and introduction;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' entering into the laboratory or facility;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' interaction and discussion with the public.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' Throughout the initiative, a fundamental role is played by the researchers who carry out the activity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' In fact, they not only guide the public in the laboratory (in our case piloting the Belle2VR application) but also share their emotions and experiences with students, thus helping to paint a realistic representation of their working environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' Following the discussion with a focus group of 7 high school teachers who participated in the activity together with their classes, we can state that our proposal was very well received by school and therefore we are strongly motivated to replicate it with other school groups in the future.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' In fact, the teachers greatly appreciated the activity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' They underlined several aspects that this proposal manages to achieve: visualising and understanding phenomena otherwise impossible to see such as those related to particle physics;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' spreading VR technology;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' intriguing students about physics and science;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' giving participants a more realistic view of the scientific research world and of the work of a scientist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' All these elements contribute to strengthening physics teaching and bringing students closer to STEM careers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' The teachers also helped us to identify some aspects we can work on to improve our activity: the limited number of students that can be involved and the too passive role experienced by a small part of them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' These aspects seem to be easily overcome, for example adding more parallel VR stations, where more students can virtually enter the experiment at the same time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' A very significant aspect of our proposal consists in the possibility of involving schools easily in any place without them having to face high travel expenses or heavy time commitment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' In this sense, our initiative could provide a valuable example of a method to introduce a visit to a research laboratory on a permanent basis in physics school curricula of all students, regardless of their availability of financial resources and their geographical location.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' For this reason, we believe that our proposal is worth being exported to other research centres or facilities, even in fields other than particle physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' Acknowledgements This work was supported by the Italian Project ‘Piano Lauree Scientifiche’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' We thank the teachers and students who participated in our activity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' References [1] Dimopoulos K, Koulaidis V, Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' of Learn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' Ann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' 12 (2006) 10 http://dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content='doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content='18848/1447-9494/CGP/v12i10/48219 [2] Italian National Indication, Ministry of Education, 2010 https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content='istruzione.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content='it/alternanza/allegati/NORMATIVA%20ASL/INDICAZIONI% 20NAZIONALI%20PER%20I%20LICEI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content='pdf [3] Neresini F, Dimopoulos K, Kallfass M and Peters H P, Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' Comm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' 30 (2009) 506 https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content='1177%2F1075547009332650 [4] Snˇetinov´a M and K´acovsk´y P 2019 J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' : Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' Ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' 1287 012049 https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content='1088/1742-6596/1287/1/012049 [5] Soko�lowska D and Michelini M The Role of Laboratory Work in Improving Physics Teaching and Learning (2018) Springer Cham https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content='1007/978-3-319-96184-2 4 [6] Postiglione A and De Angelis I Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' Educ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' 56 (2021) 025019 https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content='1088/1361-6552/abcab4 [7] Postiglione A and De Angelis I, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' Educ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' 56 (2021) 025020 https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content='1088/1361-6552/abd1c4 [8] Postiglione A, Il Nuovo Cimento 45 C(2022) 91 http://dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content='doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content='1393/ncc/i2022-22091-x [9] https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content='lngs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content='infn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content='it/en/educational [10] http://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content='srt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content='inaf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content='it/outreach/guided-tours-srt/ [11] Ellis J (2000) https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content='48550/arXiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content='physics/0005021 [12] Cecire K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' (2011) DPF-2011 Conference https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content='48550/arXiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content='1109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content='2559 [13] Cecire K and Dower R, DPF2019 Conference(2019) https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content='48550/arXiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content='1910.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content='00522 [14] De Angelis I, Postiglione A, La Franca F, Il Nuovo Cimento C 4-5 (2021) 162 http://dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content='doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content='1393/ncc/i2021-21162-x [15] Duer Z, Piilonen L and Glasson G, IEEE Comp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' Graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' and App.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' 38 (2018) 3 33 https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content='1109/MCG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content='2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content='032421652 [16] Kou et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=', Prog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' Theor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' Exp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content=', 12 (2019) 123C01, 2019 https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} +page_content='1093/ptep/ptz106 5' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdAzT4oBgHgl3EQfjP3_/content/2301.01515v1.pdf'} diff --git a/INE1T4oBgHgl3EQfFwM8/content/tmp_files/2301.02905v1.pdf.txt b/INE1T4oBgHgl3EQfFwM8/content/tmp_files/2301.02905v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..81f058c38e08ea717788db65304c69a328143077 --- /dev/null +++ b/INE1T4oBgHgl3EQfFwM8/content/tmp_files/2301.02905v1.pdf.txt @@ -0,0 +1,2817 @@ +REaaS: Enabling Adversarially Robust Downstream +Classifiers via Robust Encoder as a Service +Wenjie Qu1, Jinyuan Jia2, Neil Zhenqiang Gong3 +1 Huazhong University of Science and Technology, wen jie qu@outlook.com +2 University of Illinois Urbana-Champaign, jinyuan@illinois.edu +3 Duke University, neil.gong@duke.edu +Abstract—Encoder as a service is an emerging cloud service. +Specifically, a service provider first pre-trains an encoder (i.e., a +general-purpose feature extractor) via either supervised learning +or self-supervised learning and then deploys it as a cloud service +API. A client queries the cloud service API to obtain feature +vectors for its training/testing inputs when training/testing its +classifier (called downstream classifier). A downstream classifier +is vulnerable to adversarial examples, which are testing inputs +with carefully crafted perturbation that the downstream classifier +misclassifies. Therefore, in safety and security critical applications, +a client aims to build a robust downstream classifier and certify +its robustness guarantees against adversarial examples. +What APIs should the cloud service provide, such that a +client can use any certification method to certify the robustness +of its downstream classifier against adversarial examples while +minimizing the number of queries to the APIs? How can a service +provider pre-train an encoder such that clients can build more +certifiably robust downstream classifiers? We aim to answer the +two questions in this work. For the first question, we show that +the cloud service only needs to provide two APIs, which we +carefully design, to enable a client to certify the robustness of +its downstream classifier with a minimal number of queries to +the APIs. For the second question, we show that an encoder pre- +trained using a spectral-norm regularization term enables clients +to build more robust downstream classifiers. +I. +INTRODUCTION +In an encoder as a service, a service provider (e.g., OpenAI, +Google, and Amazon) pre-trains a general-purpose feature +extractor (called encoder) and deploys it as a cloud service; +and a client queries the cloud service APIs for the feature +vectors of its training/testing inputs when training/testing a +downstream classifier. For instance, the encoder could be pre- +trained using supervised learning on a large amount of labeled +data or self-supervised learning [1], [2] on a large amount of +unlabeled data. A client could be a smartphone, IoT device, +self-driving car, or edge device in the era of edge computing. +Encoder as a service has been widely deployed by industry, e.g., +OpenAI’s GPT-3 API [3] and Clarifai’s General Embedding +API [4]. In the Standard Encoder as a Service (SEaaS), the +service provides a single API (called Feature-API) for clients +Wenjie Qu performed this research when he was an intern in Gong’s group. +and the encoder is pre-trained without taking the robustness +of downstream classifiers into consideration. A client sends its +training/testing inputs to the Feature-API, which returns their +feature vectors to the client. +A downstream classifier is vulnerable to adversarial exam- +ples [5], [6]. Suppose a testing input is correctly classified by the +downstream classifier. An attacker adds a small carefully crafted +perturbation to the testing input to induce misclassification. +Such testing input with carefully crafted perturbation is called +an adversarial example. Therefore, in security and safety +critical applications such as user authentication and traffic sign +recognition, a client desires to build a downstream classifier +robust against adversarial examples. Many methods have +been developed for an attacker to craft adversarial examples +and the community keeps developing new, stronger ones. +Therefore, instead of defending against a specific class of +adversarial examples, a client aims to defend against all +bounded adversarial perturbations via building a certifiably +robust downstream classifier. A classifier is certifiably robust if +its predicted label for a testing input is unaffected by arbitrary +perturbation added to the testing input once its size (measured +by ℓ2-norm in this work) is less than a threshold, which is +known as certified radius. A larger certified radius indicates +better certified robustness against adversarial examples. +In general, there are two categories of complementary +methods to build a certifiably robust classifier and derive +its certified radius for a testing input, i.e., base classifier +(BC) based certification [7], [8], [9], [10] and smoothed +classifier (SC) based certification (also known as randomized +smoothing) [11], [12], [13]. BC based certification aims to +directly derive the certified radius of a given classifier (called +base classifier) for a testing input. BC based certification +requires white-box access to the base classifier as it often +requires propagating the perturbation from the input layer to +the output layer of the base classifier layer by layer. SC based +certification first builds a smoothed classifier based on the +base classifier via adding random noise (e.g., Gaussian noise) +to a testing input and then derives the certified radius of the +smoothed classifier for the testing input. To increase the testing +inputs’ certified radii, SC based certification often requires +training the base classifier using training inputs with random +noise. Moreover, to derive the predicted label and certified +radius for a testing input, SC based certification requires the +base classifier to predict the labels of multiple noisy versions +of the testing input. +SEaaS faces three challenges when a client aims to build a +certifiably robust downstream classifier and derive its certified +Network and Distributed System Security (NDSS) Symposium 2023 +28 February - 4 March 2023, San Diego, CA, USA +ISBN 1-891562-83-5 +https://dx.doi.org/10.14722/ndss.2023.24444 +www.ndss-symposium.org +arXiv:2301.02905v1 [cs.CR] 7 Jan 2023 + +SEaaS +REaaS +Feature-API +Feature-API +F2IPerturb-API +[0.1, ⋯, 0.2] +Cloud Server +Client +Client +Cloud Server +Encoder +Encoder +� +[0.1, ⋯, 0.2] +Downstream +Classifier +Step 1 +Step 2 +Step 3 +BC/SC +Fig. 1: SEaaS vs. REaaS. +radii for testing inputs. The first challenge is that a client +cannot use BC based certification. In particular, the composition +of the encoder and the client’s downstream classifier is the +base classifier that the client needs to certify in BC based +certification. However, the client does not have white-box +access to the encoder deployed on the cloud server, making +BC based certification not applicable. The second challenge +is that, although a client can use SC based certification by +treating the composition of the encoder and its downstream +classifier as a base classifier, it incurs a large communication +cost for the client and a large computation cost for the cloud +server. Specifically, the client needs to query the Feature-API +once for each noisy training input in each training epoch of +the downstream classifier because SC based certification trains +the base classifier using noisy training inputs. Therefore, the +client requires e queries to the Feature-API per training input, +where e is the number of epochs used to train the downstream +classifier. Moreover, to derive the predicted label and certified +radius for a testing input, SC based certification requires the +base classifier to predict the labels of N noisy testing inputs. +Therefore, the client requires N queries to the Feature-API +per testing input. Note that N is often a large number (e.g., +10,000) [13]. The large number of queries to the Feature- +API imply 1) large communication cost, which is intolerable +for resource-constrained clients such as smartphone and IoT +devices, and 2) large computation cost for the cloud server. +The third challenge is that SC based certification achieves +suboptimal certified radii. This is because the base classifier +is the composition of the encoder and a client’s downstream +classifier, but a client cannot train/fine-tune the encoder as it +is deployed on the cloud server. +Our work: We propose Robust Encoder as a Service (REaaS) +to address the three challenges of SEaaS. Figure 1 compares +SEaaS with REaaS. Our key idea is to provide another API +called F2IPerturb-API.1 A downstream classifier essentially +takes a feature vector as input and outputs a label. Our +F2IPerturb-API enables a client to treat its downstream classifier +alone as a base classifier and certify the robustness of its +base or smoothed downstream classifier in the feature space. +Specifically, a client performs three steps to derive the certified +radius of a testing input in REaaS. First, the client obtains the +feature vector of the testing input via querying the Feature-API. +Second, the client views its downstream classifier alone as a +base classifier and derives a feature-space certified radius RF +for the testing input using any BC/SC certification method. The +client’s base or smoothed downstream classifier predicts the +same label for the testing input if the ℓ2-norm of the adversarial +perturbation added to the testing input’s feature vector is less +1‘F’ stands for Feature and ‘I’ stands for Input. +than RF . Third, the client sends the testing input and its feature- +space certified radius RF to query the F2IPerturb-API, which +returns the corresponding input-space certified radius R to +the client. Our input-space certified radius R guarantees the +client’s base or smoothed downstream classifier predicts the +same label for the testing input if the ℓ2-norm of the adversarial +perturbation added to the testing input is less than R. +The key challenge of implementing our F2IPerturb-API is +how to find the largest input-space certified radius R for a +given testing input and its feature-space certified radius RF . +To address the challenge, we formulate finding the largest R +as an optimization problem, where the objective function is +to find the maximum R and the constraint is that the feature- +space perturbation is less than RF . However, the optimization +problem is challenging to solve due to the highly non-linear +constraint. To address the challenge, we propose a binary search +based solution. The key component of our solution is to check +whether the constraint is satisfied for a specific R in each +iteration of binary search. Towards this goal, we derive an +upper bound of the feature-space perturbation for a given R +and we treat the constraint satisfied if the upper bound is less +than RF . Our upper bound can be computed efficiently. +F2IPerturb-API addresses the first two challenges of SEaaS. +Specifically, BC based certification is applicable in REaaS. +Moreover, SC based certification requires much less queries to +the APIs in REaaS. Specifically, for any certification method, a +client only requires one query to Feature-API per training input +and two queries (one to Feature-API and one to F2IPerturb-API) +per testing input in our REaaS. +To address the third challenge of SEaaS, we propose a new +method to pre-train a robust encoder, so a client can derive +larger certified radii even though it cannot train/fine-tune the +encoder. Our method can be combined with standard supervised +learning or self-supervised learning to enhance the robustness of +a pre-trained encoder. An encoder is more robust if it produces +more similar feature vectors for an input and its adversarially +perturbed version. Our key idea is to derive an upper bound for +the Euclidean distance between the feature vectors of an input +and its adversarial version, where our upper bound is a product +of a spectral-norm term and the perturbation size. The spectral- +norm term depends on the parameters of the encoder, but it +does not depend on the input nor the adversarial perturbation. +An encoder with a smaller spectral-norm term may produce +more similar feature vectors for an input and its adversarial +version. Thus, we use the spectral-norm term as a regularization +term to regularize the pre-training of an encoder. +We perform a systematic evaluation on multiple datasets +including CIFAR10, SVHN, STL10, and Tiny-ImageNet. Our +2 + +evaluation results show that REaaS addresses the three chal- +lenges of SEaaS. First, REaaS makes BC based certification ap- +plicable. Second, REaaS incurs orders of magnitude less queries +to the cloud service than SEaaS for SC based certification. For +instance, REaaS reduces the number of queries to the cloud +service APIs respectively by 25× and 5, 000× per training and +testing input when a client trains its downstream classifier for +e = 25 epochs and uses N = 10, 000 for certification. Third, +in the framework of REaaS, our robust pre-training method +achieves larger average certified radius (ACR) for the testing +inputs than existing methods to pre-train encoders for both BC +and SC based certification. For instance, when the encoder is +pre-trained on Tiny-ImageNet and the downstream classifier is +trained on SVHN, the ACRs for MoCo (a standard non-robust +self-supervised learning method) [1], RoCL (an adversarial +training based state-of-the-art robust self-supervised learning +method) [14], and our method are respectively 0.011, 0.014, +and 0.275 when a client uses SC based certification. +In summary, we make the following contributions: +• +We propose REaaS, which enables a client to build +a certifiably robust downstream classifier and derive +its certified radii using any certification method with a +minimal number of queries to the cloud service. +• +We propose a method to implement F2IPerturb-API. +• +We propose a spectral-norm term to regularize the +pre-training of a robust encoder. +• +We extensively evaluate REaaS and compare it with +SEaaS on multiple datasets. +II. +RELATED WORK +A. Adversarial Examples +We discuss adversarial examples [5], [15] in the context of +encoder as a service. We denote by f a pre-trained encoder +and g a downstream classifier. Given a testing input x, the +encoder outputs a feature vector for it, while the downstream +classifier takes the feature vector as input and outputs a label. +For simplicity, we denote by f(x) the feature vector and g◦f(x) +the predicted label for x, where ◦ represents the composition +of the encoder and downstream classifier. In an adversarial +example, an attacker adds a carefully crafted small perturbation +δ to x such that its predicted label changes, i.e., g ◦f(x+δ) ̸= +g ◦ f(x). The carefully perturbed input x + δ is called an +adversarial example. Many methods (e.g., [5], [6], [16]) have +been proposed to find an adversarial perturbation δ for a given +input x. In our work, we focus on certified defenses, which +aim to defend against any bounded adversarial perturbations +no matter how they are found. Therefore, we omit the details +on how an attacker can find an adversarial perturbation. +B. Certifying Robustness of a Classifier +Definition of certified radius: A classifier is certifiably robust +against adversarial examples if its predicted label for an input +is unaffected by any perturbation once its size is bounded [7], +[12], [13]. Formally, a classifier h is certifiably robust if we +have the following guarantee for an input x: +h(x + δ) = h(x), ∀ ∥δ∥2 < R, +(1) +where R is known as certified radius. Note that certified radius +R may be different for different inputs x, but we omit the +explicit dependency on x in the notation for simplicity. +A certification method against adversarial examples aims +to build a certifiably robust classifier and derive its certified +radius R for any input x. There are two general categories +of certification methods, i.e., base classifier (BC) based +certification [7], [8], [9], [10] and smoothed classifier (SC) +based certification [11], [12], [13]. Both categories of methods +may be adopted in different scenarios depending on certification +needs. On one hand, BC based certification often produces +deterministic guarantees (i.e., the derived certified radius is +absolutely correct), while SC based certification often provides +probabilistic guarantees (i.e., the derived certified radius may +be incorrect with a small error probability). On the other hand, +SC based certification often derives a larger certified radius +than BC based certification due to its probabilistic guarantees. +Base classifier (BC) based certification: +BC based certi- +fication aims to directly derive the certified radius R of a +given classifier (called base classifier) for an input x. These +methods often propagate perturbation from the input x to +the output of the base classifier layer by layer in order to +derive the certified radius. Therefore, they require white-box +access to the base classifier. Suppose F is a base classifier +that maps an input x to one of c classes {1, 2, · · · , c}. We use +H(x) to denote the base classifier’s last-layer output vector +for x, where Hl(x) represents the lth entry of H(x) and +l = 1, 2, · · · , c. F(x) denotes the predicted label for x, i.e., +F(x) = argmaxl=1,2,··· ,c Hl(x). Next, we overview how to +derive the certified radius R using CROWN [9], a state-of-the- +art BC based certification method. CROWN shows that each +entry Hl(x) can be bounded by two linear functions HL +l (x) and +HU +l (x). Suppose the base classifier predicts label y for x when +there is no adversarial perturbation, i.e., F(x) = y. CROWN +finds the largest r such that the lower bound of the yth entry +(i.e., min∥δ∥2 β do +ρk = ρL+ρU +2 +for i = 1, 2, · · · , d do +f L +i , f U +i ← CROWN(i, x, f) +Li = min∥δ∥2≤ρk f L +i (x + δ) − fi(x) +Ui = max∥δ∥2≤ρk f U +i (x + δ) − fi(x) +end for +R′ +F = +√︂∑︁d +i=1 max(L2 +i , U 2 +i ) +if R′ +F < RF then +ρL = ρk +else +ρU = ρk +end if +end while +return ρL +where f is an encoder and δ is an adversarial perturbation. +However, the optimization problem is challenging to solve +because the constraint is highly non-linear when the encoder is +a complex neural network. To address the challenge, we propose +a binary search based method to solve R in the optimization +problem. In particular, we search in the range [ρL +k , ρU +k ] in the +kth round of binary search, where we set ρL +1 to be 0 and ρU +1 +to be a large value (e.g., 10 in our experiments) in the first +round. Moreover, we denote ρk = ρL +k +ρU +k +2 +for simplicity. In the +kth round, we check whether r = ρk satisfies the constraint in +Equation (4). If the constraint is satisfied, then we can search +the range [ρk, ρU +k ] in the (k + 1)th round, i.e., ρL +k+1 = ρk and +ρU +k+1 = ρU +k . Otherwise, we search the range [ρL +k , ρk] in the +(k + 1)th round, i.e., ρL +k+1 = ρL +k and ρU +k+1 = ρk. We stop the +binary search when ρU +k − ρL +k ≤ β and treat ρL +k as R, where β +is a parameter characterizing the binary-search precision. +Our binary search based solution faces a key challenge, +i.e., how to check whether r = ρk satisfies the constraint +in Equation (4). Our key idea to address the challenge is to +derive an upper bound for the left hand side of the constraint +(i.e., max∥δ∥2<ρk ∥f(x + δ) − f(x)∥2) and decide that the +constraint is satisfied if the upper bound is smaller than RF , +where the upper bound can be efficiently computed for any ρk. +Suppose the encoder f maps an input x to a d-dimensional +feature vector f(x), where fi(x) represents the ith entry of +f(x). An encoder f is essentially a deep neural network. +Therefore, according to CROWN [9], we have the following +lower bound and upper bound for fi(x + δ) when ∥δ∥2 < ρk: +min +∥δ∥2<ρk f L +i (x + δ) ≤ fi(x + δ) ≤ +max +∥δ∥2<ρk f U +i (x + δ), +(5) +where f L +i +and f U +i +are two linear functions and i += +1, 2, · · · , d. In Appendix D, we show that Equation 5 is tight +when f consists of one linear layer. As min∥δ∥2≤ρk f L +i (x + +δ) ≤ min∥δ∥2<ρk f L +i (x + δ) and max∥δ∥2<ρk f U +i (x + δ) ≤ +max∥δ∥2≤ρk f U +i (x+δ), we have the following when ∥δ∥2 < ρk: +min +∥δ∥2≤ρk f L +i (x + δ) ≤ fi(x + δ) ≤ +max +∥δ∥2≤ρk f U +i (x + δ), +(6) +Therefore, we have the following inequalities for ∀ ∥δ∥2 < ρk: +fi(x + δ) − fi(x) ≥ Li, +(7) +fi(x + δ) − fi(x) ≤ Ui, +(8) +where Li += min∥δ∥2≤ρk f L +i (x + δ) − fi(x) and Ui += +max∥δ∥2≤ρk f U +i (x + δ) − fi(x). +Based on the above two +inequalities, we have the following: +max +∥δ∥2<ρk(fi(x + δ) − fi(x))2 ≤ max(L2 +i , U 2 +i ). +(9) +Therefore, +we +can +derive +an +upper +bound +for +max∥δ∥2<ρk ∥f(x + δ) − f(x)∥2 as follows: +max +∥δ∥2<ρk ∥f(x + δ) − f(x)∥2 +(10) +≤ +⌜ +⃓ +⃓ +⎷ +d +∑︂ +i=1 +max +∥δ∥2<ρk(fi(x + δ) − fi(x))2 +(11) +≤ +⌜ +⃓ +⃓ +⎷ +d +∑︂ +i=1 +max(L2 +i , U 2 +i ) +(12) +≜R′ +F . +(13) +If the upper bound R′ +F is smaller than RF , then we have r = ρk +satisfies the constraint in Equation (4). We note that r = ρk +may also satisfy the constraint even if the upper bound R′ +F is +no smaller than RF . However, such cases do not influence the +correctness of our binary search. Note that min∥δ∥2≤ρk f L +i (x + +δ) and max∥δ∥2≤ρk f U +i (x + δ) have closed-form solutions for +i = 1, 2, · · · , d [9]. Therefore, Li, Ui, and the upper bound R′ +F +can be computed efficiently. In other words, we can efficiently +check whether r = ρk satisfies the constraint in Equation (4) +for any ρk. Algorithm 1 shows our F2IPerturb-API, where the +function CROWN obtains the lower bound and upper bound +linear functions for each fi(x). +Our binary search based solution correctly finds a lower +bound of the optimal R of the optimization problem in Equa- +tion (3) because the constraint in Equation (4) is guaranteed to +be satisfied in each round of our binary search. +Image rescaling: We note that, in our above discussion on +the two APIs, a client’s input image size is the same as +the input size of the cloud server’s encoder. When the size +of a client’s input image is different, the cloud server can +rescale it to be the input size of its encoder using the standard +bilinear interpolation. The bilinear interpolation can be viewed +as a linear transformation. In particular, suppose xb and xa +respectively represent the image before and after rescaling. +Then, we have xa = W · xb, where W is the matrix used +to represent the linear transformation. The cloud server can +implement this linear transformation (i.e., rescaling) by adding +a linear layer whose weight matrix is W before the encoder. +Moreover, the cloud server can view the linear layer + the +encoder as a “new” encoder to implement the two APIs. +6 + +C. Pre-training Robust Encoder +Our REaaS is applicable to any encoder. However, a more +robust encoder enables a client to derive a larger certified radius +for its testing input. Therefore, we further propose a method +to pre-train robust encoders. An encoder f is more robust if +it produces more similar feature vectors for an input and its +adversarially perturbed version, i.e., if f(x + δ) and f(x) are +more similar. In particular, based on our implementation of +the F2IPerturb-API, if ∥f(x + δ) − f(x)∥2 is smaller for any +adversarial perturbation δ, then F2IPerturb-API would return +a larger input-space certified radius to a client for a given +feature-space certified radius. Therefore, our key idea is to +reduce ∥f(x + δ) − f(x)∥2 when pre-training an encoder f. +Next, we derive an upper bound of ∥f(x + δ) − f(x)∥2, based +on which we design a regularization term to regularize the +pre-training of an encoder. +A neural network (e.g., an encoder) can often be de- +composed into the composition of a series of linear trans- +formations [5]. In particular, we can do so if each layer +of the neural network (e.g., linear layer, convolutional layer, +and batch normalization layer) can be expressed as a linear +transformation. We denote an encoder as the composition of n +linear transformations, i.e., f(·) = T n ◦ T n−1 ◦ · · · ◦ T 1(·). [5] +showed that the difference between the outputs of any neural +network f (f is an encoder in our case) for an input and its +adversarially perturbed version can be bounded as follows: +∥f(x + δ) − f(x)∥2 ≤ +n +∏︂ +j=1 +⃦⃦T j⃦⃦ +s · ∥δ∥2 , +(14) +where x is an input, δ is an adversarial perturbation, and ∥·∥s +represents spectral norm. The product of the spectral norms of +the n linear transformations (i.e., ∏︁n +j=1 +⃦⃦T j⃦⃦ +s) is independent +with input x and adversarial perturbation δ. Therefore, our idea +is to add ∏︁n +j=1 +⃦⃦T j⃦⃦ +s as a regularization term (called spectral- +norm regularization) when pre-training an encoder. Minimizing +such regularization term may enforce the encoder to produce +more similar feature vectors for an input and its adversarially +perturbed version, i.e., ∥f(x + δ) − f(x)∥2 may be smaller. In +particular, we minimize the following loss function for each +mini-batch of inputs when pre-training an encoder: +1 +m · +m +∑︂ +i=1 +ℓ(i) + λ · +n +∏︂ +j=1 +⃦⃦T j⃦⃦ +s , +(15) +where ℓ(i) is a loss for a training input in pre-training, m +is batch size, and λ is a hyper-parameter used to balance the +two terms. For instance, when using supervised learning to +train a classifier, whose layers excluding the output layer are +used as an encoder, the loss ℓ(i) is often the cross-entropy loss; +when using self-supervised learning algorithm MoCo [1] to +pre-train an encoder, ℓ(i) is defined in Equation (2). We adopt +the power method [21] to estimate the spectral norms of the +linear transformations when pre-training an encoder. +D. Certifying Robustness for a Client +In REaaS, a client can treat its own downstream classifier +as a base classifier. We discuss how a client can use our +two APIs to train a base downstream classifier and derive +the certified radius of the base downstream classifier in BC +TABLE I: Comparing the communication and computation +cost per training/testing input in SEaaS and REaaS. e is +the number of epochs used to train a base downstream +classifier. N is the number of noisy inputs per testing input +in SC. Tf (or Tg) and Mf (or Mg) are respectively the +number of layers and the maximum number of neurons +in a layer in an encoder (or a downstream classifier). Kf +(or Kg) is the number of parameters in an encoder (or a +downstream classifier). +(a) Communication cost +Service +#Queries +Per training input Per testing input +BC +SC +BC +SC +SEaaS N/A +e +N/A +N +REaaS +1 +2 +(b) Computation cost +Service Entity +Computational complexity +Per training input +Per testing input +BC +SC +BC +SC +SEaaS +Cloud +server +N/A +O(e · Kf ) +N/A +O(N · Kf ) +Client +O(e · Kg) +O(N · Kg) +REaaS +Cloud +server +O(Kf ) +O(Kf ) +O(Kf + T 2 +f · M 3 +f ) O(Kf + T 2 +f · M 3 +f ) +Client O(e · Kg) O(e · Kg) O(Kg + T 2 +g · M 3 +g ) +O(N · Kg) +based certification or the smoothed downstream classifier in +SC based certification for a testing input. +BC based certification: When training a base downstream +classifier, a client queries the Feature-API to obtain a feature +vector for each training input. Then, given the feature vectors +and the corresponding training labels, the client can use any +training method (e.g., standard supervised learning) to train a +base downstream classifier. Given a testing input, the client +queries the Feature-API to obtain its feature vector and uses the +base downstream classifier to predict its label. Moreover, the +client can use any BC based certification method to derive a +feature-space certified radius for the testing input by treating its +feature vector as an “input” to the base downstream classifier. +Then, the client queries the F2IPerturb-API to transform the +feature-space certified radius to an input-space certified radius. +SC based certification: Similar to BC based certification, a +client queries the Feature-API to obtain a feature vector for +each training input when training a base downstream classifier. +However, unlike BC based certification, the client adds noise +to the training feature vectors in SC based certification. In +particular, the client adds random noise (e.g., Gaussian noise) to +each feature vector in each mini-batch of training feature vectors +in each training epoch. Note that the client does not need to +query the Feature-API again for the noisy feature vector. Given +a testing input, the client queries the Feature-API to obtain its +feature vector and uses the smoothed downstream classifier to +predict its label and derive its feature-space certified radius. +In particular, the client constructs N noisy feature vectors +by adding random noise to the feature vector and uses it’s +base downstream classifier to predict their labels. Based on +the predicted labels, the client can derive the predicted label +and feature-space certified radius for the original feature vector. +Then, the client queries the F2IPerturb-API to transform the +feature-space certified radius to an input-space certified radius. +7 + +E. Theoretical Communication and Computation Cost Analysis +Communication cost: +The number of queries to the APIs +characterizes the communication cost for a client and the cloud +server. In both BC and SC based certification, a client only +queries the Feature-API once for each training input in REaaS. +Therefore, the number of queries per training input is 1 in +REaaS. In both BC and SC based certification, a client only +queries the Feature-API and F2IPerturb-API once to derive +the predicted label and certified radius for a testing input. +Therefore, the number of queries per testing input is 2 in +REaaS. Note that the client only sends an image x to the cloud +server when querying the Feature-API, while it also sends +the feature-space certified radius Rf to the cloud server when +querying the F2IPerturb-API. However, Rf is a real number +whose communication cost is negligible, compared to that of +the image x. Thus, we consider querying Feature-API and +querying F2IPerturb-API have the same communication cost in +our analysis for simplicity. Table Ia compares the number +of queries per training/testing input in SEaaS and REaaS. +Compared with SEaaS, REaaS makes BC based certification +applicable and incurs a much smaller communication cost in +SC based certification. +Computation cost: +Table Ib compares the computational +complexity of REaaS and SEaaS for the cloud server and +a client. In both REaaS and SEaaS, the computation cost for +the cloud server to process a query to the Feature-API is linear +to the number of encoder parameters, i.e., O(Kf), where Kf +is the number of parameters in the encoder. In REaaS, we use +binary search to process a query to the F2IPerturb-API. Given +the initial search range [ρL +1 , ρU +1 ] and binary-search precision +β, the number of rounds of binary search is ⌈log2( ρU +1 −ρL +1 +β +)⌉. +In practice, we can set ρL +1 , ρU +1 , and β to be constants, e.g., +ρL +1 = 0, ρU +1 = 10, and β = 10−50, and thus ⌈log2( ρU +1 −ρL +1 +β +)⌉ +can be viewed as a constant. From [9], the computational +complexity is O(T 2 +f · M 3 +f ) in each round of binary search, +where Tf and Mf are respectively the number of layers and +the maximum number of neurons in a layer in an encoder. Thus, +the computational complexity for the cloud server to process a +query to the F2IPerturb-API is O(T 2 +f · M 3 +f ). +On the client side, the computational complexity of gradient +descent is O(Kg) for each training input per epoch when +training a base downstream classifier in both BC and SC +based certification, where Kg is the number of parameters +in the base downstream classifier. Therefore, the computational +complexity of training a base downstream classifier is O(e·Kg) +per training input, where e is the number of training epochs. The +computational complexity for a client to derive the feature-space +certified radius of a testing input is O(T 2 +g · M 3 +g ) in BC based +certification [9], where Tg and Mg are respectively the number +of layers and the maximum number of neurons in a layer in +the base downstream classifier. Moreover, the computational +complexity of using the base downstream classifier to predict +a label for a (noisy) feature vector is O(Kg). +As SEaaS does not support BC based certification, we focus +on comparing the computation cost of SEaaS and REaaS for +SC based certification. First, we observe that the computation +cost per training/testing input is the same for a client in SEaaS +and REaaS. Second, REaaS incurs a smaller computation cost +per training input for the cloud server than SEaaS, because +REaaS incurs much fewer queries than SEaaS. Third, REaaS +often incurs a smaller computation cost per testing input for the +cloud server than SEaaS, because N is often large to achieve +a large certified radius as shown in our experiments. +V. +EVALUATION +A. Experimental Setup +Datasets: We use CIFAR10 [22], SVHN [23], STL10 [24], +and Tiny-ImageNet [25] in our experiments. CIFAR10 has +50,000 training and 10,000 testing images from ten classes. +SVHN contains 73,257 training and 26,032 testing images from +ten classes. STL10 contains 5,000 training and 8,000 testing +images from ten classes, as well as 100,000 unlabeled images. +Tiny-ImageNet contains 100,000 training and 10,000 testing +images from 200 classes. +We rescale each image in all datasets to 32 × 32 by the +standard bi-linear interpolation. Therefore, the input image size +in a downstream dataset is the same as the input size of the pre- +trained encoder. However, we will also explicitly explore the +scenarios in which the input image size of a downstream dataset +is different from the input size of the pre-trained encoder. +Pre-training encoders: We use STL-10 and Tiny-ImageNet +as pre-training datasets to pre-train encoders. We adopt these +two datasets because they contain more images than CIFAR10 +and SVHN. In particular, we use the unlabeled data of STL10 +to pre-train an encoder when STL10 is used as a pre-training +dataset. When Tiny-ImageNet is used as a pre-training dataset, +we use its training dataset to pre-train an encoder. Unless +otherwise mentioned, we adopt MoCo [1] as the pre-training +algorithm in SEaaS, while we adopt MoCo with our spectral- +norm regularization as the pre-training algorithm in REaaS, +since they only need unlabeled data. Moreover, we adopt the +public implementation of MoCo [26] in our experiments. When +calculating the spectral norm of the encoder during pre-training, +we run 10 iterations of power iteration in each mini-batch. The +architecture of the encoder can be found in Table XIII in +Appendix. We pre-train an encoder for 500 epochs with a +learning rate 0.06 and a batch size 512. +Training downstream classifiers: As we have four datasets, +we use the other three datasets as downstream datasets when +a dataset is used as a pre-training dataset. Moreover, when a +dataset is used as a downstream dataset, we adopt its training +dataset as the downstream training dataset and testing dataset as +the downstream testing dataset. We use the downstream training +dataset to train a base downstream classifier. In particular, in +BC based certification, we use standard supervised learning to +train a base downstream classifier on the feature vectors of the +training inputs. We note that some works [27], [28] proposed +new methods to train a base classifier to improve its certified +robustness in BC based certification. These methods are also +applicable in our REaaS, but we do not evaluate them since our +focus is to show the applicability of BC based certification in +REaaS instead of its optimal certified robustness. For SC based +certification, we train a base downstream classifier via adding +Gaussian noise N(0, σ2I) to the training inputs in SEaaS and +the feature vectors of the training inputs in REaaS. +We use a fully connected neural network with two hidden +layers as a base downstream classifier. We respectively adopt +8 + +ReLU and Softmax as the activation functions in the two hidden +layers and the output layer. The number of neurons in both +hidden layers is 256. We train a base downstream classifier +for 25 epochs using cross-entropy loss, a learning rate of 0.06, +and a batch size of 512. +Certification methods: For BC based certification, we adopt +CROWN [9] to derive the certified radius of a base downstream +classifier for a testing input in REaaS. We adopt the public +implementation of CROWN [29]. For SC based certification, +we adopt Gaussian noise based randomized smoothing [13] to +build a smoothed classifier and derive its certified radius for +a testing input. In SEaaS, a client treats the composition of +the encoder and its downstream classifier as a base classifier, +while a client treats its downstream classifier alone as a base +classifier in REaaS. We use the public code [30] for Gaussian +noise based randomized smoothing. Appendix B and C show +the technical details of CROWN and Gaussian noise based +randomized smoothing, respectively. +Evaluation metrics: Recall that REaaS aims to achieve three +design goals. We can evaluate the generality goal by showing +that REaaS supports both BC and SC based certification. For +the efficiency goal, we use #Queries per training (or testing) +input to measure the communication cost between a client and +the cloud server. Moreover, we use running time per testing +input on the cloud server to measure its computation cost. We +do not consider running time on a client as it is the same in +SEaaS and REaaS. Note that #Queries per training input also +characterizes the computation cost per training input for the +cloud server as it is linear to the number of queries. For the +robustness goal, we use average certified radius (ACR) of the +correctly classified testing examples to measure the certified +robustness of a base or smoothed classifier. +Note that there often exists a trade-off between robustness +and accuracy for a classifier. Therefore, we further consider +accuracy under adversarial perturbation as an evaluation metric. +In particular, we consider the widely adopted certified accuracy +@ a perturbation size, which is the fraction of testing inputs +in a downstream testing dataset whose labels are correctly +predicted and whose certified radii are no smaller than the given +perturbation size. Certified accuracy @ a perturbation size is +the least testing accuracy that a classifier can achieve no matter +what adversarial perturbation is added to each testing input once +its ℓ2-norm is at most the given perturbation size. The certified +accuracy @ a perturbation size decreases as the perturbation +size increases. ACR is the area under the certified accuracy +vs. perturbation size curve (details are shown in Appendix A). +Therefore, ACR can also be viewed as a metric to measure +the robustness-accuracy trade-off of a classifier, where a larger +ACR indicates a better trade-off. +Parameter settings: F2IPerturb-API has the following three +parameters: ρL +1 and ρU +1 which specify the range of R in the +first round of binary search, and β which characterizes the +binary-search precision. We set ρL +1 to be 0 and set ρU +1 to be +10. Note that they do not impact experimental results once +ρL +1 is set to 0 and ρU +1 is set to a large value (e.g., 10). We +set the default value of β as 0.001. We note that β has a +negligible impact on certified accuracy and ACR. In particular, +the absolute difference between the certified accuracy (or ACR) +TABLE II: ACR and #Queries in SEaaS and REaaS. +(a) Pre-training dataset is Tiny-ImageNet +Service Certification +method +Downstre- +am dataset +ACR +#Queries +Per train- +ing input +Per test- +ing input +SEaaS +BC +CIFAR10 +N/A +SVHN +STL10 +SC +CIFAR10 +0.157 +25 +1 × 105 +SVHN +0.226 +STL10 +0.134 +REaaS +BC +CIFAR10 +0.138 +1 +2 +SVHN +0.258 +STL10 +0.090 +SC +CIFAR10 +0.171 +SVHN +0.275 +STL10 +0.143 +(b) Pre-training dataset is STL10 +Service Certification +method +Downstre- +am dataset +ACR +#Queries +Per train- +ing input +Per test- +ing input +SEaaS +BC +CIFAR10 +NA +SVHN +Tiny- +ImageNet +SC +CIFAR10 +0.155 +25 +1 × 105 +SVHN +0.244 +Tiny- +ImageNet +0.016 +REaaS +BC +CIFAR10 +0.139 +1 +2 +SVHN +0.272 +Tiny- +ImageNet +0.027 +SC +CIFAR10 +0.173 +SVHN +0.278 +Tiny- +ImageNet +0.033 +when β = 0.001 and that when β is an arbitrarily small value +(e.g., 10−50) is smaller than 0.001. +Randomized smoothing has the following three parameters: +the number of Gaussian noise N, standard deviation σ of +the Gaussian noise, and error probability α. Following prior +work [13], unless otherwise mentioned, we set N = 100, 000, +σ = 0.5, and α = 0.001. We set the default value of the +hyperparameter λ in our pre-training method as 0.00075. We +normalize pixel values to [0, 1]. +B. Experimental Results +We first show that REaaS achieves our three design goals, +but SEaaS does not. Then, we show the impact of relevant +factors on REaaS. In particular, we consider 1) different ways +to pre-train an encoder, 2) image scaling, and 3) different +hyperparameters of certification methods such as N, σ, and α +for randomized smoothing. Note that we fix all other parameters +to their default values when studying the impact of one +parameter on REaaS. +9 + +TABLE III: Comparing the running time per testing input +for the cloud server in SC for SEaaS and REaaS. The +pre-training dataset is Tiny-ImageNet. +Service Downstream +dataset +Running time (s) per testing input +SEaaS +CIFAR10 +73.77 +SVHN +72.65 +STL10 +73.48 +REaaS +CIFAR10 +1.05 +SVHN +1.06 +STL10 +1.04 +TABLE IV: Training without noise vs. training with +noise for SC in SEaaS. The pre-training dataset is Tiny- +ImageNet. +Downstream +dataset +ACR +Training with noise Training without noise +CIFAR10 +0.157 +0.106 +SVHN +0.226 +0.155 +STL10 +0.134 +0.088 +TABLE V: Impact of N on ACR for SC in SEaaS. The +pre-training dataset is Tiny-ImageNet. +Downstream +dataset +N +100 +1,000 10,000 100,000 +CIFAR10 +0.091 0.132 +0.148 +0.157 +SVHN +0.130 0.186 +0.211 +0.226 +STL10 +0.079 0.111 +0.127 +0.134 +REaaS achieves the generality, efficiency, and robustness +goals: +In SC based certification, a client respectively adds +Gaussian noise to images and their feature vectors to train a base +downstream classifier in SEaaS and REaaS. Thus, the certified +robustness of the smoothed classifiers are not comparable even +if we use the same standard deviation σ of Gaussian noise in +SEaaS and REaaS. Therefore, we try multiple values of σ and +report the largest ACR for each service. Moreover, we select σ +values such that the largest ACR is not reached at the smallest +or largest value of σ, to ensure the largest ACR is found for +each service. In particular, we try σ = 0.125, 0.25, 0.5, 0.75, 1 +for both SEaaS and REaaS. We note that σ controls a tradeoff +between certified accuracy without attacks (i.e., perturbation +size is 0) and robustness. Specifically, a smaller σ can achieve +a larger certified accuracy without attacks but also make the +curve drop more quickly (i.e., less robust). ACR measures such +trade-off, and thus we adopt the σ that achieves the largest +ACR for each method when comparing the certified accuracy +of SC based certification in SEaaS and REaaS. +Table II compares ACR and #Queries per training/testing +input in SEaaS and REaaS, while Table III compares the running +time per testing input for the server in SC for SEaaS and REaaS. +We have the following observations. First, REaaS supports both +BC and SC. Therefore, REaaS achieves the generality goal. +In contrast, SEaaS only supports SC. Second, REaaS achieves +the efficiency goal as it is much more efficient than SEaaS. +TABLE VI: Comparing the ACRs in REaaS for different +downstream datasets when the encoders are pre-trained +by different self-supervised learning methods. The pre- +training dataset is Tiny-ImageNet. +(a) CIFAR10 +Certification Method Pre-training Method ACR +BC +Non-robust MoCo +0.012 +RoCL +0.016 +Ours +0.138 +SC +Non-robust MoCo +0.020 +RoCL +0.024 +Ours +0.171 +(b) SVHN +Certification Method Pre-training Method ACR +BC +Non-robust MoCo +0.009 +RoCL +0.015 +Ours +0.258 +SC +Non-robust MoCo +0.011 +RoCL +0.014 +Ours +0.275 +(c) STL10 +Certification Method Pre-training Method ACR +BC +Non-robust MoCo +0.011 +RoCL +0.014 +Ours +0.090 +SC +Non-robust MoCo +0.015 +RoCL +0.020 +Ours +0.143 +Specifically, #Queries per training/testing input in REaaS is +orders of magnitude smaller than that in SEaaS for SC. We +note that a client using SEaaS could choose to train a base +downstream classifier without adding noise to its training inputs +to reduce the #Queries per training input to 1 or use a small N +to reduce the #Queries per testing input. However, the smoothed +classifier achieves (much) smaller ACRs in such cases as shown +in Table IV and V. Base on Table III, REaaS also incurs a +much lower computation cost for the server than SEaaS. +Third, REaaS achieves the robustness goal as it achieves +larger ACRs than SEaaS for SC. The reason is that, in SEaaS, +the base classifier is the composition of an encoder and a +base downstream classifier, but the client can only train the +base downstream classifier with noise. In contrast, a client can +build a smoothed classifier upon a base downstream classifier +alone which can be trained with noise and the encoder is pre- +trained in a robust way in REaaS. Figure 7 in Appendix further +compares the certified accuracy vs. perturbation size of SC in +SEaaS and REaaS. We find that REaaS can achieve a better +trade-off between accuracy without attacks and robustness than +SEaaS. Specifically, REaaS achieves larger certified accuracy +than SEaaS when the perturbation size is small. Moreover, the +gap between the certified accuracy of SEaaS and REaaS is +much larger when the perturbation size is small than that when +the perturbation size is large. +Impact of methods to pre-train encoders: +We can use +different methods to pre-train an encoder in REaaS. Table VI +and VII show ACRs in REaaS when different self-supervised +10 + +TABLE VII: Comparing the ACRs in REaaS for different +downstream datasets when the encoders are pre-trained +by different self-supervised learning methods. The pre- +training dataset is STL10. +(a) CIFAR10 +Certification Method Pre-training Method ACR +BC +Non-robust MoCo +0.010 +RoCL +0.012 +Ours +0.139 +SC +Non-robust MoCo +0.014 +RoCL +0.017 +Ours +0.173 +(b) SVHN +Certification Method Pre-training Method ACR +BC +Non-robust MoCo +0.006 +RoCL +0.009 +Ours +0.272 +SC +Non-robust MoCo +0.007 +RoCL +0.012 +Ours +0.278 +(c) Tiny-ImageNet +Certification Method Pre-training Method ACR +BC +Non-robust MoCo +0.003 +RoCL +0.004 +Ours +0.027 +SC +Non-robust MoCo +0.003 +RoCL +0.004 +Ours +0.033 +0.0 +0.2 +0.4 +0.6 +0.8 +1.0 +Perturbation size +0.0 +0.1 +0.2 +0.3 +0.4 +0.5 +0.6 +0.7 +Certified accuracy += 0.00025 += 0.0005 += 0.00075 += 0.001 +(a) BC +0.0 +0.2 +0.4 +0.6 +0.8 +1.0 +Perturbation size +0.0 +0.1 +0.2 +0.3 +0.4 +0.5 +0.6 +0.7 +Certified accuracy += 0.00025 += 0.0005 += 0.00075 += 0.001 +(b) SC +Fig. 2: Impact of λ on certified accuracy vs. perturbation +size for BC and SC in REaaS. The pre-training dataset is +Tiny-ImageNet and the downstream dataset is CIFAR10. +learning methods are used to pre-train encoders. In particular, +we consider non-robust MoCo [1], RoCL [14], and our robust +pre-training method (i.e., MoCo with our spectral-norm regu- +larization). Table VIII shows ACRs of REaaS when different +supervised learning methods are used to pre-train encoders. +In particular, we consider a standard, non-robust supervised +learning method, adversarial training [16] (we use the default +parameter settings in the authors’ public implementation), +and our robust pre-training method (i.e., standard supervised +learning with our spectral-norm regularization). We only show +results when the pre-training dataset is Tiny-ImageNet for +supervised pre-training methods, as STL10 dataset only has a +small number of labeled training images which are insufficient +to pre-train high-quality encoders using supervised learning. +We try σ = 0.125, 0.25, 0.5, 0.75, 1 and report the largest +ACR for each pre-training method. As the results show, our +TABLE VIII: Comparing the ACRs in REaaS for different +downstream datasets when the encoders are pre-trained +by different supervised learning (SL) methods. The pre- +training dataset is Tiny-ImageNet. +(a) CIFAR10 +Certification Method Pre-training Method +ACR +BC +Non-robust SL +0.019 +Adversarial Training 0.035 +Ours +0.174 +SC +Non-robust SL +0.022 +Adversarial Training 0.041 +Ours +0.172 +(b) SVHN +Certification Method Pre-training Method +ACR +BC +Non-robust SL +0.008 +Adversarial Training 0.018 +Ours +0.268 +SC +Non-robust SL +0.011 +Adversarial Training 0.021 +Ours +0.292 +(c) STL10 +Certification Method Pre-training Method +ACR +BC +Non-robust SL +0.012 +Adversarial Training 0.026 +Ours +0.100 +SC +Non-robust SL +0.018 +Adversarial Training 0.034 +Ours +0.114 +0.00025 +0.00050 +0.00075 +0.00100 +0.00 +0.02 +0.04 +0.06 +0.08 +0.10 +0.12 +0.14 +0.16 +ACR +(a) BC +0.00025 +0.00050 +0.00075 +0.00100 +0.00 +0.02 +0.04 +0.06 +0.08 +0.10 +0.12 +0.14 +0.16 +ACR +(b) SC +Fig. 3: Impact of λ on ACR for BC and SC in REaaS. The +pre-training dataset is Tiny-ImageNet and the downstream +dataset is CIFAR10. +robust pre-training method achieves substantially larger ACRs +than existing methods for both supervised learning and self- +supervised learning. Our method is better than RoCL and +adversarial training because they aim to train empirically robust +rather than certifiably robust encoders, and is better than MoCo +and standard supervised learning because the encoders pre- +trained by them are non-robust. +Impact of hyperparameter λ: Figure 2 shows the impact of λ +on certified accuracy in REaaS. We find that λ measures a trade- +off between accuracy without attacks (i.e., perturbation size is +0) and robustness. In particular, when λ is smaller, the accuracy +without attacks is larger, but the certified accuracy decreases +11 + +100 +1,000 +10,000 +100,000 +N +0.10 +0.11 +0.12 +0.13 +0.14 +0.15 +0.16 +0.17 +0.18 +ACR +0.125 +0.25 +0.5 +0.75 +0.10 +0.11 +0.12 +0.13 +0.14 +0.15 +0.16 +0.17 +0.18 +ACR +0.0001 +0.001 +0.01 +0.1 +0.10 +0.11 +0.12 +0.13 +0.14 +0.15 +0.16 +0.17 +0.18 +ACR +Fig. 4: Impact of N, σ, and α on ACR of SC in REaaS. The pre-training dataset is Tiny-ImageNet and the downstream +dataset is CIFAR10. +0.0 +0.2 +0.4 +0.6 +0.8 +1.0 +Perturbation size +0.0 +0.1 +0.2 +0.3 +0.4 +0.5 +0.6 +Certified accuracy +16x16 +32x32 +64x64 +(a) BC +0.0 +0.2 +0.4 +0.6 +0.8 +1.0 +Perturbation size +0.0 +0.1 +0.2 +0.3 +0.4 +0.5 +0.6 +Certified accuracy +16x16 +32x32 +64x64 +(b) SC +Fig. 5: Impact of downstream input size on certified accu- +racy vs. perturbation size for BC and SC in REaaS. The +pre-training dataset is Tiny-ImageNet and the downstream +dataset is (or created from) CIFAR10. The input size of +the pre-trained encoder is 32x32. +more quickly as the perturbation size increases. Figure 3 shows +the impact of λ on ACR. Our results show that, for both BC +and SC, ACR first increases as λ increases and then decreases +after λ is larger than a certain value. The reason is that a +larger or smaller λ leads to a worse trade-off between accuracy +without attacks and robustness as shown in Figure 2. +Impact of image rescaling: To study the impact of image +rescaling, we create downstream datasets with different input +image sizes via resizing images in CIFAR10. Table IX shows +the results on ACR and Figure 5 shows the results on certified +accuracy. We find that, when the size of the images in a +downstream dataset is larger (or smaller) than the input size +of the encoder, the downstream input-space ACR is larger (or +smaller) for both BC and SC. The reason is that down-scaling +(or up-scaling) the downstream input images to be the same +size as the input size of the encoder reduces (or enlarges) the +perturbation in the downstream image space. +Impact of N, σ, and α for SC: Figure 4 and 8 (in Appendix) +shows the impact of N, σ, and α on ACR and certified accuracy +of SC in REaaS. We have the following observations. First, +both ACR and certified accuracy increase as N or α increases. +The reason is that the estimated certified radii are larger when +N or α is larger. Second, we find that σ achieves a trade- +off between accuracy without attacks (i.e., perturbation size +is 0) and robustness. In particular, a smaller σ can achieve a +larger accuracy without attacks, but the curve drops faster as +the perturbation size increases. Third, ACR first increases and +TABLE IX: Impact of image rescaling on ACR in REaaS. +The pre-training dataset is Tiny-ImageNet and the down- +stream dataset is (or created from) CIFAR10. The input +size of the encoder is 32x32. +Certification Method +Size of Images in +Downstream Dataset ACR +BC +16x16 +0.082 +32x32 +0.138 +64x64 +0.303 +SC +16x16 +0.068 +32x32 +0.153 +64x64 +0.305 +then decreases as σ increases. The reason is that a smoothed +classifier is less accurate without attacks when σ is larger and +is less robust when σ is smaller. +REaaS vs. white-box access to the encoder: In REaaS, a +client has black-box access to the encoder. We compare REaaS +with the scenario where a client has white-box access to the +encoder, e.g., the cloud server shares its encoder with a client. +Specifically, with white-box access to the encoder, a client +can use either BC or SC by treating the composition of the +encoder and its downstream classifier as a base classifier. For +BC, the client can use CROWN [29] to derive the certified +radius of its base classifier for a testing input. For SC, the +client can train/fine-tune the base classifier (both the encoder +and downstream classifier) using training inputs with noise. +The white-box scenario represents the upper-bound robustness +a client can achieve. Therefore, comparing with the robustness +in the white-box scenario enables us to understand how close +our REaaS with the two APIs is to such upper bound. Table X +compares the ACRs of REaaS and such white-box scenario. +We find that REaaS can achieve comparable ACRs with the +white-box scenario. +VI. +DISCUSSION +Extension to ℓp-norm adversarial perturbations: We focus +on certified robustness against ℓ2-norm adversarial perturbation +in this work. The certified robustness can be extended to other +ℓp-norms, e.g., via leveraging the relationship between ℓ2-norm +and other ℓp-norms. For instance, suppose the certified radius +is R for an image in ℓ2-norm; the certified radius in ℓ1-norm +12 + +TABLE X: Comparing the ACRs of REaaS and the white- +box scenario for different downstream datasets. The pre- +training dataset is Tiny-ImageNet. +(a) CIFAR10 +Certification Method +Service +ACR +BC +White-box 0.157 +REaaS +0.138 +SC +White-box 0.188 +REaaS +0.171 +(b) SVHN +Certification Method +Service +ACR +BC +White-box 0.286 +REaaS +0.258 +SC +White-box 0.302 +REaaS +0.275 +(c) STL10 +Certification Method +Service +ACR +BC +White-box 0.102 +REaaS +0.090 +SC +White-box 0.151 +REaaS +0.143 +and ℓ∞-norm can respectively be computed as R and +R +√ +dim, +where dim is the product of the number of pixels and the +number of channels in the image. Figure 6 shows the certified +accuracy of SC in REaaS for ℓ1-norm and ℓ∞-norm adversarial +perturbations, where the ℓ1-norm and ℓ∞-norm certified radii +are obtained from ℓ2-norm certified radius with N = 100, 000, +σ = 0.5, and α = 0.001. +Extending REaaS to natural language processing (NLP) +domain: An attacker can make a text classifier predict an +incorrect label for a text by substituting a small number of +words as their synonyms [31], [32], [33]. Our REaaS can +also be applied to enable adversarially robust downstream +text classifiers against those attacks by slightly adapting our +F2IPerturb-API (please refer to Appendix E for details). Given a +text and a feature-space certified radius, our adapted F2IPerturb- +API returns an input-space certified radius, which is the +maximum number of words that can be substituted such that +the downstream classifier’s predicted label for the text is +unchanged. Table XI shows our experimental results (please +refer to Appendix E for details of the experimental setup). Our +results show that our REaaS is also applicable to NLP domain. +Encoder stealing: Our REaaS introduces a new F2IPerturb- +API. A natural question is whether the new F2IPerturb-API +makes the encoder more vulnerable to stealing attacks. We +argue that the answer is probably no. The reason is that our +new API returns a certified radius for a query image, which +can also be obtained by an attacker via calling the existing +Feature-API many times. However, an attacker may obtain +such certified radius with less queries using our new API. +We explore whether certified radii can be exploited to assist +encoder stealing. In particular, we extend StolenEncoder [34], +TABLE XI: ACR and #Queries of REaaS in NLP domain, +where BC is used. The pre-training dataset is SST-2 [35] +and the downstream dataset is IMDB [36]. +ACR +#Queries +Per training input Per testing input +2.517 +1 +2 +TABLE XII: Comparing StolenEncoder and its extended +version +using +our +F2IPerturb-API. +The +pre-training +dataset is Tiny-ImageNet and the downstream dataset is +CIFAR10. +StolenEncoder +Extended StolenEncoder +γ +0 +10−4 10−3 10−2 10−1 +Stolen Accuracy (%) +62.3 +62.6 +63.4 +61.5 +59.4 +0.0 +0.2 +0.4 +0.6 +0.8 +1.0 +Perturbation size +0.0 +0.1 +0.2 +0.3 +0.4 +0.5 +0.6 +0.7 +Certified accuracy +(a) ℓ1-norm +0.000 +0.005 +0.010 +0.015 +0.020 +0.025 +Perturbation size +0.0 +0.1 +0.2 +0.3 +0.4 +0.5 +0.6 +0.7 +Certified accuracy +(b) ℓ∞-norm +Fig. 6: Certified accuracy vs. perturbation size of SC in +REaaS under ℓ1-norm and ℓ∞-norm adversarial perturba- +tions. The pre-training dataset is Tiny-ImageNet and the +downstream dataset is CIFAR10. +which uses Feature-API to steal encoder, to steal encoders using +both Feature-API and F2IPerturb-API (see Appendix F for the +details of StolenEncoder and its extended version as well as the +experimental setup). Table XII shows our experimental results, +where γ is a hyperparameter. Note that the total number of +queries to the APIs made by the extended StolenEncoder is +twice of StolenEncoder in our comparison. Our results show that +the downstream classifiers built upon stolen encoders obtained +by StolenEncoder and its extended version achieve comparable +accuracy, which implies that certified radii may not be able to +assist encoder stealing. +Privacy-preserving encoder as a service: In both SEaaS and +REaaS, a client sends his/her raw images to the cloud server. +Therefore, an untrusted service provider may compromise the +privacy of the client, especially when the downstream datasets +contain sensitive images such as facial and medical images. +We believe it is an interesting future work to develop privacy- +preserving encoder as a service. For instance, we can leverage +(local) differential privacy [37], [38], [39], secure hardware [40], +and cryptography [41], [42] based methods. +Other attacks to pre-trained encoders: In this work, we +focus on adversarial examples [5], [6]. Some recent studies [43], +[44], [45] show that pre-trained encoders are also vulnerable +to poisoning and backdoor attacks, which are orthogonal to +our work. We believe it is an interesting future work to extend +our framework to defend against those attacks. +13 + +VII. +CONCLUSION AND FUTURE WORK +In this work, we show that, via providing two APIs, a cloud +server 1) makes it possible for a client to certify robustness of +its downstream classifier against adversarial perturbations using +any certification method and 2) makes it orders of magnitude +more communication efficient and more computation efficient to +certify robustness using smoothed classifier based certification. +Moreover, when the cloud server pre-trains the encoder via +considering our spectral-norm regularization term, it achieves +better certified robustness for the clients’ downstream classifiers. +Interesting future work includes extending REaaS to poisoning +and backdoor attacks as well as designing both robust and +privacy-preserving encoder as a service. +ACKNOWLEDGEMENTS +We thank the anonymous reviewers for the constructive +comments. This work was supported by NSF under grant No. +2131859, 2112562, and 1937786, as well as ARO under grant +No. W911NF2110182. +REFERENCES +[1] +K. He, H. Fan, Y. Wu, S. Xie, and R. Girshick, “Momentum contrast +for unsupervised visual representation learning,” in CVPR, 2020. +[2] +T. Chen, S. Kornblith, M. Norouzi, and G. Hinton, “A simple framework +for contrastive learning of visual representations,” in ICML, 2020. +[3] +GPT-3 API, https://openai.com/blog/customized-gpt-3/. +[4] +“General Image Embedding Model,” https://www.clarifai.com/models/ +general-image-embedding. +[5] +C. Szegedy, W. Zaremba, I. Sutskever, J. Bruna, D. Erhan, I. Goodfellow, +and R. Fergus, “Intriguing properties of neural networks,” in ICLR, 2014. +[6] +N. Carlini and D. Wagner, “Towards evaluating the robustness of neural +networks,” in IEEE S & P, 2017. +[7] +E. Wong and J. Z. Kolter, “Provable defenses against adversarial +examples via the convex outer adversarial polytope,” in ICML, 2018. +[8] +A. Raghunathan, J. Steinhardt, and P. Liang, “Certified defenses against +adversarial examples,” in ICLR, 2018. +[9] +H. Zhang, T.-W. Weng, P.-Y. Chen, C.-J. Hsieh, and L. Daniel, “Efficient +neural network robustness certification with general activation functions,” +in NeurIPS, 2018. +[10] +S. Wang, K. Pei, J. Whitehouse, J. Yang, and S. Jana, “Formal security +analysis of neural networks using symbolic intervals,” in USENIX +Security, 2018. +[11] +X. Cao and N. Z. Gong, “Mitigating evasion attacks to deep neural +networks via region-based classification,” in ACSAC, 2017. +[12] +M. Lecuyer, V. Atlidakis, R. Geambasu, D. Hsu, and S. Jana, “Certified +robustness to adversarial examples with differential privacy,” in IEEE S +& P, 2019. +[13] +J. M. Cohen, E. Rosenfeld, and J. Z. Kolter, “Certified adversarial +robustness via randomized smoothing,” ICML, 2019. +[14] +M. Kim, J. Tack, and S. J. Hwang, “Adversarial self-supervised +contrastive learning,” in NeurIPS, 2020. +[15] +I. J. Goodfellow, J. Shlens, and C. Szegedy, “Explaining and harnessing +adversarial examples,” in ICLR, 2015. +[16] +A. Madry, A. Makelov, L. Schmidt, D. Tsipras, and A. Vladu, “Towards +deep learning models resistant to adversarial attacks,” in ICLR, 2018. +[17] +H. Salman, M. Sun, G. Yang, A. Kapoor, and J. Z. Kolter, “Denoised +smoothing: A provable defense for pretrained classifiers,” NeurIPS, 2020. +[18] +S. J. Pan and Q. Yang, “A survey on transfer learning,” TKDE, 2009. +[19] +T. Chen, S. Liu, S. Chang, Y. Cheng, L. Amini, and Z. Wang, +“Adversarial robustness: From self-supervised pre-training to fine-tuning,” +in CVPR, 2020. +[20] +Z. Jiang, T. Chen, T. Chen, and Z. Wang, “Robust pre-training by +adversarial contrastive learning.” in NeurIPS, 2020. +[21] +R. Mises and H. Pollaczek-Geiringer, “Praktische verfahren der gle- +ichungsaufl¨osung.” ZAMM-Journal of Applied Mathematics and Mechan- +ics, 1929. +[22] +A. Krizhevsky, G. Hinton et al., “Learning multiple layers of features +from tiny images,” Tech Report, 2009. +[23] +Y. Netzer, T. Wang, A. Coates, A. Bissacco, B. Wu, and A. Y. Ng, +“Reading digits in natural images with unsupervised feature learning,” +in NeurIPS Workshop on Deep Learning and Unsupervised Feature +Learning, 2011. +[24] +A. Coates, A. Ng, and H. Lee, “An analysis of single-layer networks in +unsupervised feature learning,” in AISTATS, 2011. +[25] +“Tiny-ImageNet,” https://www.kaggle.com/c/tiny-imagenet/overview. +[26] +“MoCo,” https://github.com/facebookresearch/moco. +[27] +M. Balunovic and M. Vechev, “Adversarial training and provable +defenses: Bridging the gap,” in ICLR, 2019. +[28] +H. Zhang, H. Chen, C. Xiao, S. Gowal, R. Stanforth, B. Li, D. Boning, +and C.-J. Hsieh, “Towards stable and efficient training of verifiably +robust neural networks,” ICLR, 2020. +[29] +“CROWN,” https://github.com/huanzhang12/CROWN-IBP. +[30] +“Randomized Smoothing,” https://github.com/locuslab/smoothing. +[31] +M. Alzantot, Y. Sharma, A. Elgohary, B.-J. Ho, M. Srivastava, and K.-W. +Chang, “Generating natural language adversarial examples,” in EMNLP, +2018. +[32] +S. Ren, Y. Deng, K. He, and W. Che, “Generating natural language +adversarial examples through probability weighted word saliency,” in +ACL, 2019. +[33] +P.-S. Huang, R. Stanforth, J. Welbl, C. Dyer, D. Yogatama, S. Gowal, +K. Dvijotham, and P. Kohli, “Achieving verified robustness to symbol +substitutions via interval bound propagation,” EMNLP-IJCNLP, 2019. +[34] +Y. Liu, J. Jia, H. Liu, and N. Z. Gong, “Stolenencoder: Stealing pre- +trained encoders in self-supervised learning,” in CCS, 2022. +[35] +R. Socher, A. Perelygin, J. Wu, J. Chuang, C. D. Manning, A. Ng, and +C. Potts, “Recursive deep models for semantic compositionality over a +sentiment treebank,” in EMNLP, 2013. +[36] +A. Maas, R. E. Daly, P. T. Pham, D. Huang, A. Y. Ng, and C. Potts, +“Learning word vectors for sentiment analysis,” in ACL, 2011. +[37] +J. C. Duchi, M. I. Jordan, and M. J. Wainwright, “Local privacy and +statistical minimax rates,” in FOCS, 2013. +[38] +´U. Erlingsson, V. Pihur, and A. Korolova, “Rappor: Randomized +aggregatable privacy-preserving ordinal response,” in CCS, 2014. +[39] +T. Wang, J. Blocki, N. Li, and S. Jha, “Locally differentially private +protocols for frequency estimation,” in USENIX Security, 2017. +[40] +V. Costan and S. Devadas, “Intel sgx explained.” IACR Cryptol. ePrint +Arch., 2016. +[41] +R. Bost, R. A. Popa, S. Tu, and S. Goldwasser, “Machine learning +classification over encrypted data.” in NDSS, 2015. +[42] +R. Gilad-Bachrach, N. Dowlin, K. Laine, K. Lauter, M. Naehrig, and +J. Wernsing, “Cryptonets: Applying neural networks to encrypted data +with high throughput and accuracy,” in ICML, 2016. +[43] +J. Jia, Y. Liu, and N. Z. Gong, “Badencoder: Backdoor attacks to +pre-trained encoders in self-supervised learning,” in IEEE S&P, 2022. +[44] +N. Carlini and A. Terzis, “Poisoning and backdooring contrastive +learning,” in ICLR, 2021. +[45] +H. Liu, J. Jia, and N. Z. Gong, “Poisonedencoder: Poisoning the +unlabeled pre-training data in contrastive learning,” in USENIX Security, +2022. +[46] +C. J. Clopper and E. S. Pearson, “The use of confidence or fiducial +limits illustrated in the case of the binomial,” Biometrika, 1934. +[47] +K. Xu, Z. Shi, H. Zhang, Y. Wang, K.-W. Chang, M. Huang, B. Kailkhura, +X. Lin, and C.-J. Hsieh, “Automatic perturbation analysis for scalable +certified robustness and beyond,” in NeurIPS, 2020. +[48] +R. Socher, A. Perelygin, J. Wu, J. Chuang, C. D. Manning, A. Y. Ng, +and C. Potts, “Recursive deep models for semantic compositionality +over a sentiment treebank,” in EMMLP, 2013. +[49] +R. Jia, A. Raghunathan, K. G¨oksel, and P. Liang, “Certified robustness to +adversarial word substitutions,” arXiv preprint arXiv:1909.00986, 2019. +14 + +TABLE XIII: Architecture of the neural network for the +encoder. +Layer Type +Layer Parameters +Input 32 × 32 +Convolution +16 × 3 × 3, strides=(1, 1), padding=1 +Activation +ReLU +Convolution +16 × 4 × 4, strides=(2, 2), padding=1 +Activation +ReLU +Convolution +32 × 3 × 3, strides=(1, 1), padding=1 +Activation +ReLU +Convolution +32 × 4 × 4, strides=(2, 2), padding=1 +Activation +ReLU +Fully Connected +256 +Output +APPENDIX A +ACR IS THE AREA UNDER THE CERTIFIED ACCURACY VS. +PERTURBATION SIZE CURVE +Suppose the largest certified radius of a testing input is +Rmax and the certified radius of the testing inputs follows +a probability distribution in the interval [0, Rmax], whose +probability density function is p(R). The certified accuracy +(CA) at a perturbation size R can be formally defined as +follows: +CA(R) = +∫︂ Rmax +R +p(r)dr. +(16) +By definition, the area under the certified accuracy vs. pertur- +bation size curve is calculated as follows: +Area = +∫︂ Rmax +0 +CA(R)dR +(17) += CA(R) · R|Rmax +0 +− +∫︂ Rmax +0 +R · dCA(R) +(18) += 0 + +∫︂ Rmax +0 +R · p(R) · dR +(19) += ACR, +(20) +where ACR is the average certified radius of the testing inputs. +APPENDIX B +TECHNICAL DETAILS OF CROWN [9] +Suppose F is a base classifier that maps an input x to +one of c classes {1, 2, · · · , c}. For instance, the composition +of the encoder and downstream classifier g ◦ f is the base +classifier F in SEaaS, and a client can treat the downstream +classifier g as the base classifier F in REaaS. We use +H(x) to denote the base classifier’s last-layer output vector +for x, where Hl(x) represents the lth entry of H(x) and +l = 1, 2, · · · , c. F(x) denotes the predicted label for x, i.e., +F(x) = argmaxl=1,2,··· ,c Hl(x). Suppose the base classifier +predicts label y for x when there is no adversarial perturbation, +i.e., F(x) = y. A base classifier based certification method +derives a certified radius R such that F(x + δ) = y for all +∥δ∥2 < R, where δ is adversarial perturbation. Next, we discuss +how to derive the certified radius R for CROWN [9], a state- +of-the-art base classifier based certification method. +The key idea of CROWN is to bound each entry of the +output vector, i.e., Hl(x). In particular, when the output of +the activation function (e.g., ReLU) can be bounded by two +linear functions, CROWN shows that each entry Hl(x) can be +bounded by two linear functions HL +l (x) and HU +l (x). Formally, +we have HL +l (x) ≤ Hl(x) ≤ HU +l (x), where l ∈ {1, 2, · · · , c}. +Suppose an adversarial perturbation δ that satisfies ∥δ∥2 < r +is added to x. Then, we have the following: +min +∥δ∥2 max +l̸=y +max +∥δ∥2 max∥δ∥2<ρk f U +i (x + δ). We first derive +an upper bound of max∥δ∥2<ρk f U +i (x + δ). +max +∥δ∥2<ρk f U +i (x + δ) +(25) += max +∥δ∥2<ρk(W[i, :]x + W[i, :]δ + b[i]) +(26) +=W[i, :]x + b[i] + +max +∥δ∥2<ρk W[i, :]δ +(27) +≤W[i, :]x + b[i] + +max +∥δ∥2<ρk ∥W[i, :]∥2 ∥δ∥2 +(28) + max∥δ∥2<ρk f U +i (x + δ). Thus, we prove the +tightness of the right-hand side of Equation 5. Similarly, we +can prove the tightness of the left-hand side of Equation 5. +APPENDIX E +APPLYING REAAS TO NLP DOMAIN +Our REaaS provides two APIs: Feature-API and F2IPerturb- +API. The Feature-API can be directly applied to the NLP +domain. In particular, given a text as input, the Feature-API +returns the feature vector produced by a text encoder for it. +Next, we discuss how to adapt our F2IPerturb-API to the NLP +domain. +Adapting our F2IPerturb-API to NLP domain: Given a text +input and a feature-space certified radius, we can adapt our +F2IPerturb-API to provide the input-space certified radius for +the input text. In particular, we consider an attacker can replace +a small number of words in a text with their synonyms such that +the downstream classifier of a client makes incorrect prediction +for it. For simplicity, given a text input x, we use x[i] to denote +the ith word in x. Moreover, we use δ to denote an adversarial +text perturbation whose length is the same as x, where δ[i] +is an empty string if we don’t perturb x[i]; we use x ⊕ δ to +denote the perturbed text obtained by replacing x[i] as δ[i] if +δ[i] is not an empty string; we use ∥δ∥0 to denote the number +of words in δ that are not empty string. +The input-space certified radius returned by our adapted +F2IPerturb-API is the maximum number of words that can be +replaced by their synonyms such that the predicted label by +the downstream classifier is unchanged. Formally, given a text +input x and a feature-space certified radius RF , our adapted +F2IPerturb-API aims to solve the following optimization +problem: +R = max +r +r +(33) +s.t. +max +∥δ∥0 1 do +ρk = ⌈ ρL+ρU +2 +⌉ +for i = 1, 2, · · · , d do +f L +i , f U +i ← EXTENDEDCROWN(i, x, f) +Li = min∥δ∥0≤ρk f L +i (x + δ) − fi(x) +Ui = max∥δ∥0≤ρk f U +i (x + δ) − fi(x) +end for +R′ +F = +√︂∑︁d +i=1 max(L2 +i , U 2 +i ) +if R′ +F < RF then +ρL = ρk +else +ρU = ρk +end if +end while +return ρL +upper bounds (denoted as f L +i (x⊕δ) and f U +i (x⊕δ)) of fi(x⊕δ). +Moreover, they also provide a computation-efficient method +to compute min∥δ∥0 Rx +F ), +where I is an indicator function whose output is 1 if the +condition is satisfied and 0 otherwise. Intuitively, the loss term +in L′(D) for an input x is 0 if d(fs(x), fs(x+δx)) ≤ Rx +F and is +non-zero otherwise. Combining with the loss of StolenEncoder, +our final optimization problem is as follows: +min +fs L1(D) = L(D) + γL′(D), +(38) +where γ is a hyperparameter and L is defined in Equation 35. +The total number of queries is 2|D| as we respectively make +one query to the Feature-API and F2IPerturb-API for each input +in D. Similarly, we use stochastic gradient descent to solve the +optimization problem. Note that our extended StolenEncoder +reduces to StolenEncoder when γ = 0. +Experimental setup: We use Tiny-ImageNet as the pre-training +dataset and use CIFAR10 as the downstream task. Moreover, +we randomly sample 10,000 images from STL10 dataset as +the surrogate dataset D. We adopt the same κ, d, and A as +StolenEncoder. We set Rmin +F +and Rmax +F +to be 0.01 and 0.5, +respectively. As we use the same surrogate dataset, we give +advantages to the extended StolenEncoder since its total number +of queries is twice of StolenEncoder. Following [34], we use +Stolen Accuracy as evaluation metrics. In particular, given a +stolen encoder and a downstream task, Stolen Accuracy is the +classification accuracy of the downstream classifier built upon +the stolen encoder for the downstream task. +17 + +0.0 +0.2 +0.4 +0.6 +0.8 +1.0 +Perturbation size +0.0 +0.1 +0.2 +0.3 +0.4 +0.5 +0.6 +0.7 +Certified accuracy +SEaaS +REaaS +(a) CIFAR10 +0.0 +0.2 +0.4 +0.6 +0.8 +1.0 +Perturbation size +0.0 +0.1 +0.2 +0.3 +0.4 +0.5 +0.6 +0.7 +Certified accuracy +SEaaS +REaaS +(b) SVHN +0.0 +0.2 +0.4 +0.6 +0.8 +1.0 +Perturbation size +0.0 +0.1 +0.2 +0.3 +0.4 +0.5 +0.6 +0.7 +Certified accuracy +SEaaS +REaaS +(c) STL10 +0.0 +0.2 +0.4 +0.6 +0.8 +1.0 +Perturbation size +0.0 +0.1 +0.2 +0.3 +0.4 +0.5 +0.6 +0.7 +Certified accuracy +SEaaS +REaaS +(d) CIFAR10 +0.0 +0.2 +0.4 +0.6 +0.8 +1.0 +Perturbation size +0.0 +0.1 +0.2 +0.3 +0.4 +0.5 +0.6 +0.7 +Certified accuracy +SEaaS +REaaS +(e) SVHN +0.0 +0.2 +0.4 +0.6 +0.8 +1.0 +Perturbation size +0.0 +0.1 +0.2 +0.3 +0.4 +0.5 +0.6 +0.7 +Certified accuracy +SEaaS +REaaS +(f) Tiny-ImageNet +Fig. 7: Comparing certified accuracy vs. perturbation size of SC in SEaaS and REaaS for different downstream datasets, +where the pre-training dataset is Tiny-ImageNet (first row) and STL10 (second row). +0.0 +0.2 +0.4 +0.6 +0.8 +1.0 +Perturbation size +0.0 +0.1 +0.2 +0.3 +0.4 +0.5 +0.6 +0.7 +Certified accuracy +N = 100 +N = 1, 000 +N = 10, 000 +N = 100, 000 +(a) N +0.0 +0.2 +0.4 +0.6 +0.8 +1.0 +Perturbation size +0.0 +0.1 +0.2 +0.3 +0.4 +0.5 +0.6 +0.7 +Certified accuracy += 0.125 += 0.25 += 0.5 += 0.75 +(b) σ +0.0 +0.2 +0.4 +0.6 +0.8 +1.0 +Perturbation size +0.0 +0.1 +0.2 +0.3 +0.4 +0.5 +0.6 +0.7 +Certified accuracy += 0.0001 += 0.001 += 0.01 += 0.1 +(c) α +Fig. 8: Impact of N, σ, and α on certified accuracy of SC in REaaS. The pre-training dataset is Tiny-ImageNet and the +downstream dataset is CIFAR10. +18 + diff --git a/INE1T4oBgHgl3EQfFwM8/content/tmp_files/load_file.txt b/INE1T4oBgHgl3EQfFwM8/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..5c44802bf3eec901c603e23f7e0794f7169b9d2c --- /dev/null +++ b/INE1T4oBgHgl3EQfFwM8/content/tmp_files/load_file.txt @@ -0,0 +1,1570 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf,len=1569 +page_content='REaaS: Enabling Adversarially Robust Downstream Classifiers via Robust Encoder as a Service Wenjie Qu1, Jinyuan Jia2, Neil Zhenqiang Gong3 1 Huazhong University of Science and Technology, wen jie qu@outlook.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content='com 2 University of Illinois Urbana-Champaign, jinyuan@illinois.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content='edu 3 Duke University, neil.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content='gong@duke.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content='edu Abstract—Encoder as a service is an emerging cloud service.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' Specifically, a service provider first pre-trains an encoder (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=', a general-purpose feature extractor) via either supervised learning or self-supervised learning and then deploys it as a cloud service API.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' A client queries the cloud service API to obtain feature vectors for its training/testing inputs when training/testing its classifier (called downstream classifier).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' A downstream classifier is vulnerable to adversarial examples, which are testing inputs with carefully crafted perturbation that the downstream classifier misclassifies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' Therefore, in safety and security critical applications, a client aims to build a robust downstream classifier and certify its robustness guarantees against adversarial examples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' What APIs should the cloud service provide, such that a client can use any certification method to certify the robustness of its downstream classifier against adversarial examples while minimizing the number of queries to the APIs?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' How can a service provider pre-train an encoder such that clients can build more certifiably robust downstream classifiers?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' We aim to answer the two questions in this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' For the first question, we show that the cloud service only needs to provide two APIs, which we carefully design, to enable a client to certify the robustness of its downstream classifier with a minimal number of queries to the APIs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' For the second question, we show that an encoder pre- trained using a spectral-norm regularization term enables clients to build more robust downstream classifiers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' INTRODUCTION In an encoder as a service, a service provider (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=', OpenAI, Google, and Amazon) pre-trains a general-purpose feature extractor (called encoder) and deploys it as a cloud service;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' and a client queries the cloud service APIs for the feature vectors of its training/testing inputs when training/testing a downstream classifier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' For instance, the encoder could be pre- trained using supervised learning on a large amount of labeled data or self-supervised learning [1], [2] on a large amount of unlabeled data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' A client could be a smartphone, IoT device, self-driving car, or edge device in the era of edge computing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' Encoder as a service has been widely deployed by industry, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=', OpenAI’s GPT-3 API [3] and Clarifai’s General Embedding API [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' In the Standard Encoder as a Service (SEaaS), the service provides a single API (called Feature-API) for clients Wenjie Qu performed this research when he was an intern in Gong’s group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' and the encoder is pre-trained without taking the robustness of downstream classifiers into consideration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' A client sends its training/testing inputs to the Feature-API, which returns their feature vectors to the client.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' A downstream classifier is vulnerable to adversarial exam- ples [5], [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' Suppose a testing input is correctly classified by the downstream classifier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' An attacker adds a small carefully crafted perturbation to the testing input to induce misclassification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' Such testing input with carefully crafted perturbation is called an adversarial example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' Therefore, in security and safety critical applications such as user authentication and traffic sign recognition, a client desires to build a downstream classifier robust against adversarial examples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' Many methods have been developed for an attacker to craft adversarial examples and the community keeps developing new, stronger ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' Therefore, instead of defending against a specific class of adversarial examples, a client aims to defend against all bounded adversarial perturbations via building a certifiably robust downstream classifier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' A classifier is certifiably robust if its predicted label for a testing input is unaffected by arbitrary perturbation added to the testing input once its size (measured by ℓ2-norm in this work) is less than a threshold, which is known as certified radius.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' A larger certified radius indicates better certified robustness against adversarial examples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' In general, there are two categories of complementary methods to build a certifiably robust classifier and derive its certified radius for a testing input, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=', base classifier (BC) based certification [7], [8], [9], [10] and smoothed classifier (SC) based certification (also known as randomized smoothing) [11], [12], [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' BC based certification aims to directly derive the certified radius of a given classifier (called base classifier) for a testing input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' BC based certification requires white-box access to the base classifier as it often requires propagating the perturbation from the input layer to the output layer of the base classifier layer by layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' SC based certification first builds a smoothed classifier based on the base classifier via adding random noise (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=', Gaussian noise) to a testing input and then derives the certified radius of the smoothed classifier for the testing input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' To increase the testing inputs’ certified radii, SC based certification often requires training the base classifier using training inputs with random noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' Moreover, to derive the predicted label and certified radius for a testing input, SC based certification requires the base classifier to predict the labels of multiple noisy versions of the testing input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' SEaaS faces three challenges when a client aims to build a certifiably robust downstream classifier and derive its certified Network and Distributed System Security (NDSS) Symposium 2023 28 February - 4 March 2023, San Diego, CA, USA ISBN 1-891562-83-5 https://dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content='doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content='14722/ndss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content='2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content='24444 www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content='ndss-symposium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content='org arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content='02905v1 [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content='CR] 7 Jan 2023 SEaaS REaaS Feature-API Feature-API F2IPerturb-API [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content='1, ⋯, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content='2] Cloud Server Client Client Cloud Server Encoder Encoder � [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content='1, ⋯, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content='2] Downstream Classifier Step 1 Step 2 Step 3 BC/SC Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' 1: SEaaS vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' REaaS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' radii for testing inputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' The first challenge is that a client cannot use BC based certification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' In particular, the composition of the encoder and the client’s downstream classifier is the base classifier that the client needs to certify in BC based certification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' However, the client does not have white-box access to the encoder deployed on the cloud server, making BC based certification not applicable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' The second challenge is that, although a client can use SC based certification by treating the composition of the encoder and its downstream classifier as a base classifier, it incurs a large communication cost for the client and a large computation cost for the cloud server.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' Specifically, the client needs to query the Feature-API once for each noisy training input in each training epoch of the downstream classifier because SC based certification trains the base classifier using noisy training inputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' Therefore, the client requires e queries to the Feature-API per training input, where e is the number of epochs used to train the downstream classifier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' Moreover, to derive the predicted label and certified radius for a testing input, SC based certification requires the base classifier to predict the labels of N noisy testing inputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' Therefore, the client requires N queries to the Feature-API per testing input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' Note that N is often a large number (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=', 10,000) [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' The large number of queries to the Feature- API imply 1) large communication cost, which is intolerable for resource-constrained clients such as smartphone and IoT devices, and 2) large computation cost for the cloud server.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' The third challenge is that SC based certification achieves suboptimal certified radii.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' This is because the base classifier is the composition of the encoder and a client’s downstream classifier, but a client cannot train/fine-tune the encoder as it is deployed on the cloud server.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' Our work: We propose Robust Encoder as a Service (REaaS) to address the three challenges of SEaaS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' Figure 1 compares SEaaS with REaaS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' Our key idea is to provide another API called F2IPerturb-API.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content='1 A downstream classifier essentially takes a feature vector as input and outputs a label.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' Our F2IPerturb-API enables a client to treat its downstream classifier alone as a base classifier and certify the robustness of its base or smoothed downstream classifier in the feature space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' Specifically, a client performs three steps to derive the certified radius of a testing input in REaaS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' First, the client obtains the feature vector of the testing input via querying the Feature-API.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' Second, the client views its downstream classifier alone as a base classifier and derives a feature-space certified radius RF for the testing input using any BC/SC certification method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' The client’s base or smoothed downstream classifier predicts the same label for the testing input if the ℓ2-norm of the adversarial perturbation added to the testing input’s feature vector is less 1‘F’ stands for Feature and ‘I’ stands for Input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' than RF .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' Third, the client sends the testing input and its feature- space certified radius RF to query the F2IPerturb-API, which returns the corresponding input-space certified radius R to the client.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' Our input-space certified radius R guarantees the client’s base or smoothed downstream classifier predicts the same label for the testing input if the ℓ2-norm of the adversarial perturbation added to the testing input is less than R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' The key challenge of implementing our F2IPerturb-API is how to find the largest input-space certified radius R for a given testing input and its feature-space certified radius RF .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' To address the challenge, we formulate finding the largest R as an optimization problem, where the objective function is to find the maximum R and the constraint is that the feature- space perturbation is less than RF .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' However, the optimization problem is challenging to solve due to the highly non-linear constraint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' To address the challenge, we propose a binary search based solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' The key component of our solution is to check whether the constraint is satisfied for a specific R in each iteration of binary search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' Towards this goal, we derive an upper bound of the feature-space perturbation for a given R and we treat the constraint satisfied if the upper bound is less than RF .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' Our upper bound can be computed efficiently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' F2IPerturb-API addresses the first two challenges of SEaaS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' Specifically, BC based certification is applicable in REaaS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' Moreover, SC based certification requires much less queries to the APIs in REaaS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' Specifically, for any certification method, a client only requires one query to Feature-API per training input and two queries (one to Feature-API and one to F2IPerturb-API) per testing input in our REaaS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' To address the third challenge of SEaaS, we propose a new method to pre-train a robust encoder, so a client can derive larger certified radii even though it cannot train/fine-tune the encoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' Our method can be combined with standard supervised learning or self-supervised learning to enhance the robustness of a pre-trained encoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' An encoder is more robust if it produces more similar feature vectors for an input and its adversarially perturbed version.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' Our key idea is to derive an upper bound for the Euclidean distance between the feature vectors of an input and its adversarial version, where our upper bound is a product of a spectral-norm term and the perturbation size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' The spectral- norm term depends on the parameters of the encoder, but it does not depend on the input nor the adversarial perturbation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' An encoder with a smaller spectral-norm term may produce more similar feature vectors for an input and its adversarial version.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' Thus, we use the spectral-norm term as a regularization term to regularize the pre-training of an encoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' We perform a systematic evaluation on multiple datasets including CIFAR10, SVHN, STL10, and Tiny-ImageNet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' Our 2 evaluation results show that REaaS addresses the three chal- lenges of SEaaS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' First, REaaS makes BC based certification ap- plicable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' Second, REaaS incurs orders of magnitude less queries to the cloud service than SEaaS for SC based certification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' For instance, REaaS reduces the number of queries to the cloud service APIs respectively by 25× and 5, 000× per training and testing input when a client trains its downstream classifier for e = 25 epochs and uses N = 10, 000 for certification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' Third, in the framework of REaaS, our robust pre-training method achieves larger average certified radius (ACR) for the testing inputs than existing methods to pre-train encoders for both BC and SC based certification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' For instance, when the encoder is pre-trained on Tiny-ImageNet and the downstream classifier is trained on SVHN, the ACRs for MoCo (a standard non-robust self-supervised learning method) [1], RoCL (an adversarial training based state-of-the-art robust self-supervised learning method) [14], and our method are respectively 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content='011, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content='014, and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content='275 when a client uses SC based certification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' In summary, we make the following contributions: We propose REaaS, which enables a client to build a certifiably robust downstream classifier and derive its certified radii using any certification method with a minimal number of queries to the cloud service.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' We propose a method to implement F2IPerturb-API.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' We propose a spectral-norm term to regularize the pre-training of a robust encoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' We extensively evaluate REaaS and compare it with SEaaS on multiple datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' RELATED WORK A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' Adversarial Examples We discuss adversarial examples [5], [15] in the context of encoder as a service.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' We denote by f a pre-trained encoder and g a downstream classifier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' Given a testing input x, the encoder outputs a feature vector for it, while the downstream classifier takes the feature vector as input and outputs a label.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' For simplicity, we denote by f(x) the feature vector and g◦f(x) the predicted label for x, where ◦ represents the composition of the encoder and downstream classifier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' In an adversarial example, an attacker adds a carefully crafted small perturbation δ to x such that its predicted label changes, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=', g ◦f(x+δ) ̸= g ◦ f(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' The carefully perturbed input x + δ is called an adversarial example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' Many methods (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=', [5], [6], [16]) have been proposed to find an adversarial perturbation δ for a given input x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' In our work, we focus on certified defenses, which aim to defend against any bounded adversarial perturbations no matter how they are found.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' Therefore, we omit the details on how an attacker can find an adversarial perturbation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' Certifying Robustness of a Classifier Definition of certified radius: A classifier is certifiably robust against adversarial examples if its predicted label for an input is unaffected by any perturbation once its size is bounded [7], [12], [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' Formally, a classifier h is certifiably robust if we have the following guarantee for an input x: h(x + δ) = h(x), ∀ ∥δ∥2 < R, (1) where R is known as certified radius.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' Note that certified radius R may be different for different inputs x, but we omit the explicit dependency on x in the notation for simplicity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' A certification method against adversarial examples aims to build a certifiably robust classifier and derive its certified radius R for any input x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' There are two general categories of certification methods, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=', base classifier (BC) based certification [7], [8], [9], [10] and smoothed classifier (SC) based certification [11], [12], [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' Both categories of methods may be adopted in different scenarios depending on certification needs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' On one hand, BC based certification often produces deterministic guarantees (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=', the derived certified radius is absolutely correct), while SC based certification often provides probabilistic guarantees (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=', the derived certified radius may be incorrect with a small error probability).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' On the other hand, SC based certification often derives a larger certified radius than BC based certification due to its probabilistic guarantees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' Base classifier (BC) based certification: BC based certi- fication aims to directly derive the certified radius R of a given classifier (called base classifier) for an input x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' These methods often propagate perturbation from the input x to the output of the base classifier layer by layer in order to derive the certified radius.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' Therefore, they require white-box access to the base classifier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' Suppose F is a base classifier that maps an input x to one of c classes {1, 2, · · · , c}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' We use H(x) to denote the base classifier’s last-layer output vector for x, where Hl(x) represents the lth entry of H(x) and l = 1, 2, · · · , c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' F(x) denotes the predicted label for x, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=', F(x) = argmaxl=1,2,··· ,c Hl(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' Next, we overview how to derive the certified radius R using CROWN [9], a state-of-the- art BC based certification method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' CROWN shows that each entry Hl(x) can be bounded by two linear functions HL l (x) and HU l (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' Suppose the base classifier predicts label y for x when there is no adversarial perturbation, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=', F(x) = y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=' CROWN finds the largest r such that the lower bound of the yth entry (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/INE1T4oBgHgl3EQfFwM8/content/2301.02905v1.pdf'} +page_content=', min∥δ∥2 0. +Let P = |g⟩⟨g|. Note this is not necessarily a projector because |g⟩ does not have to be +normalized, but it is a Hermitian operator. Applying the Aharonov-Vaidman identity to P +and |f⟩ gives +P |f⟩ = ⟨P⟩ |f⟩ + ∆P +��f ⊥ +P +� +, +(39) +or equivalently +|g⟩ ⟨g|f⟩ = ⟨f|g⟩ ⟨g|f⟩ +⟨f|f⟩ +|f⟩ + ∆P +��f ⊥ +P +� +. +(40) +Taking the inner product with +��f ⊥ +P +� +gives +� +f ⊥ +P +��g +� +⟨g|f⟩ = ∆P ⟨f|f⟩ , +(41) +where we used the fact that +� +f ⊥ +P +��f ⊥ +P +� += ⟨f|f⟩ Rearranging and taking the complex conjugate +gives +� +g +��f ⊥ +P +� += ∆P ⟨f|f⟩ +⟨f|g⟩ +. +(42) +9 + +Now, taking the inner product of eq. (40) with |g⟩ gives +⟨g|g⟩ ⟨g|f⟩ = ⟨f|g⟩ ⟨g|f⟩ +⟨f|f⟩ +⟨g|f⟩ + ∆P +� +g +��f ⊥ +P +� +. +(43) +Multiplying both sides by ⟨f|f⟩ / ⟨g|f⟩ gives +⟨f|f⟩ ⟨g|g⟩ = ⟨f|g⟩ ⟨g|f⟩ + ∆P +� +g +��f ⊥ +P +� +⟨f|f⟩ +⟨g|f⟩ +. +(44) +Substituting eq. (42) into this gives +⟨f|f⟩ ⟨g|g⟩ = ⟨f|g⟩ ⟨g|f⟩ + (∆P)2 |⟨f|f⟩|2 +⟨f|g⟩ ⟨g|f⟩ +, +(45) +or +⟨f|f⟩ ⟨g|g⟩ = |⟨f|g⟩|2 + (∆P)2 |⟨f|f⟩|2 +|⟨f|g⟩|2 +. +(46) +Now, the terms ∆P, ⟨f|f⟩ and |⟨f|g⟩| are all real and non-negative. Hence, +⟨f|f⟩ ⟨g|g⟩ ≥ |⟨f|g⟩|2 . +(47) +5 +Pedagogical Notes +In order to teach the Robertson uncertainty relation via the Aharonov-Vaidman identity, +you first have to establish the Aharonov-Vaidman identity. For the purposes of proving the +Robertson uncertainty relation, it is sufficient to restrict the operator in the identity to be +Hermitian and the vector |ψ⟩ to be a unit vector, as I shall in this section. +In my experience, not all students immediately understand why, given a unit vector |ψ⟩, +any other unit vector |φ⟩ can be written as +|φ⟩ = α |ψ⟩ + β +��ψ⊥� +, +(48) +where +��ψ⊥� +is a unit vector orthogonal to |ψ⟩. They will probably have seen Gram-Schmidt +orthogonalization in a linear algebra class, but may have difficulty using that knowledge +here due to the jump to abstract Hilbert spaces and Dirac notation. To aid intuition, I +remark that |ψ⟩ and |φ⟩ span a two-dimensional subspace of H and show them fig. 1. By +the process of Gram-Schmidt orthogonalization, we can construct an orthornormal basis for +this subspace consisting of |ψ⟩ and +��ψ⊥� += +1 +� +1 − |⟨φ|ψ⟩|2 (|φ⟩ − |ψ⟩ ⟨ψ|φ⟩) , +(49) +10 + +|ψ⟩ +|φ⟩ +|ψ⊥⟩ +Figure 1: Diagram showing that there exists a unit vector +��ψ⊥� +such that |ψ⟩ and +��ψ⊥� +form +an orthogonal basis for the two dimensional subspace of H spanned by |ψ⟩ and |φ⟩. +from which we have eq. (48) with α = ⟨ψ|φ⟩ and β = +� +1 − |⟨φ|ψ⟩|2. +In my quantum mechanics classes, I set students in-class activities that involve things +like deriving important equations or making order of magnitude estimates. These take about +5-10 minutes each and are done in pairs. I usually do two or three such activities per class. +I believe this increases active engagement and retention of the main principles. I try to +reduce the number of long derivations that I do myself on the board because I think they +cause confusion about what the most important equations are and the derivations are rarely +remembered by the students. However, I also do not want to set the students a long and +complicated derivation to do themselves in class, so I try to find shorter derivations that +they can do with guidance instead. The proof of the Robertson relation from the Aharonov- +Vaidman relation is better suited to this approach than the standard proof. +After establishing eq. (48), I set students the following activity. +In Class Activity +Given that A |ψ⟩ = α |ψ⟩ + β +��ψ⊥� +, find α and β in terms of the expectation value ⟨A⟩ +and standard deviation ∆A of A in the state |ψ⟩. +Although some students can do this straight away, most need some help. During the +course of the activity, I walk around the class to get an idea of how they are doing. When +it seems like many students are stuck, I reveal the following three hints in sequence. +Hints +1. Try taking the inner product of A |ψ⟩ = α |ψ⟩ + β +��ψ⊥� +with other states. +2. Try taking the inner product of A |ψ⟩ with |ψ⟩. +3. Try taking the inner product of A |ψ⟩ with itself. +Although most students can get α = ⟨A⟩ either straight away or after the first hint, +|β| = ∆A is more challenging. After taking the inner product with |ψ⟩, the obvious instinct +is to take the inner product with +��ψ⊥� +, which does not help, so the third hint is usually +needed. After this, it is a short hop to the Robertson relation via the proof given in section 3. +I think it would be more difficult to teach the standard proof in this way. One would +either have to ask the students to derive the Cauchy-Schwarz inequality for themselves or +11 + +derive the Robertson relation from Cauchy-Schwarz. +The former is a bit abstract for a +quantum mechanics class and the latter involves a lot of algebra and cancellations with a +high potential for making mistakes. Both would require a large number of hints. In contrast, +the proof of the Aharonov-Vaidman identity is relatively short, and I think that students +who retain the identity are more likely to be able to reconstruct the proof of the Robertson +relation for themselves. +6 +Other Uncertainty Relations for Standard Deviations +Despite the ubiquity of the Schrödinger-Robertson uncertainty relations in quantum me- +chanics classes, there are good reasons to go beyond them. For example, consider a spin- +1/2 particle with spin operators Sx, Sy and Sz. For this case, the Robertson uncertainty +is ∆Sx∆Sy ≥ ℏ |⟨Sz⟩|. Let |x+⟩ be the spin-up state in the x direction. For this state +we have ⟨Sz⟩ = 0, which is perfectly valid because |x+⟩ is an eigenstate of Sx and hence +∆Sx = 0. However, because [Sx, Sy] ̸= 0 there is necessarily some uncertainty in Sy and in +fact ∆Sy = ℏ/2. The Schrödinger relation also yields ∆Sx∆Sy ≥ 0. So the Schrödinger- +Robertson relations do not capture all uncertainty trade-offs that necessarily exist in quan- +tum mechanics. +More generally, for bounded operators A and B, any uncertainty relation of the form +∆A∆B ≥ f (A, B, |ψ⟩) for some function f must necessarily have f (A, B, |ψ⟩) = 0 whenever +|ψ⟩ is an eigenstate of A or B. For this reason, it makes sense to seek uncertainty relations +that bound the sum of standard deviations ∆A + ∆B, the sum of variances (∆A)2 + (∆B)2, +or more exotic combinations. We shall discuss the Maccone-Pati relations, and some simple +generalizations, in this section. +Uncertainty relations are classified as either state dependent or state independent, de- +pending on whether the right hand side of the inequality depends on the state |ψ⟩. For two +observables A and B, a state dependent uncertainty relation is of the form f(∆A, ∆B) ≥ +g(A, B, |ψ⟩), where f and g are specified functions, whereas a state independent uncertainty +relation would be of the form f(∆A, ∆B) ≥ g(A, B), noting that g is no longer allowed to +depend on |ψ⟩. +On the face of it, a state dependent uncertainty relation is a strange idea, since, for any +given normalized state |ψ⟩, we can always just calculate the uncertainties ∆A and ∆B and +get the exact value of f(∆A, ∆B). Therefore, bounds on uncertainty that apply to all states +seem more useful. +However, a state dependent uncertainty relation can be a useful step in deriving a state +independent one. This can happen in two ways. First, it may happen that, for a particular +choice of the observables A and B, the function g(A, B, |ψ⟩) turns out not to depend on |ψ⟩. +For example, the Robertson relation ∆A∆B ≥ 1 +2 |⟨ψ|[A, B]|ψ⟩| is state dependent, but if we +choose A = x, B = p, then |⟨ψ|[A, B]|ψ⟩| = 1 and so we get the Heisenberg relation ∆x∆p ≥ +ℏ +2, which is state independent. Since the main point of proving the Robertson uncertainty +relation in a quantum mechanics class is to give a rigorous derivation of the Heisenberg +relation, its state dependence does no harm. However, the utility of the Robertson relation +12 + +for other classes of observable, such as spin components, is more questionable. Despite the +fact that I have asked students to compute it for states of a spin-1/2 particle as a homework +problem, I do not think there is ever a need to do this in practice, as it is just as easy to +calculate the exact uncertainties. +The second way of obtaining a state independent uncertainty relation from a state de- +pendent one is to optimize, i.e. if f(∆A, ∆B) ≥ g(A, B, |ψ⟩) then2 +f(∆A, ∆B) ≥ min +|ψ⟩ g(A, B, |ψ⟩). +(50) +Of course, if f(∆A, ∆B) = ∆A∆B and A and B are bounded operators then this leads +to the trivial relation ∆A∆B ≥ 0 because we can choose |ψ⟩ to be an eigenstate of either +A or B. However, for sums and more general combinations of observables, optimization can +lead to a nontrivial relation. +Further, if we are considering a set of experiments that can only prepare a subset of +the possible states, then we can get an uncertainty relation that applies to those states by +optimizing over the subset. An example might be experiments in which we can only prepare +the system in a Gaussian state. Although this does not yield a state independent uncertainty +relation, it is more useful than a completely state dependent one, as it allows us to bound +the possible uncertainties for a class of relevant states. +To summarize, state dependent uncertainty relations are a strange idea, and I am not +sure whether they would ever have been considered had not Robertson introduced one as +a way-point in proving the Heisenberg relation. However, they can be useful in proving +more generally applicable uncertainty relations. The relations that we discuss here are state +dependent. +The remainder of this section is structured as follows. In section 6.1 we prove two propo- +sitions called the sum relations that will be used repeatedly using the Aharonov-Vaidman +identity. In section 6.2, we give an Aharonov-Vaidman based proof of the Maccone-Pati +uncertainty relations, and in in section 6.3 we give some simple generalizations. +6.1 +The Sum Relations +Proposition 6.1. Let A and B be linear operators acting on H. Then, for any |ψ⟩ ∈ H, +∆(A + B) +��ψ⊥ +A+B +� += ∆A +��ψ⊥ +A +� ++ ∆B +��ψ⊥ +B +� +. +Proof. Apply the Aharonov-Vaidman identity to A + B in two different ways. The first way +is +(A + B) |ψ⟩ = ⟨A + B⟩ |ψ⟩ + ∆(A + B) +��ψ⊥ +A+B +� += (⟨A⟩ + ⟨B⟩) |ψ⟩ + ∆(A + B) +��ψ⊥ +A+B +� +, +(51) +2The minimum in eq. (50) may have to be replaced by an infimum, depending on the Hilbert space that +the observables are defined on. +13 + +and the second is +(A + B) |ψ⟩ = A |ψ⟩ + B |ψ⟩ += (⟨A⟩ + ⟨B⟩) |ψ⟩ + ∆A +��ψ⊥A� ++ ∆B +��ψ⊥ +B +� +. +(52) +Subtracting eq. (52) from eq. (51) and rearranging gives the desired result. +The next proposition comes from [19]. Here, the proof relies on proposition 6.1 and so is +based on the Aharonov-Vaidman relation. The original proof uses a different method and is +a little more complicated. +Proposition 6.2 (The Sum Relation). Let A and B be two linear operators acting on a +Hilbert space H. Then, +∆(A + B) ≤ ∆A + ∆B. +Proof. Let |ψ⟩ in proposition 6.1 be a unit vector. Then, starting from ∆(A + B) +��ψ⊥ +A+B +� += +∆A +��ψ⊥ +A +� ++ ∆B +��ψ⊥ +B +� +and taking the inner product with +��ψ⊥ +A+B +� +gives +∆(A + B) = ∆A +� +ψ⊥ +A+B +��ψ⊥ +A +� ++ ∆B +� +ψ⊥A+B��ψ⊥ +B +� +. +The left hand side of this equation is a real number, so the right hand side must be too. +Therefore, we can take the real part of each term to give +∆(A + B) = ∆ARe +�� +ψ⊥ +A+B +��ψ⊥ +A +�� ++ ∆BRe +�� +ψ⊥A+B��ψ⊥ +B +�� +, +but the real part of an inner product between two unit vectors is ≤ 1, so we have +∆(A + B) ≤ ∆A + ∆B. +From the proof, we see that the equality condition for the sum relation is +Rcorr(A + B, A) = Rcorr(A + B, B) = 1. +Remark 6.3. For a set of linear operators A1, A2, · · · , An on a Hilbert space H, Proposi- +tion 6.1 is easily generalized to +∆ +� n +� +j=1 +Aj +� ���ψ⊥ +�n +j=1 Aj +� += +n +� +j=1 +∆Aj +���ψ⊥ +Aj +� +, +(53) +by applying the Aharonov-Vaidman identity to �n +j=1 Aj. Similarly, proposition 6.2 is easily +generalized to +∆ +� n +� +j=1 +Aj +� +≤ +n +� +j=1 +∆Aj. +(54) +by taking the inner product of eq. (53) with +���ψ⊥ +�n +j=1 Aj +� +. We will also refer to the generaliza- +tion in eq. (54) as the sum relation. +14 + +6.2 +The Maccone-Pati Uncertainty Relations +Between the time of Robertson’s uncertainty relation and now, there has always been some +literature on uncertainty relations for variances and standard deviations. However, the field +was reinvigorated in 2014, when Maccone and Pati [20] proved a pair of uncertainty relations +for sums of variances, which always give a nontrivial bound, even in the case of an eigenstate +of an observable. +Here, we give Aharonov-Vaidman based proofs of the Maccone-Pati relations3. +Theorem 6.4 (The First Maccone-Pati Uncertainty Relation). Let A and B be Hermitian +operators on a Hilbert space H and let |ψ⟩ ∈ H be a unit vector. Then, +(∆A)2 + (∆B)2 ≥ ±i ⟨[A, B]⟩ + +��� +ψ⊥��(A ∓ iB) +��ψ +���2 , +(55) +where +��ψ⊥� +is any unit vector orthogonal to |ψ⟩. +Proof. We will prove (∆A)2 + (∆B)2 ≥ −i ⟨[A, B]⟩ + +��� +ψ⊥��(A + iB) +��ψ +���2 by applying the +Aharonov-Vaidman identity to (A + iB). The proof of the other inequality follows by re- +placing A + iB with A − iB. Note that, even though A and B are Hermitian, A + iB is not, +so it is crucial that we previously generalized the Aharonov-Vaidman identity to arbitrary +linear operators. +Applying the Aharonov-Vaidman identity to A + iB gives +(A + iB) |ψ⟩ = (⟨A⟩ + i ⟨B⟩) |ψ⟩ + ∆(A + iB) +��ψ⊥ +A+iB +� +. +Taking the inner product with any unit vector +��ψ⊥� +orthogonal to |ψ⟩ gives +� +ψ⊥��(A + iB) +��ψ +� += ∆(A + iB) +� +ψ⊥��ψ⊥ +A+iB +� +, +and taking the modulus squared of this gives +��� +ψ⊥��(A + iB) +��ψ +���2 = (∆(A + iB))2 ��� +ψ⊥��ψ⊥ +A+iB +���2 . +Now, +��� +ψ⊥��ψ⊥ +A+iB +��� ≤ 1, so +(∆(A + iB))2 ≥ +��� +ψ⊥��(A + iB) +��ψ +���2 . +The result now follows by expanding (∆(A + iB))2 as follows. +(∆(A + iB))2 = ⟨(A − iB)(A + iB)⟩ − ⟨A − iB⟩ ⟨A + iB⟩ += +� +A2� ++ +� +B2� ++ i ⟨[A, B]⟩ − ⟨A⟩2 − ⟨B⟩2 += (∆A)2 + (∆B)2 + i ⟨[A, B]⟩ . +3Although the Aharonov-Vaidman identity is used in [20], it is not used in the proofs of the uncertainty +relations. +15 + +Theorem 6.5 (The Second Maccone-Pati Uncertainty Relation). Let A and B be linear +operators on a Hilbert space H and let |ψ⟩ ∈ H be a unit vector. Then, +(∆A)2 + (∆B)2 ≥ 1 +2 +��� +ψ⊥ +A+B +��(A + B) +��ψ +���2 . +(56) +Proof. Applying the Aharonov-Vaidman identity to A + B gives +(A + B) |ψ⟩ = (⟨A⟩ + ⟨B⟩) |ψ⟩ + ∆(A + B) +��ψ⊥ +A+B +� +. +Taking the inner product with +��ψ⊥ +A+B +� +gives +� +ψ⊥ +A+B +��(A + B) +��ψ +� += ∆(A + B) +≤ ∆A + ∆B, +where the second line follows from the sum relation. +We could stop here and regard ∆A+∆B ≥ +� +ψ⊥ +A+B +��(A + B) +��ψ +� +as an uncertainty relation, +but Maccone and Pati wanted a relation in terms of variances to compare to their first result. +To do this, we take the modulus squared of both sides to obtain +(∆A + ∆B)2 ≥ +��� +ψ⊥ +A+B +��(A + B) +��ψ +���2 . +The result now follows from the real number inequality x2 + y2 ≥ 1 +2(x + y)2 with x = ∆A +and y = ∆B. For completeness, this inequality is proved as follows. +0 ≤ (x − y)2 = x2 + y2 − 2xy +⇒ +x2 + y2 ≥ 2xy +⇒ +2x2 + 2y2 ≥ x2 + y2 + 2xy +⇒ +2x2 + 2y2 ≥ (x + y)2 +⇒ +x2 + y2 ≥ 1 +2(x + y)2. +6.3 +Generalizations +Generalizations of the Maccone-Pati Uncertainty relations can be obtained by applying the +Aharonov-Vaidman identity to more general linear combinations αA + βB, where α, β ∈ C. +This gives +(αA + βB) |ψ⟩ = (α ⟨A⟩ + β ⟨B⟩) |ψ⟩ + ∆(αA + βB) +��ψ⊥ +αA+βB +� +. +(57) +Applying the strategy we used to prove theorem 6.4, we can take the inner product of this +with an arbitrary unit vector +��ψ⊥� +that is orthogonal to |ψ⟩, which gives +� +ψ⊥��(αA + βB) +��ψ +� += ∆(αA + βB) +� +ψ⊥��ψ⊥ +αA+βB +� +. +16 + +We can now take the modulus squared of this and recognize that 0 ≤ +��� +ψ⊥��ψ⊥ +αA+βB +���2 ≤ 1 +to obtain +��� +ψ⊥��(αA + βB) +��ψ +���2 ≤ ∆(αA + βB). +Next, we can expand ∆(αA + βB) and rearrange to obtain +|α|2 (∆A)2 + |β|2 (∆B)2 ≥ −Re(α∗β) (⟨{A, B}⟩ − 2 ⟨A⟩ ⟨B⟩) − iIm (α∗β) ⟨[A, B]⟩ ++ +��� +ψ⊥��(αA + βB) +��ψ +���2 . +(58) +Substituting α = 1, β = i and α = 1, β = −i immediately yields the first Maccone-Pati +Uncertainty Relation. +Alternatively, we can apply the strategy used to prove theorem 6.5. Starting from eq. (57), +we can take the inner product with +��ψ⊥ +αA+βB +� +and rearrange to obtain +∆(αA + βB) = +� +ψ⊥ +αA+βB +��(αA + βB) +��ψ +� +. +Using the sum relation, together with ∆(αA) = |α|∆A gives +|α|∆A + |β|∆B ≥ +� +ψ⊥ +αA+βB +��(αA + βB) +��ψ +� +. +Finally, squaring and using the inequality x2 + y2 ≥ 1 +2(x + y)2 gives +|α|2 (∆A)2 + |β|2 (∆B)2 ≥ 1 +2 +��� +ψ⊥ +αA+βB +��(αA + βB) +��ψ +���2 . +(59) +The inequalities eq. (58) and eq. (59) are related to some of the generalizations of the +Maccone-Pati uncertainty relations that have previously appeared in the literature [21, 28]. +For example, eq. (58) can be used to derive an uncertainty relation that has appeared in the +literature under the name “weighted uncertainty relation” [28]. To do so, we set α = +√ +λ, +β = ±i/ +√ +λ in eq. (58), where λ > 0. This yields +λ (∆A)2 + 1 +λ (∆B)2 ≥ ±i ⟨[A, B]⟩ + 1 +λ +��� +ψ⊥��(λA ∓ iB) +��ψ +���2 . +This is an uncertainty relation in its own right, but the relation in [28] comes from adding +this to eq. (55), which yields +(1+λ) (∆A)2+ +� +1 + 1 +λ +� +(∆B)2 ≥ ±2i ⟨[A, B]⟩ +��� +ψ⊥ +1 +��(A ∓ iB) +��ψ +���2+1 +λ +��� +ψ⊥ +2 +��(λA ∓ iB) +��ψ +���2 , +where +��ψ⊥ +1 +� +and +��ψ⊥ +2 +� +are (possibly different) unit vectors that are orthogonal to |ψ⟩. +This is intended as a simple example of a generalization that is easily obtained from the +Aharonov-Vaidman identity, but I expect many other uncertainty relations that are usually +proved using the Cauchy-Schwarz inequality or the parallelogram law would also have simple +Aharonov-Vaidman based proofs. +17 + +7 +Quantum Propagation of Uncertainty +In this section, we develop generalizations of the classical formulas for the propagation of +uncertainty. We start with the case of linear functions in section 7.1, for which exact formulas +are easy to obtain, before moving on to the general, possibly nonlinear, case in section 7.2, +for which we have to employ a Taylor series approximation. +7.1 +Linear Functions +We start with the simplest case: a sum of two observables. Classically, if A and B are +random variables then +[∆(A + B)]2 = (∆A)2 + (∆B)2 + 2∆A∆B corrA,B. +(60) +Consider an experiment consisting of multiple runs. On each run, the quantities A and B +are measured. These quantities are formalized as random variables because we assume that +our experiments are subject to random statistical fluctuations, and that the “true” values +that we are seeking are the means ⟨A⟩ and ⟨B⟩ of these random processes. We then use +the average values calculated from the data as estimates of ⟨A⟩ and ⟨B⟩, and the standard +deviations as a measure of the error in our experiment. If we are actually interested in the +quantity A + B then we would sum the averages to form our estimate of ⟨A + B⟩, and we +would use eq. (60) to determine the error in our estimate of ⟨A + B⟩. Using eq. (60) in this +way is called the propagation of uncertainty or propagation of error. +If the random variables, A and B are independent, which would be the case if the ran- +domness were due to independent statistical errors, then corrA,B = 0 and we would have +[∆(A + B)]2 = (∆A)2 + (∆B)2 , +which is the formula for propagation of uncertainty that is most commonly used in practice. +We now want to generalize these formulas by replacing classical random variables with +quantum observables. The generalization of eq. (60) is as follows. +Theorem 7.1. Let A and B be Hermitian operators on a Hilbert space H. Then, +[∆(A + B)]2 = (∆A)2 + (∆B)2 + 2∆A∆B RcorrA,B +(61) += (∆A)2 + (∆B)2 + ⟨{A, B}⟩ − 2 ⟨A⟩ ⟨B⟩ +(62) +Proof. Proposition 6.1 implies that, for any unit vector |ψ⟩ ∈ H, +∆(A + B) +��ψ⊥ +A+B +� += ∆A +��ψ⊥ +A +� ++ ∆B +��ψ⊥ +B +� +. +Taking the inner product of this with itself gives +[∆ (A + B)]2 = (∆A)2 + (∆B)2 + ∆A∆B +�� +ψ⊥ +A +��ψ⊥ +B +� ++ +� +ψ⊥ +B +��ψ⊥ +A +�� += (∆A)2 + (∆B)2 + 2∆A∆B Re +�� +ψ⊥ +A +��ψ⊥ +B +�� +. +Applying eq. (13) completes the proof. +18 + +Remark 7.2. For operators A1, A2, · · · , An and real numbers α1, α2, · · · , αn, theorem 7.1 is +easily generalized to +� +∆ +� n +� +j=1 +αjAj +��2 += +n +� +j=1 +α2 +j (∆Aj)2 + +� +j̸=k +αjαk∆Aj∆Ak RcorrAj,Ak += +n +� +j=1 +α2 +j (∆Aj)2 + +� +j̸=k +αjαk (⟨{Aj, Ak}⟩ − 2 ⟨Aj⟩ ⟨Ak⟩) . +Although theorem 7.1 is a true theorem about quantum observables, it cannot be used +to propagate uncertainty in the same way as its classical counterpart. Classically, we can +measure A and B together in the same run of the experiment. We can then estimate A + B +by summing the average values of A and B that we found in the experiment. We also have +all the information we need to calculate the uncertainty ∆(A + B), i.e. ∆A, ∆B, ⟨A⟩, ⟨B⟩ +and ⟨AB⟩, so we can determine the uncertainty without doing any more experiments. +In quantum mechanics, this is not the case. When A and B do not commute, they cannot +both be accurately measured on the same run of an experiment. We can still estimate their +expectation values by measuring A on half of the runs of the experiment and B on the other +half and taking averages. Since ⟨A + B⟩ = ⟨A⟩ + ⟨B⟩, summing these averages is still a way +of estimating ⟨A + B⟩. However, we do not have enough information to calculate ∆(A + B). +The reason is that ∆(A + B) is the uncertainty in a direct measurement of A + B. Since A +and B do not commute, this requires a different experimental setup from a measurement of +A and B alone. +If we wanted to use eq. (61) to calculate ∆(A + B), we would also have to estimate +⟨{A, B}⟩. The most straightforward way of doing this would be to measure the observable +{A, B} = AB +BA, but this requires yet another different experimental setup, and one that +is likely to be at least as complicated as measuring A + B directly. +An exception to this are cases where {A, B} = cI for some constant c, in which case +⟨{A, B}⟩ = c regardless of the state. In particular, this is true of the Pauli observables σx, +σy, σz of a qubit for which {σj, σk} = δjkI, where j and k run over x, y, z. Therefore, if we +measure σx on many qubits prepared in the same way and σy on another set of such qubits, +we can estimate ⟨σx + σy⟩ and ∆(σx + σy) without doing any further experiments using the +formula +[∆ (σx + σy)]2 = (∆σx)2 + (∆σy)2 − 2 ⟨σx⟩ ⟨σy⟩ . +When {A, B} ̸= cI, I do not know of any situations in which eq. (61) would be useful in +practice, but from a theoretical point of view it is the appropriate generalization of eq. (60) +to quantum mechanics, and this bolsters the case that RcorrA,B is the appropriate quantum +generalization of the classical correlation. +7.2 +Nonlinear Functions +For nonlinear functions f(A, B) of two random variables A and B, it is common to use a first +order Taylor expansion of f(A, B) about the point f(⟨A⟩ , ⟨B⟩) to derive an approximation +19 + +for the variance [∆f(A, B)]2 to second order in ∆A and ∆B. This yields the formula +[∆f(A, B)]2 ≈ +� +∂f +∂A +���� +A=⟨A⟩,B=⟨B⟩ +�2 +(∆A)2 + +� +∂f +∂B +���� +A=⟨A⟩,B=⟨B⟩ +�2 +(∆B)2 ++ ∂f +∂A +���� +A=⟨A⟩,B=⟨B⟩ +∂f +∂B +���� +A=⟨A⟩,B=⟨B⟩ +∆A∆B corrA,B. +To avoid cluttering notation, I will write ¯A for A = ⟨A⟩, so that we can more compactly +write +[∆f(A, B)]2 ≈ ∂f +∂A +���� +2 +¯ +A, ¯B +(∆A)2 + ∂f +∂B +���� +2 +¯ +A, ¯B +(∆B)2 + ∂f +∂A +���� ¯ +A, ¯B +∂f +∂B +���� ¯ +A, ¯B +∆A∆B corrA,B. +(63) +When A and B are independent, this reduces to +[∆f(A, B)]2 ≈ ∂f +∂A +���� +2 +¯ +A, ¯B +(∆A)2 + ∂f +∂B +���� +2 +¯ +A, ¯B +(∆B)2 , +which is the most commonly used form. +The quantum generalization of eq. (63) is as follows. +Theorem 7.3. Let A and B be Hermitian operators on a Hilbert space H and consider a +function f : H(H) × H(H) → H(H) where H(H) is the space of Hermitian operators on H. +Then +[∆f(A, B)]2 ≈ ∂f +∂A +���� +2 +¯ +A, ¯B +(∆A)2 + ∂f +∂B +���� +2 +¯ +A, ¯B +(∆B)2 + ∂f +∂A +���� ¯ +A, ¯B +∂f +∂B +���� ¯ +A, ¯B +∆A∆B RcorrA,B +(64) +where ≈ means equality to second order in ∆A and ∆B +Proof. Consider the first order Taylor expansion of f(A, B) about the point f0 = f(⟨A⟩ , ⟨B⟩), +f(A, B) ≈ f0 + ∂f +∂A +���� ¯ +A, ¯B +A + ∂f +∂B +���� ¯ +A, ¯B +B. +Applying proposition 6.1 to this gives +[∆f(A, B)] +��ψ⊥ +f(A,B) +� +≈ ∂f +∂A +���� ¯ +A, ¯B +∆A +��ψ⊥ +A +� ++ ∂f +∂B +���� ¯ +A, ¯B +∆B +��ψ⊥ +B +� +. +Taking the inner product of this with itself gives +[∆f(A, B)]2 ≈ ∂f +∂A +���� +2 +¯ +A, ¯B +(∆A)2 + ∂f +∂B +���� +2 +¯ +A, ¯B +(∆B)2 + ∂f +∂A +���� ¯ +A, ¯B +∂f +∂B +���� ¯ +A, ¯B +∆A∆B Re +�� +ψ⊥ +A +��ψ⊥ +B +�� += ∂f +∂A +���� +2 +¯ +A, ¯B +(∆A)2 + ∂f +∂B +���� +2 +¯ +A, ¯B +(∆B)2 + ∂f +∂A +���� ¯ +A, ¯B +∂f +∂B +���� ¯ +A, ¯B +∆A∆B RcorrA,B +20 + +Remark 7.4. For operators A1, A2, · · · , An and a function f(A1, A2, · · · , An), theorem 7.3 is +easily generalized to +[∆f (A1, A2, · · · , An)]2 ≈ +n +� +j=1 +∂f +∂Aj +���� +2 +¯ +A +(∆Aj)2 + +� +j̸=k +∂f +∂Aj +���� ¯ +A +∂f +∂Ak +���� ¯ +A +∆Aj∆Ak RcorrAj,Ak, +where ¯A is shorthand for A1 = ⟨A1⟩ , A2 = ⟨A2⟩ , · · · An = ⟨An⟩. +As a formula for propagating uncertainty, eq. (64) inherits all of the problems of eq. (61), +but the problems are compounded further by use of the first order Taylor approximation. +This approximation is valid when ∆A and ∆B are suitably small compared to ⟨A⟩, ⟨B⟩, +f(⟨A⟩ , ⟨B⟩) and the derivatives of f(A, B) at A = ⟨A⟩, B = ⟨B⟩. This is often the case +in classical experiments where everything can be measured with a small statistical error. +However, in quantum mechanics, when A and B do not commute, the (various) uncertainty +relations tell us that there is necessarily a trade-off between the size of ∆A and ∆B. If one +of them is small, then the other might necessarily have to be large. For example, for the +Pauli observables σx and σy, at least one of the uncertainties must be comparable in size to +1, which is the largest possible value of ⟨σx⟩ or ⟨σy⟩. +A case where the formula will work well is for a continuous variable system where ∆x ∼ +∆p ∼ +√ +ℏ, and ⟨x⟩, ⟨p⟩ are large compared to +√ +ℏ. But this is a case where you would expect +classical physics to be a good approximation anyway. +I do not know whether there is a practical use of eq. (64), but it is nonetheless a correct +formal generalization of eq. (63). +8 +Dealing with Mixed States +So far, we have dealt exclusively with the case of pure state vectors |ψ⟩. However, all of +our results can be extended to more general density operators ρ, which can represent mixed +states. The most familiar way to do this is to make use of the concept of a purification +of a density operator. Given a density operator on a Hilbert space HS, where S stands +for “system”, we can always find a pure state vector |ψ⟩SE ∈ HS ⊗ HE, where E is the +“environment”, such that +ρS = TrE (|ψ⟩⟨ψ|SE) , +and TrE is the partial trace over HE. You can then apply the Aharonov-Vaidman identity +to operators of the form AS ⊗ IE acting on a purification to obtain results about the density +operator ρS. +However, to make the parallels to the pure state case as close as possible, I prefer to use +an equivalent concept, called an amplitude operator. The equivalence between amplitude +operators and purifications is discussed in appendix A +Definition 8.1. Given a density operator ρS on a Hilbert space HS, an amplitude operator +for ρS is a linear operator LS : HE → HS, where HE is any Hilbert space, such that +ρS = LSL† +S. +21 + +The reason for the name amplitude operator is that, in pure-state quantum mechanics, an +amplitude is a complex number α such that |α|2 is a probability. A density operator is a non- +commutative generalization of a probability distribution [42, 43], and hence an amplitude +operator ought to be an operator that “squares” to a density operator. +Given a density operator ρS, one obvious way of constructing an amplitude operator is +to set HE = HS and LS = √ρS, but there are an infinite number of alternatives, as the +following proposition shows +Proposition 8.2. An operator LS : HE → HS is an amplitude operator for ρS if and only +if +LS = √ρSUS|E, +where US|E : HE → HS is a semi-unitary operator, i.e. it satisfies US|EU † +S|E = IS +Proof. An operator of the form LS = √ρSUS|E obviously satisfies definition 8.1. For the other +direction, assume LS is an amplitude operator. Like any operator, it may be decomposed in +its polar decomposition LS = PSUS|E where PS is a positive semi-definite operator on HS, +and US|E : HE → HS is semi-unitary4. The definition of an amplitude operator then implies +that ρS = PSUS|EU † +S|EPS = P 2 +S, so we must have PS = √ρS. +Going back to the analogy between amplitudes and amplitude operators, multiplying an +amplitude α by a phase factor eiφ does not change the probability it represents. Similarly, +multiplying an amplitude operator LS by a semi-unitary VE|E′, i.e. an operator VE|E′ : HE′ → +HE satisfying VE|E′V † +E|E′ = IE, on the right does not change the density operator it represents. +Although one might think it desirable to work directly with probabilities or density operators +in order to eliminate these ambiguities, the mathematical manipulations we need to do in +quantum mechanics are often linear in the amplitudes or amplitude operators, but would be +nonlinear if you used probabilities or density operators. Therefore, it is often more convenient +to live with the ambiguity. +Since every operator has a polar decomposition, the only requirement for LS to be an +amplitude operator for some density operator is that TrS +� +LSL† +S +� += 1. +If we want to +work with unnormalized density operators, i.e. any positive operator, then any operator +LS : HE → HS is the amplitude operator for some (possibly unnormalized) density operator. +This is analogous to the fact that any vector in HS represents a (possibly unnormalized) pure +state. +The strategy for generalizing the Aharonov-Vaidman identity, and everything that follows +from it, is to replace the state vector |ψ⟩S with an amplitude operator LS. The reason this +works is that the space of linear operators mapping HE to HS, which we denote LS|E, is itself +a Hilbert space with inner product ⟨LS, MS⟩ = TrE +� +L† +SMS +� +, known as the Hilbert-Schmidt +4The polar decomposition is often only defined for square matrices, in which case HE = HS and US|E is +unitary. Here, we use the generalization to non-square matrices (see e.g. [44]). +22 + +inner product5. Since the Aharonov-Vaidman identity is valid for any Hilbert space, it must +be valid on LS|E as well. +Proposition 8.3 (The Aharonov-Vaidman Identity for Operators). Let AS be a linear op- +erator on a Hilbert space HS and let LS : HE → HS. Then, +ASLS = ⟨AS⟩ LS + (∆AS) L⊥ +AS, +(65) +where ⟨AS⟩ = TrS +� +ASLSL† +S +� +/TrS +� +LSL† +S +� +, ∆A = +�� +A† +SAS +� +− |⟨AS⟩|2, and L⊥ +AS : HE → +HS is an amplitude operator that is orthogonal to LS, i.e. +TrE +� +L† +SL⊥ +AS +� += 0, satisfies +TrS +� +L⊥ +ASL⊥† +AS +� += TrS +� +LSL† +S +� +, and depends on both LS and AS. +The proof of this proposition is essentially the same as the proof of the vector Aharonov- +Vaidman identity (proposition 2.1) with the standard inner product replaced by the Hilbert- +Schmidt inner product. The only difference is that the cyclic property of the trace is also +needs to be used to write things in the exact form given in proposition 8.3. I leave this as +an exercise for the reader. +Since ρS = LSL† +S is always a (possibly unnormalized) density operator, we can write +⟨AS⟩ = +TrS +� +ASLSL† +S +� +TrE +� +L† +SLS +� += TrS (ASρS) +TrE (ρS) . +We can also introduce the density operator ρ⊥ +AS = L⊥ +ASL⊥† +AS, which will be normalized in the +same way as ρS, i.e., TrS +� +ρ⊥ +AS +� += TrS (ρS). +When LS is normalized so that ρS = LSL† +S is a normalized density operator, i.e., +TrS +� +LSL† +S +� += 1, then ρ⊥ +AS is also normalized, i.e., TrS +� +ρ⊥ +AS +� += 1. +As defined, ρ⊥ +AS = L⊥ +ASL⊥† +AS looks like it depends on the choice of amplitude operator +LS. In fact, it does not. It only depends on ρS and AS. To see this, rewrite the operator +Aharonov-Vaidman identity as +L⊥ +AS = +1 +∆AS +(AS − ⟨AS⟩ IS) LS, +and then we have, +ρ⊥ +AS = L⊥ +ASL⊥† +AS += +1 +(∆AS)2 (AS − ⟨AS⟩ IS) LSL† +S +� +A† +S − ⟨AS⟩∗ IS +� += +1 +(∆AS)2 (AS − ⟨AS⟩ IS) ρS +� +A† +S − ⟨AS⟩∗ IS +� +, +5By the cyclic property of the trace, we can also write ⟨LS, MS⟩ = TrS +� +MSL† +S +� +. +23 + +which is clearly independent of the choice of LS. +Note that, although LS and L⊥ +AS are +Hilbert-Schmidt orthogonal, ρS and ρ⊥ +AS are generally not. +To generalize the results of this paper from state vectors to density operators, we replace +the vector Aharonov-Vaidman identity with its operator counterpart applied to amplitude +operators, and we replace the usual inner product with the Hilbert-Schmidt inner product. +In many cases, the final result is independent of the amplitude operator used to represent +the state. Although we use it in the proof, it drops out in the final result by only appearing +in the combination LSL† +S, as in the expression we derived for ρ⊥ +AS. In fact, the final formulas +are usually the same as in the pure state case, except that we have to interpret ⟨AS⟩ as +TrS (ASρS) rather than ⟨ψ|AS|ψ⟩. +However, this is not true for the Maccone-Pati uncertainty relations and their general- +izations, which do depend on the choice of amplitude operator LS. +Theorem 8.4 (The First Maccone-Pati Uncertainty Relation for amplitude operators). Let +AS and BS be Hermitian operators on a Hilbert space HS and let ρS be a normalized density +operator on HS. Then, +(∆A)2 + (∆B)2 ≥ ±i ⟨[A, B]⟩ + +���TrE +� +L⊥† +S (A ∓ iB)LS +���� +2 +, +(66) +where LS : HE → HS is any amplitude operator for ρS, and L⊥ +S : HE → HS is any normalized +amplitude operator orthogonal to LS that has the same input space HE. +Note that, in order to obtain the tightest possible bound on (∆A)2 + (∆B)2, the right +hand side of eq. (66) should be maximized over all possible choices of LS and L⊥ +S . To do this +in practice, a bound on the largest dimension dE required to obtain the maximum is needed. +I conjecture that dE = 2dS is sufficient because this allows LS and L⊥ +S to have orthogonal +kernels on HE, but I do not have a proof of this. +Theorem 8.5 (The Second Maccone-Pati Uncertainty Relation for amplitude operators). +Let AS and BS be linear operators on a Hilbert space HS and let ρS be a normalized density +operator on HS. Then, +(∆AS)2 + (∆BS)2 ≥ 1 +2 +���TrE +� +L⊥† +AS+BS(A + B)LS +���� +2 +, +(67) +where LS is any amplitude operator for ρS and +L⊥ +AS+BS = +1 +∆(AS + BS) (AS + BS − ⟨AS + BS⟩ IS) LS. +In this case, to obtain the tightest bound, we have to maximize the right hand side over +LS. We do not have to separately optimize over L⊥ +AS+BS because it is a function of LS, AS +and BS. However, its dependence on LS makes the problem into a complicated nonlinear +optimization. +24 + +9 +Summary and Conclusions +In this paper, I discussed how the standard textbook uncertainty relations of Robertson and +Schrödinger can be derived from the Aharonov-Vaidman identity in a more direct way than +the standard proof. I also demonstrated the identity’s usefulness in proving other uncertainty +relations, such as the Maccone-Pati relations, and the quantum formulas for propagation of +uncertainty. Finally, I gave a mixed-state generalization of the Aharonov-Vaidman identity +in terms of amplitude operators. I hope that this has persuaded you that the Aharonov- +Vaidman identity belongs in undergraduate textbooks and that it ought to be a first-line +tool in proving relationships between standard deviations in quantum mechanics. I am sure +there are other uncertainty relations that have an elegant Aharonov-Vaidman based proofs, +and I hope to find new and useful uncertainty relations that have not been discovered before +via this method. +The Aharonov-Vaidman identity naturally gives rise to two quantum generalizations of +the correlation, corrA,B and RcorrA,B. It would be interesting to determine whether these +quantities have an operational meaning in the case where A and B do not commute. On the +more formal side, perhaps there is a pseudo-probability representation of quantum mechanics, +such as the Wigner function [45, 46, 47] or the Kirkwood-Dirac distribution [48, 49, 50], +for which these are the correlations for observables as defined on the appropriate phase +space. This might help to find uses for the propagation of error formulas in cases where the +observables do not commute. +Acknowledgments +I would like to thank Yakir Aharonov for introducing me to the Aharonov-Vaidman iden- +tity and emphasizing its importance. I would like to acknowledge (but not thank) the role +played by the COVID19 pandemic shutdowns in giving me the opportunity to think about +uncertainty relations and their pedagogy. This research was supported in part by the Fetzer +Franklin Fund of the John E. Fetzer Memorial Trust and by grant number FQXi-RFPIPW- +1905 from the Foundational Questions Institute and Fetzer Franklin Fund, a donor advised +fund of Silicon Alley Community Foundation. This research was also supported in part by +Perimeter Institute for Theoretical Physics. Research at Perimeter Institute is supported +by the Government of Canada through the Department of Innovation, Science, and Eco- +nomic Development, and by the Province of Ontario through the Ministry of Colleges and +Universities. +References +[1] Y. Aharonov and L. Vaidman. Properties of a quantum system during the time interval +between two measurements. Phys. Rev. A, 41(1):11–20, 1990. doi:10.1103/PhysRevA. +41.11. +25 + +[2] Y. Aharonov. +Visiting researcher presentation. +Talk at Perimeter Institute to PSI +Masters Students: comment is made at 41:16, August 2011. URL: https://pirsa. +org/11080091. +[3] L. Vaidman. Minimum time for the evolution to an orthogonal state. Am. J. Phys., +60(2):182, 1992. doi:10.1119/1.16940. +[4] H. P. Robertson. The Uncertainty Principle. Phys. Rev., 34(1):163–164, 1929. doi: +10.1103/PhysRev.34.163. +[5] E. Schrödinger. Zum heisenbergschen unschärfeprinzip. Sitzungsberichte der Preussis- +chen Akademie der Wissenschaften, Physikalisch-mathematische Klasse, 14:296–303, +1930. +[6] L. Goldenberg and L. Vaidman. Applications of a simple quantum mechanical formula. +Am. J. Phys., 64(8):1059, 1996. arXiv:quant-ph/9506030, doi:10.1119/1.18307. +[7] Y. Aharonov and D. Rohrlich. Quantum Paradoxes: Quantum Theory for the Perplexed. +Wiley, 2005. doi:10.1002/9783527619115. +[8] M. +J. +Steele. +The +Cauchy-Schwarz +Master +Class: +An +Introduction +to +the +Art +of +Mathematical +Inequalities, +chapter +1, +page +1. +Mathematical +Association +of +America +Problem +Books. +Cambridge +University +Press, +2004. +URL: +http://www-stat.wharton.upenn.edu/~steele/Publications/Books/CSMC/ +CSMC_index.html, doi:CBO9780511817106. +[9] C. A. Fuchs and A. Peres. Quantum-state disturbance versus information gain: Un- +certainty relations for quantum information. Phys. Rev. A, 53(4):2038, 1996. arXiv: +quant-ph/9512023, doi:10.1103/PhysRevA.53.2038. +[10] H. F. Hofmann and S. Takeuchi. Violation of local uncertainty relations as a signature +of entanglement. Phys. Rev. A, 68(3):032103, 2003. arXiv:quant-ph/0212090, doi: +10.1103/PhysRevA.68.032103. +[11] O. Gühne. +Characterizing entanglement via uncertainty relations. +Phys. Rev. +Lett., 92(11):117903, 2004. +arXiv:quant-ph/0306194, doi:10.1103/PhysRevLett. +92.117903. +[12] M. Koashi. Unconditional security of quantum key distribution and the uncertainty +principle. +J. Phys.: Conf. Ser., 36:98–102, 2006. +arXiv:quant-ph/0505108, doi: +10.1088/1742-6596/36/1/016. +[13] M. Berta, M. Christandl, R. Colbeck, J. M. Renes, and R. Renner. The uncertainty +principle in the presence of quantum memory. Nature Physics, 6:659–662, 2010. arXiv: +0909.0950, doi:doi.org/10.1038/nphys1734. +26 + +[14] A. S. Majumdar and T. Pramanik. Some applications of uncertainty relations in quan- +tum information. International Journal of Quantum Information, 14(6):1640022, 2016. +arXiv:1410.5974, doi:10.1142/S0219749916400220. +[15] N. Yunger Halpern, A. Bartolotta, and J. Pollack. Entropic uncertainty relations for +quantum information scrambling. +Commun. Phys., 2:92, 2019. +arXiv:1806.04147, +doi:10.1038/s42005-019-0179-8. +[16] J. Oppenheim and S. Wehner. The uncertainty principle determines the nonlocality +of quantum mechanics. Science, 330(6007):1072–1074, 2010. arXiv:1004.2507, doi: +10.1126/science.119206. +[17] L. Catani, M. Leifer, G. Scala, D. Schmid, and R. W. Spekkens. What is nonclassical +about uncertainty relations? +Phys. Rev. Lett., 129(24):240401, 2022. arXiv:2207. +11779, doi:10.1103/PhysRevLett.129.240401. +[18] P. J. Coles, M. Berta, M. Tomamichel, and S. Wehner. Entropic uncertainty relations +and their applications. Rev. Mod. Phys., 89(1):015002, 2017. arXiv:1511.04857, doi: +10.1103/RevModPhys.89.015002. +[19] A. K. Pati and P. K. Sahu. Sum uncertainty relation in quantum theory. Phys. Lett. +A, 367(3):177–181, 2007. arXiv:quant-ph/0608092, doi:10.1016/j.physleta.2007. +03.005. +[20] L. Maccone and A. K. Pati. Stronger uncertainty relations for all incompatible ob- +servables. Phys. Rev. Lett., 113(26):039902, 2015. arXiv:1407.0338, doi:10.1103/ +PhysRevLett.113.260401. +[21] V. M. Bannur. General and stronger uncertainty relation. 2015. arXiv:1503.00405, +doi:10.48550/arXiv.1503.00405. +[22] J. L. Li and C. F. Qiao. Reformulating the quantum uncertainty relation. Scientific +Reports, 5:12708, 2015. arXiv:1502.06292, doi:10.1038/srep12708. +[23] Y. Yao, X. Xiao, X. Wang, and C. P. Sun. Implications and applications of the variance- +based uncertainty equalities. Phys. Rev. A, 91:062113, 2015. arXiv:1503.00239, doi: +10.1103/PhysRevA.91.062113. +[24] A. A. Abbott, P. Alzieu, M. J. W. Hall, and C. Branciard. Tight state-independent +uncertainty relations for qubits. Mathematics, 4(1):8, 2016. arXiv:1512.02383, doi: +10.3390/math4010008. +[25] B. Chen, N. Cao, S. Fei, and G. Long. Variance-based uncertainty relations for in- +compatible observables. Quantum Information Processing, 15:3909–3917, 2016. arXiv: +1608.06075, doi:10.1007/s11128-016-1365-1. +27 + +[26] H. Qin, S. Fei, and X. Li-Jost. Multi-observable uncertainty relations in product form +of variances. +Scientific Reports, 6:31192, 2016. +arXiv:1608.03089, doi:10.1038/ +srep31192. +[27] Q. Song and C. Qiao. +Stronger Schrödinger-like uncertainty relations. +Phys. Lett. +A, 380(37):2925–2930, 2016. arXiv:1504.01137, doi:10.1016/j.physleta.2016.06. +054. +[28] Y. Xiao, N. Jing, X. Li-Jost, and S. Fei. Weighted uncertainty relations. Scientific +Reports, 6:23201, 2016. arXiv:1603.01004, doi:10.1038/srep23201. +[29] D. Mondal, S. Bagchi, and A. K. Pati. Tighter uncertainty and reverse uncertainty rela- +tions. Phys. Rev. A, 95(5):052117, 2017. arXiv:1607.06712, doi:10.1103/PhysRevA. +95.052117. +[30] Q. Song, G. Li, J. annd Peng, and C. Qiao. A stronger multi-observable uncertainty re- +lation. Scientific Reports, 7:44764, 2017. arXiv:1701.01072, doi:10.1038/srep44764. +[31] J. Zhang, Y. Zhang, and C. Yu. Stronger uncertainty relations with improvable upper +and lower bounds. Quantum Information Processing, 16:131, 2017. arXiv:1607.08223, +doi:10.1007/s11128-017-1585-z. +[32] X. Zheng and G. Zhang. Variance-based uncertainty relation for incompatible observers. +Quantum Information Processing, 16:167, 2017. +arXiv:1705.07396, doi:10.1007/ +s11128-017-1619-6. +[33] V. V. Dodonov. Variance uncertainty relations without covariances for three and four +observables. +Phys. Rev. A, 97(2):022105, 2018. +arXiv:1711.04037, doi:10.1103/ +PhysRevA.97.022105. +[34] H. de Guise, L. Maccone, B. C. Sanders, and N. Shukla. +State-independent un- +certainty relations. +Phys. Rev. A, 98(4):042121, 2018. +arXiv:1804.06794, doi: +10.1103/PhysRevA.98.042121. +[35] P. Busch and O. Reaerdon-Smith. On quantum uncertainty relations and uncertainty +regions. 2019. arXiv:1901.03695, doi:10.48550/arXiv.1901.03695. +[36] P. Giorda, L. Maccone, and A. Riccardi. State-independent uncertainty relations from +eigenvalue minimization. Phys. Rev. A, 99(5):052121, 2019. arXiv:1810.09775, doi: +10.1103/PhysRevA.99.052121. +[37] X. Zheng, S. Ma, G. Zhang, H. Fan, and W. Liu. Unified and exact framework for +variance-based uncertainty relations. Scientific Reports, 10:150, 2020. arXiv:1803. +08720, doi:10.1038/s41598-019-56803-2. +28 + +[38] J. Li and C. Qiao. +The generalized uncertainty principle. +Annalen der Physik, +533(1):2000335, 2021. +arXiv:2003.08705, doi:https://doi.org/10.1002/andp. +202000335. +[39] L. Zhang, S. Luo, S. Fei, and J. Wu. Uncertainty regions of observables and state- +independent uncertainty relations. +Quantum Information Processing, 20:357, 2021. +arXiv:2110.14134, doi:10.1007/s11128-021-03303-w. +[40] S. Chiew and M. Gessner. Improving sum uncertainty relations with the quantum Fisher +information. Phys. Rev. Res., 4(1):013076, 2022. arXiv:2109.06900, doi:10.1103/ +PhysRevResearch.4.013076. +[41] Y. Xiao, N. Jing, B. Yu, S. Fei, and X. Li-Jost. Near-optimal variance-based uncertainty +relations. Front. Phys., 10:846330, 2022. arXiv:1610.01692, doi:10.3389/fphy.2022. +846330. +[42] M. Rédei and S. J. Summers. Quantum probability theory. Stud. Hist. Phil. Mod. Phys., +38(2):390–417, 2007. arXiv:quant-ph/0601158, doi:10.1016/j.shpsb.2006.05.006. +[43] M. S. Leifer and R. W. Spekkens. +Towards a formulation of quantum theory as a +causally neutral theory of bayesian inference. Phys. Rev. A, 88(5):052130, 2013. arXiv: +1107.5849, doi:10.1103/PhysRevA.88.052130. +[44] A. Ben-Israel and T. N. Greville. Generalized Inverses: Theory and Applications, chap- +ter chapter 6, pages 220–221. CMS Books in Mathematics. Springer, 2nd edition, 2003. +doi:doi.org/10.1007/b97366. +[45] E. Wigner. On the quantum correction for thermodynamic equilibrium. Phys. Rev., +40(5):749–759, 1932. doi:10.1103/PhysRev.40.749. +[46] D. Gross. Hudson’s theorem for finite-dimensional quantum systems. J. Math. Phys., +47:122107, 2006. arXiv:quant-ph/0602001, doi:10.1063/1.2393152. +[47] T. L. Curtright, D. B. Fairlie, and C. K. Zachos. A Concise Treatise on Quantum +Mechanics in Phase Space. World Scientific, 2014. doi:10.1142/8870. +[48] J. G. Kirkwood. Quantum statistics of almost classical assemblies. Phys. Rev., 44(1):31– +37, 1933. doi:10.1103/PhysRev.44.31. +[49] P. A. M. Dirac. On the analogy between classical and quantum mechanics. Rev. Mod. +Phys., 17(2-3):195–199, 1945. doi:10.1103/RevModPhys.17.195. +[50] M. Lostaglio, A. Belenchia, A. Levy, S. Hernández-Gómez, N. Fabbri, and S. Gherardini. +Kirkwood-dirac quasiprobability approach to quantum fluctuations: Theoretical and ex- +perimental perspectives. 2022. arXiv:2206.11783, doi:10.48550/arXiv.2206.11783. +29 + +A +Amplitude Operators and Purifications +Proposition A.1. Given a density operator ρS on a Hilbert space HS, let HS′ be another +copy of the same Hilbert space and let {|j⟩} be an orthonormal basis for HS and HS′. Define +the vector +��Φ+� +SS′ = +� +j +|j⟩S |j⟩S′ . +Let LS : HE → HS be an amplitude operator for ρS and let {|k⟩E} be an orthonormal +basis for HE. Then IS ⊗LT +S′ |Φ+⟩SS′ is a purification of ρS, where T denotes transpose in the +|j⟩⟨k|SE basis. Similarly, if |ψ⟩SE ∈ HS⊗HE is a purification of ρS then LS = ⟨ψ∗|S′E |Φ+⟩SS′ +is an amplitude operator for ρS, where ∗ denotes complex conjugation in the |jk⟩S′E basis. +Proof. If LS is an amplitude operator for ρS then ρS = LSL† +S. We have to show that this +implies that TrE +� +IS ⊗ LT +S′ |Φ+⟩⟨Φ+|SS′ IS ⊗ +� +LT +S′ +�†� += ρS. Note that +� +LT +S′ +�† = L∗ +S′, where ∗ +denotes complex conjugate in the |j⟩⟨k|SE basis. Therefore, we have +TrE +� +IS ⊗ LT +S′ +��Φ+�� +Φ+�� +SS′ IS ⊗ L∗ +S′ +� += +� +j,k +|j⟩⟨k|S TrE +� +LT +S′ |j⟩⟨k|S′ L∗ +S′ +� +(68) += +� +j,k +|j⟩⟨k|S +� +k +��L∗ +SLT +S +��j +� +S , +(69) +where we have changed the index S′ to S because they refer to the same Hilbert space and +� +k +��LT +SL∗ +S +��j +� +S is a scalar. Rearranging this, we have +TrE +� +IS ⊗ LT +S′ +��Φ+�� +Φ+�� +SS′ IS ⊗ L∗ +S′ +� += +� +j,k +|j⟩S +� +k +��L∗ +SLT +S +��j +� +S ⟨k|S +(70) += +� +j,k +|j⟩⟨j|S +� +L∗ +SLT +S +�T |k⟩⟨k|S +(71) += +� +L∗ +SLT +S +�T = LSL† +S = ρS. +(72) +For the other direction, we have to prove that LSL† +S = ρS, where LS = ⟨ψ∗|S′E |Φ+⟩SS′ +and |ψ⟩SE is any purification of ρS, i.e. TrE (|ψ⟩⟨ψ|SE) = ρS. +First, let |ψ⟩SE = � +jk αjk |j⟩S ⊗ |k⟩E be the decomposition of |ψ⟩SE in the |jk⟩SE basis. +We have |ψ∗⟩SE = � +jk α∗ +jk |j⟩S ⊗ |k⟩E and the condition TrE (|ψ⟩⟨ψ|SE) = ρS is equivalent +to � +j,k,l αjkα∗ +lk |j⟩⟨l|S = ρS. Note also that ⟨j|S′ |Φ+⟩SS′ = |j⟩S. +30 + +Hence, we have +LSL† +S = +� +⟨ψ∗|S′E +��Φ+� +SS′ +� � +⟨ψ∗|S′E +��Φ+� +SS′ +�† +(73) += ⟨ψ∗|S′E +��Φ+� +SS′ +� +Φ+�� +SS′ |ψ∗⟩S′E +(74) += +� +jklm +αjk ⟨j|S′ ⟨k|E′ +��Φ+�� +Φ+�� +SS′ α∗ +lm |l⟩S′ |m⟩E +(75) += +� +jklm +αjkα∗ +lm ⟨k|m⟩E +� +⟨j|S′ +��Φ+� +SS′ +� �� +Φ+�� +SS′ |l⟩S′ +� +(76) += +� +jkl +αjkα∗ +lk |j⟩⟨l|S +(77) += ρS. +(78) +31 + diff --git a/KtFAT4oBgHgl3EQfwB6h/content/tmp_files/load_file.txt b/KtFAT4oBgHgl3EQfwB6h/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..fc8bad554e9d8e976d461c21bb78d1c247641d5a --- /dev/null +++ b/KtFAT4oBgHgl3EQfwB6h/content/tmp_files/load_file.txt @@ -0,0 +1,1135 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf,len=1134 +page_content='Uncertainty from the Aharonov-Vaidman Identity Matthew S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Leifer Institute for Quantum Studies and Schmid College of Science and Technology Chapman University, One University Drive, Orange, CA 92866, USA January 23, 2023 Abstract In this article, I show how the Aharonov-Vaidman identity A |ψ⟩ = ⟨A⟩ |ψ⟩ + ∆A ��ψ⊥ A � can be used to prove relations between the standard deviations of observ- ables in quantum mechanics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' In particular, I review how it leads to a more direct and less abstract proof of the Robertson uncertainty relation ∆A∆B ≥ 1 2 |⟨[A, B]⟩| than the textbook proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' I discuss the relationship between these two proofs and show how the Cauchy-Schwarz inequality can be derived from the Aharonov-Vaidman identity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' I give Aharonov-Vaidman based proofs of the Maccone-Pati uncertainty relations and I show how the Aharonov-Vaidman identity can be used to handle propagation of uncertainty in quantum mechanics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Finally, I show how the Aharonov-Vaidman identity can be extended to mixed states and discuss how to generalize the results to the mixed case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' 1 Introduction Let A be a Hermitian operator on a Hilbert space H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Then, for any (not necessarily nor- malized) vector |ψ⟩ ∈ H, A |ψ⟩ = ⟨A⟩ |ψ⟩ + ∆A ��ψ⊥ A � , (1) where ⟨A⟩ = ⟨ψ|A|ψ⟩ / ⟨ψ|ψ⟩ is the expectation value of A, ∆A = � ⟨A2⟩ − ⟨A⟩2 is its standard deviation, and ��ψ⊥ A � is a vector that is orthogonal to |ψ⟩, has equal norm � ψ⊥ A ��ψ⊥ A � = ⟨ψ|ψ⟩, and depends on the operator A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Equation (1) is the Aharonov-Vaidman Identity, which first appeared in [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Yakir Aharonov has stated that he “[does not] understand why it doesn’t appear in every quantum book” [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' The main purpose of this article is to explain why it should appear in undergrad- uate quantum mechanics textbooks1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' 1Other demonstrations of the usefulness of the Aharonov-Vaidman identity include its use in the proof that, for any state |ψ⟩ and any observable A, |ψ⟩⊗n is an approximate eigenstate of the observable ¯A = 1 n �n j=1 Aj for large n, where Aj refers to A acting on the jth subsystem [1], and its use in deriving the minimum time required for evolution to an orthogonal quantum state [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' 1 arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='08679v1 [quant-ph] 20 Jan 2023 The uncertainty relation that is proved most often in quantum mechanics classes and textbooks is the Robertson relation [4]: ∆A∆B ≥ 1 2 |⟨[A, B]⟩| , (2) where [A, B] = AB − BA is the commutator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' As pointed out by Schrödinger [5], the Robertson relation can be extended to (∆A)2 (∆B)2 ≥ ���� 1 2 ⟨{A, B}⟩ − ⟨A⟩ ⟨B⟩ ���� 2 + ���� 1 2 ⟨[A, B]⟩ ���� 2 , (3) where {A, B} = AB + BA is the anti-commutator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Although not often emphasized in quantum mechanics classes, the Schrödinger relation is not harder to prove than the Robertson relation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' In fact, the standard textbook proof of the Robertson relation effectively proves the Schrödinger relation and then throws away the anti-commutator term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' The proof almost universally adopted in textbooks is based on the Cauchy-Schwarz in- equality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' While this proof is elementary for those familiar with the mathematics of Hilbert spaces, it can be daunting for undergraduate physics students, who are likely encountering Hilbert spaces for the first time along with quantum mechanics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' In this article, I will review more direct proofs of eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (2) and eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (3) from the Aharonov- Vaidman identity that only make use of basic properties of complex numbers and inner products.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' These proofs previously appeared in [6] and the proof of the Robertson relation is also problem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='10 in Aharonov and Rohrlich’s book “Quantum Paradoxes” [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' The proof of the Aharonov-Vaidman identity itself is uses similar ideas to one of the standard proofs of the Cauchy-Schwarz identity, but is perhaps more memorable to undergraduate physics students because it uses concepts that have a physical meaning, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' expectation values and standard deviations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' The proof of the Robertson and Schrödinger relations so obtained is not independent of the standard Cauchy-Schwarz based proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' I shall discuss their relationship and show that the Cauchy-Schwarz inequality can itself be derived from eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' The main virtue of using the Aharonov-Vaidman based proof of the uncertainty relation is that it is more direct and involves fewer abstractions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' To be clear, I am not against using or teaching the Cauchy-Schwarz inequality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' It has been called “one of the most widely used and important inequalities in all of mathematics” [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' In fact, the Aharonov-Vaidman based proof still uses one instance of the Cauchy-Schwarz inequality, namely that if |ψ⟩ and |φ⟩ are unit vectors then |⟨φ|ψ⟩| ≤ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' But this is easily motivated by the idea that ⟨φ|ψ⟩ is a generalization of the cosine of an angle, and it is used in a more direct way than in the standard proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Students of quantum mechanics also need to know the Cauchy-Schwarz inequality to prove that the Born rule always yields well-defined probabilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Physics students should learn the Cauchy-Schwarz inequality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' I just think it should be used in a less abstract way where possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Besides the Robertson and Schrödinger relations, many other uncertainty relations are known.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Indeed, since uncertainty relations have found applications in quantum information 2 science [9, 10, 11, 12, 13, 14, 15] and quantum foundations [16, 17], proving new ones has become something of a sport.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' The two most common classes of uncertainty relations are those based on entropy [18] and those based on standard deviations [4, 5, 19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Many of the standard deviation based relations can be derived from the Aharonov-Vaidman relation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' I include a proof of the Maccone-Pati uncertainty relations [20] to illustrate this.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' While these are not the most recent or tightest known uncertainty relations, I include them because they have a simple and elegant Aharonov-Vaidman based proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' For more recent work on standard deviation uncertainty relations, see [21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Another place where relationships between standard deviations are important is in the propagation of uncertainty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' In classical statistics, if random variables X1, X2, · · · , Xn have standard deviations ∆X1, ∆X2, · · · ∆Xn then a function of them f(X1, X2, · · · , Xn) has stan- dard deviation ∆f that is a function of ∆X1, ∆X2, · · · ∆Xn (and their correlations if the variables are not independent).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Formulas for the propagation of uncertainty tell us how to compute this function, and are commonly used to estimate experimental errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' In quantum mechanics, similar formulas can be derived relating the standard deviations of observables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' They differ from their classical counterparts due to the fact that quantum observables do not commute, but provided this is taken care of they can be derived by the same methods as in the classical case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' However, they can alternatively be derived from the Aharonov-Vaidman identity, as I shall explain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Although the Aharonov-Vaidman identity is usually discussed for pure quantum states, it can be extended to mixed states, either by use of purification or an equivalent concept called an amplitude operator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Relations between standard deviations can be extended to mixed states, but obtaining tight bounds is sometimes more difficult than in the pure case due to the need to optimize over all purifications or amplitude operators that can represent a given mixed state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' The remainder of this article is structured as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Section 2 gives the proof of the Aharonov-Vaidman identity and a corollary that is useful for understanding the equality conditions in uncertainty relations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Section 3 presents the proof of the Robertson and Schrödinger relations based on the Aharonov-Vaidman identity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Section 4 explains the rela- tionship with the standard textbook proof of the Robertson relation and explains how the Cauchy-Schwarz inequality can be derived from the Aharonov-Vaidman identity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Section 5 comments on the effective teaching of the Robertson uncertainty relations via the Aharonov- Vaidman identity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Section 6 presents Aharonov-Vaidman based proofs of the Maccone-Pati uncertainty relations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Section 7 describes how to use the Aharonov-Vaidman identity to derive formulas for the propagation of quantum uncertainty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Section 8 explains how to gen- eralize the Aharonov-Vaidman relation to mixed states using amplitude operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (The relationship between amplitude operators and purifications is discussed in appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=') Fi- nally, section 9 presents the summary and conclusions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' I intend this article to be pedagogical and self-contained, so as to be accessible to under- graduate students and anyone teaching introductory quantum mechanics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' 3 2 Proof of the Aharonov Vaidman Identity Sometimes, it is useful to generalize the Aharonov-Vaidman identity to non-Hermitian op- erators, so we prove the more general version here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1 (The Aharonov-Vaidman Identity).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Let A be a linear operator on a Hilbert space H and let |ψ⟩ be a (not necessarily normalized) vector in H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Then, A |ψ⟩ = ⟨A⟩ |ψ⟩ + ∆A ��ψ⊥ A � , (4) where ⟨A⟩ = ⟨ψ|A|ψ⟩ / ⟨ψ|ψ⟩, ∆A = � ⟨A†A⟩ − |⟨A⟩|2, and ��ψ⊥ A � is a vector orthogonal to |ψ⟩ that depends on both |ψ⟩ and A and satisfies � ψ⊥ A ��ψ⊥ A � = ⟨ψ|ψ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Note that, if A is Hermitian, then this reduces to eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (1), where ⟨A⟩ and ∆A are the expectation value and standard deviation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' In general, ⟨A⟩ is a complex number, but ∆A is always real and non-negative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' For most of what we need to do, it is sufficient to consider the case where |ψ⟩ is a unit vector, in which case ��ψ⊥ A � is also a unit vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' The exception is the proof of the Cauchy-Schwarz inequality (proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1 in section 4), which uses the identity with an unnormalized vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Given a vector |ψ⟩ ∈ H, any other vector |φ⟩ ∈ H can be written as |φ⟩ = α |ψ⟩ + β ��ψ⊥� , where α and β are complex coefficients and ��ψ⊥� is some vector that is orthogonal to |ψ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' By an appropriate rescaling of β, we can ensure that � ψ⊥��ψ⊥� = ⟨ψ|ψ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Applying this to |φ⟩ = A |ψ⟩ gives A |ψ⟩ = α |ψ⟩ + β ��ψ⊥� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (5) To determine α, take the inner product of eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (5) with |ψ⟩, which gives ⟨ψ|A|ψ⟩ = α ⟨ψ|ψ⟩ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (6) Rearranging this gives α = ⟨A⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' To determine β, substitute α = ⟨A⟩ into eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (5) and take the inner product of A |ψ⟩ with itself to obtain ⟨ψ| A†A |ψ⟩ = |⟨A⟩|2 ⟨ψ|ψ⟩ + |β|2 � ψ⊥��ψ⊥� = |⟨A⟩|2 ⟨ψ|ψ⟩ + |β|2 ⟨ψ|ψ⟩ , where we have used � ψ⊥��ψ⊥� = ⟨ψ|ψ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Rearranging and using � A†A � = � ψ ��A†A ��ψ � / ⟨ψ|ψ⟩ gives |β|2 = � A†A � − |⟨A⟩|2 = (∆A)2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (7) This means that β = (∆A)eiθ for some phase angle θ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' If we define ��ψ⊥ A � = eiθ ��ψ⊥� then ��ψ⊥ A � is still orthogonal to |ψ⟩, its norm is unchanged, and we have eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' 4 The following corollary is useful for finding the conditions for equality in uncertainty relations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' In general, for two operators A and B, and for a unit vector |ψ⟩, � ψ⊥ A ��ψ⊥ B � = � A†B � − ⟨A⟩∗ ⟨B⟩ ∆A∆B .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (8) Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' From proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1, we have A |ψ⟩ = ⟨A⟩ |ψ⟩ + ∆A ��ψ⊥ A � , (9) B |ψ⟩ = ⟨B⟩ |ψ⟩ + ∆B ��ψ⊥ B � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (10) Taking the inner product of these gives ⟨ψ| A†B |ψ⟩ = ⟨A⟩∗ ⟨B⟩ + ∆A∆B � ψ⊥ A ��ψ⊥ B � , (11) Rearranging gives the desired result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Note that, if A and B are Hermitian then we have � ψ⊥ A ��ψ⊥ B � = ⟨AB⟩ − ⟨A⟩ ⟨B⟩ ∆A∆B .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (12) If it is also the case that [A, B] = 0 then eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (12) is the correlation, denoted corrA,B, that would be obtained from a joint measurement of A and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' The correlation is a well-known statistical measure of how two random variables are related to one another.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Equation (12) is a formal generalization of the correlation, so we will also denote it corrA,B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' However, if A and B do not commute then corrA,B is generally a complex number, there is no joint measurement of A and B of which corrA,B could be the correlation, and AB is not an observable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' The real and imaginary parts of corrA,B are Re (corrA,B) = 1 2 �� ψ⊥ A ��ψ⊥ B � + � ψ⊥ B ��ψ⊥ A �� = 1 2 ⟨{A, B}⟩ − ⟨A⟩ ⟨B⟩ ∆A∆B (13) Im (corrA,B) = 1 2i �� ψ⊥ A ��ψ⊥ B � − � ψ⊥ B ��ψ⊥ A �� = ⟨[A, B]⟩ 2i∆A∆B , (14) The real part is also a formal generalization of the correlation in that it reduces to the classical formula when A and B commute.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' We denote it RcorrA,B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' 3 The Robertson and Schrödinger Uncertainty Relations We are now in a position to prove the Robertson and Schrödinger uncertainty relations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1 (The Robertson Uncertainty Relation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Let A and B be two Hermitian operators on a Hilbert space H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Then, for any unit vector |ψ⟩ ∈ H ∆A∆B ≥ 1 2 |⟨[A, B]⟩| .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (15) 5 Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' From the Aharonov-Vaidman identity, we have A |ψ⟩ = ⟨A⟩ |ψ⟩ + ∆A ��ψ⊥ A � , (16) B |ψ⟩ = ⟨B⟩ |ψ⟩ + ∆B ��ψ⊥ B � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (17) Taking the inner product of these two equations and its complex conjugate gives ⟨ψ|AB|ψ⟩ = ⟨A⟩ ⟨B⟩ + ∆A∆B � ψ⊥ A ��ψ⊥ B � (18) ⟨ψ|BA|ψ⟩ = ⟨A⟩ ⟨B⟩ + ∆A∆B � ψ⊥ B ��ψ⊥ A � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (19) Subtracting these two equations gives ⟨ψ|(AB − BA)|ψ⟩ = ∆A∆B �� ψ⊥ A ��ψ⊥ B � − � ψ⊥ B ��ψ⊥ A �� , (20) or, ⟨[A, B]⟩ = ∆A∆B �� ψ⊥ A ��ψ⊥ B � − � ψ⊥ B ��ψ⊥ A �� , (21) Since � ψ⊥ B ��ψ⊥ A � is the complex conjugate of � ψ⊥ A ��ψ⊥ B � , we can rewrite this as ⟨[A, B]⟩ = 2i∆A∆BIm �� ψ⊥ A ��ψ⊥ B �� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (22) Taking the absolute value of both sides and rearranging gives ∆A∆B ��Im �� ψ⊥ A ��ψ⊥ B ���� = 1 2 |⟨[A, B]⟩| .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (23) Because ��ψ⊥ A � and ��ψ⊥ B � are unit vectors, 0 ≤ ��� ψ⊥ A ��ψ⊥ B ���2 ≤ 1, and hence the absolute value of the imaginary part of � ψ⊥ B ��ψ⊥ A � is also bounded between 0 and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Hence, we have ∆A∆B ≥ 1 2 |⟨[A, B]⟩| .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (24) The condition for equality in the Robertson relation is ��Im �� ψ⊥ A ��ψ⊥ B ���� = 1 or, equiva- lently, corrA,B = ±i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' States that saturate the inequality are called (Robertson) intelligent states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' The condition corrA,B = ±i can be used to find intelligent states, although this is not easier than solving for equality in the Robertson relation directly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='2 (The Schrödinger Uncertainty Relation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Let A and B be two Hermitian operators on a Hilbert space H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Then, for any unit vector |ψ⟩ ∈ H (∆A)2 (∆B)2 ≥ ���� 1 2 ⟨{A, B}⟩ − ⟨A⟩ ⟨B⟩ ���� 2 + ���� 1 2 ⟨[A, B]⟩ ���� 2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (25) 6 Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Taking the sum of eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (18) and eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (19) gives ⟨{A, B}⟩ = 2 ⟨A⟩ ⟨B⟩ + ∆A∆B �� ψ⊥ A ��ψ⊥ B � + � ψ⊥ B ��ψ⊥ A �� , (26) or, ⟨{A, B}⟩ − 2 ⟨A⟩ ⟨B⟩ = ∆A∆B �� ψ⊥ A ��ψ⊥ B � + � ψ⊥ B ��ψ⊥ A �� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (27) Adding this to eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (21) gives ⟨{A, B}⟩ − 2 ⟨A⟩ ⟨B⟩ + ⟨[A, B]⟩ = 2∆A∆B � ψ⊥ A ��ψ⊥ B � , (28) or, ∆A∆B � ψ⊥ A ��ψ⊥ B � = 1 2 ⟨{A, B}⟩ − ⟨A⟩ ⟨B⟩ + 1 2 ⟨[A, B]⟩ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (29) Now, because A and B are Hermitian, {A, B} is Hermitian and [A, B] is anti-Hermitian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Therefore ⟨{A, B}⟩ is real and ⟨[A, B]⟩ is imaginary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Further ⟨A⟩, ⟨B⟩, ∆A and ∆B are real.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Therefore, taking the modulus squared of eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (29) gives (∆A)2(∆B)2 ��� ψ⊥ A ��ψ⊥ B ���2 = ���� 1 2 ⟨{A, B}⟩ − ⟨A⟩ ⟨B⟩ ���� 2 + ���� 1 2 ⟨[A, B]⟩ ���� 2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (30) Finally, because ��ψ⊥ A � and ��ψ⊥ B � are unit vectors, we have 0 ≤ ��� ψ⊥ A ��ψ⊥ B ���2 ≤ 1, from which the result follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' The condition for equality in the Schrödinger relation is ��� ψ⊥ A ��ψ⊥ B ���2 = |corrA,B|2 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' States that saturate the inequality are called (Schrödinger) intelligent states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' The condition |corrA,B|2 = 1 can be used to find intelligent states, although this is not easier than solving for equality in the Schrödinger relation directly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' 4 The Textbook Proof and The Cauchy-Schwarz Inequal- ity The textbook proofs of the Robertson and Schrödinger uncertainty relations are based on the Cauchy-Schwarz inequality |⟨f|g⟩|2 ≤ ⟨f|f⟩ ⟨g|g⟩ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (31) Note that the proofs given in section 3 also make use of a special case of this inequality: that for unit vectors |⟨f|g⟩|2 ≤ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' This is applied to |f⟩ = ��ψ⊥ A � , |g⟩ = ��ψ⊥ B � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' My aim is not to eliminate any use of the Cauchy-Schwarz inequality, but just to argue that the proof is more memorable if the inequality is applied in a different way than in the standard proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' In the standard proof, the Cauchy-Schwarz inequality is applied to the two vectors |f⟩ = (A − ⟨A⟩) |ψ⟩ and |g⟩ = (B − ⟨B⟩) |ψ⟩ to obtain |⟨ψ|(A − ⟨A⟩)(B − ⟨B⟩)|ψ⟩|2 ≤ � ψ ��(A − ⟨A⟩)2��ψ � � ψ ��(B − ⟨B⟩)2��ψ � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (32) 7 A few lines of messy algebra and cancellations, which I will spare you the details of, yields (∆A)2 (∆B)2 ≥ ���� 1 2 ⟨{A, B}⟩ − ⟨A⟩ ⟨B⟩ + 1 2 ⟨[A, B]⟩ ���� 2 , (33) from which we can derive the Schrödinger and Robertson relations by recognizing the real and imaginary parts of the right hand side.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' As physics students do not often see the Cauchy-Schwarz inequality prior to their first course on quantum mechanics, most textbooks include a proof of this as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' One of the common proofs uses reasoning similar to that which we used to establish the Aharonov- Vaidman identity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' It starts by recognizing that |g⟩ can be written as |g⟩ = α |f⟩ + β ��f ⊥� , (34) where ��f ⊥� is a unit vector that is orthogonal to |f⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' To find α, take the inner product of this with |f⟩, which yields α = ⟨f|g⟩ / ⟨f|f⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Substituting this back into eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (34) and then taking the inner product of |g⟩ with itself gives ⟨g|g⟩ = |⟨f|g⟩|2 ⟨f|f⟩ + |β|2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (35) The Cauchy-Schwarz inequality follows from this by recognizing that |β|2 is real and non- negative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Summarizing, the standard proof of the Robertson inequality consists of: proving the Cauchy-Schwarz inequality and then finding convenient vectors to insert into the inequality that will yield terms involving ∆A and ∆B after some algebra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' From the Aharonov-Vaidman identity, we can see that the reason the choice |f⟩ = (A − ⟨A⟩) |ψ⟩ and |g⟩ = (B − ⟨B⟩) |ψ⟩ is guaranteed work is that |f⟩ = ∆A ��ψ⊥ A � and |g⟩ = ∆B ��ψ⊥ B � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' After inserting these choices, one has to multiply out and simplify the expressions in the Cauchy-Schwarz inequality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' This involves recognizing things like ⟨A⟩ ⟨ψ|A|ψ⟩ = ⟨A⟩2 and then canceling several terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' It is difficult for students to follow the full details of this in a lecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' In the approach using the Aharonov-Vaidman relation, we already have expressions involving ∆A and ∆B, so it is easier to see how to get an expression involving ∆A∆B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' This expression has fewer terms and there is less cancellation to do.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Although the approach using the Aharonov-Vaidman identity uses the Cauchy-Schwarz inequality in a less convoluted way, it uses similar mathematical ideas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' For vectors |f⟩ and |g⟩, we can write |g⟩ in terms of |f⟩ and an orthogonal vector, as in the proof of Cauchy- Schwarz, or we can write both vectors in terms of a third vector |h⟩ as |f⟩ = α1 |h⟩ + β1 ��h⊥ f � (36) |g⟩ = α2 |h⟩ + β2 ��h⊥ g � , (37) where ��h⊥ f � and ��h⊥ g � are (generally different) vectors orthogonal to |h⟩ and α1, β1, α2, β2 are complex coefficients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' This is what we do in the proof of the Aharonov-Vaidman identity with 8 the choices |f⟩ = A |ψ⟩, |g⟩ = B |ψ⟩ and |h⟩ = |ψ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' The advantage of this approach is that it immediately yields expressions involving the expectation values and standard deviations of the observables, which it is easy to see what to do with in order to get the uncertainty relations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' From this point of view, the standard proof looks like shoehorning something into the Cauchy-Schwarz inequality that will yield standard deviations, and then backtracking to a point more easily obtained from the Aharonov-Vaidman identity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' At the end of the day, both approaches use the same mathematics, but the Aharonov-Vaidman approach does so in a simpler and more direct way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' I would go so far as to say that whenever you are tempted to use the Cauchy-Schwarz inequality to prove a relationship between standard deviations of observables in quantum mechanics, you will have an easier time working from the Aharonov-Vaidman identity (and the special case |⟨f|g⟩|2 ≤ 1 of the Cauchy-Schwarz inequality for unit vectors) instead.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Section 6 and Section 7 give more examples of this.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' I end this section by showing that you can prove the Cauchy-Schwarz inequality from the Aharonov-Vaidman identity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' I include this not because I think it is the best way to prove the Cauchy-Schwarz inequality, but because finding alternative proofs of the Cauchy-Schwarz inequality is the mathematician’s equivalent of the sport of finding new uncertainty relations in quantum mechanics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' It also shows that, in principle, there is nothing that can be proved using the Cauchy-Schwarz inequality that could not be proved using the Aharonov-Vaidman identity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Of course, outside the context of standard deviations in quantum mechanics, using the Aharonov-Vaidman identity instead of the Cauchy-Schwarz inequality is unlikely to yield a better proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1 (Cauchy-Schwarz Inequality).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Let |f⟩ and |g⟩ be two vectors in a Hilbert space H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Then |⟨f|g⟩|2 ≤ ⟨f|f⟩ ⟨g|g⟩ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (38) Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' First note that the inequality trivially holds whenever ⟨f|g⟩ = 0 and that ⟨f|f⟩ = 0 implies ⟨f|g⟩ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Therefore, we can assume that both ⟨f|g⟩ ̸= 0 and ⟨f|f⟩ > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Let P = |g⟩⟨g|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Note this is not necessarily a projector because |g⟩ does not have to be normalized, but it is a Hermitian operator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Applying the Aharonov-Vaidman identity to P and |f⟩ gives P |f⟩ = ⟨P⟩ |f⟩ + ∆P ��f ⊥ P � , (39) or equivalently |g⟩ ⟨g|f⟩ = ⟨f|g⟩ ⟨g|f⟩ ⟨f|f⟩ |f⟩ + ∆P ��f ⊥ P � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (40) Taking the inner product with ��f ⊥ P � gives � f ⊥ P ��g � ⟨g|f⟩ = ∆P ⟨f|f⟩ , (41) where we used the fact that � f ⊥ P ��f ⊥ P � = ⟨f|f⟩ Rearranging and taking the complex conjugate gives � g ��f ⊥ P � = ∆P ⟨f|f⟩ ⟨f|g⟩ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (42) 9 Now, taking the inner product of eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (40) with |g⟩ gives ⟨g|g⟩ ⟨g|f⟩ = ⟨f|g⟩ ⟨g|f⟩ ⟨f|f⟩ ⟨g|f⟩ + ∆P � g ��f ⊥ P � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (43) Multiplying both sides by ⟨f|f⟩ / ⟨g|f⟩ gives ⟨f|f⟩ ⟨g|g⟩ = ⟨f|g⟩ ⟨g|f⟩ + ∆P � g ��f ⊥ P � ⟨f|f⟩ ⟨g|f⟩ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (44) Substituting eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (42) into this gives ⟨f|f⟩ ⟨g|g⟩ = ⟨f|g⟩ ⟨g|f⟩ + (∆P)2 |⟨f|f⟩|2 ⟨f|g⟩ ⟨g|f⟩ , (45) or ⟨f|f⟩ ⟨g|g⟩ = |⟨f|g⟩|2 + (∆P)2 |⟨f|f⟩|2 |⟨f|g⟩|2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (46) Now, the terms ∆P, ⟨f|f⟩ and |⟨f|g⟩| are all real and non-negative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Hence, ⟨f|f⟩ ⟨g|g⟩ ≥ |⟨f|g⟩|2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (47) 5 Pedagogical Notes In order to teach the Robertson uncertainty relation via the Aharonov-Vaidman identity, you first have to establish the Aharonov-Vaidman identity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' For the purposes of proving the Robertson uncertainty relation, it is sufficient to restrict the operator in the identity to be Hermitian and the vector |ψ⟩ to be a unit vector, as I shall in this section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' In my experience, not all students immediately understand why, given a unit vector |ψ⟩, any other unit vector |φ⟩ can be written as |φ⟩ = α |ψ⟩ + β ��ψ⊥� , (48) where ��ψ⊥� is a unit vector orthogonal to |ψ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' They will probably have seen Gram-Schmidt orthogonalization in a linear algebra class, but may have difficulty using that knowledge here due to the jump to abstract Hilbert spaces and Dirac notation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' To aid intuition, I remark that |ψ⟩ and |φ⟩ span a two-dimensional subspace of H and show them fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' By the process of Gram-Schmidt orthogonalization, we can construct an orthornormal basis for this subspace consisting of |ψ⟩ and ��ψ⊥� = 1 � 1 − |⟨φ|ψ⟩|2 (|φ⟩ − |ψ⟩ ⟨ψ|φ⟩) , (49) 10 |ψ⟩ |φ⟩ |ψ⊥⟩ Figure 1: Diagram showing that there exists a unit vector ��ψ⊥� such that |ψ⟩ and ��ψ⊥� form an orthogonal basis for the two dimensional subspace of H spanned by |ψ⟩ and |φ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' from which we have eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (48) with α = ⟨ψ|φ⟩ and β = � 1 − |⟨φ|ψ⟩|2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' In my quantum mechanics classes, I set students in-class activities that involve things like deriving important equations or making order of magnitude estimates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' These take about 5-10 minutes each and are done in pairs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' I usually do two or three such activities per class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' I believe this increases active engagement and retention of the main principles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' I try to reduce the number of long derivations that I do myself on the board because I think they cause confusion about what the most important equations are and the derivations are rarely remembered by the students.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' However, I also do not want to set the students a long and complicated derivation to do themselves in class, so I try to find shorter derivations that they can do with guidance instead.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' The proof of the Robertson relation from the Aharonov- Vaidman relation is better suited to this approach than the standard proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' After establishing eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (48), I set students the following activity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' In Class Activity Given that A |ψ⟩ = α |ψ⟩ + β ��ψ⊥� , find α and β in terms of the expectation value ⟨A⟩ and standard deviation ∆A of A in the state |ψ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Although some students can do this straight away, most need some help.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' During the course of the activity, I walk around the class to get an idea of how they are doing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' When it seems like many students are stuck, I reveal the following three hints in sequence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Hints 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Try taking the inner product of A |ψ⟩ = α |ψ⟩ + β ��ψ⊥� with other states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Try taking the inner product of A |ψ⟩ with |ψ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Try taking the inner product of A |ψ⟩ with itself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Although most students can get α = ⟨A⟩ either straight away or after the first hint, |β| = ∆A is more challenging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' After taking the inner product with |ψ⟩, the obvious instinct is to take the inner product with ��ψ⊥� , which does not help, so the third hint is usually needed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' After this, it is a short hop to the Robertson relation via the proof given in section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' I think it would be more difficult to teach the standard proof in this way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' One would either have to ask the students to derive the Cauchy-Schwarz inequality for themselves or 11 derive the Robertson relation from Cauchy-Schwarz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' The former is a bit abstract for a quantum mechanics class and the latter involves a lot of algebra and cancellations with a high potential for making mistakes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Both would require a large number of hints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' In contrast, the proof of the Aharonov-Vaidman identity is relatively short, and I think that students who retain the identity are more likely to be able to reconstruct the proof of the Robertson relation for themselves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' 6 Other Uncertainty Relations for Standard Deviations Despite the ubiquity of the Schrödinger-Robertson uncertainty relations in quantum me- chanics classes, there are good reasons to go beyond them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' For example, consider a spin- 1/2 particle with spin operators Sx, Sy and Sz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' For this case, the Robertson uncertainty is ∆Sx∆Sy ≥ ℏ |⟨Sz⟩|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Let |x+⟩ be the spin-up state in the x direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' For this state we have ⟨Sz⟩ = 0, which is perfectly valid because |x+⟩ is an eigenstate of Sx and hence ∆Sx = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' However, because [Sx, Sy] ̸= 0 there is necessarily some uncertainty in Sy and in fact ∆Sy = ℏ/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' The Schrödinger relation also yields ∆Sx∆Sy ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' So the Schrödinger- Robertson relations do not capture all uncertainty trade-offs that necessarily exist in quan- tum mechanics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' More generally, for bounded operators A and B, any uncertainty relation of the form ∆A∆B ≥ f (A, B, |ψ⟩) for some function f must necessarily have f (A, B, |ψ⟩) = 0 whenever |ψ⟩ is an eigenstate of A or B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' For this reason, it makes sense to seek uncertainty relations that bound the sum of standard deviations ∆A + ∆B, the sum of variances (∆A)2 + (∆B)2, or more exotic combinations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' We shall discuss the Maccone-Pati relations, and some simple generalizations, in this section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Uncertainty relations are classified as either state dependent or state independent, de- pending on whether the right hand side of the inequality depends on the state |ψ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' For two observables A and B, a state dependent uncertainty relation is of the form f(∆A, ∆B) ≥ g(A, B, |ψ⟩), where f and g are specified functions, whereas a state independent uncertainty relation would be of the form f(∆A, ∆B) ≥ g(A, B), noting that g is no longer allowed to depend on |ψ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' On the face of it, a state dependent uncertainty relation is a strange idea, since, for any given normalized state |ψ⟩, we can always just calculate the uncertainties ∆A and ∆B and get the exact value of f(∆A, ∆B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Therefore, bounds on uncertainty that apply to all states seem more useful.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' However, a state dependent uncertainty relation can be a useful step in deriving a state independent one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' This can happen in two ways.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' First, it may happen that, for a particular choice of the observables A and B, the function g(A, B, |ψ⟩) turns out not to depend on |ψ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' For example, the Robertson relation ∆A∆B ≥ 1 2 |⟨ψ|[A, B]|ψ⟩| is state dependent, but if we choose A = x, B = p, then |⟨ψ|[A, B]|ψ⟩| = 1 and so we get the Heisenberg relation ∆x∆p ≥ ℏ 2, which is state independent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Since the main point of proving the Robertson uncertainty relation in a quantum mechanics class is to give a rigorous derivation of the Heisenberg relation, its state dependence does no harm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' However, the utility of the Robertson relation 12 for other classes of observable, such as spin components, is more questionable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Despite the fact that I have asked students to compute it for states of a spin-1/2 particle as a homework problem, I do not think there is ever a need to do this in practice, as it is just as easy to calculate the exact uncertainties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' The second way of obtaining a state independent uncertainty relation from a state de- pendent one is to optimize, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' if f(∆A, ∆B) ≥ g(A, B, |ψ⟩) then2 f(∆A, ∆B) ≥ min |ψ⟩ g(A, B, |ψ⟩).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (50) Of course, if f(∆A, ∆B) = ∆A∆B and A and B are bounded operators then this leads to the trivial relation ∆A∆B ≥ 0 because we can choose |ψ⟩ to be an eigenstate of either A or B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' However, for sums and more general combinations of observables, optimization can lead to a nontrivial relation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Further, if we are considering a set of experiments that can only prepare a subset of the possible states, then we can get an uncertainty relation that applies to those states by optimizing over the subset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' An example might be experiments in which we can only prepare the system in a Gaussian state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Although this does not yield a state independent uncertainty relation, it is more useful than a completely state dependent one, as it allows us to bound the possible uncertainties for a class of relevant states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' To summarize, state dependent uncertainty relations are a strange idea, and I am not sure whether they would ever have been considered had not Robertson introduced one as a way-point in proving the Heisenberg relation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' However, they can be useful in proving more generally applicable uncertainty relations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' The relations that we discuss here are state dependent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' The remainder of this section is structured as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' In section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1 we prove two propo- sitions called the sum relations that will be used repeatedly using the Aharonov-Vaidman identity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' In section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='2, we give an Aharonov-Vaidman based proof of the Maccone-Pati uncertainty relations, and in in section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='3 we give some simple generalizations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1 The Sum Relations Proposition 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Let A and B be linear operators acting on H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Then, for any |ψ⟩ ∈ H, ∆(A + B) ��ψ⊥ A+B � = ∆A ��ψ⊥ A � + ∆B ��ψ⊥ B � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Apply the Aharonov-Vaidman identity to A + B in two different ways.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' The first way is (A + B) |ψ⟩ = ⟨A + B⟩ |ψ⟩ + ∆(A + B) ��ψ⊥ A+B � = (⟨A⟩ + ⟨B⟩) |ψ⟩ + ∆(A + B) ��ψ⊥ A+B � , (51) 2The minimum in eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (50) may have to be replaced by an infimum, depending on the Hilbert space that the observables are defined on.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' 13 and the second is (A + B) |ψ⟩ = A |ψ⟩ + B |ψ⟩ = (⟨A⟩ + ⟨B⟩) |ψ⟩ + ∆A ��ψ⊥A� + ∆B ��ψ⊥ B � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (52) Subtracting eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (52) from eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (51) and rearranging gives the desired result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' The next proposition comes from [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Here, the proof relies on proposition 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1 and so is based on the Aharonov-Vaidman relation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' The original proof uses a different method and is a little more complicated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Proposition 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='2 (The Sum Relation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Let A and B be two linear operators acting on a Hilbert space H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Then, ∆(A + B) ≤ ∆A + ∆B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Let |ψ⟩ in proposition 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1 be a unit vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Then, starting from ∆(A + B) ��ψ⊥ A+B � = ∆A ��ψ⊥ A � + ∆B ��ψ⊥ B � and taking the inner product with ��ψ⊥ A+B � gives ∆(A + B) = ∆A � ψ⊥ A+B ��ψ⊥ A � + ∆B � ψ⊥A+B��ψ⊥ B � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' The left hand side of this equation is a real number, so the right hand side must be too.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Therefore, we can take the real part of each term to give ∆(A + B) = ∆ARe �� ψ⊥ A+B ��ψ⊥ A �� + ∆BRe �� ψ⊥A+B��ψ⊥ B �� , but the real part of an inner product between two unit vectors is ≤ 1, so we have ∆(A + B) ≤ ∆A + ∆B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' From the proof, we see that the equality condition for the sum relation is Rcorr(A + B, A) = Rcorr(A + B, B) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Remark 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' For a set of linear operators A1, A2, · · · , An on a Hilbert space H, Proposi- tion 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1 is easily generalized to ∆ � n � j=1 Aj � ���ψ⊥ �n j=1 Aj � = n � j=1 ∆Aj ���ψ⊥ Aj � , (53) by applying the Aharonov-Vaidman identity to �n j=1 Aj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Similarly, proposition 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='2 is easily generalized to ∆ � n � j=1 Aj � ≤ n � j=1 ∆Aj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (54) by taking the inner product of eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (53) with ���ψ⊥ �n j=1 Aj � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' We will also refer to the generaliza- tion in eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (54) as the sum relation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' 14 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='2 The Maccone-Pati Uncertainty Relations Between the time of Robertson’s uncertainty relation and now, there has always been some literature on uncertainty relations for variances and standard deviations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' However, the field was reinvigorated in 2014, when Maccone and Pati [20] proved a pair of uncertainty relations for sums of variances, which always give a nontrivial bound, even in the case of an eigenstate of an observable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Here, we give Aharonov-Vaidman based proofs of the Maccone-Pati relations3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Theorem 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='4 (The First Maccone-Pati Uncertainty Relation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Let A and B be Hermitian operators on a Hilbert space H and let |ψ⟩ ∈ H be a unit vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Then, (∆A)2 + (∆B)2 ≥ ±i ⟨[A, B]⟩ + ��� ψ⊥��(A ∓ iB) ��ψ ���2 , (55) where ��ψ⊥� is any unit vector orthogonal to |ψ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' We will prove (∆A)2 + (∆B)2 ≥ −i ⟨[A, B]⟩ + ��� ψ⊥��(A + iB) ��ψ ���2 by applying the Aharonov-Vaidman identity to (A + iB).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' The proof of the other inequality follows by re- placing A + iB with A − iB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Note that, even though A and B are Hermitian, A + iB is not, so it is crucial that we previously generalized the Aharonov-Vaidman identity to arbitrary linear operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Applying the Aharonov-Vaidman identity to A + iB gives (A + iB) |ψ⟩ = (⟨A⟩ + i ⟨B⟩) |ψ⟩ + ∆(A + iB) ��ψ⊥ A+iB � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Taking the inner product with any unit vector ��ψ⊥� orthogonal to |ψ⟩ gives � ψ⊥��(A + iB) ��ψ � = ∆(A + iB) � ψ⊥��ψ⊥ A+iB � , and taking the modulus squared of this gives ��� ψ⊥��(A + iB) ��ψ ���2 = (∆(A + iB))2 ��� ψ⊥��ψ⊥ A+iB ���2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Now, ��� ψ⊥��ψ⊥ A+iB ��� ≤ 1, so (∆(A + iB))2 ≥ ��� ψ⊥��(A + iB) ��ψ ���2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' The result now follows by expanding (∆(A + iB))2 as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (∆(A + iB))2 = ⟨(A − iB)(A + iB)⟩ − ⟨A − iB⟩ ⟨A + iB⟩ = � A2� + � B2� + i ⟨[A, B]⟩ − ⟨A⟩2 − ⟨B⟩2 = (∆A)2 + (∆B)2 + i ⟨[A, B]⟩ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' 3Although the Aharonov-Vaidman identity is used in [20], it is not used in the proofs of the uncertainty relations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' 15 Theorem 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='5 (The Second Maccone-Pati Uncertainty Relation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Let A and B be linear operators on a Hilbert space H and let |ψ⟩ ∈ H be a unit vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Then, (∆A)2 + (∆B)2 ≥ 1 2 ��� ψ⊥ A+B ��(A + B) ��ψ ���2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (56) Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Applying the Aharonov-Vaidman identity to A + B gives (A + B) |ψ⟩ = (⟨A⟩ + ⟨B⟩) |ψ⟩ + ∆(A + B) ��ψ⊥ A+B � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Taking the inner product with ��ψ⊥ A+B � gives � ψ⊥ A+B ��(A + B) ��ψ � = ∆(A + B) ≤ ∆A + ∆B, where the second line follows from the sum relation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' We could stop here and regard ∆A+∆B ≥ � ψ⊥ A+B ��(A + B) ��ψ � as an uncertainty relation, but Maccone and Pati wanted a relation in terms of variances to compare to their first result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' To do this, we take the modulus squared of both sides to obtain (∆A + ∆B)2 ≥ ��� ψ⊥ A+B ��(A + B) ��ψ ���2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' The result now follows from the real number inequality x2 + y2 ≥ 1 2(x + y)2 with x = ∆A and y = ∆B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' For completeness, this inequality is proved as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' 0 ≤ (x − y)2 = x2 + y2 − 2xy ⇒ x2 + y2 ≥ 2xy ⇒ 2x2 + 2y2 ≥ x2 + y2 + 2xy ⇒ 2x2 + 2y2 ≥ (x + y)2 ⇒ x2 + y2 ≥ 1 2(x + y)2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='3 Generalizations Generalizations of the Maccone-Pati Uncertainty relations can be obtained by applying the Aharonov-Vaidman identity to more general linear combinations αA + βB, where α, β ∈ C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' This gives (αA + βB) |ψ⟩ = (α ⟨A⟩ + β ⟨B⟩) |ψ⟩ + ∆(αA + βB) ��ψ⊥ αA+βB � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (57) Applying the strategy we used to prove theorem 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='4, we can take the inner product of this with an arbitrary unit vector ��ψ⊥� that is orthogonal to |ψ⟩, which gives � ψ⊥��(αA + βB) ��ψ � = ∆(αA + βB) � ψ⊥��ψ⊥ αA+βB � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' 16 We can now take the modulus squared of this and recognize that 0 ≤ ��� ψ⊥��ψ⊥ αA+βB ���2 ≤ 1 to obtain ��� ψ⊥��(αA + βB) ��ψ ���2 ≤ ∆(αA + βB).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Next, we can expand ∆(αA + βB) and rearrange to obtain |α|2 (∆A)2 + |β|2 (∆B)2 ≥ −Re(α∗β) (⟨{A, B}⟩ − 2 ⟨A⟩ ⟨B⟩) − iIm (α∗β) ⟨[A, B]⟩ + ��� ψ⊥��(αA + βB) ��ψ ���2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (58) Substituting α = 1, β = i and α = 1, β = −i immediately yields the first Maccone-Pati Uncertainty Relation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Alternatively, we can apply the strategy used to prove theorem 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Starting from eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (57), we can take the inner product with ��ψ⊥ αA+βB � and rearrange to obtain ∆(αA + βB) = � ψ⊥ αA+βB ��(αA + βB) ��ψ � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Using the sum relation, together with ∆(αA) = |α|∆A gives |α|∆A + |β|∆B ≥ � ψ⊥ αA+βB ��(αA + βB) ��ψ � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Finally, squaring and using the inequality x2 + y2 ≥ 1 2(x + y)2 gives |α|2 (∆A)2 + |β|2 (∆B)2 ≥ 1 2 ��� ψ⊥ αA+βB ��(αA + βB) ��ψ ���2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (59) The inequalities eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (58) and eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (59) are related to some of the generalizations of the Maccone-Pati uncertainty relations that have previously appeared in the literature [21, 28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' For example, eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (58) can be used to derive an uncertainty relation that has appeared in the literature under the name “weighted uncertainty relation” [28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' To do so, we set α = √ λ, β = ±i/ √ λ in eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (58), where λ > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' This yields λ (∆A)2 + 1 λ (∆B)2 ≥ ±i ⟨[A, B]⟩ + 1 λ ��� ψ⊥��(λA ∓ iB) ��ψ ���2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' This is an uncertainty relation in its own right, but the relation in [28] comes from adding this to eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (55), which yields (1+λ) (∆A)2+ � 1 + 1 λ � (∆B)2 ≥ ±2i ⟨[A, B]⟩ ��� ψ⊥ 1 ��(A ∓ iB) ��ψ ���2+1 λ ��� ψ⊥ 2 ��(λA ∓ iB) ��ψ ���2 , where ��ψ⊥ 1 � and ��ψ⊥ 2 � are (possibly different) unit vectors that are orthogonal to |ψ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' This is intended as a simple example of a generalization that is easily obtained from the Aharonov-Vaidman identity, but I expect many other uncertainty relations that are usually proved using the Cauchy-Schwarz inequality or the parallelogram law would also have simple Aharonov-Vaidman based proofs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' 17 7 Quantum Propagation of Uncertainty In this section, we develop generalizations of the classical formulas for the propagation of uncertainty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' We start with the case of linear functions in section 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1, for which exact formulas are easy to obtain, before moving on to the general, possibly nonlinear, case in section 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='2, for which we have to employ a Taylor series approximation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1 Linear Functions We start with the simplest case: a sum of two observables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Classically, if A and B are random variables then [∆(A + B)]2 = (∆A)2 + (∆B)2 + 2∆A∆B corrA,B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (60) Consider an experiment consisting of multiple runs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' On each run, the quantities A and B are measured.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' These quantities are formalized as random variables because we assume that our experiments are subject to random statistical fluctuations, and that the “true” values that we are seeking are the means ⟨A⟩ and ⟨B⟩ of these random processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' We then use the average values calculated from the data as estimates of ⟨A⟩ and ⟨B⟩, and the standard deviations as a measure of the error in our experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' If we are actually interested in the quantity A + B then we would sum the averages to form our estimate of ⟨A + B⟩, and we would use eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (60) to determine the error in our estimate of ⟨A + B⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Using eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (60) in this way is called the propagation of uncertainty or propagation of error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' If the random variables, A and B are independent, which would be the case if the ran- domness were due to independent statistical errors, then corrA,B = 0 and we would have [∆(A + B)]2 = (∆A)2 + (∆B)2 , which is the formula for propagation of uncertainty that is most commonly used in practice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' We now want to generalize these formulas by replacing classical random variables with quantum observables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' The generalization of eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (60) is as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Theorem 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Let A and B be Hermitian operators on a Hilbert space H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Then, [∆(A + B)]2 = (∆A)2 + (∆B)2 + 2∆A∆B RcorrA,B (61) = (∆A)2 + (∆B)2 + ⟨{A, B}⟩ − 2 ⟨A⟩ ⟨B⟩ (62) Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Proposition 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1 implies that, for any unit vector |ψ⟩ ∈ H, ∆(A + B) ��ψ⊥ A+B � = ∆A ��ψ⊥ A � + ∆B ��ψ⊥ B � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Taking the inner product of this with itself gives [∆ (A + B)]2 = (∆A)2 + (∆B)2 + ∆A∆B �� ψ⊥ A ��ψ⊥ B � + � ψ⊥ B ��ψ⊥ A �� = (∆A)2 + (∆B)2 + 2∆A∆B Re �� ψ⊥ A ��ψ⊥ B �� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Applying eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (13) completes the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' 18 Remark 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' For operators A1, A2, · · · , An and real numbers α1, α2, · · · , αn, theorem 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1 is easily generalized to � ∆ � n � j=1 αjAj ��2 = n � j=1 α2 j (∆Aj)2 + � j̸=k αjαk∆Aj∆Ak RcorrAj,Ak = n � j=1 α2 j (∆Aj)2 + � j̸=k αjαk (⟨{Aj, Ak}⟩ − 2 ⟨Aj⟩ ⟨Ak⟩) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Although theorem 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1 is a true theorem about quantum observables, it cannot be used to propagate uncertainty in the same way as its classical counterpart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Classically, we can measure A and B together in the same run of the experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' We can then estimate A + B by summing the average values of A and B that we found in the experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' We also have all the information we need to calculate the uncertainty ∆(A + B), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' ∆A, ∆B, ⟨A⟩, ⟨B⟩ and ⟨AB⟩, so we can determine the uncertainty without doing any more experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' In quantum mechanics, this is not the case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' When A and B do not commute, they cannot both be accurately measured on the same run of an experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' We can still estimate their expectation values by measuring A on half of the runs of the experiment and B on the other half and taking averages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Since ⟨A + B⟩ = ⟨A⟩ + ⟨B⟩, summing these averages is still a way of estimating ⟨A + B⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' However, we do not have enough information to calculate ∆(A + B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' The reason is that ∆(A + B) is the uncertainty in a direct measurement of A + B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Since A and B do not commute, this requires a different experimental setup from a measurement of A and B alone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' If we wanted to use eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (61) to calculate ∆(A + B), we would also have to estimate ⟨{A, B}⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' The most straightforward way of doing this would be to measure the observable {A, B} = AB +BA, but this requires yet another different experimental setup, and one that is likely to be at least as complicated as measuring A + B directly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' An exception to this are cases where {A, B} = cI for some constant c, in which case ⟨{A, B}⟩ = c regardless of the state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' In particular, this is true of the Pauli observables σx, σy, σz of a qubit for which {σj, σk} = δjkI, where j and k run over x, y, z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Therefore, if we measure σx on many qubits prepared in the same way and σy on another set of such qubits, we can estimate ⟨σx + σy⟩ and ∆(σx + σy) without doing any further experiments using the formula [∆ (σx + σy)]2 = (∆σx)2 + (∆σy)2 − 2 ⟨σx⟩ ⟨σy⟩ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' When {A, B} ̸= cI, I do not know of any situations in which eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (61) would be useful in practice, but from a theoretical point of view it is the appropriate generalization of eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (60) to quantum mechanics, and this bolsters the case that RcorrA,B is the appropriate quantum generalization of the classical correlation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='2 Nonlinear Functions For nonlinear functions f(A, B) of two random variables A and B, it is common to use a first order Taylor expansion of f(A, B) about the point f(⟨A⟩ , ⟨B⟩) to derive an approximation 19 for the variance [∆f(A, B)]2 to second order in ∆A and ∆B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' This yields the formula [∆f(A, B)]2 ≈ � ∂f ∂A ���� A=⟨A⟩,B=⟨B⟩ �2 (∆A)2 + � ∂f ∂B ���� A=⟨A⟩,B=⟨B⟩ �2 (∆B)2 + ∂f ∂A ���� A=⟨A⟩,B=⟨B⟩ ∂f ∂B ���� A=⟨A⟩,B=⟨B⟩ ∆A∆B corrA,B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' To avoid cluttering notation, I will write ¯A for A = ⟨A⟩, so that we can more compactly write [∆f(A, B)]2 ≈ ∂f ∂A ���� 2 ¯ A, ¯B (∆A)2 + ∂f ∂B ���� 2 ¯ A, ¯B (∆B)2 + ∂f ∂A ���� ¯ A, ¯B ∂f ∂B ���� ¯ A, ¯B ∆A∆B corrA,B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (63) When A and B are independent, this reduces to [∆f(A, B)]2 ≈ ∂f ∂A ���� 2 ¯ A, ¯B (∆A)2 + ∂f ∂B ���� 2 ¯ A, ¯B (∆B)2 , which is the most commonly used form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' The quantum generalization of eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (63) is as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Theorem 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Let A and B be Hermitian operators on a Hilbert space H and consider a function f : H(H) × H(H) → H(H) where H(H) is the space of Hermitian operators on H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Then [∆f(A, B)]2 ≈ ∂f ∂A ���� 2 ¯ A, ¯B (∆A)2 + ∂f ∂B ���� 2 ¯ A, ¯B (∆B)2 + ∂f ∂A ���� ¯ A, ¯B ∂f ∂B ���� ¯ A, ¯B ∆A∆B RcorrA,B (64) where ≈ means equality to second order in ∆A and ∆B Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Consider the first order Taylor expansion of f(A, B) about the point f0 = f(⟨A⟩ , ⟨B⟩), f(A, B) ≈ f0 + ∂f ∂A ���� ¯ A, ¯B A + ∂f ∂B ���� ¯ A, ¯B B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Applying proposition 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1 to this gives [∆f(A, B)] ��ψ⊥ f(A,B) � ≈ ∂f ∂A ���� ¯ A, ¯B ∆A ��ψ⊥ A � + ∂f ∂B ���� ¯ A, ¯B ∆B ��ψ⊥ B � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Taking the inner product of this with itself gives [∆f(A, B)]2 ≈ ∂f ∂A ���� 2 ¯ A, ¯B (∆A)2 + ∂f ∂B ���� 2 ¯ A, ¯B (∆B)2 + ∂f ∂A ���� ¯ A, ¯B ∂f ∂B ���� ¯ A, ¯B ∆A∆B Re �� ψ⊥ A ��ψ⊥ B �� = ∂f ∂A ���� 2 ¯ A, ¯B (∆A)2 + ∂f ∂B ���� 2 ¯ A, ¯B (∆B)2 + ∂f ∂A ���� ¯ A, ¯B ∂f ∂B ���� ¯ A, ¯B ∆A∆B RcorrA,B 20 Remark 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' For operators A1, A2, · · · , An and a function f(A1, A2, · · · , An), theorem 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='3 is easily generalized to [∆f (A1, A2, · · · , An)]2 ≈ n � j=1 ∂f ∂Aj ���� 2 ¯ A (∆Aj)2 + � j̸=k ∂f ∂Aj ���� ¯ A ∂f ∂Ak ���� ¯ A ∆Aj∆Ak RcorrAj,Ak, where ¯A is shorthand for A1 = ⟨A1⟩ , A2 = ⟨A2⟩ , · · · An = ⟨An⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' As a formula for propagating uncertainty, eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (64) inherits all of the problems of eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (61), but the problems are compounded further by use of the first order Taylor approximation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' This approximation is valid when ∆A and ∆B are suitably small compared to ⟨A⟩, ⟨B⟩, f(⟨A⟩ , ⟨B⟩) and the derivatives of f(A, B) at A = ⟨A⟩, B = ⟨B⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' This is often the case in classical experiments where everything can be measured with a small statistical error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' However, in quantum mechanics, when A and B do not commute, the (various) uncertainty relations tell us that there is necessarily a trade-off between the size of ∆A and ∆B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' If one of them is small, then the other might necessarily have to be large.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' For example, for the Pauli observables σx and σy, at least one of the uncertainties must be comparable in size to 1, which is the largest possible value of ⟨σx⟩ or ⟨σy⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' A case where the formula will work well is for a continuous variable system where ∆x ∼ ∆p ∼ √ ℏ, and ⟨x⟩, ⟨p⟩ are large compared to √ ℏ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' But this is a case where you would expect classical physics to be a good approximation anyway.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' I do not know whether there is a practical use of eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (64), but it is nonetheless a correct formal generalization of eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (63).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' 8 Dealing with Mixed States So far, we have dealt exclusively with the case of pure state vectors |ψ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' However, all of our results can be extended to more general density operators ρ, which can represent mixed states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' The most familiar way to do this is to make use of the concept of a purification of a density operator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Given a density operator on a Hilbert space HS, where S stands for “system”, we can always find a pure state vector |ψ⟩SE ∈ HS ⊗ HE, where E is the “environment”, such that ρS = TrE (|ψ⟩⟨ψ|SE) , and TrE is the partial trace over HE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' You can then apply the Aharonov-Vaidman identity to operators of the form AS ⊗ IE acting on a purification to obtain results about the density operator ρS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' However, to make the parallels to the pure state case as close as possible, I prefer to use an equivalent concept, called an amplitude operator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' The equivalence between amplitude operators and purifications is discussed in appendix A Definition 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Given a density operator ρS on a Hilbert space HS, an amplitude operator for ρS is a linear operator LS : HE → HS, where HE is any Hilbert space, such that ρS = LSL† S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' 21 The reason for the name amplitude operator is that, in pure-state quantum mechanics, an amplitude is a complex number α such that |α|2 is a probability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' A density operator is a non- commutative generalization of a probability distribution [42, 43], and hence an amplitude operator ought to be an operator that “squares” to a density operator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Given a density operator ρS, one obvious way of constructing an amplitude operator is to set HE = HS and LS = √ρS, but there are an infinite number of alternatives, as the following proposition shows Proposition 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' An operator LS : HE → HS is an amplitude operator for ρS if and only if LS = √ρSUS|E, where US|E : HE → HS is a semi-unitary operator, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' it satisfies US|EU † S|E = IS Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' An operator of the form LS = √ρSUS|E obviously satisfies definition 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' For the other direction, assume LS is an amplitude operator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Like any operator, it may be decomposed in its polar decomposition LS = PSUS|E where PS is a positive semi-definite operator on HS, and US|E : HE → HS is semi-unitary4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' The definition of an amplitude operator then implies that ρS = PSUS|EU † S|EPS = P 2 S, so we must have PS = √ρS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Going back to the analogy between amplitudes and amplitude operators, multiplying an amplitude α by a phase factor eiφ does not change the probability it represents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Similarly, multiplying an amplitude operator LS by a semi-unitary VE|E′, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' an operator VE|E′ : HE′ → HE satisfying VE|E′V † E|E′ = IE, on the right does not change the density operator it represents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Although one might think it desirable to work directly with probabilities or density operators in order to eliminate these ambiguities, the mathematical manipulations we need to do in quantum mechanics are often linear in the amplitudes or amplitude operators, but would be nonlinear if you used probabilities or density operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Therefore, it is often more convenient to live with the ambiguity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Since every operator has a polar decomposition, the only requirement for LS to be an amplitude operator for some density operator is that TrS � LSL† S � = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' If we want to work with unnormalized density operators, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' any positive operator, then any operator LS : HE → HS is the amplitude operator for some (possibly unnormalized) density operator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' This is analogous to the fact that any vector in HS represents a (possibly unnormalized) pure state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' The strategy for generalizing the Aharonov-Vaidman identity, and everything that follows from it, is to replace the state vector |ψ⟩S with an amplitude operator LS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' The reason this works is that the space of linear operators mapping HE to HS, which we denote LS|E, is itself a Hilbert space with inner product ⟨LS, MS⟩ = TrE � L† SMS � , known as the Hilbert-Schmidt 4The polar decomposition is often only defined for square matrices, in which case HE = HS and US|E is unitary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Here, we use the generalization to non-square matrices (see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' [44]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' 22 inner product5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Since the Aharonov-Vaidman identity is valid for any Hilbert space, it must be valid on LS|E as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Proposition 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='3 (The Aharonov-Vaidman Identity for Operators).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Let AS be a linear op- erator on a Hilbert space HS and let LS : HE → HS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Then, ASLS = ⟨AS⟩ LS + (∆AS) L⊥ AS, (65) where ⟨AS⟩ = TrS � ASLSL† S � /TrS � LSL† S � , ∆A = �� A† SAS � − |⟨AS⟩|2, and L⊥ AS : HE → HS is an amplitude operator that is orthogonal to LS, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' TrE � L† SL⊥ AS � = 0, satisfies TrS � L⊥ ASL⊥† AS � = TrS � LSL† S � , and depends on both LS and AS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' The proof of this proposition is essentially the same as the proof of the vector Aharonov- Vaidman identity (proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1) with the standard inner product replaced by the Hilbert- Schmidt inner product.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' The only difference is that the cyclic property of the trace is also needs to be used to write things in the exact form given in proposition 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' I leave this as an exercise for the reader.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Since ρS = LSL† S is always a (possibly unnormalized) density operator, we can write ⟨AS⟩ = TrS � ASLSL† S � TrE � L† SLS � = TrS (ASρS) TrE (ρS) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' We can also introduce the density operator ρ⊥ AS = L⊥ ASL⊥† AS, which will be normalized in the same way as ρS, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=', TrS � ρ⊥ AS � = TrS (ρS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' When LS is normalized so that ρS = LSL† S is a normalized density operator, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=', TrS � LSL† S � = 1, then ρ⊥ AS is also normalized, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=', TrS � ρ⊥ AS � = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' As defined, ρ⊥ AS = L⊥ ASL⊥† AS looks like it depends on the choice of amplitude operator LS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' In fact, it does not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' It only depends on ρS and AS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' To see this, rewrite the operator Aharonov-Vaidman identity as L⊥ AS = 1 ∆AS (AS − ⟨AS⟩ IS) LS, and then we have, ρ⊥ AS = L⊥ ASL⊥† AS = 1 (∆AS)2 (AS − ⟨AS⟩ IS) LSL† S � A† S − ⟨AS⟩∗ IS � = 1 (∆AS)2 (AS − ⟨AS⟩ IS) ρS � A† S − ⟨AS⟩∗ IS � , 5By the cyclic property of the trace, we can also write ⟨LS, MS⟩ = TrS � MSL† S � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' 23 which is clearly independent of the choice of LS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Note that, although LS and L⊥ AS are Hilbert-Schmidt orthogonal, ρS and ρ⊥ AS are generally not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' To generalize the results of this paper from state vectors to density operators, we replace the vector Aharonov-Vaidman identity with its operator counterpart applied to amplitude operators, and we replace the usual inner product with the Hilbert-Schmidt inner product.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' In many cases, the final result is independent of the amplitude operator used to represent the state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Although we use it in the proof, it drops out in the final result by only appearing in the combination LSL† S, as in the expression we derived for ρ⊥ AS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' In fact, the final formulas are usually the same as in the pure state case, except that we have to interpret ⟨AS⟩ as TrS (ASρS) rather than ⟨ψ|AS|ψ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' However, this is not true for the Maccone-Pati uncertainty relations and their general- izations, which do depend on the choice of amplitude operator LS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Theorem 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='4 (The First Maccone-Pati Uncertainty Relation for amplitude operators).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Let AS and BS be Hermitian operators on a Hilbert space HS and let ρS be a normalized density operator on HS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Then, (∆A)2 + (∆B)2 ≥ ±i ⟨[A, B]⟩ + ���TrE � L⊥† S (A ∓ iB)LS ���� 2 , (66) where LS : HE → HS is any amplitude operator for ρS, and L⊥ S : HE → HS is any normalized amplitude operator orthogonal to LS that has the same input space HE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Note that, in order to obtain the tightest possible bound on (∆A)2 + (∆B)2, the right hand side of eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (66) should be maximized over all possible choices of LS and L⊥ S .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' To do this in practice, a bound on the largest dimension dE required to obtain the maximum is needed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' I conjecture that dE = 2dS is sufficient because this allows LS and L⊥ S to have orthogonal kernels on HE, but I do not have a proof of this.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Theorem 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='5 (The Second Maccone-Pati Uncertainty Relation for amplitude operators).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Let AS and BS be linear operators on a Hilbert space HS and let ρS be a normalized density operator on HS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Then, (∆AS)2 + (∆BS)2 ≥ 1 2 ���TrE � L⊥† AS+BS(A + B)LS ���� 2 , (67) where LS is any amplitude operator for ρS and L⊥ AS+BS = 1 ∆(AS + BS) (AS + BS − ⟨AS + BS⟩ IS) LS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' In this case, to obtain the tightest bound, we have to maximize the right hand side over LS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' We do not have to separately optimize over L⊥ AS+BS because it is a function of LS, AS and BS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' However, its dependence on LS makes the problem into a complicated nonlinear optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' 24 9 Summary and Conclusions In this paper, I discussed how the standard textbook uncertainty relations of Robertson and Schrödinger can be derived from the Aharonov-Vaidman identity in a more direct way than the standard proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' I also demonstrated the identity’s usefulness in proving other uncertainty relations, such as the Maccone-Pati relations, and the quantum formulas for propagation of uncertainty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Finally, I gave a mixed-state generalization of the Aharonov-Vaidman identity in terms of amplitude operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' I hope that this has persuaded you that the Aharonov- Vaidman identity belongs in undergraduate textbooks and that it ought to be a first-line tool in proving relationships between standard deviations in quantum mechanics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' I am sure there are other uncertainty relations that have an elegant Aharonov-Vaidman based proofs, and I hope to find new and useful uncertainty relations that have not been discovered before via this method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' The Aharonov-Vaidman identity naturally gives rise to two quantum generalizations of the correlation, corrA,B and RcorrA,B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' It would be interesting to determine whether these quantities have an operational meaning in the case where A and B do not commute.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' On the more formal side, perhaps there is a pseudo-probability representation of quantum mechanics, such as the Wigner function [45, 46, 47] or the Kirkwood-Dirac distribution [48, 49, 50], for which these are the correlations for observables as defined on the appropriate phase space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' This might help to find uses for the propagation of error formulas in cases where the observables do not commute.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Acknowledgments I would like to thank Yakir Aharonov for introducing me to the Aharonov-Vaidman iden- tity and emphasizing its importance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' I would like to acknowledge (but not thank) the role played by the COVID19 pandemic shutdowns in giving me the opportunity to think about uncertainty relations and their pedagogy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' This research was supported in part by the Fetzer Franklin Fund of the John E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Fetzer Memorial Trust and by grant number FQXi-RFPIPW- 1905 from the Foundational Questions Institute and Fetzer Franklin Fund, a donor advised fund of Silicon Alley Community Foundation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' This research was also supported in part by Perimeter Institute for Theoretical Physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Research at Perimeter Institute is supported by the Government of Canada through the Department of Innovation, Science, and Eco- nomic Development, and by the Province of Ontario through the Ministry of Colleges and Universities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' References [1] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Aharonov and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Vaidman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Properties of a quantum system during the time interval between two measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' A, 41(1):11–20, 1990.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1103/PhysRevA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' 41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' 25 [2] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Aharonov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Visiting researcher presentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Talk at Perimeter Institute to PSI Masters Students: comment is made at 41:16, August 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' URL: https://pirsa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' org/11080091.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' [3] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Vaidman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Minimum time for the evolution to an orthogonal state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Am.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=', 60(2):182, 1992.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1119/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='16940.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' [4] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Robertson.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' The Uncertainty Principle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=', 34(1):163–164, 1929.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1103/PhysRev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='163.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' [5] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Schrödinger.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Zum heisenbergschen unschärfeprinzip.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Sitzungsberichte der Preussis- chen Akademie der Wissenschaften, Physikalisch-mathematische Klasse, 14:296–303, 1930.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' [6] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Goldenberg and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Vaidman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Applications of a simple quantum mechanical formula.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Am.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=', 64(8):1059, 1996.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' arXiv:quant-ph/9506030, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1119/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='18307.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' [7] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Aharonov and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Rohrlich.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Quantum Paradoxes: Quantum Theory for the Perplexed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Wiley, 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1002/9783527619115.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' [8] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Steele.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' The Cauchy-Schwarz Master Class: An Introduction to the Art of Mathematical Inequalities, chapter 1, page 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Mathematical Association of America Problem Books.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Cambridge University Press, 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' URL: http://www-stat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='wharton.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='upenn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='edu/~steele/Publications/Books/CSMC/ CSMC_index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='html, doi:CBO9780511817106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' [9] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Fuchs and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Peres.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Quantum-state disturbance versus information gain: Un- certainty relations for quantum information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' A, 53(4):2038, 1996.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' arXiv: quant-ph/9512023, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1103/PhysRevA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='2038.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' [10] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Hofmann and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Takeuchi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Violation of local uncertainty relations as a signature of entanglement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' A, 68(3):032103, 2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' arXiv:quant-ph/0212090, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1103/PhysRevA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='032103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' [11] O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Gühne.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Characterizing entanglement via uncertainty relations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=', 92(11):117903, 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' arXiv:quant-ph/0306194, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1103/PhysRevLett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' 92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='117903.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' [12] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Koashi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Unconditional security of quantum key distribution and the uncertainty principle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' : Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=', 36:98–102, 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' arXiv:quant-ph/0505108, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1088/1742-6596/36/1/016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' [13] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Berta, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Christandl, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Colbeck, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Renes, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Renner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' The uncertainty principle in the presence of quantum memory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Nature Physics, 6:659–662, 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' arXiv: 0909.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='0950, doi:doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1038/nphys1734.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' 26 [14] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Majumdar and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Pramanik.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Some applications of uncertainty relations in quan- tum information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' International Journal of Quantum Information, 14(6):1640022, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' arXiv:1410.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='5974, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1142/S0219749916400220.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' [15] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Yunger Halpern, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Bartolotta, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Pollack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Entropic uncertainty relations for quantum information scrambling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=', 2:92, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' arXiv:1806.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='04147, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1038/s42005-019-0179-8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' [16] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Oppenheim and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Wehner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' The uncertainty principle determines the nonlocality of quantum mechanics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Science, 330(6007):1072–1074, 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' arXiv:1004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='2507, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1126/science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='119206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' [17] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Catani, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Leifer, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Scala, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Schmid, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Spekkens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' What is nonclassical about uncertainty relations?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=', 129(24):240401, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' arXiv:2207.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' 11779, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1103/PhysRevLett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='129.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='240401.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' [18] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Coles, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Berta, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Tomamichel, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Wehner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Entropic uncertainty relations and their applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=', 89(1):015002, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' arXiv:1511.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='04857, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1103/RevModPhys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='015002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' [19] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Pati and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Sahu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Sum uncertainty relation in quantum theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' A, 367(3):177–181, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' arXiv:quant-ph/0608092, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='physleta.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' 03.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' [20] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Maccone and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Pati.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Stronger uncertainty relations for all incompatible ob- servables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=', 113(26):039902, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' arXiv:1407.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='0338, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1103/ PhysRevLett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='113.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='260401.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' [21] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Bannur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' General and stronger uncertainty relation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' arXiv:1503.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='00405, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='48550/arXiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1503.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='00405.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' [22] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Li and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Qiao.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Reformulating the quantum uncertainty relation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Scientific Reports, 5:12708, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' arXiv:1502.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='06292, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1038/srep12708.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' [23] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Yao, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Xiao, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Wang, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Sun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Implications and applications of the variance- based uncertainty equalities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' A, 91:062113, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' arXiv:1503.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='00239, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1103/PhysRevA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='062113.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' [24] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Abbott, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Alzieu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Hall, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Branciard.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Tight state-independent uncertainty relations for qubits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Mathematics, 4(1):8, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' arXiv:1512.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='02383, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='3390/math4010008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' [25] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Chen, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Cao, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Fei, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Long.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Variance-based uncertainty relations for in- compatible observables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Quantum Information Processing, 15:3909–3917, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' arXiv: 1608.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='06075, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1007/s11128-016-1365-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' 27 [26] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Qin, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Fei, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Li-Jost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Multi-observable uncertainty relations in product form of variances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Scientific Reports, 6:31192, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' arXiv:1608.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='03089, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1038/ srep31192.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' [27] Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Song and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Qiao.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Stronger Schrödinger-like uncertainty relations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' A, 380(37):2925–2930, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' arXiv:1504.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='01137, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='physleta.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='06.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' 054.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' [28] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Xiao, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Jing, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Li-Jost, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Fei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Weighted uncertainty relations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Scientific Reports, 6:23201, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' arXiv:1603.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='01004, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1038/srep23201.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' [29] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Mondal, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Bagchi, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Pati.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Tighter uncertainty and reverse uncertainty rela- tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' A, 95(5):052117, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' arXiv:1607.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='06712, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1103/PhysRevA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' 95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='052117.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' [30] Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Song, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Li, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' annd Peng, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Qiao.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' A stronger multi-observable uncertainty re- lation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Scientific Reports, 7:44764, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' arXiv:1701.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='01072, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1038/srep44764.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' [31] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Zhang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Zhang, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Yu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Stronger uncertainty relations with improvable upper and lower bounds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Quantum Information Processing, 16:131, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' arXiv:1607.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='08223, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1007/s11128-017-1585-z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' [32] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Zheng and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Zhang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Variance-based uncertainty relation for incompatible observers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Quantum Information Processing, 16:167, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' arXiv:1705.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='07396, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1007/ s11128-017-1619-6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' [33] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Dodonov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Variance uncertainty relations without covariances for three and four observables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' A, 97(2):022105, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' arXiv:1711.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='04037, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1103/ PhysRevA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='022105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' [34] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' de Guise, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Maccone, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Sanders, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Shukla.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' State-independent un- certainty relations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' A, 98(4):042121, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' arXiv:1804.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='06794, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1103/PhysRevA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='042121.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' [35] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Busch and O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Reaerdon-Smith.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' On quantum uncertainty relations and uncertainty regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' arXiv:1901.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='03695, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='48550/arXiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1901.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='03695.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' [36] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Giorda, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Maccone, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Riccardi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' State-independent uncertainty relations from eigenvalue minimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' A, 99(5):052121, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' arXiv:1810.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='09775, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1103/PhysRevA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='052121.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' [37] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Zheng, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Ma, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Zhang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Fan, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Liu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Unified and exact framework for variance-based uncertainty relations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Scientific Reports, 10:150, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' arXiv:1803.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' 08720, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1038/s41598-019-56803-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' 28 [38] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Li and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Qiao.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' The generalized uncertainty principle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Annalen der Physik, 533(1):2000335, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' arXiv:2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='08705, doi:https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1002/andp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' 202000335.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' [39] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Zhang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Luo, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Fei, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Wu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Uncertainty regions of observables and state- independent uncertainty relations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Quantum Information Processing, 20:357, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' arXiv:2110.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='14134, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1007/s11128-021-03303-w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' [40] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Chiew and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Gessner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Improving sum uncertainty relations with the quantum Fisher information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=', 4(1):013076, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' arXiv:2109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='06900, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1103/ PhysRevResearch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='013076.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' [41] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Xiao, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Jing, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Yu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Fei, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Li-Jost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Near-optimal variance-based uncertainty relations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Front.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=', 10:846330, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' arXiv:1610.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='01692, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='3389/fphy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' 846330.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' [42] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Rédei and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Summers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Quantum probability theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Stud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Hist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Phil.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=', 38(2):390–417, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' arXiv:quant-ph/0601158, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='shpsb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' [43] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Leifer and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Spekkens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Towards a formulation of quantum theory as a causally neutral theory of bayesian inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' A, 88(5):052130, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' arXiv: 1107.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='5849, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1103/PhysRevA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='052130.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' [44] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Ben-Israel and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Greville.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Generalized Inverses: Theory and Applications, chap- ter chapter 6, pages 220–221.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' CMS Books in Mathematics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Springer, 2nd edition, 2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' doi:doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1007/b97366.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' [45] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Wigner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' On the quantum correction for thermodynamic equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=', 40(5):749–759, 1932.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1103/PhysRev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='749.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' [46] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Gross.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Hudson’s theorem for finite-dimensional quantum systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=', 47:122107, 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' arXiv:quant-ph/0602001, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='2393152.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' [47] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Curtright, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Fairlie, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Zachos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' A Concise Treatise on Quantum Mechanics in Phase Space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' World Scientific, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1142/8870.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' [48] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Kirkwood.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Quantum statistics of almost classical assemblies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=', 44(1):31– 37, 1933.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1103/PhysRev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' [49] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Dirac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' On the analogy between classical and quantum mechanics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=', 17(2-3):195–199, 1945.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1103/RevModPhys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='195.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' [50] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Lostaglio, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Belenchia, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Levy, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Hernández-Gómez, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Fabbri, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Gherardini.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Kirkwood-dirac quasiprobability approach to quantum fluctuations: Theoretical and ex- perimental perspectives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' arXiv:2206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='11783, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='48550/arXiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='2206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='11783.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' 29 A Amplitude Operators and Purifications Proposition A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Given a density operator ρS on a Hilbert space HS, let HS′ be another copy of the same Hilbert space and let {|j⟩} be an orthonormal basis for HS and HS′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Define the vector ��Φ+� SS′ = � j |j⟩S |j⟩S′ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Let LS : HE → HS be an amplitude operator for ρS and let {|k⟩E} be an orthonormal basis for HE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Then IS ⊗LT S′ |Φ+⟩SS′ is a purification of ρS, where T denotes transpose in the |j⟩⟨k|SE basis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Similarly, if |ψ⟩SE ∈ HS⊗HE is a purification of ρS then LS = ⟨ψ∗|S′E |Φ+⟩SS′ is an amplitude operator for ρS, where ∗ denotes complex conjugation in the |jk⟩S′E basis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' If LS is an amplitude operator for ρS then ρS = LSL† S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' We have to show that this implies that TrE � IS ⊗ LT S′ |Φ+⟩⟨Φ+|SS′ IS ⊗ � LT S′ �†� = ρS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Note that � LT S′ �† = L∗ S′, where ∗ denotes complex conjugate in the |j⟩⟨k|SE basis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Therefore, we have TrE � IS ⊗ LT S′ ��Φ+�� Φ+�� SS′ IS ⊗ L∗ S′ � = � j,k |j⟩⟨k|S TrE � LT S′ |j⟩⟨k|S′ L∗ S′ � (68) = � j,k |j⟩⟨k|S � k ��L∗ SLT S ��j � S , (69) where we have changed the index S′ to S because they refer to the same Hilbert space and � k ��LT SL∗ S ��j � S is a scalar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Rearranging this, we have TrE � IS ⊗ LT S′ ��Φ+�� Φ+�� SS′ IS ⊗ L∗ S′ � = � j,k |j⟩S � k ��L∗ SLT S ��j � S ⟨k|S (70) = � j,k |j⟩⟨j|S � L∗ SLT S �T |k⟩⟨k|S (71) = � L∗ SLT S �T = LSL† S = ρS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (72) For the other direction, we have to prove that LSL† S = ρS, where LS = ⟨ψ∗|S′E |Φ+⟩SS′ and |ψ⟩SE is any purification of ρS, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' TrE (|ψ⟩⟨ψ|SE) = ρS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' First, let |ψ⟩SE = � jk αjk |j⟩S ⊗ |k⟩E be the decomposition of |ψ⟩SE in the |jk⟩SE basis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' We have |ψ∗⟩SE = � jk α∗ jk |j⟩S ⊗ |k⟩E and the condition TrE (|ψ⟩⟨ψ|SE) = ρS is equivalent to � j,k,l αjkα∗ lk |j⟩⟨l|S = ρS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' Note also that ⟨j|S′ |Φ+⟩SS′ = |j⟩S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' 30 Hence, we have LSL† S = � ⟨ψ∗|S′E ��Φ+� SS′ � � ⟨ψ∗|S′E ��Φ+� SS′ �† (73) = ⟨ψ∗|S′E ��Φ+� SS′ � Φ+�� SS′ |ψ∗⟩S′E (74) = � jklm αjk ⟨j|S′ ⟨k|E′ ��Φ+�� Φ+�� SS′ α∗ lm |l⟩S′ |m⟩E (75) = � jklm αjkα∗ lm ⟨k|m⟩E � ⟨j|S′ ��Φ+� SS′ � �� Φ+�� SS′ |l⟩S′ � (76) = � jkl αjkα∗ lk |j⟩⟨l|S (77) = ρS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} +page_content=' (78) 31' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KtFAT4oBgHgl3EQfwB6h/content/2301.08679v1.pdf'} diff --git a/L9E0T4oBgHgl3EQfSwBA/content/tmp_files/2301.02226v1.pdf.txt b/L9E0T4oBgHgl3EQfSwBA/content/tmp_files/2301.02226v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..b8340fb39a30c59f57acf20d5eb1798e2c0cad3c --- /dev/null +++ b/L9E0T4oBgHgl3EQfSwBA/content/tmp_files/2301.02226v1.pdf.txt @@ -0,0 +1,956 @@ +arXiv:2301.02226v1 [hep-ph] 5 Jan 2023 +Resolving RD and RD∗ Anomalies in Adjoint SU(5) +A. Ismael1,2 and S. Khalil2 +1Physics Department, Faculty of Science, Ain Shams University, Cairo 11566, Egypt. and +2Center for Fundamental Physics, Zewail City of Science and Technology, 6th of October City, Giza 12578, Egypt. +(Dated: January 6, 2023) +We investigate the RD and RD∗ anomalies in the context of non-minimal SU(5), where Higgs +sector is extended by adjoint 45-dimensional multiplet. One of the light spectrum of this model +could be the scalar triplet leptoquark that is contained in this multiplet. We demonstrate that +this particular scalar leptogquark mediation of the transition b → cτν is capable of simultaneously +accounting for both RD and RD∗ anomalies. We further emphasize that another Yukawa coupling +controls its contribution to b → sℓ+ℓ−, ensuring that RK and RK∗ remain consistent with the +standard model predictions. +I. +INTRODUCTION +Semileptonic decays B → {D, D∗}τν have received a +lot of attention in recent years because they provide a +good opportunity to test the Standard Model (SM) and +look for possible new physics beyond. +Recent intrigu- +ing measurements of RD,D∗ by BaBar [1, 2], Belle [3–6], +and LHCb collaborations [7] are significant hints of new +physics that violate lepton flavor universality. The ratios +RD,D∗ are defined by +RD∗,D ≡ BR(Bq → {D∗, D}τν) +BR(Bq → {D∗, D}lν) , +(1) +where l = e, µ. The current experimental averages of RD +and RD∗ are given by [8] +RD = 0.339 ± 0.026 ± 0.014 , +(2) +RD∗ = 0.295 ± 0.010 ± 0.010 . +(3) +However, the SM predictions are given as follows: [9–11] +RSM +D += 0.298 ± 0.004 , +(4) +RSM +D∗ = 0.254 ± 0.005 . +(5) +This shows that the measured RD and RD∗ results devi- +ate from the SM expectations by 1.9σ and 3.2σ, respec- +tively. On the other hand, the LHCb recently announced +new results for the ratios +RK = BR(B+ → K+µ+µ−) +BR(B+ → K+e+e−) , +(6) +RK∗ = BR(B0 → K∗0µ+µ−) +BR(B0 → K∗0e+e−) . +(7) +It has been reported that RK and RK∗ are given for two +dilepton invariant mass-squared bins by [12, 13] +Low − q2 + + + + + +RK = 0.994 +0.09 +−0.082 (stat) +0.027 +−0.029 (syst) +RK∗ = 0.927 +0.0933 +−0.087 (stat) +0.034 +−0.033 (syst) +(8) +Central − q2 + + + + + +RK = 0.949 +0.042 +−0.041 (stat) +0.023 +−0.023 (syst) +RK∗ = 1.027 +0.072 +−0.068 (stat) +0.027 +−0.027 (syst) +These measurements are consistent with the SM predic- +tions: RK,K∗ ≃ 1 [14]. As a result, they would impose +sever constraints on any new physics contributions that +could lead to lepton flavor non-universality. +In this paper, we argue that the scalar triplet lepto- +quark within the adjoint SU(5) framework can account +for the discrepancy between RD,D∗ experimental results +and SM expectations, while preserving RSM +K,K∗ results. +The Adjoint SU(5) is the simplest extension of minimal +SU(5) Grand Unified Theory (GUT), in which the Higgs +sector is extended by a 45-dimensional multiplet (45H). +As is well known, minimal SU(5) has a number of se- +rious problems, such as the incorrect prediction for the +fermion mass relation: mµ(e) = ms(d). One possible so- +lution to some of these flaws is to introduce an extra +45H. The scalar triplet is one of the 45H components, +with the following (3∗, 2, −7/6) representation under the +SM gauge group. Because of its special interactions with +quarks and leptons, this scalar triplet, which is a lepto- +quark type particle, does not contribute to proton de- +cay, as explained in [15]. This distinguishes SU(5) scalar +triplet from previous leptoquark scenarios discussed in + +2 +the literature. [16–19]. Although the scalar letptoquark +contributes to the semileptonic decays b → cτν at the +tree level, it is still subdominant because the leptoquark’s +mass is quite heavy of order TeV, which is sufficient to +account for the given ∼ 10% discrepancy. Controlling the +contribution of scalar leptoquarks to the b → sℓ+ℓ− can +be accomplished by constraining one of the free Yukawa +couplings. +The paper is organized as follows. In section 2 we in- +troduce the SU(5) scalar leptoquark and its associated +interactions, emphasizing that it does not contribute to +proton decay but can play important role in the following +decays: b → cτν and b → sℓ+ℓ−. Section 3 is devoted to +anlayzing the new contribution of our scalar leptoquark +to RD,D∗. RK,K∗ analysis is discussed in section 4. Fi- +nally our conclusions and prospects are give in section +5. +II. +SCALAR LEPTOQUARK IN ADJOINT SU(5) +As previously advocated, extending the Higgs sector of +SU(5) by 45H helps to solve some of the problems that +this simple example of GUT model faces [20–23]. The +45H transforms under the SM gauge as +45H = (8, 2)1/2 ⊕ (1, 2)1/2 ⊕ (3, 1)−1/3 ⊕ (3, 3)−1/3 +⊕ (6∗, 1)−1/3 ⊕ (3∗, 2)−7/6 ⊕ (3∗, 1)4/3. +(9) +It also satisfies the following constraints: 45αβ +γ += −45βα +γ +and �5 +α(45)αβ +α += 0. +Through non-vanishing Vacuum +Expectation Values (VEVs) of 5H and 45H: +⟨5H⟩ = +v5, ⟨45H⟩15 +1 += ⟨45H⟩25 +2 += ⟨45H⟩35 +3 += v45, ⟨45H⟩45 +4 += +−3v45, the electroweak symmetry SU(2)L × U(1)Y is +spontaneously broken into U(1)em. +The 45H scalar triplets are defined as: +(3∗, 2)ij +c −7/6 ≡ (45H)ij +c ≡ Φij +c , +(10) +(3∗, 1)ab +k 4/3 ≡ (45H)ab +k ≡ Φab +k , +[(3, 1)ib +c ⊕ (3, 3)ib +c ]−1/3 ≡ (45H)ib +c ≡ Φib +c . +It has been emphasized [15] that while the scalar triplets +Φab +k +and Φib +c +contribute to the proton decay and they +must be superheavy, the scalar triplet Φij +c does not. It +has no interaction terms that would cause proton decay. +By writing Φij +c as (φi +1, φi +2)T , one can demonstrate that +the scalar triplet has the following peculiar interactions: +L=2Y 2 +ABeT +ACuc +Biφi1∗+4(Y 4 +AB−Y 4 +BA)uiT +A Cec +Bφi1 +−2Y 2 +ABνT +ACuc +Biφi2∗+4(Y 4 +AB−Y 4 +BA)diT +A Cec +Bφi2. (11) +The first two interaction terms would imply the decay of +b → sℓ+ℓ− through scalar triplet leptoquark φi1 media- +tion, while the last two interaction terms clearly account +for the decay b → cτν via scalar triplet leptoquark φi2 +mediation. These terms can be written as +L = 2Y 2 +AB¯uBiPLνAφi2∗ − 4Y 4′ +AB¯eBPLdi +Aφi2 + h.c., +(12) +where we used CT = −C and ¯Ψ = ΨcT +L , and define +Y 4′ +AB ≡ (Y 4 +AB −Y 4 +BA). In the mass eignestate basis, where +dA → V CKM +AB +dB, νA → V PMNS +AB +νB, uA → uA, eA → eA, +the above Lagrangian takes the form: +L = 2Y 2 +AB ¯u′BiPLV PMNS +AK +ν′ +kφi2∗ − 4Y 4′ +AB ¯e′BPLV CKM +AK +d′ +Kφi2 ++h.c. +(13) +In this regards, the amplitude of b → cτν transition is +given by +M=−8Y 4′ +13V CKM +13 +M 2 +φ +�1 +2(¯uτPLvντ )(¯uCPLub) ++ 1 +8(¯uτσµνPLvντ )(¯uCPLσµνub) × +� +Y 2 +12V PMNS +13 +(14) ++Y 2 +22V PMNS +23 ++Y 2 +32V PMNS +33 +�� ++ +� +Y 4′ +13 V CKM +13 +→Y 4′ +23 V CKM +23 +� +. +Because V CKM +13 +and V CKM +23 +are so small (10−3 and 10−2, +respectively), the amplitude of b → cτν is essentially +determined by the leptoquark masses Mφ, Y 2 +22, Y 2 +32, and +Y 4′ +13. +III. +SU(5) LEPTOQUARK CONTRIBUTION TO +RD,D∗ +The general expression of the effective Hamiltonian for +b → cl ¯νl can be written as [24] +Heff = 4GF Vcb +√ +2 +� +(1 + gVL)[¯cγµPLb][¯lγµPLνl] ++ gVR[¯cγµPRb][¯lγµPLνl] + gSL[¯cPLb][¯lPLνl] ++ gSR[¯cPRb][¯lPLνl] + gT [¯cσµντ PLb][¯lσµνPLνl] +� +,(15) +where GF is the Fermi coupling constant, Vcb is the +Cabibbo-Kobayashi-Maskawa (CKM) matrix element be- +tween charm and bottom quarks while PL/R = (1 ∓ + +3 +γ5)/2. +Here, gi is defined as gi = CNP +i +/CSM, i ≡ +VL, VR, SL, SR, T , with CSM = +4GF Vcb +√ +2 +. Eq. 15 shows +that gVL = gVR = gSR = 0, whereas gSL and gT are given +by +gSL = − +√ +2Z +M 2 +φGF +, +gST = gSL +4 += − +Z +2 +√ +2M 2 +φGF +, (16) +with +Z = +� +Y 2 +12V PMNS +13 ++ Y 2 +22V PMNS +23 ++ Y 2 +32V PMNS +33 +� +� +Y 4′ +13V CKM +13 +V CKM +23 ++ Y 4′ +23 +� +(17) +Substituting with the SM parameters as well as the +form factors involved in the definition of the matrix ele- +ments to their central values, one finds [25] +R(D) = R(D)SM� +1 + 1.02|gSL|2 + 0.9|gT|2 ++ 1.49 Re[g∗ +SL] + 1.14 Re[g∗ +T ] +� +, +(18) +R(D∗) = R(D∗)SM� +1 + 0.04|gSL|2 + 16.07|gT|2 +− 0.11 Re[g∗ +SL] − 5.12 Re[g∗ +T ] +� +. +(19) +A few remarks are in order. First, the gSL and gT can +be complex due to non-zero phases in U PMNS as well as +complex values of the Yukawa couplings Y 2 and Y 4′. Sec- +ond, because the tree-level scalar leptoquark contributes +to the branching ratio of the tauonic decay B− +c → τ −¯ντ, +experimental constraints from this decay must be in- +cluded in our analysis. +The modified branching ratio +BR(B− +c → τ −¯ντ) is given by [25–27] +BR(B− +c →τ −¯ντ)=BR(B− +c →τ −¯ντ)SM|1−4.065gSL|2, (20) +with BR(B− +c +→ τ −¯ντ)SM = (2.25 ± 0.21) × 10−2 [28]. +The experimental bound on BR(B− +c → τ −¯ντ) varies from +≤ 10% to ≤ 60% [28–31]. Third, it is also worth noting +that our type of scalar leptoquarks would not contribute +to lepton flavor violation, like τ → µγ or B − ¯B mixing. +Fourth, we impose the constraints of the D∗ and τ lon- +gitudinal polarizations that come from Belle experiment. +Their expressions depend on the same Wilson coefficients +affecting RD and RD∗, which are written as [25, 27] +F D∗ +L +F D∗ +L,SM += +� RD∗ +RSM +D∗ +�−1� +1 + 0.08|gSL|2 + 7.02|gT|2 +− 0.24 Re[g∗ +SL] − 4.37 Re[g∗ +T] +� +(21) +P D∗ +τ +P D∗ +τ,SM += +� RD∗ +RSM +D∗ +�−1� +1 − 0.07|gSL|2 − 1.86|gT|2 ++ 0.22 Re[g∗ +SL] − 3.37 Re[g∗ +T] +� +(22) +The experimental values of F D +L and P D∗ +τ +are given by +0.60 ± 0.08 ± 0.035 [32] and −0.38 ± 0.51+0.21 +−0.16 [4, 5, 33] +respectively, whereas their SM predictions are 0.46±0.04 +[34] and −0.497 ± 0.013 [35] Finally, running the coeffi- +cients gSL and gT from the scale µ = 1T eV to the scale +mb = 4.2GeV implies that [36, 37]: +� +gSL +gT +� += +� +1.71 0 +0 +1 +� � +gSL(µ = 1T eV ) +gT (µ = 1T eV ) +� +. +(23) +In the presence of the aforementioned experimental +constraints, we performed a numerical analysis of RD +and RD∗. In Fig. 1, we show the dependence of RD and +RD∗ on the most relevant parameters, which are the mass +of leptoquark Mφ (left panel) and the real and imag- +inary parts of the Yukawa coupling Y 4′ +23 (right panel). +The other parameters in these plots were set as follows: +Y 2 +12 = −1.5, Y 2 +22 = Y 2 +32 = Y 4′ +13 = 1.5. Furthermore, the +coupling Y 4′ +23 is fixed with 1.48 + 0.1i in the plot of RD +and RD∗ versus Mφ (left panel), whereas in the 3D plot +of RD and RD∗ versus real and imaginary parts of Y 4′ +23 +(right panel), the mass Mφ varies along the [800, 1500] +GeV, while real and imaginary parts of Y 4′ +23 vary along +the [−1.5, 1.5] and [−0.5, 0.5], respectively. +The correlation between RD and RD∗ is shown in Fig. +2, left-panel, and the correlation between the constraints +on the BR(B− +c → τ −¯ντ) and RD and RD∗ is highlighted +in the right-panel of this plot. The parameters are set in +the same way as in the previous plots. +These plots show that in this class of models, both RD +and RD∗ can be significantly enhanced and lie within +one sigma of the recent experimental limits, with scalar +leptoquark masses of order one TeV, which is consistent +with experimental constraints. + +4 +1000 +1050 +1100 +1150 +1200 +1250 +1300 +1350 +1400 +1450 +M (GeV) +0.28 +0.3 +0.32 +0.34 +0.36 +0.38 +0.4 +0.42 +RD & R D * +RD +* +RD +0.26 +0.28 +0.4 +0.3 +0.32 +0.34 +0.2 +RD&R D * +0.36 +1 +0.38 +(Y 23 +4' ) +0 +0.5 +0.4 +(Y 23 +4' ) +0.42 +0 +-0.2 +-0.5 +-1 +-0.4 +RD +* +RD +FIG. 1. RD and RD∗ as function of the Letoquark mass and and real and imaginary parts of the Yukawa coupling Y23. The +other parameters are fixed as mentioned in the text. +0.3 +0.32 +0.34 +0.36 +0.38 +0.4 +0.42 +RD +0.25 +0.26 +0.27 +0.28 +0.29 +0.3 +0.31 +0.32 +RD * +0.05 +0.1 +0.15 +0.2 +0.25 +BR (B +) +0.26 +0.28 +0.3 +0.32 +0.34 +0.36 +0.38 +0.4 +0.42 +RD & R D * +RD +* +RD +FIG. 2. The correlation between RD and RD∗ (left) and between both RD and RD∗ and BR(B− +c → τ −¯ντ) (right). The scan +is conducted over the regions of parameter space mentioned above. +IV. +SU(5) LEPTOQUARK CONTRIBUTION TO +RK,K∗ +In this section, we show that, while the scalar lep- +toquark causes non-universality of lepton flavor in the +process B → Dℓν, it does not necessarily cause non- +universality in the process B → Kℓ+ℓ−. The Lagrangian +that generates the b → sℓ+ℓ− transition is given by +L=−4Y 4′ +AB ¯e′BPLV CKM +AK +di′ +Kφi2−4Y 4′ +AB ¯d′iKV CKM∗ +AK +PR e +′ +Bφ∗ +i2. +(24) +Thus, for b → s µ µ+, the Lagrangian is given as +L ⊃ −4Y 4′ +32 ¯µ′PLbi′φi2 − 4Y 4′∗ +12 +¯ +Si′V CKM∗ +12 +PR µ +′φ∗ +i2 +− 4Y 4′∗ +32 +¯ +Si′V CKM∗ +32 +PR µ +′φ∗ +i2, +(25) +where V CKM +13 +≈ 0 and V CKM +33 +≈ 1 are assumed. Also, +we may neglect V CKM +32 +respect V CKM +12 +(although we in- +clude all terms in our numerical calculations). Thus, the +amplitude of this process is given by +M = 8Y 4′ +32Y 4′∗ +12 V CKM∗ +12 +M 2 +φ +� ¯UsγµPLUb +�� ¯UµγµPLVν +� +. (26) +We used the Fierz transformation identity +� ¯UsPRVµ +�� ¯ +UµPLUb +� += 1 +2 +� ¯UsγµPLUb +�� ¯UµγµPLvµ +� +. +(27) +As a result, the Wilson coefficient Cµ +9 for b → s µ µ+ +process is written as +Cµ +9 (Λ) = 8Y 4′ +32Y 4′∗ +12 V CKM∗ +12 +M 2 +φ +. +(28) + +5 +where the scale Λ ≈ 1TeV, and Cµ +10(Λ) = −Cµ +9 (Λ). On +the other hand, the Lagrangian that generates the pro- +cess b → s e e+ is given by +L = − 4Y 4′ +31 ¯e +′PLbi′φi2 − 4Y 4′∗ +21 +¯ +Si′PRe +′φ∗ +i2. +(29) +After applying Fierz identity, the amplitude of b → s e e+ +is given by +M = 8Y 4′ +31Y 4′∗ +21 +M 2 +φ +� ¯UsγµPLUb +�� ¯UeγµPLVe +� +. +(30) +Hence, the Wilson coefficient Ce +9(Λ) for b → s e e+ will +be +Ce +9(Λ) = 8Y 4′ +31Y 4′∗ +21 +M 2 +φ +. +(31) +Moreover, Ce +10(Λ) = −Ce +9(Λ). The effective Hamiltonian +Heff for RK process is given by +Heff = +� +i +� +Ci(µb)Oi(µb) + ˜Ci(µb) ˜Oi(µb) +� +. +(32) +Through renormalization group equation (RGE), we ob- +tain +Ce,µ +9,10(Λ) = 1.2 Ce,µ +9,10(µb), +(33) +where Oi(µb) are ∆B = 1 transition operator, which is +evaluated at the mb scale. ˜Ci(µb), ˜Oi(µb) are obtained by +replacing L ↔ R. The relevant operators that describe +the Rk and Rk∗ in our model are +O9 = +� +¯sγµPLb +��¯lγµl), +O10 = +� +¯sγµPLb +��¯lγµγ5l). (34) +The Rk and Rk∗ expressions are written as +Rk ≈1 + ∆+, +(35) +Rk∗ ≈1 + ∆+ + p(∆+ − ∆−), +(36) +where p is a function of q2 +min and q2 +max and ∆± is given +by +∆± = +2 +|CSM +9 +|2 + |CSM +10 |2 +� +ℜ +� +CSM +9 +(CNP,µ +9 +± ˜ +C9 +NP,µ)∗� ++ ℜ +� +CSM +10 (CNP,µ +10 +± ˜ +C10 +NP,µ)∗� +− (µ ↔ e) +� +(37) +For our model, ˜CNP +9,10 = 0. Therefore, we obtain +∆+ = ∆− = 2.4 +� +CSM +9 +− CSM +10 +� +|CSM +9 +|2 + |CSM +10 |2 ℜ +� +CNP,µ +9 +(µb)−CNP,e +9 +(µb) +�∗ +(38) +It is worth mentioning that, whereas RK,K∗ is essen- +tially dependent on the couplings Y 4′ +21 and Y 4′ +32, RD,D∗ is +dependent on Y 2 +22, Y 2 +33 and Y 4′ +23 . As a result, it is entirely +possible to keep RK,K∗ equal to the SM expectation, con- +sistently with the new LHCb results, while leaving RD,D∗ +intact. To make RK,K∗ close to one, ∆+ should be very +small. This can be accomplished by having Y 4′ +12 ≪ 1. +V. +CONCLUSIONS +In this paper we have demonstrated that, in the pres- +ence of experimental constraints on flavor and lepton +violation observables, measured values of RD and RD∗ +within 1σ can be explained in non-minimal SU(5) with +adjoint 45-dimensional Higgs multiplet. Enhancements +for both RD and RD∗ are made possible by a tree level +transition of b → cτν, which is mediated by the associ- +ated scalar leptoquark. We also emphasized that even +though this leptoquark may contribute to RK and RK∗, +they remain independent of RD and RD∗ enhancements +because they are given in terms of different Yukawa cou- +plings. As a result, their contributions can be easily sup- +pressed, and RK and RK∗ continue to be identical to SM +predictions, which are consistent with the most recent +LHCb data. +ACKNOWLEDGEMENTS +This work is partially supported by Science, Tech- +nology & Innovation Funding Authority (STDF) under +grant number 37272. + +6 +REFERENCES +[1] J. P. Lees et al. [BaBar Collaboration], Phys. Rev. Lett. +109, 101802 (2012) [arXiv:1205.5442 [hep-ex]]. +[2] J. P. Lees et al. [BaBar Collaboration], Phys. Rev. D 88, +no. 7, 072012 (2013) [arXiv:1303.0571 [hep-ex]]. +[3] M. Huschle et al. [Belle Collaboration], Phys. Rev. D 92, +no. 7, 072014 (2015) [arXiv:1507.03233 [hep-ex]]. +[4] S. Hirose et al. [Belle Collaboration], Phys. Rev. Lett. +118, no. 21, 211801 (2017) [arXiv:1612.00529 [hep-ex]]. +[5] S. Hirose et al. [Belle Collaboration], Phys. Rev. D 97, +no. 1, 012004 (2018) [arXiv:1709.00129 [hep-ex]]. +[6] G. Caria et al. [Belle Collaboration], Phys. Rev. Lett. +124, no. 16, 161803 (2020) [arXiv:1910.05864 [hep-ex]]. +[7] LHCb Collaboration, https://indico.cern.ch/event/1187939/ +(2022). +[8] https://hflav-eos.web.cern.ch/hflav- +eos/semi/spring21/html/RDsDsstar/RDRDs.html +(2022). +[9] D. Bigi and P. Gambino, Phys. Rev. D 94, no. 7, 094008 +(2016). [arXiv:1606.08030 [hep-ph]] +[10] P. Gambino, M. Jung and S. Schacht, Phys. Lett. B 795, +386-390 (2019) [arXiv:1905.08209 [hep-ph]]. +[11] M. Bordone, M. Jung and D. van Dyk, Eur. Phys. J. C +80, no. 2, 74 (2020) [arXiv:1908.09398 [hep-ph]]. +[12] LHCb collaboration, arXiv.2212.09152 [hep-ex] (2022). +[13] LHCb collaboration, arXiv.2212.09153 [hep-ex] (2022). +[14] Marzia Bordone, Gino Isidori and Andrea Pattori,Eur. +Phys. J. C 76, no. 8, 440 (2016) [arXiv:1605.07633 [hep- +ph]]. +[15] Ilja Dorsner, Svjetlana Fajfer, Nejc Kosnik, Phys. Rev. D +86, no. 1, 015013 (2012) [ arXiv:1204.0674v2 [hep-ph]]. +[16] Syuhei Iguro, Michihisa Takeuchi and Ryoutaro Watan- +abe, +Eur. +Phys. +J. +C +81, +no. +5, +406 +(2021) +[arXiv:2011.02486 [hep-ph]]. +[17] David Marzocca and Sokratis Trifinopoulos, Phys. Rev. +Lett. 127, no. 6, 061803 (2021) [arXiv:2104.05730 [hep- +ph]]. +[18] Arvind Bhaskar and Anirudhan A. Madathil and Tanu- +moy Mandal and Subhadip Mitra, Phys. Rev. D 106, no. +11, 115009 (2022) [arXiv:2204.09031 [hep-ph]]. +[19] Peter +Cox, +Alexander +Kusenko, +Olcyr +Sumensari +and +Tsutomu +T. +Yanagida, +JHEP +05, +35 +(2017) +[arXiv:1612.03923 [hep-ph]]. +[20] Bartosz Fornal and Benjam´ın Grinstein, Phys. Rev. Lett. +119, no. 24, 241801 (2017) [ arXiv:1706.08535 [hep-ph]. +[21] Ilja Dorsner, Pavel Fileviez Perez, Phys. Lett. B 642, no. +03, 248-252 (2006) [arXiv:0606062 [hep-ph]]. +[22] S. Khalil, S. Salem, M. Allam, Phys. Rev. D 89, no. 09, +095011 (2015) [arXiv:1401.1482v2 [hep-ph]]. +[23] S. Khalil, S. Salem, Nucl. Phys. B 876, 473 (2013) +[arXiv:1304.3689 [hep-ph]] +[24] Minoru Tanaka and Ryoutaro Watanabe, Phys. Rev. D +87, no. 3, 034028 (2013) [arXiv:1212.1878 [hep-ph]]. +[25] Syuhei Iguro, Teppei Kitahara, Yuji Omura, Ryoutaro +Watanabe and Kei Yamamoto,JHEP 02, 194 (2019) +[arXiv 1811.08899 [hep-ph]]. +[26] Pouya Asadi, Matthew R. Buckley and David Shih, +JHEP 09, 10 (2018) [arXiv:1804.04135 [hep-ph]]. +[27] Pouya Asadi, Matthew R. Buckley and David Shih, Phys. +Rev. D 99, no. 3, 035015 (2019) [arXiv:1810.06597 [hep- +ph]]. +[28] Robert +Fleischer, +Ruben +Jaarsma +and +Gilberto +Tetlalmatzi-Xolocotzi, +Eur. +Phys. +J. +C +81, +no.7, +658 (2021) [arXiv:2104.04023 [hep-ph]]. +[29] Debjyoti Bardhan and Diptimoy Ghosh, Phys. Rev. D +100, no. 1, 011701 (2019) [arXiv:1904.10432 [hep-ph]]. +[30] Monika Blanke, +Andreas Crivellin, +Stefan de Boer, +Teppei Kitahara, Marta Moscati, Ulrich Nierste and +Ivan Nisandzic,Phys. Rev. D 99, no.7, 075006 (2019) +[arXiv:1811.09603 [hep-ph]]. +[31] Monika Blanke, Andreas Crivellin, Teppei Kitahara, +Marta Moscati, Ulrich Nierste and Ivan Nisandzic,Phys. +Rev. D 100, no. 3, 035035 (2019) [arXiv:1905.08253 [hep- +ph]]. +[32] A. +Abdesselam +et +al. +[Belle +Collaboration], +arXiv:1903.03102 [hep-ex] (2019). +[33] Karol Adamczyk, arXiv:1901.06380 [hep-ex] (2019). +[34] Ashutosh Kumar Alok, Dinesh Kumar, Suman Kumb- +hakar and S Uma Sankar, Phys. Rev. D 95, no. 11, +115038 (2017), [arXiv:1606.03164 [hep-ph]]. +[35] Minoru Tanaka and Ryoutaro Watanabe, Phys. Rev. D +87, no. 3, 034028 (2013), [arXiv:1212.1878v3 [hep-ph]]. +[36] Mart´ın Gonz´alez-Alonso, Jorge Martin Camalich and +Kin +Mimouni,Phys. +Lett. +B +772, +777-785 +(2017), +[arXiv:1706.00410v2 [hep-ph]]. +[37] Syuhei +Iguro, +Michihisa +Takeuchi +and +Ryoutaro +Watanabe,Eur. Phys. J. C 81, +no. 5, +406 (2021), +[arXiv2011.02486v4 [hep-ph]]. + diff --git a/L9E0T4oBgHgl3EQfSwBA/content/tmp_files/load_file.txt b/L9E0T4oBgHgl3EQfSwBA/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..a9a285530d6d5aded071f07ce6d8869d73a09d50 --- /dev/null +++ b/L9E0T4oBgHgl3EQfSwBA/content/tmp_files/load_file.txt @@ -0,0 +1,437 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf,len=436 +page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='02226v1 [hep-ph] 5 Jan 2023 Resolving RD and RD∗ Anomalies in Adjoint SU(5) A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Ismael1,2 and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Khalil2 1Physics Department, Faculty of Science, Ain Shams University, Cairo 11566, Egypt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' and 2Center for Fundamental Physics, Zewail City of Science and Technology, 6th of October City, Giza 12578, Egypt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' (Dated: January 6, 2023) We investigate the RD and RD∗ anomalies in the context of non-minimal SU(5), where Higgs sector is extended by adjoint 45-dimensional multiplet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' One of the light spectrum of this model could be the scalar triplet leptoquark that is contained in this multiplet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' We demonstrate that this particular scalar leptogquark mediation of the transition b → cτν is capable of simultaneously accounting for both RD and RD∗ anomalies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' We further emphasize that another Yukawa coupling controls its contribution to b → sℓ+ℓ−, ensuring that RK and RK∗ remain consistent with the standard model predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' INTRODUCTION Semileptonic decays B → {D, D∗}τν have received a lot of attention in recent years because they provide a good opportunity to test the Standard Model (SM) and look for possible new physics beyond.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Recent intrigu- ing measurements of RD,D∗ by BaBar [1, 2], Belle [3–6], and LHCb collaborations [7] are significant hints of new physics that violate lepton flavor universality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' The ratios RD,D∗ are defined by RD∗,D ≡ BR(Bq → {D∗, D}τν) BR(Bq → {D∗, D}lν) , (1) where l = e, µ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' The current experimental averages of RD and RD∗ are given by [8] RD = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='339 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='026 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='014 , (2) RD∗ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='295 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='010 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='010 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' (3) However, the SM predictions are given as follows: [9–11] RSM D = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='298 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='004 , (4) RSM D∗ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='254 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='005 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' (5) This shows that the measured RD and RD∗ results devi- ate from the SM expectations by 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='9σ and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='2σ, respec- tively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' On the other hand, the LHCb recently announced new results for the ratios RK = BR(B+ → K+µ+µ−) BR(B+ → K+e+e−) , (6) RK∗ = BR(B0 → K∗0µ+µ−) BR(B0 → K∗0e+e−) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' (7) It has been reported that RK and RK∗ are given for two dilepton invariant mass-squared bins by [12, 13] Low − q2 \uf8f1 \uf8f4 \uf8f2 \uf8f4 \uf8f3 RK = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='994 +0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='09 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='082 (stat) +0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='027 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='029 (syst) RK∗ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='927 +0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='0933 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='087 (stat) +0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='034 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='033 (syst) (8) Central − q2 \uf8f1 \uf8f4 \uf8f2 \uf8f4 \uf8f3 RK = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='949 +0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='042 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='041 (stat) +0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='023 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='023 (syst) RK∗ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='027 +0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='072 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='068 (stat) +0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='027 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='027 (syst) These measurements are consistent with the SM predic- tions: RK,K∗ ≃ 1 [14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' As a result, they would impose sever constraints on any new physics contributions that could lead to lepton flavor non-universality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' In this paper, we argue that the scalar triplet lepto- quark within the adjoint SU(5) framework can account for the discrepancy between RD,D∗ experimental results and SM expectations, while preserving RSM K,K∗ results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' The Adjoint SU(5) is the simplest extension of minimal SU(5) Grand Unified Theory (GUT), in which the Higgs sector is extended by a 45-dimensional multiplet (45H).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' As is well known, minimal SU(5) has a number of se- rious problems, such as the incorrect prediction for the fermion mass relation: mµ(e) = ms(d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' One possible so- lution to some of these flaws is to introduce an extra 45H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' The scalar triplet is one of the 45H components, with the following (3∗, 2, −7/6) representation under the SM gauge group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Because of its special interactions with quarks and leptons, this scalar triplet, which is a lepto- quark type particle, does not contribute to proton de- cay, as explained in [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' This distinguishes SU(5) scalar triplet from previous leptoquark scenarios discussed in 2 the literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' [16–19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Although the scalar letptoquark contributes to the semileptonic decays b → cτν at the tree level, it is still subdominant because the leptoquark’s mass is quite heavy of order TeV, which is sufficient to account for the given ∼ 10% discrepancy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Controlling the contribution of scalar leptoquarks to the b → sℓ+ℓ− can be accomplished by constraining one of the free Yukawa couplings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' The paper is organized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' In section 2 we in- troduce the SU(5) scalar leptoquark and its associated interactions, emphasizing that it does not contribute to proton decay but can play important role in the following decays: b → cτν and b → sℓ+ℓ−.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Section 3 is devoted to anlayzing the new contribution of our scalar leptoquark to RD,D∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' RK,K∗ analysis is discussed in section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Fi- nally our conclusions and prospects are give in section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' SCALAR LEPTOQUARK IN ADJOINT SU(5) As previously advocated, extending the Higgs sector of SU(5) by 45H helps to solve some of the problems that this simple example of GUT model faces [20–23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' The 45H transforms under the SM gauge as 45H = (8, 2)1/2 ⊕ (1, 2)1/2 ⊕ (3, 1)−1/3 ⊕ (3, 3)−1/3 ⊕ (6∗, 1)−1/3 ⊕ (3∗, 2)−7/6 ⊕ (3∗, 1)4/3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' (9) It also satisfies the following constraints: 45αβ γ = −45βα γ and �5 α(45)αβ α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Through non-vanishing Vacuum Expectation Values (VEVs) of 5H and 45H: ⟨5H⟩ = v5, ⟨45H⟩15 1 = ⟨45H⟩25 2 = ⟨45H⟩35 3 = v45, ⟨45H⟩45 4 = −3v45, the electroweak symmetry SU(2)L × U(1)Y is spontaneously broken into U(1)em.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' The 45H scalar triplets are defined as: (3∗, 2)ij c −7/6 ≡ (45H)ij c ≡ Φij c , (10) (3∗, 1)ab k 4/3 ≡ (45H)ab k ≡ Φab k , [(3, 1)ib c ⊕ (3, 3)ib c ]−1/3 ≡ (45H)ib c ≡ Φib c .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' It has been emphasized [15] that while the scalar triplets Φab k and Φib c contribute to the proton decay and they must be superheavy, the scalar triplet Φij c does not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' It has no interaction terms that would cause proton decay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' By writing Φij c as (φi 1, φi 2)T , one can demonstrate that the scalar triplet has the following peculiar interactions: L=2Y 2 ABeT ACuc Biφi1∗+4(Y 4 AB−Y 4 BA)uiT A Cec Bφi1 −2Y 2 ABνT ACuc Biφi2∗+4(Y 4 AB−Y 4 BA)diT A Cec Bφi2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' (11) The first two interaction terms would imply the decay of b → sℓ+ℓ− through scalar triplet leptoquark φi1 media- tion, while the last two interaction terms clearly account for the decay b → cτν via scalar triplet leptoquark φi2 mediation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' These terms can be written as L = 2Y 2 AB¯uBiPLνAφi2∗ − 4Y 4′ AB¯eBPLdi Aφi2 + h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=', (12) where we used CT = −C and ¯Ψ = ΨcT L , and define Y 4′ AB ≡ (Y 4 AB −Y 4 BA).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' In the mass eignestate basis, where dA → V CKM AB dB, νA → V PMNS AB νB, uA → uA, eA → eA, the above Lagrangian takes the form: L = 2Y 2 AB ¯u′BiPLV PMNS AK ν′ kφi2∗ − 4Y 4′ AB ¯e′BPLV CKM AK d′ Kφi2 +h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' (13) In this regards, the amplitude of b → cτν transition is given by M=−8Y 4′ 13V CKM 13 M 2 φ �1 2(¯uτPLvντ )(¯uCPLub) + 1 8(¯uτσµνPLvντ )(¯uCPLσµνub) × � Y 2 12V PMNS 13 (14) +Y 2 22V PMNS 23 +Y 2 32V PMNS 33 �� + � Y 4′ 13 V CKM 13 →Y 4′ 23 V CKM 23 � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Because V CKM 13 and V CKM 23 are so small (10−3 and 10−2, respectively), the amplitude of b → cτν is essentially determined by the leptoquark masses Mφ, Y 2 22, Y 2 32, and Y 4′ 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' SU(5) LEPTOQUARK CONTRIBUTION TO RD,D∗ The general expression of the effective Hamiltonian for b → cl ¯νl can be written as [24] Heff = 4GF Vcb √ 2 � (1 + gVL)[¯cγµPLb][¯lγµPLνl] + gVR[¯cγµPRb][¯lγµPLνl] + gSL[¯cPLb][¯lPLνl] + gSR[¯cPRb][¯lPLνl] + gT [¯cσµντ PLb][¯lσµνPLνl] � ,(15) where GF is the Fermi coupling constant, Vcb is the Cabibbo-Kobayashi-Maskawa (CKM) matrix element be- tween charm and bottom quarks while PL/R = (1 ∓ 3 γ5)/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Here, gi is defined as gi = CNP i /CSM, i ≡ VL, VR, SL, SR, T , with CSM = 4GF Vcb √ 2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' 15 shows that gVL = gVR = gSR = 0, whereas gSL and gT are given by gSL = − √ 2Z M 2 φGF , gST = gSL 4 = − Z 2 √ 2M 2 φGF , (16) with Z = � Y 2 12V PMNS 13 + Y 2 22V PMNS 23 + Y 2 32V PMNS 33 � � Y 4′ 13V CKM 13 V CKM 23 + Y 4′ 23 � (17) Substituting with the SM parameters as well as the form factors involved in the definition of the matrix ele- ments to their central values, one finds [25] R(D) = R(D)SM� 1 + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='02|gSL|2 + 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='9|gT|2 + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='49 Re[g∗ SL] + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='14 Re[g∗ T ] � , (18) R(D∗) = R(D∗)SM� 1 + 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='04|gSL|2 + 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='07|gT|2 − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='11 Re[g∗ SL] − 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='12 Re[g∗ T ] � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' (19) A few remarks are in order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' First, the gSL and gT can be complex due to non-zero phases in U PMNS as well as complex values of the Yukawa couplings Y 2 and Y 4′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Sec- ond, because the tree-level scalar leptoquark contributes to the branching ratio of the tauonic decay B− c → τ −¯ντ, experimental constraints from this decay must be in- cluded in our analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' The modified branching ratio BR(B− c → τ −¯ντ) is given by [25–27] BR(B− c →τ −¯ντ)=BR(B− c →τ −¯ντ)SM|1−4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='065gSL|2, (20) with BR(B− c → τ −¯ντ)SM = (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='25 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='21) × 10−2 [28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' The experimental bound on BR(B− c → τ −¯ντ) varies from ≤ 10% to ≤ 60% [28–31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Third, it is also worth noting that our type of scalar leptoquarks would not contribute to lepton flavor violation, like τ → µγ or B − ¯B mixing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Fourth, we impose the constraints of the D∗ and τ lon- gitudinal polarizations that come from Belle experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Their expressions depend on the same Wilson coefficients affecting RD and RD∗, which are written as [25, 27] F D∗ L F D∗ L,SM = � RD∗ RSM D∗ �−1� 1 + 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='08|gSL|2 + 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='02|gT|2 − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='24 Re[g∗ SL] − 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='37 Re[g∗ T] � (21) P D∗ τ P D∗ τ,SM = � RD∗ RSM D∗ �−1� 1 − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='07|gSL|2 − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='86|gT|2 + 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='22 Re[g∗ SL] − 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='37 Re[g∗ T] � (22) The experimental values of F D L and P D∗ τ are given by 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='60 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='08 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='035 [32] and −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='38 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='51+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='21 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='16 [4, 5, 33] respectively, whereas their SM predictions are 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='46±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='04 [34] and −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='497 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='013 [35] Finally, running the coeffi- cients gSL and gT from the scale µ = 1T eV to the scale mb = 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='2GeV implies that [36, 37]: � gSL gT � = � 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='71 0 0 1 � � gSL(µ = 1T eV ) gT (µ = 1T eV ) � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' (23) In the presence of the aforementioned experimental constraints, we performed a numerical analysis of RD and RD∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' 1, we show the dependence of RD and RD∗ on the most relevant parameters, which are the mass of leptoquark Mφ (left panel) and the real and imag- inary parts of the Yukawa coupling Y 4′ 23 (right panel).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' The other parameters in these plots were set as follows: Y 2 12 = −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='5, Y 2 22 = Y 2 32 = Y 4′ 13 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Furthermore, the coupling Y 4′ 23 is fixed with 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='48 + 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='1i in the plot of RD and RD∗ versus Mφ (left panel), whereas in the 3D plot of RD and RD∗ versus real and imaginary parts of Y 4′ 23 (right panel), the mass Mφ varies along the [800, 1500] GeV, while real and imaginary parts of Y 4′ 23 vary along the [−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='5, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='5] and [−0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='5, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='5], respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' The correlation between RD and RD∗ is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' 2, left-panel, and the correlation between the constraints on the BR(B− c → τ −¯ντ) and RD and RD∗ is highlighted in the right-panel of this plot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' The parameters are set in the same way as in the previous plots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' These plots show that in this class of models, both RD and RD∗ can be significantly enhanced and lie within one sigma of the recent experimental limits, with scalar leptoquark masses of order one TeV, which is consistent with experimental constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' 4 1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 M (GeV) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='28 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='32 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='34 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='36 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='38 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='42 RD & R D * RD RD 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='26 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='28 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='32 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='34 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='2 RD&R D * 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='36 1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content="38 (Y 23 4' ) 0 0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content="4 (Y 23 4' ) 0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='42 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='5 1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='4 RD RD FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' RD and RD∗ as function of the Letoquark mass and and real and imaginary parts of the Yukawa coupling Y23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' The other parameters are fixed as mentioned in the text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='32 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='34 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='36 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='38 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='42 RD 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='26 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='27 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='28 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='29 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='31 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='32 RD * 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='25 BR (B ) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='26 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='28 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='32 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='34 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='36 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='38 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='42 RD & R D * RD RD FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' The correlation between RD and RD∗ (left) and between both RD and RD∗ and BR(B− c → τ −¯ντ) (right).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' The scan is conducted over the regions of parameter space mentioned above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' SU(5) LEPTOQUARK CONTRIBUTION TO RK,K∗ In this section, we show that, while the scalar lep- toquark causes non-universality of lepton flavor in the process B → Dℓν, it does not necessarily cause non- universality in the process B → Kℓ+ℓ−.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' The Lagrangian that generates the b → sℓ+ℓ− transition is given by L=−4Y 4′ AB ¯e′BPLV CKM AK di′ Kφi2−4Y 4′ AB ¯d′iKV CKM∗ AK PR e ′ Bφ∗ i2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' (24) Thus, for b → s µ µ+, the Lagrangian is given as L ⊃ −4Y 4′ 32 ¯µ′PLbi′φi2 − 4Y 4′∗ 12 ¯ Si′V CKM∗ 12 PR µ ′φ∗ i2 − 4Y 4′∗ 32 ¯ Si′V CKM∗ 32 PR µ ′φ∗ i2, (25) where V CKM 13 ≈ 0 and V CKM 33 ≈ 1 are assumed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Also, we may neglect V CKM 32 respect V CKM 12 (although we in- clude all terms in our numerical calculations).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Thus, the amplitude of this process is given by M = 8Y 4′ 32Y 4′∗ 12 V CKM∗ 12 M 2 φ � ¯UsγµPLUb �� ¯UµγµPLVν � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' (26) We used the Fierz transformation identity � ¯UsPRVµ �� ¯ UµPLUb � = 1 2 � ¯UsγµPLUb �� ¯UµγµPLvµ � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' (27) As a result, the Wilson coefficient Cµ 9 for b → s µ µ+ process is written as Cµ 9 (Λ) = 8Y 4′ 32Y 4′∗ 12 V CKM∗ 12 M 2 φ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' (28) 5 where the scale Λ ≈ 1TeV, and Cµ 10(Λ) = −Cµ 9 (Λ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' On the other hand, the Lagrangian that generates the pro- cess b → s e e+ is given by L = − 4Y 4′ 31 ¯e ′PLbi′φi2 − 4Y 4′∗ 21 ¯ Si′PRe ′φ∗ i2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' (29) After applying Fierz identity, the amplitude of b → s e e+ is given by M = 8Y 4′ 31Y 4′∗ 21 M 2 φ � ¯UsγµPLUb �� ¯UeγµPLVe � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' (30) Hence, the Wilson coefficient Ce 9(Λ) for b → s e e+ will be Ce 9(Λ) = 8Y 4′ 31Y 4′∗ 21 M 2 φ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' (31) Moreover, Ce 10(Λ) = −Ce 9(Λ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' The effective Hamiltonian Heff for RK process is given by Heff = � i � Ci(µb)Oi(µb) + ˜Ci(µb) ˜Oi(µb) � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' (32) Through renormalization group equation (RGE), we ob- tain Ce,µ 9,10(Λ) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='2 Ce,µ 9,10(µb), (33) where Oi(µb) are ∆B = 1 transition operator, which is evaluated at the mb scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' ˜Ci(µb), ˜Oi(µb) are obtained by replacing L ↔ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' The relevant operators that describe the Rk and Rk∗ in our model are O9 = � ¯sγµPLb ��¯lγµl), O10 = � ¯sγµPLb ��¯lγµγ5l).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' (34) The Rk and Rk∗ expressions are written as Rk ≈1 + ∆+, (35) Rk∗ ≈1 + ∆+ + p(∆+ − ∆−), (36) where p is a function of q2 min and q2 max and ∆± is given by ∆± = 2 |CSM 9 |2 + |CSM 10 |2 � ℜ � CSM 9 (CNP,µ 9 ± ˜ C9 NP,µ)∗� + ℜ � CSM 10 (CNP,µ 10 ± ˜ C10 NP,µ)∗� − (µ ↔ e) � (37) For our model, ˜CNP 9,10 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Therefore, we obtain ∆+ = ∆− = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='4 � CSM 9 − CSM 10 � |CSM 9 |2 + |CSM 10 |2 ℜ � CNP,µ 9 (µb)−CNP,e 9 (µb) �∗ (38) It is worth mentioning that, whereas RK,K∗ is essen- tially dependent on the couplings Y 4′ 21 and Y 4′ 32, RD,D∗ is dependent on Y 2 22, Y 2 33 and Y 4′ 23 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' As a result, it is entirely possible to keep RK,K∗ equal to the SM expectation, con- sistently with the new LHCb results, while leaving RD,D∗ intact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' To make RK,K∗ close to one, ∆+ should be very small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' This can be accomplished by having Y 4′ 12 ≪ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' CONCLUSIONS In this paper we have demonstrated that, in the pres- ence of experimental constraints on flavor and lepton violation observables, measured values of RD and RD∗ within 1σ can be explained in non-minimal SU(5) with adjoint 45-dimensional Higgs multiplet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Enhancements for both RD and RD∗ are made possible by a tree level transition of b → cτν, which is mediated by the associ- ated scalar leptoquark.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' We also emphasized that even though this leptoquark may contribute to RK and RK∗, they remain independent of RD and RD∗ enhancements because they are given in terms of different Yukawa cou- plings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' As a result, their contributions can be easily sup- pressed, and RK and RK∗ continue to be identical to SM predictions, which are consistent with the most recent LHCb data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' ACKNOWLEDGEMENTS This work is partially supported by Science, Tech- nology & Innovation Funding Authority (STDF) under grant number 37272.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' 6 REFERENCES [1] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Lees et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' [BaBar Collaboration], Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' 109, 101802 (2012) [arXiv:1205.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='5442 [hep-ex]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' [2] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Lees et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' [BaBar Collaboration], Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' D 88, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' 7, 072012 (2013) [arXiv:1303.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='0571 [hep-ex]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' [3] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Huschle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' [Belle Collaboration], Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' D 92, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' 7, 072014 (2015) [arXiv:1507.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='03233 [hep-ex]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' [4] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Hirose et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' [Belle Collaboration], Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' 118, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' 21, 211801 (2017) [arXiv:1612.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='00529 [hep-ex]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' [5] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Hirose et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' [Belle Collaboration], Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' D 97, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' 1, 012004 (2018) [arXiv:1709.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='00129 [hep-ex]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' [6] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Caria et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' [Belle Collaboration], Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' 124, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' 16, 161803 (2020) [arXiv:1910.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='05864 [hep-ex]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' [7] LHCb Collaboration, https://indico.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='cern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='ch/event/1187939/ (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' [8] https://hflav-eos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='web.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='cern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='ch/hflav- eos/semi/spring21/html/RDsDsstar/RDRDs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='html (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' [9] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Bigi and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Gambino, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' D 94, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' 7, 094008 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' [arXiv:1606.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='08030 [hep-ph]] [10] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Gambino, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Jung and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Schacht, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' B 795, 386-390 (2019) [arXiv:1905.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='08209 [hep-ph]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' [11] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Bordone, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Jung and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' van Dyk, Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' C 80, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' 2, 74 (2020) [arXiv:1908.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='09398 [hep-ph]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' [12] LHCb collaboration, arXiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='2212.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='09152 [hep-ex] (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' [13] LHCb collaboration, arXiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='2212.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='09153 [hep-ex] (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' [14] Marzia Bordone, Gino Isidori and Andrea Pattori,Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' C 76, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' 8, 440 (2016) [arXiv:1605.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='07633 [hep- ph]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' [15] Ilja Dorsner, Svjetlana Fajfer, Nejc Kosnik, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' D 86, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' 1, 015013 (2012) [ arXiv:1204.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='0674v2 [hep-ph]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' [16] Syuhei Iguro, Michihisa Takeuchi and Ryoutaro Watan- abe, Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' C 81, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' 5, 406 (2021) [arXiv:2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='02486 [hep-ph]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' [17] David Marzocca and Sokratis Trifinopoulos, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' 127, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' 6, 061803 (2021) [arXiv:2104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='05730 [hep- ph]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' [18] Arvind Bhaskar and Anirudhan A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Madathil and Tanu- moy Mandal and Subhadip Mitra, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' D 106, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' 11, 115009 (2022) [arXiv:2204.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='09031 [hep-ph]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' [19] Peter Cox, Alexander Kusenko, Olcyr Sumensari and Tsutomu T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Yanagida, JHEP 05, 35 (2017) [arXiv:1612.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='03923 [hep-ph]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' [20] Bartosz Fornal and Benjam´ın Grinstein, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' 119, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' 24, 241801 (2017) [ arXiv:1706.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='08535 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' [21] Ilja Dorsner, Pavel Fileviez Perez, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' B 642, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' 03, 248-252 (2006) [arXiv:0606062 [hep-ph]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' [22] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Khalil, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Salem, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Allam, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' D 89, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' 09, 095011 (2015) [arXiv:1401.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='1482v2 [hep-ph]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' [23] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Khalil, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Salem, Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' B 876, 473 (2013) [arXiv:1304.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='3689 [hep-ph]] [24] Minoru Tanaka and Ryoutaro Watanabe, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' D 87, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' 3, 034028 (2013) [arXiv:1212.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='1878 [hep-ph]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' [25] Syuhei Iguro, Teppei Kitahara, Yuji Omura, Ryoutaro Watanabe and Kei Yamamoto,JHEP 02, 194 (2019) [arXiv 1811.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='08899 [hep-ph]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' [26] Pouya Asadi, Matthew R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Buckley and David Shih, JHEP 09, 10 (2018) [arXiv:1804.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='04135 [hep-ph]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' [27] Pouya Asadi, Matthew R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Buckley and David Shih, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' D 99, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' 3, 035015 (2019) [arXiv:1810.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='06597 [hep- ph]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' [28] Robert Fleischer, Ruben Jaarsma and Gilberto Tetlalmatzi-Xolocotzi, Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' C 81, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='7, 658 (2021) [arXiv:2104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='04023 [hep-ph]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' [29] Debjyoti Bardhan and Diptimoy Ghosh, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' D 100, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' 1, 011701 (2019) [arXiv:1904.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='10432 [hep-ph]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' [30] Monika Blanke, Andreas Crivellin, Stefan de Boer, Teppei Kitahara, Marta Moscati, Ulrich Nierste and Ivan Nisandzic,Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' D 99, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='7, 075006 (2019) [arXiv:1811.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='09603 [hep-ph]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' [31] Monika Blanke, Andreas Crivellin, Teppei Kitahara, Marta Moscati, Ulrich Nierste and Ivan Nisandzic,Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' D 100, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' 3, 035035 (2019) [arXiv:1905.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='08253 [hep- ph]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' [32] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Abdesselam et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' [Belle Collaboration], arXiv:1903.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='03102 [hep-ex] (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' [33] Karol Adamczyk, arXiv:1901.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='06380 [hep-ex] (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' [34] Ashutosh Kumar Alok, Dinesh Kumar, Suman Kumb- hakar and S Uma Sankar, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' D 95, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' 11, 115038 (2017), [arXiv:1606.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='03164 [hep-ph]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' [35] Minoru Tanaka and Ryoutaro Watanabe, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' D 87, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' 3, 034028 (2013), [arXiv:1212.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='1878v3 [hep-ph]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' [36] Mart´ın Gonz´alez-Alonso, Jorge Martin Camalich and Kin Mimouni,Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' B 772, 777-785 (2017), [arXiv:1706.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='00410v2 [hep-ph]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' [37] Syuhei Iguro, Michihisa Takeuchi and Ryoutaro Watanabe,Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' C 81, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content=' 5, 406 (2021), [arXiv2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} +page_content='02486v4 [hep-ph]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E0T4oBgHgl3EQfSwBA/content/2301.02226v1.pdf'} diff --git a/M9E2T4oBgHgl3EQfBgYX/content/2301.03602v1.pdf b/M9E2T4oBgHgl3EQfBgYX/content/2301.03602v1.pdf new file mode 100644 index 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b/MdAyT4oBgHgl3EQf6vqH/content/tmp_files/2301.00827v1.pdf.txt @@ -0,0 +1,1870 @@ +CERN-TH-2023-002 +Anomaly Cancellation in Effective Field Theories +From the Covariant Derivative Expansion +Timothy Cohen,1,2,3 Xiaochuan Lu,4,3 and Zhengkang Zhang5 +1 Theoretical Physics Department, CERN, 1211 Geneva, Switzerland +2 Theoretical Particle Physics Laboratory, EPFL, 1015 Lausanne, Switzerland +3 Institute for Fundamental Science, University of Oregon, Eugene, OR 97403, USA +4 Department of Physics, University of California, San Diego, La Jolla, CA 92093, USA +5 Department of Physics, University of California, Santa Barbara, CA 91106, USA +E-mail: tim.cohen@cern.ch, xil224@ucsd.edu, zkzhang@ucsb.edu +Abstract: We extend our recently-proposed formalism for calculating anomalies of +global and gauge symmetries using the Covariant Derivative Expansion to include +a general class of operators that can appear in relativistic Effective Field Theories +(EFTs). This allows us to prove that EFT operators involving general scalar, vector, +and tensor couplings to fermion bilinears only give rise to irrelevant anomalies, which +can be removed by an appropriate choice of counterterms, thereby confirming the +absence of new constraints from anomaly cancellation on the Standard Model EFT. +arXiv:2301.00827v1 [hep-ph] 2 Jan 2023 + +Contents +1 +Introduction +2 +2 +Parameterization of a General EFT +4 +3 +Regularizing and Evaluating the Anomaly with CDE +6 +4 +Higher-dimensional Operators Yield Irrelevant Anomalies +10 +4.1 +Vector Interactions +11 +4.2 +Vector and Scalar Interactions +13 +4.3 +Vector, Scalar, and Tensor Interactions +15 +4.4 +Summary +18 +5 +Discussion and Future Directions +18 +Acknowledgments +19 +References +19 +1 +Introduction +Anomalies provide critical consistency conditions on gauge theories such as the Stan- +dard Model; see e.g. Ref. [1, 2] for reviews. Anomaly cancellation in the Standard +Model itself is of course well understood. However, anomaly cancellation for Ef- +fective Field Theories (EFTs) with higher-dimensional operators is a more subtle +issue, which has received renewed interest recently in the context of the Standard +Model Effective Field Theory (SMEFT) [3, 4] (see also Refs. [5–10] for earlier stud- +ies). As shown in these papers, demonstrating anomaly cancellation for SMEFT +involves carefully accounting for the interplay of various interactions encoded in the +higher-dimensional operators. +In this paper, we generalize the method developed in Ref. [11] for computing +anomalies with the Covariant Derivative Expansion (CDE) [12–16] to the case of +EFTs. This will allow us to confirm that the anomaly cancellation condition is un- +changed by the presence of a general class of higher-dimensional operators. More +precisely, contributions to anomalies from higher-dimensional operators are in the +form of the gauge variation of local operators. These are known as irrelevant anoma- +lies and can be removed by the renormalization procedure with appropriate countert- +erms (see e.g. Ref. [17] for a recent systematic study of such counterterms focused on +– 2 – + +renormalizable theories). In contrast, relevant anomalies are IR effects and are not +affected by higher-dimensional operators. We will demonstrate this explicitly with a +CDE calculation. +To see that anomalies a priori may depend on the detailed form of the interac- +tions in the theory, let us briefly review its definition. We extract anomalies from +the gauge variation of the bosonic effective action W[Gµ], defined as +eiW[Gµ] ≡ +� +DχDχ† eiS[χ,χ†,Gµ] . +(1.1) +Even when the classical action is gauge invariant, S[χα, χ† +α, Gµ +α] = S[χ, χ†, Gµ] (where +subscript α denotes the gauge-transformed quantity), the bosonic effective action +after integrating out the fermions may not be: +W[Gµ +α] +?= W[Gµ] . +(1.2) +This possible discrepancy is due to the path integral measure DχDχ†: +eiW[Gµ +α] = +� +DχDχ† eiS[χ,χ†,Gµ +α] = +� +DχαDχ† +α eiS[χα,χ† +α,Gµ +α] += +� +J −1 +α DχDχ† eiS[χ,χ†,Gµ] = eiW[Gµ] � +J −1 +α +� +G , +(1.3) +or equivalently +W[Gµ +α] − W[Gµ] = −i log +� +J −1 +α +� +G = A[α] + O(α2) . +(1.4) +We see that the anomaly functional A[α] (which we will often just refer to as the +anomaly), as defined by the first-order gauge variation of the bosonic effective action, +is related to the expectation value of the Jacobian factor ⟨J −1 +α ⟩G. As emphasized +by the subscript G, this expectation value may a priori depend on the details of the +theory, namely what interactions it contains (just as expectation values of generic +operators would). So one needs a general formalism to calculate the anomalies for +theories with generic interactions. +In Ref. [11], we focused on the case of chiral fermions minimally coupled to gauge +fields and introduced a regularization prescription – a generalized version of the clas- +sic Fujikawa’s method [18–21] – to efficiently evaluate the anomaly in d = 4 spacetime +dimensions using CDE. This approach leads to unambiguous evaluation results, in +the form of a master formula for the anomaly functional A[α] that integrates various +known results about anomalies. In this paper, we extend this formalism to include +a more general set of interactions in Lorentz-invariant EFTs such as SMEFT. +The rest of this paper is organized as follows. In Sec. 2 we present our param- +eterization of a general class of EFT operators, involving scalar, vector, and tensor +– 3 – + +couplings to fermion bilinears. In Sec. 3 we generalize the formalism in Ref. [11] +and explain how to calculate the anomaly in such EFTs with CDE. We complete +the detailed evaluation of the anomaly in Sec. 4 and show that extra contributions +from the interactions beyond minimal coupling are all irrelevant anomalies. Finally, +in Sec. 5 we conclude and discuss some future directions. +2 +Parameterization of a General EFT +We are interested in anomalies of both gauge and global symmetries in a general +Lorentz-invariant EFT. As in Ref. [11], we introduce auxiliary gauge fields for all the +global symmetries of interest. Putting them together with the physical gauge fields, +we denote the whole collection by Gµ, which can be a sum over multiple (Abelian +and/or non-Abelian) group sectors: +Gµ ≡ +� +a +Ga +µta . +(2.1) +The (Hermitian) covariant derivative is +Pµ ≡ iDµ = i∂µ + Gµ , +(2.2) +and the gauge field strength is given by +Fµν = +� +a +F a +µν ta = −i [Pµ, Pν] = (∂µGν) − (∂νGµ) − i [Gµ, Gν] . +(2.3) +We consider a general theory of n left-handed Weyl fermions χ1, . . . , χn, with each χi +transforming in an irreducible representation of the (global and gauge) symmetries. +The theory may also contain an arbitrary number of scalar fields, collectively denoted +as φ. The EFT Lagrangian we consider has the following general form: +L = LG,φ + +n +� +i=1 +χ† +i σµPµ χi ++ +n +� +i,j=1 +� +χ† +i σµV µ +ij χj + +� +χi +� +Sij + iσµσνT µν +ij +� +χj + h.c. +�� +. +(2.4) +Here LG,φ collects the interactions that do not involve fermions. The rest of the +first line encodes the minimal couplings between the fermions χi and gauge fields +Gµ. In the second line, we parameterize an extended set of interactions with fermion +bilinears, categorizing them into scalar, vector, and tensor interactions: +χi Sij χj , +χ† +i σµV µ +ij χj , +χi iσµσνT µν +ij χj , +(2.5) +– 4 – + +where Sij[G, φ], V µ +ij [G, φ], T µν +ij [G, φ] are functions made of Gµ, φ and their derivatives +and can have arbitrarily high operator dimensions. Note that due to the Clifford +algebra σµσν + σνσµ = 2ηµν1, the µ ↔ ν symmetric components of T µν +ij +can be +absorbed into the scalar interactions Sij, so we define the tensor interactions to be +antisymmetric, T νµ +ij = −T µν +ij . +In the equations above, we have been using the standard two-component notation +and have suppressed the spinor indices. Taking the scalar interactions for example, +if we write out the spinor indices and put the expression into matrix form, we have +χiχj = (χi)α(χj)α = (χi)β +� +−ϵβα� +(χj)α +−→ +χT +i +� +−iσ2� +χj , +(2.6) +which is symmetric under i ↔ j. Absorbing the i, j indices also into matrix form, +we can write +χi Sij χj +−→ +χT � +−iσ2S +� +χ , +(2.7a) +χ† +i σµV µ +ij χj +−→ +χ† (σµVµ) χ , +(2.7b) +χi iσµσνT µν +ij χj +−→ +χT � +−iσ2iσµσνTµν +� +χ . +(2.7c) +We see that without loss of generality we can require +� +−iσ2S +�T = − +� +−iσ2S +� +=⇒ +ST = S , +(2.8a) +� +−iσ2iσµσνTµν +�T = − +� +−iσ2iσµσνTµν +� +=⇒ +T T +µν = Tνµ = −Tµν . +(2.8b) +Furthermore, Hermiticity of the Lagrangian in Eq. (2.4) requires V † +µ = Vµ. +A general symmetry transformation of the fermions can be parameterized as +χ +→ +χα ≡ Uα χ = eiα χ , +(2.9) +where, similar to the gauge fields in Eq. (2.1), α ≡ αata is a sum over all symmetry +group generators (across multiple sectors). For the Lagrangian in Eq. (2.4) to respect +the (global and gauge) symmetries, we need the following transformation properties +of various quantities: +P µ +−→ +P µ +α = Uα P µ U † +α , +δαP µ = δαGµ = i[α, P µ] , +(2.10a) +V µ +−→ +V µ +α = Uα V µ U † +α , +δαV µ = i[α, V µ] , +(2.10b) +S +−→ +Sα = U ∗ +α S U † +α , +δαS = −i(αTS + Sα) , +(2.10c) +T µν +−→ +T µν +α += U ∗ +α T µν U † +α , +δαT µν = −i(αTT µν + T µνα) , (2.10d) +LG,φ +−→ +LG,φ[Gα, φα] = LG,φ[G, φ] , +δαLG,φ = 0 , +(2.10e) +– 5 – + +where δα denotes the first order (in α) gauge variation, e.g. δαP µ ≡ (P µ +α − P µ)|O(α). +The Lagrangian in Eq. (2.4) incorporates the most general scalar, vector, and +tensor couplings to fermion bilinears. For example, in SMEFT, the vector interac- +tions V µ +ij cover current-current operators such as +� +H†i←→ +D µH +�� ¯ψγµψ +� +, +|H|2� +H†i←→ +D µH +�� ¯ψγµψ +� +, +· · · +(2.11) +where H is the Higgs doublet and ψ may represent any of the SM fermions ψ ∈ +{q, u, d, ℓ, e}, written in four-component notation here. The scalar interactions Sij +cover Yukawa-type operators such as +¯ℓeH , +|H|2 ¯ℓeH , +· · · +(2.12) +The tensor interactions T µν +ij cover dipole operators like +¯ℓσµνeBµνH , +|H|2 ¯ℓσµνeBµνH , +· · · +(2.13) +where σµν ≡ +i +2[γµ, γν]. +At dimension six, these include all but the four-fermion +operators in the Warsaw basis [22]. In fact, all operators in SMEFT involving up +to two powers of fermions and no derivatives acting on them, up to arbitrarily high +dimensions, are captured by Eq. (2.4). Furthermore, as argued in Refs. [4, 9], four- +fermion operators can be captured by introducing auxiliary fields, and we believe this +argument may be extended to operators with six and more fermions by perturbatively +including interactions among such auxiliary fields. Therefore, our calculation in what +follows should apply quite generally to all higher-dimensional SMEFT (as well as +other relativistic EFT) operators1 with no derivatives acting on the fermions. +3 +Regularizing and Evaluating the Anomaly with CDE +To facilitate the calculation of anomalies, we first recast the fermionic interactions +in Eq. (2.4) into the following matrix form +L = LG,φ + 1 +2 +� +χ† χT (−iσ2) +� +� +P +� +χ +iσ2χ∗ +� +, +(3.1) +where +� +P ≡ +� +� σµ(i∂µ + Gµ + Vµ) +S† − i σνσµ T † +µν +S + iσµσν Tµν +σµ(i∂µ − GT +µ − V T +µ ) +� +� . +(3.2) +1Throughout this paper we use the term ‘higher-dimensional operators’ to emphasize the rel- +evance of our analysis for the infinite series of EFT operators, though technically the operators +considered here include also renormalizable ones like dimension-four Yukawa interactions (as part +of S – see Eq. (2.12)). +– 6 – + +For the Lagrangian to be real and symmetry preserving, the matrix � +P needs to be +hermitian, � +P † = � +P , and transform as +� +P +−→ +� +Pα = eiα � +P e−iα , +δα � +P = i +� +α, � +P +� +with +α ≡ +� +α +0 +0 −αT +� +. +(3.3) +Clearly, these properties of � +P can be verified using its explicit expression in Eq. (3.2) +together with the transformation properties given in Eq. (2.10). +As reviewed in Ref. [11] (see also Refs [1, 2]), anomalies can be derived from +the gauge variation of the bosonic effective action obtained by integrating out the +fermion fields. In the present case, the bosonic effective action depends on both +gauge and scalar fields (i.e., we integrate out the fermions in the path integral while +treating all bosonic fields as classical backgrounds). Formally, we have +eiW[G,φ] = +� +DχDχ† eiS[χ,χ†,G,φ] = eiSG,φ� +det � +P +�1/2 . +(3.4) +Following Eq. (3.3), a gauge transformation yields +eiW[Gα,φα] = eiSG,φ� +det � +Pα +�1/2 = eiSG,φ +� +det +� +eiα � +P e−iα��1/2 +. +(3.5) +As in Eq. (1.4), the anomaly functional (or simply the anomaly) is defined by the +first-order gauge variation of the bosonic effective action: +A[α] ≡ δαW[G, φ] = +� +W[Gα, φα] − W[G, φ] +���� +O(α) +≃ − i +2 Tr log +� +1 + 1 +� +P +� +iα � +P − � +P iα +������ +O(α) +≃ 1 +2 Tr +� 1 +� +P +� +α � +P − � +P α +�� +. +(3.6) +As explained in detail in Ref. [11], we use the notation ‘≃’ to emphasize that the +expressions are not exactly equal unless they are regularized in the same way. +To proceed further, we need to introduce a regulator. Following similar steps as +in Sec. 3 of Ref. [11], we see that in the present case, each term in the expansion is +proportional to +tr +� +�σµ1σν1 . . . σµnσνn +· +· +σµ1σν1 . . . σµnσνn +� +� = tr +� +γµ1γν1 . . . γµnγνn +� +� +1−γ5 +2 +· +· +1+γ5 +2 +� +� +� +. (3.7) +We can therefore replace all the 2×2 Pauli matrices by 4×4 gamma matrices while +freely inserting chirality projection factors 1∓γ5 +2 +β 1±γ5 +2 , such that terms proportional +to β will hit the opposite chirality projection operator when anti-commuted to the +– 7 – + +right and vanish. To this end, let us define +� +Pβ ≡ +� +i/∂+/G +� +1−γ5 +2 ++βG +1+γ5 +2 +� ++ /V +� +1−γ5 +2 ++βV +1+γ5 +2 +� +S†� +1+γ5 +2 ++βS +1−γ5 +2 +� ++σµνT † +µν +� +1+γ5 +2 ++βT +1−γ5 +2 +� +S +� +1−γ5 +2 ++βS +1+γ5 +2 +� ++σµνTµν +� +1−γ5 +2 ++βT +1+γ5 +2 +� +i/∂−/GT� +1+γ5 +2 ++βG +1−γ5 +2 +� +− /V T � +1+γ5 +2 ++βV +1−γ5 +2 +� +� +, +(3.8) +We clarify that /G +T, /V +T are defined as +/G +T ≡ γµGT +µ , +/V +T ≡ γµV T +µ , +(3.9) +in which the gamma matrices are not transposed. Here βG, βS, βV , βT can all be +different in principle, and we denote them collectively as β in the subscript of � +Pβ +(and also Aβ below). +Replacing � +P → � +Pβ in Eq. (3.6), we see that similarly to +Ref. [11], a damping factor f +� +− � +P 2 +β /Λ2� +emerges as a natural regulator, with any +function f(u) that satisfies the following conditions +f(0) = 1 ; +f(+∞) = 0 ; +� ∞ +0 +duf(u) +well defined , +(3.10a) +undnf +dun +���� +u=0 += undnf +dun +���� +u→+∞ += 0 +for +n ≥ 1 . +(3.10b) +The regularized anomaly is then defined by +AΛ +β[α] ≡ 1 +2 Tr +� +f +� +− +� +P 2 +β +Λ2 +� +� +P −1 +β +� +α � +Pβ − � +Pβα +� 1 − Γ5 +2 +� +, +(3.11) +where we have introduced the notation +Γ5 ≡ +� +γ5 +0 +0 −γ5 +� +satisfying +� +PβΓ5 = −Γ5 � +Pβ . +(3.12) +Now using the cyclicity of the trace and commuting � +Pβ through f +� +− +� +P 2 +β +Λ2 +� +, we obtain +AΛ +β[α] = 1 +2 Tr +� +f +� +− +� +P 2 +β +Λ2 +� +Γ5 α +� +. +(3.13) +The renormalized anomaly is then defined by +Aβ[α] ≡ lim +Λ→∞ +� +AΛ +β[α] + δα +� +d4x LΛ +ct +� +, +(3.14) +where LΛ +ct is the local counterterm Lagrangian. Since AΛ +β[α] may be quadratically +divergent, we must include appropriate O(Λ2) counterterms to make the renormalized +anomaly finite in the limit Λ → ∞. Meanwhile, the finite part of LΛ +ct defines the +renormalization scheme. Generically AΛ +β[α] also contains O(1/Λ) terms, which we +– 8 – + +will suppress throughout the paper since they vanish when Λ → ∞. +Eq. (3.13) is a generalization of the minimal coupling (mc) case formula in +Ref. [11]. To see the connection explicitly, we note that when S = Vµ = Tµν = 0, � +Pβ +becomes block diagonal with the two blocks related by charge conjugation:2 +� +P mc +β += +� �Pβ +0 +0 +�P β +� += +� +i/∂+γµGµ +� +1−γ5 +2 ++βG +1+γ5 +2 +� +0 +0 +−i/∂T−γµGT +µ +� +1+γ5 +2 ++βG +1−γ5 +2 +� +� +, +(3.15) +where ‘charge conjugation’ is the operation +�P β ≡ γ0γ2 �P T +β γ0γ2 , +(3.16) +under which the gamma matrices transform as +γµ = −γµ , +σµν = −σµν , +γ5 = γ5 . +(3.17) +It satisfies the expected properties: +A = A , +tr +� +ABC · · · +� += tr +� +· · · C B A +� +. +(3.18) +Therefore, the two blocks in � +P mc +β +contribute equally, and Eq. (3.13) reduces to the +result derived in Ref. [11]: +AΛ,mc +β +[α] = Tr +� +f +� +− +�P 2 +β +Λ2 +� +γ5 α +� +. +(3.19) +It is useful to introduce an extended version of this charge conjugation operation. +For a matrix A acting on the field multiplet space, we define +A ≡ γ0γ2� +0 1 +1 0 +� +AT γ0γ2� +0 1 +1 0 +� +. +(3.20) +Clearly, the properties in Eq. (3.18) hold for this extended version as well, and one +can also check that +� +P β = � +Pβ , +α = −α , +Γ5 = −Γ5 . +(3.21) +The CDE evaluation of the functional trace in Eq. (3.13) proceeds in a similar +way to the minimal coupling case detailed in Ref. [11]. After performing the loop +integrals, we obtain +AΛ +β[α] = +i +32π2 +� +d4x +� +− Λ2 +�� ∞ +0 +duf(u) +� +tr0 + 1 +6 +� +tr1 + tr2 + tr3 +�� +, +(3.22) +2Note that (∂µ)T = ←−∂ µ = −∂µ upon integration by parts. +– 9 – + +with a few (non-functional) traces over the field multiplet and internal indices (de- +noted by lowercase ‘tr’): +tr0 = tr +� � +P 2 +β Γ5α +� +, +(3.23a) +tr1 = tr +� � +P 4 +β Γ5α +� +, +(3.23b) +tr2 = − 1 +2 tr +�� � +P 2 +β γµ � +Pβγµ � +Pβ + � +Pβγµ � +Pβγµ � +P 2 +β +� +Γ5α +� +, +(3.23c) +tr3 = − 1 +2 tr +� � +Pβγµ � +P 2 +β γµ � +Pβ Γ5α +� +. +(3.23d) +These are generalizations of tr0–tr3 (unbolded) in Ref. [11], although (obviously) +their evaluation result is twice as large, tri = 2 tri, in the minimal coupling case. It +is also useful to note that the two terms in tr2 are related by charge conjugation and +therefore equal,3 which simplifies its calculation later on. +4 +Higher-dimensional Operators Yield Irrelevant Anomalies +In this section, we complete the evaluation of the regularized anomaly AΛ +β[α] by com- +puting the traces in Eq. (3.23). For general values of βG, βS, βV , βT, the calculation +is very tedious and does not give new insights. The reason is that most β choices +lead to results that do not satisfy the Wess-Zumino consistency condition [23], which +means they do not correspond to consistent regularization schemes of the effective +action and there is no meaningful notion of relevant vs. irrelevant anomalies. This +point has been discussed in detail in Ref. [11] in the minimal coupling case where only +βG is present; for example, βG = 0 is the only choice that satisfies the Wess-Zumino +consistency condition for the case of a nontrivial non-Abelian anomaly. Motivated +by the results in Ref. [11], we will set all the β’s to zero in the present analysis: +βG = βS = βV = βT = 0 . +(4.1) +With this regularization scheme choice, we will show that all the additional contri- +butions to the anomaly are irrelevant, namely: +AΛ +β=0[α] = AΛ,mc +β=0 [α] − δα +� +d4x ∆LΛ +ct . +(4.2) +This means that by appropriately adjusting the local counterterms (i.e. choosing the +renormalization scheme), the renormalized anomaly defined in Eq. (3.14) is the same +3Note that we need to use cyclic permutation inside the internal trace ‘tr’ for this argument. +See App. A of Ref. [11] for a detailed discussion about the legitimacy of such operations, which will +be assumed throughout this paper. +– 10 – + +as that in the minimal coupling case: +Aβ=0[α] = Amc +β=0[α] . +(4.3) +Setting β = 0 significantly simplifies the presentation; we now have +� +Pβ=0 ≡ i/∂ + +� +/G+ /V +S†+σµνT † +µν +S+σµνTµν +−/GT− /V T +� 1 − Γ5 +2 +. +(4.4) +Nevertheless, the calculation including S, Vµ, Tµν all at once is still quite lengthy. So +in what follows, we will work up to the full results gradually, adding one type of +interactions at each step. +4.1 +Vector Interactions +We begin with the case of having vector interactions Vµ only, while setting S and +Tµν to zero. In this case, there is actually a shortcut. From the expression of � +Pβ=0 +in Eq. (4.4) we see that, instead of directly calculating the traces in Eq. (3.23), we +can simply take the minimal coupling result and replace Gµ → Gµ + Vµ: +AΛ +β=0[α] +��� +S=Tµν=0 = AΛ,mc +β=0 [α] +��� +Gµ→Gµ+Vµ . +(4.5) +In Ref. [11], we obtained the result for the minimal coupling case +AΛ,mc +β=0 [α] = +� +d4x +� +1 +48π2 εµνρσ tr +� +(∂µα) (GνFρσ + iGνGρGσ) +� +− δαLΛ +ct,0 +� +. +(4.6) +The first term is the standard result for the consistent anomaly. The second term, +being the gauge variation of a local counterterm +LΛ +ct,0 = +1 +16π2 +� +Λ2 +� ∞ +0 +duf(u) +� +tr +� +GµGµ +� ++ +1 +96π2 tr +� +(∂µGµ)2 − 2i F µνGµGν + 1 +2 GµGνGµGν +� +, +(4.7) +is an irrelevant anomaly. +Upon making the substitution Gµ → Gµ + Vµ, we first note that the irrelevant +term in Eq. (4.6) remains irrelevant, because the two operations ‘taking the gauge +variation’ and ‘substituting Gµ → Gµ + Vµ’ commute with each other: +� +δαLΛ +ct,0 +���� +Gµ→Gµ+Vµ = δα +� +LΛ +ct,0 +��� +Gµ→Gµ+Vµ +� +, +(4.8) +– 11 – + +due to the fact +δα(Gµ + Vµ) = (∂µα) + i [α, Gµ] + i [α, Vµ] = (∂µα) + i [α, Gµ + Vµ] . +(4.9) +For the relevant part of AΛ,mc +β=0 (first term in Eq. (4.6)), the substitution Gµ → +Gµ + Vµ produces additional terms that we need to track carefully. Using +Fµν +�� +Gµ→Gµ+Vµ = Fµν + (DµVν) − (DνVµ) − i [Vµ, Vν] , +(4.10) +where (DµVν) ≡ (∂µVν) − i [Gµ, Vν], we get +AΛ +β=0[α] +�� +S=Tµν=0 = AΛ,mc +β=0 [α] − δα +� +d4x +� +LΛ +ct,0 +��� +Gµ→Gµ+Vµ − LΛ +ct,0 +� +− +� +d4x +1 +48π2 εµνρσ tr +� +(∂µα) +� +− (VνGρσ + GρσVν) +− i (GνGρVσ + VνGρGσ − GνVρGσ) − 2Vν (DρVσ) +− iVνGρVσ + i (GνVρVσ − VνVρGσ) + iVνVρVσ +�� +. (4.11) +Using the gauge transformation properties of the various quantities: +δαGµ = (∂µα) + i [α, Gµ] , +δαGµν = i [α, Gµν] , +(4.12a) +δαVµ = i [α, Vµ] , +δα(DµVν) = i [α, (DµVν)] , +(4.12b) +we can organize the terms beyond the first line in Eq. (4.11) into the gauge variation +of the following local counterterm: +∆L(V ) +ct += +1 +48π2 εµνρσ tr +� +− Gµ (VνFρσ + FρσVν) − iGµGνGρVσ − 2GµVν (DρVσ) +− i +2 GµVνGρVσ + iGµGνVρVσ + iGµVνVρVσ +� +. (4.13) +Note that when taking the gauge variation of the expression above, all the commuta- +tor terms generated through Eq. (4.12) cancel out, which leaves us only with terms +proportional to (∂µα), reproducing the expression in Eq. (4.11). In summary, we +have shown that +AΛ +β=0[α] +��� +S=Tµν=0 = AΛ,mc +β=0 [α] − δα +� +d4x +� +LΛ +ct,0 +��� +Gµ→Gµ+Vµ − LΛ +ct,0 + ∆L(V ) +ct +� +. (4.14) +We conclude that all additional contributions to the anomaly due to the vector +interactions Vµ are irrelevant. +– 12 – + +4.2 +Vector and Scalar Interactions +In this subsection, we turn on both the scalar interactions S and vector interactions +Vµ while keeping Tµν = 0. We will further include the tensor interactions Tµν in the +next subsection. +To calculate the traces in Eq. (3.23) in the presence of S and/or Tµν, it is useful +to decompose � +Pβ=0 in Eq. (4.4) as +� +Pβ=0 = (SL + γµV µ +L + σµνT µν +L ) 1 − γ5 +2 ++ (SR + γµV µ +R + σµνT µν +R ) 1 + γ5 +2 +≡ (SL + VL + TL) 1 − γ5 +2 ++ (SR + VR + TR) 1 + γ5 +2 +, +(4.15) +where we have introduced the notation: +VL = +� i/∂+/G+ /V +0 +0 +i/∂ +� +, +SL = +� +0 0 +S 0 +� +, +TL = σµν +� +0 +0 +T µν 0 +� +, +(4.16a) +VR = +� +i/∂ +0 +0 +i/∂−/GT− /V T +� +, +SR = +� +0 S† +0 0 +� +, +TR = σµν +� +0 T †µν +0 +0 +� +. +(4.16b) +These components satisfy the following relations under the (extended) charge conju- +gation defined in Eq. (3.20): +V L/R = VR/L , +SL/R = SL/R , +T L/R = TL/R . +(4.17) +With the decomposition in Eq. (4.15), we can expand the traces in Eq. (3.23) +into a set of terms, each being a product of the components +VL/R +1 ∓ γ5 +2 +, +SL/R +1 ∓ γ5 +2 +, +TL/R +1 ∓ γ5 +2 +. +(4.18) +The matrix structures of these components, their chiralities, and charge conjugation +properties lead to simplifications of the calculation: +• For the Dirac trace to be nonzero, each term must have an even power of γµ +matrices in total. Given the structures of the traces in Eq. (3.23), this implies +that only terms with an even power of VL/R will contribute. +• The matrix structure of SL/R tells us that +SL +� +· · · VL/R · · · +� +SL = SR +� +· · · VL/R · · · +� +SR = 0 , +(4.19) +where +� +· · · VL/R · · · +� +does not contain any SL/R or TL/R factors. The same is +true if we replace any of the SL/R in Eq. (4.19) with TL/R. +– 13 – + +• The product of the chirality projection factors 1∓γ5 +2 +will impose further selection +rules. +• Finally, one can make use of the charge conjugation properties in Eq. (4.17) to +merge terms and simplify the result. +Now we apply these constraints to the case of this subsection, where S, Vµ ̸= 0 +but Tµν = 0. It is easy to see that tr0 does not contain any S-dependent terms, while +the nonzero terms in tr1, tr2, tr3 must have two powers of S and two powers of V +with appropriate chirality combinations. Starting with tr1, we get +tr(S2V 2) +1 += 1 +2 tr +�� +SRVLSLVR − VLSLVRSR + SLVRSRVL − VRSRVLSL +� +α +� +, +(4.20) +where terms containing one power of γ5 have been dropped since tr(γµγνγ5) = 0. We +can use charge conjugation to further simplify this trace. Upon cyclic permutation +the four terms in Eq. (4.20) combine in pairs and give +tr(S2V 2) +1 += tr +�� +SRVLSLVR − VRSRVLSL +� +α +� += tr +� +SRVLSL [VR, α] +� +. +(4.21) +The other two traces tr2 and tr3 admit similar simplifications. The general rule we +follow is to rewrite half of the terms using charge conjugation such that the entire +expression is proportional to the commutator [VR, α]. After contracting the gamma +matrices using γµγµ = 4, γµγνγµ = −2γν, we find +tr(S2V 2) +2 += tr +�� +SRVRSL − 2VLSRSL − 2SRSLVL +� +[VR, α] +� +, +(4.22a) +tr(S2V 2) +3 += tr +� +SRSL [VR, α] +� += tr +�� +SRSLVR + VRSRSL +� +[VR, α] +� +. +(4.22b) +Combining the three traces above and substituting in the expressions for SL,R , VL,R +from Eq. (4.16), we find that the additional contribution to the anomaly from scalar +couplings is +AΛ +β=0[α] +��� +O(S2V 2) = − +1 +192π2 +� +d4x tr +�� +S†(/G +T + /V +T)S − S†S (/G + /V ) +− (/G + /V ) S†S + i +� +S†←→ +/DV S +�� +(/∂α) +� +, +(4.23) +where +� +S†←→ +/DV S +� +≡ γµ +� +S†(Dµ +V S)−(Dµ +V S†)S +� +. Here we have defined a shifted covariant +derivative Dµ +V that also contains the vector interactions V µ: +Dµ +V ≡ Dµ�� +Gµ→Gµ+V µ = ∂µ − i (Gµ + V µ) . +(4.24) +– 14 – + +Its action on S, S† follows the same substitution: +(Dµ +V S) ≡ (DµS) +�� +Gµ→Gµ+V µ , +� +Dµ +V S†� +≡ +� +DµS†��� +Gµ→Gµ+V µ . +(4.25) +If desired, one could easily evaluate the Dirac trace tr(γµγν) = 4ηµν in Eq. (4.23), +but this is unnecessary for showing that it is an irrelevant anomaly. +To find the corresponding counterterm, we recall the gauge transformation of +the scalar interactions S[Gµ, φ] from Eq. (2.10): +S +−→ +Sα = U ∗ +αSU † +α , +(4.26) +which leads to +S†S −→ UαS†SU † +α , +δα +� +S†S +� += i +� +α, S†S +� +. +(4.27) +Their covariant derivatives by definition transform in the same way. This remains +true for the shifted covariant derivative Dµ +V defined in Eq. (4.24), and therefore we +have +δα +� +S†←→ +/DV S +� += i +� +α, +� +S†←→ +/DV S +�� +. +(4.28) +From the gauge transformation properties discussed above, together with those of +Gµ, Vµ in Eq. (4.12), we can identify +AΛ +β=0[α] +��� +O(S2V 2) = −δα +� +d4x ∆L(S2V 2) +ct +, +(4.29) +where +∆L(S2V 2) +ct += +1 +192π2 +� +d4x tr +�1 +2 S†(/G +T + /V +T) S (/G + /V ) +− S†S(/G + /V )(/G + /V ) + i +� +S†←→ +/DV S +� /G +� +. +(4.30) +We therefore conclude that when both vector and scalar interactions are present, the +additional contributions to the anomaly beyond the minimal coupling case are all +irrelevant. +4.3 +Vector, Scalar, and Tensor Interactions +Finally, we also include the tensor interactions Tµν alongside vector and scalar inter- +actions in this subsection. The calculation proceeds in a similar way to the vector +and scalar interactions case in the previous subsection; the gamma matrix algebra is +slightly more tedious but it is straightforward. +Using the decomposition in Eq. (4.15), we immediately see that again, tr0 does +– 15 – + +not contain any Tµν-dependent terms. For tr1, tr2, tr3, the additional nonzero terms +are of the form TSV 2 and T 2V 2. We examine them in turn below. +T SV 2 terms: +Upon contraction of gamma matrices using γµγµ = 4, γµγνγµ = +−2γν, and noting γµTL,Rγµ = 0 (since γµγνγργµ = 4ηνρ while TL,R involves the +antisymmetric σµν), we find +tr(TSV 2) +1 += tr +�� +TRVLSL + SRVLTL +� +[VR, α] (1 + γ5) +� +, +(4.31a) +tr(TSV 2) +2 += tr +�� +TRVRSL + SRVRTL +− 2VLSRTL − 2TRSLVL +� +[VR, α] (1 + γ5) +� +, +(4.31b) +tr(TSV 2) +3 += tr +� +TRSL +� +V 2 +R, α +� +(1 + γ5) + SRTL +� +V 2 +R, α +� +(1 − γ5) +� +. +(4.31c) +To arrive at these equations we have combined terms that are related by charge +conjugation and used cyclic permutation as in the previous subsection. +We can +further show that tr(TSV 2) +3 += 0 because +� +V 2 +R, α +� += +� +V µ +R [V ν +R, α] + [V µ +R , α] V ν +R +� +γµγν += +�� +V µ +R , [V ν +R, α] +� ++ [V ν +R, α] V µ +R + [V µ +R , α] V ν +R +� +γµγν . +(4.32) +The expression in parentheses is symmetric in µ ↔ ν (note that for +� +V µ +R , [V ν +R, α] +� +, +only its upper-left block (−∂µ∂να) will eventually feed into the expressions), whereas +the Dirac traces are antisymmetric: +tr +� +γµγνσρτ +� += − tr +� +γνγµσρτ +� +, +(4.33a) +tr +� +γµγνσρτγ5� += − tr +� +γνγµσρτγ5� +. +(4.33b) +Adding up tr1 and tr2 and substituting in the expressions for SL,R, VL,R, TL,R from +Eq. (4.16), we obtain +AΛ +β=0[α] +��� +O(TSV 2) = − +1 +192π2 +� +d4x tr +�� +(σ · T †)(/G +T + /V +T)S + S†(/G +T + /V +T)(σ · T) ++ 2i +� +(σ · T †)( /DV S) − ( /DV S†)(σ · T) +�� +(/∂α)(1 + γ5) +� +, (4.34) +where we have introduced the shorthand notation +σ · T ≡ σµνT µν , +σ · T † ≡ σµνT †µν . +(4.35) +– 16 – + +From the gauge transformation properties discussed earlier we see that +AΛ +β=0[α] +��� +O(TSV 2) = −δα +� +d4x ∆L(TSV 2) +ct +(4.36) +is an irrelevant anomaly corresponding to the following local counterterm: +∆L(TSV 2) +ct += +1 +192π2 +� +d4x tr +��1 +2 +� +(σ · T †)(/G +T + /V +T)S(/G + /V ) ++ S†(/G +T + /V +T)(σ · T)(/G + /V ) +� ++ 2i +� +(σ · T †)( /DV S) − ( /DV S†)(σ · T) +� +/G +� +(1 + γ5) +� +. (4.37) +T 2V 2 terms: +Finally, for the T 2V 2 terms, we find +tr(T 2V 2) +1 += tr +� +TRVLTL [VR, α] (1 + γ5) +� +, +(4.38a) +tr(T 2V 2) +2 += tr +� +TRVRTL [VR, α] (1 + γ5) +� +, +(4.38b) +tr(T 2V 2) +3 += − tr +� +TRγµTLγν [V µ +R V ν +R, α] (1 + γ5) +� +, +(4.38c) +where we have used γµTLVRγµ = 2γµTLV µ +R to simplify tr3. Further, since the Dirac +traces involved are symmetric under the exchange of γµ and γν: +tr +� +γµσρτγνσκλ +� += tr +� +γνσρτγµσκλ +� +, +(4.39a) +tr +� +γµσρτγνσκλγ5� += tr +� +γνσρτγµσκλγ5� +, +(4.39b) +we can freely interchange µ and ν in tr3 and obtain +tr(T 2V 2) +3 += − tr +�� +TRγµTLV µ +R + V µ +R TRγµTL +� +[VR, α] (1 + γ5) +� +. +(4.40) +Adding up all three traces and substituting in the expressions for VL,R , TL,R from +Eq. (4.16), we get +AΛ +β=0[α] +��� +O(T 2V 2) = − +1 +192π2 +� +d4x tr +�� +(σ · T †)(/G +T + /V +T)(σ · T) ++ (σ · T †)γµ(σ · T)(Gµ + V µ) + (Gµ + V µ)(σ · T †)γµ(σ · T) ++ i +� +(σ · T †) +←→ +/DV (σ · T) +�� +(/∂α)(1 + γ5) +� +, +(4.41) +where +� +(σ · T †) +←→ +/DV (σ · T) +� += σρτγµσκλ +� +T †ρτ(Dµ +V T κλ) − (Dµ +V T †ρτ)T κλ� +. This again +– 17 – + +can be identified with the gauge variation of a local counterterm: +AΛ +β=0[α] +��� +O(T 2V 2) = −δα +� +d4x ∆L(T 2V 2) +ct +, +(4.42) +where +∆L(T 2V 2) +ct += +1 +192π2 +� +d4x tr +��1 +2 (σ · T †)(/G +T + /V +T)(σ · T)(/G + /V ) ++ (σ · T †)γµ(σ · T)γν(Gµ + V µ)(Gν + V ν) ++ i +� +(σ · T †) +←→ +/DV (σ · T) +�/G +� +(1 + γ5) +� +. +(4.43) +We therefore conclude that additional contributions to AΛ +β=0[α] remain irrelevant +when tensor couplings are included. +4.4 +Summary +To summarize, in this section we have completed the calculation of the regularized +anomaly AΛ +β[α] in the presence of scalar, vector, and tensor couplings to fermion +bilinears and found that, with the Wess-Zumino consistent scheme choice β = 0, the +difference with respect to the minimal coupling case is an irrelevant anomaly: +AΛ +β=0[α] = AΛ,mc +β=0 [α] − δα +� +d4x ∆LΛ +ct . +(4.44) +The corresponding local counterterm is +∆LΛ +ct = LΛ +ct,0 +��� +Gµ→Gµ+Vµ −LΛ +ct,0 +∆L(V ) +ct +∆L(S2V 2) +ct ++∆L(TSV 2) +ct ++∆L(T 2V 2) +ct +, +(4.45) +with LΛ +ct,0, ∆L(V ) +ct , ∆L(S2V 2) +ct +, ∆L(TSV 2) +ct +and ∆L(T 2V 2) +ct +given by Eqs. (4.7), (4.13), +(4.30), (4.37) and (4.43), respectively. This means that for the renormalized anomaly +Aβ[α] defined in Eq. (3.14): +There exists a renormalization scheme where Aβ=0[α] = Amc +β=0[α] . +(4.46) +5 +Discussion and Future Directions +In this paper, we generalized the CDE framework for computing anomalies in Ref. [11] +to the case of relativistic EFTs with a general class of higher-dimensional operators. +We systematically calculated the anomaly in this formalism, and demonstrated ex- +plicitly that the additional contributions from higher-dimensional operators are irrel- +evant anomalies. This means, in particular, that the (relevant) anomaly cancellation +– 18 – + +condition in SMEFT including the aforementioned higher-dimensional operators is +the same as that in the Standard Model. +Our calculation did not include higher-dimensional operators which involve deriva- +tives acting on the fermions (beyond the kinetic term), such as +ϵikϵjl (HiDµHj) +� +ℓT +k iγ0γ2Dµℓl +� +, +� +H†DµDνH +� �¯ℓγµDνℓ +� +. +(5.1) +While there is no essential obstacle to incorporate them in our present formalism, +the CDE calculation becomes more and more tedious with the inclusion of each +derivative. Nevertheless, noting that the counterterms we found in Eqs. (4.30), (4.37) +and (4.43) share similar structures, we are hopeful that there could be a more efficient +framework that would make such a calculation more manageable and potentially also +shed new light on the underlying structures of CDE. We plan to pursue this intriguing +possibility in future work. +The master functional trace evaluated in this paper, Eq. (3.13), can also be +relevant for certain EFT matching calculations, such as when integrating out heavy +fermions that acquire masses from a Yukawa interaction via spontaneous symmetry +breaking [24, 25]. Modern EFT matching calculations are typically performed with +dimensional regularization. However, we anticipate our regularization prescription, +applied in exclusively d = 4 spacetime dimensions, should produce the same anomaly- +related non-decoupling effects. We leave the exploration of this interesting question +for future study. +Acknowledgments +We thank Quentin Bonnefoy, Nathaniel Craig, Sungwoo Hong, Markus Luty and +Aneesh Manohar for useful discussions. T.C. is supported by the U.S. Department +of Energy under grant number DE-SC0011640. X.L. is supported by the U.S. De- +partment of Energy under grant numbers DE-SC0009919 and DE-SC0011640. Z.Z. +is supported by the U.S. Department of Energy under grant number DE-SC0011702. +This work was performed in part at Aspen Center for Physics, which is supported +by National Science Foundation grant PHY-1607611. +References +[1] R. A. Bertlmann, Anomalies in quantum field theory. 1996. +[2] A. Bilal, “Lectures on Anomalies,” arXiv:0802.0634 [hep-th]. +[3] Q. Bonnefoy, L. Di Luzio, C. Grojean, A. Paul, and A. N. Rossia, “Comments on +gauge anomalies at dimension-six in the Standard Model Effective Field Theory,” +JHEP 05 (2021) 153, arXiv:2012.07740 [hep-ph]. +– 19 – + +[4] F. Feruglio, “A Note on Gauge Anomaly Cancellation in Effective Field Theories,” +JHEP 03 (2021) 128, arXiv:2012.13989 [hep-ph]. +[5] S. Marculescu and L. Mezincescu, “Axial Anomaly in Nonrenormalizable Theories,”. +[6] A. Manohar and G. W. Moore, “Anomalous Inequivalence of Phenomenological +Theories,” Nucl. Phys. B 243 (1984) 55–64. +[7] J. Minn, J. Kim, and C.-k. Lee, “Spinor Loop Anomalies With Very General Local +Fermion Lagrangians,” Phys. Rev. D 35 (1987) 1872. +[8] Y. Kim, P. Y. Pac, and H. K. Shin, “Spinor Loop Anomalies in Higher Derivative +Theories,” Phys. Rev. D 39 (1989) 1251. +[9] J. Soto, “Anomaly cancellation at finite cutoff,” Phys. Rev. D 45 (1992) 4621–4631. +[10] J. A. Dixon, “Anomalies, BRS cohomology and effective theories,” Phys. Rev. Lett. +67 (1991) 797–800. +[11] T. Cohen, X. Lu, and Z. Zhang, “Anomalies From the Covariant Derivative +Expansion,” (2023) . +[12] M. K. Gaillard, “The Effective One Loop Lagrangian With Derivative Couplings,” +Nucl. Phys. B268 (1986) 669–692. +[13] L.-H. Chan, “Derivative Expansion for the One Loop Effective Actions With Internal +Symmetry,” Phys. Rev. Lett. 57 (1986) 1199. +[14] O. Cheyette, “Effective Action for the Standard Model With Large Higgs Mass,” +Nucl. Phys. B297 (1988) 183–204. +[15] B. Henning, X. Lu, and H. Murayama, “How to use the Standard Model effective +field theory,” JHEP 01 (2016) 023, arXiv:1412.1837 [hep-ph]. +[16] B. Henning, X. Lu, and H. Murayama, “One-loop Matching and Running with +Covariant Derivative Expansion,” JHEP 01 (2018) 123, arXiv:1604.01019 +[hep-ph]. +[17] C. Cornella, F. Feruglio, and L. Vecchi, “Gauge Invariance and Finite Counterterms +in Chiral Gauge Theories,” arXiv:2205.10381 [hep-ph]. +[18] K. Fujikawa, “Path Integral Measure for Gauge Invariant Fermion Theories,” Phys. +Rev. Lett. 42 (1979) 1195–1198. +[19] K. Fujikawa, “Path Integral for Gauge Theories with Fermions,” Phys. Rev. D 21 +(1980) 2848. [Erratum: Phys.Rev.D 22, 1499 (1980)]. +[20] K. Fujikawa, “On the Evaluation of Chiral Anomaly in Gauge Theories with +Gamma(5) Couplings,” Phys. Rev. D 29 (1984) 285. +[21] K. Fujikawa and H. Suzuki, Path integrals and quantum anomalies. 2004. +[22] B. Grzadkowski, M. Iskrzynski, M. Misiak, and J. Rosiek, “Dimension-Six Terms in +the Standard Model Lagrangian,” JHEP 10 (2010) 085, arXiv:1008.4884 [hep-ph]. +– 20 – + +[23] J. Wess and B. Zumino, “Consequences of anomalous Ward identities,” Phys. Lett. B +37 (1971) 95–97. +[24] E. D’Hoker and E. Farhi, “Decoupling a Fermion Whose Mass Is Generated by a +Yukawa Coupling: The General Case,” Nucl. Phys. B 248 (1984) 59–76. +[25] E. D’Hoker and E. Farhi, “Decoupling a Fermion in the Standard Electroweak +Theory,” Nucl. Phys. B 248 (1984) 77. +– 21 – + diff --git a/MdAyT4oBgHgl3EQf6vqH/content/tmp_files/load_file.txt b/MdAyT4oBgHgl3EQf6vqH/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..863b26ff97441e16064d83754c2738a985d9e52a --- /dev/null +++ b/MdAyT4oBgHgl3EQf6vqH/content/tmp_files/load_file.txt @@ -0,0 +1,616 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf,len=615 +page_content='CERN-TH-2023-002 Anomaly Cancellation in Effective Field Theories From the Covariant Derivative Expansion Timothy Cohen,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='3 Xiaochuan Lu,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='3 and Zhengkang Zhang5 1 Theoretical Physics Department,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' CERN,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' 1211 Geneva,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Switzerland 2 Theoretical Particle Physics Laboratory,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' EPFL,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' 1015 Lausanne,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Switzerland 3 Institute for Fundamental Science,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' University of Oregon,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Eugene,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' OR 97403,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' USA 4 Department of Physics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' University of California,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' San Diego,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' La Jolla,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' CA 92093,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' USA 5 Department of Physics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' University of California,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Santa Barbara,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' CA 91106,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' USA E-mail: tim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='cohen@cern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='ch, xil224@ucsd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='edu, zkzhang@ucsb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='edu Abstract: We extend our recently-proposed formalism for calculating anomalies of global and gauge symmetries using the Covariant Derivative Expansion to include a general class of operators that can appear in relativistic Effective Field Theories (EFTs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' This allows us to prove that EFT operators involving general scalar, vector, and tensor couplings to fermion bilinears only give rise to irrelevant anomalies, which can be removed by an appropriate choice of counterterms, thereby confirming the absence of new constraints from anomaly cancellation on the Standard Model EFT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='00827v1 [hep-ph] 2 Jan 2023 Contents 1 Introduction 2 2 Parameterization of a General EFT 4 3 Regularizing and Evaluating the Anomaly with CDE 6 4 Higher-dimensional Operators Yield Irrelevant Anomalies 10 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='1 Vector Interactions 11 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='2 Vector and Scalar Interactions 13 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='3 Vector, Scalar, and Tensor Interactions 15 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='4 Summary 18 5 Discussion and Future Directions 18 Acknowledgments 19 References 19 1 Introduction Anomalies provide critical consistency conditions on gauge theories such as the Stan- dard Model;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' [1, 2] for reviews.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Anomaly cancellation in the Standard Model itself is of course well understood.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' However, anomaly cancellation for Ef- fective Field Theories (EFTs) with higher-dimensional operators is a more subtle issue, which has received renewed interest recently in the context of the Standard Model Effective Field Theory (SMEFT) [3, 4] (see also Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' [5–10] for earlier stud- ies).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' As shown in these papers, demonstrating anomaly cancellation for SMEFT involves carefully accounting for the interplay of various interactions encoded in the higher-dimensional operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' In this paper, we generalize the method developed in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' [11] for computing anomalies with the Covariant Derivative Expansion (CDE) [12–16] to the case of EFTs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' This will allow us to confirm that the anomaly cancellation condition is un- changed by the presence of a general class of higher-dimensional operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' More precisely, contributions to anomalies from higher-dimensional operators are in the form of the gauge variation of local operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' These are known as irrelevant anoma- lies and can be removed by the renormalization procedure with appropriate countert- erms (see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' [17] for a recent systematic study of such counterterms focused on – 2 – renormalizable theories).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' In contrast, relevant anomalies are IR effects and are not affected by higher-dimensional operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' We will demonstrate this explicitly with a CDE calculation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' To see that anomalies a priori may depend on the detailed form of the interac- tions in the theory, let us briefly review its definition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' We extract anomalies from the gauge variation of the bosonic effective action W[Gµ], defined as eiW[Gµ] ≡ � DχDχ† eiS[χ,χ†,Gµ] .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='1) Even when the classical action is gauge invariant, S[χα, χ† α, Gµ α] = S[χ, χ†, Gµ] (where subscript α denotes the gauge-transformed quantity), the bosonic effective action after integrating out the fermions may not be: W[Gµ α] ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='= W[Gµ] .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='2) This possible discrepancy is due to the path integral measure DχDχ†: eiW[Gµ α] = � DχDχ† eiS[χ,χ†,Gµ α] = � DχαDχ† α eiS[χα,χ† α,Gµ α] = � J −1 α DχDχ† eiS[χ,χ†,Gµ] = eiW[Gµ] � J −1 α � G , (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='3) or equivalently W[Gµ α] − W[Gµ] = −i log � J −1 α � G = A[α] + O(α2) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='4) We see that the anomaly functional A[α] (which we will often just refer to as the anomaly), as defined by the first-order gauge variation of the bosonic effective action, is related to the expectation value of the Jacobian factor ⟨J −1 α ⟩G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' As emphasized by the subscript G, this expectation value may a priori depend on the details of the theory, namely what interactions it contains (just as expectation values of generic operators would).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' So one needs a general formalism to calculate the anomalies for theories with generic interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' In Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' [11], we focused on the case of chiral fermions minimally coupled to gauge fields and introduced a regularization prescription – a generalized version of the clas- sic Fujikawa’s method [18–21] – to efficiently evaluate the anomaly in d = 4 spacetime dimensions using CDE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' This approach leads to unambiguous evaluation results, in the form of a master formula for the anomaly functional A[α] that integrates various known results about anomalies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' In this paper, we extend this formalism to include a more general set of interactions in Lorentz-invariant EFTs such as SMEFT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' The rest of this paper is organized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' In Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' 2 we present our param- eterization of a general class of EFT operators, involving scalar, vector, and tensor – 3 – couplings to fermion bilinears.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' In Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' 3 we generalize the formalism in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' [11] and explain how to calculate the anomaly in such EFTs with CDE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' We complete the detailed evaluation of the anomaly in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' 4 and show that extra contributions from the interactions beyond minimal coupling are all irrelevant anomalies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Finally, in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' 5 we conclude and discuss some future directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' 2 Parameterization of a General EFT We are interested in anomalies of both gauge and global symmetries in a general Lorentz-invariant EFT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' As in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' [11], we introduce auxiliary gauge fields for all the global symmetries of interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Putting them together with the physical gauge fields, we denote the whole collection by Gµ, which can be a sum over multiple (Abelian and/or non-Abelian) group sectors: Gµ ≡ � a Ga µta .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='1) The (Hermitian) covariant derivative is Pµ ≡ iDµ = i∂µ + Gµ , (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='2) and the gauge field strength is given by Fµν = � a F a µν ta = −i [Pµ, Pν] = (∂µGν) − (∂νGµ) − i [Gµ, Gν] .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='3) We consider a general theory of n left-handed Weyl fermions χ1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' , χn, with each χi transforming in an irreducible representation of the (global and gauge) symmetries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' The theory may also contain an arbitrary number of scalar fields, collectively denoted as φ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' The EFT Lagrangian we consider has the following general form: L = LG,φ + n � i=1 χ† i σµPµ χi + n � i,j=1 � χ† i σµV µ ij χj + � χi � Sij + iσµσνT µν ij � χj + h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' �� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='4) Here LG,φ collects the interactions that do not involve fermions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' The rest of the first line encodes the minimal couplings between the fermions χi and gauge fields Gµ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' In the second line, we parameterize an extended set of interactions with fermion bilinears, categorizing them into scalar, vector, and tensor interactions: χi Sij χj , χ† i σµV µ ij χj , χi iσµσνT µν ij χj , (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='5) – 4 – where Sij[G, φ], V µ ij [G, φ], T µν ij [G, φ] are functions made of Gµ, φ and their derivatives and can have arbitrarily high operator dimensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Note that due to the Clifford algebra σµσν + σνσµ = 2ηµν1, the µ ↔ ν symmetric components of T µν ij can be absorbed into the scalar interactions Sij, so we define the tensor interactions to be antisymmetric, T νµ ij = −T µν ij .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' In the equations above, we have been using the standard two-component notation and have suppressed the spinor indices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Taking the scalar interactions for example, if we write out the spinor indices and put the expression into matrix form, we have χiχj = (χi)α(χj)α = (χi)β � −ϵβα� (χj)α −→ χT i � −iσ2� χj , (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='6) which is symmetric under i ↔ j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Absorbing the i, j indices also into matrix form, we can write χi Sij χj −→ χT � −iσ2S � χ , (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='7a) χ† i σµV µ ij χj −→ χ† (σµVµ) χ , (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='7b) χi iσµσνT µν ij χj −→ χT � −iσ2iσµσνTµν � χ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='7c) We see that without loss of generality we can require � −iσ2S �T = − � −iσ2S � =⇒ ST = S , (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='8a) � −iσ2iσµσνTµν �T = − � −iσ2iσµσνTµν � =⇒ T T µν = Tνµ = −Tµν .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='8b) Furthermore, Hermiticity of the Lagrangian in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='4) requires V † µ = Vµ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' A general symmetry transformation of the fermions can be parameterized as χ → χα ≡ Uα χ = eiα χ , (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='9) where, similar to the gauge fields in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='1), α ≡ αata is a sum over all symmetry group generators (across multiple sectors).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' For the Lagrangian in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='4) to respect the (global and gauge) symmetries, we need the following transformation properties of various quantities: P µ −→ P µ α = Uα P µ U † α , δαP µ = δαGµ = i[α, P µ] , (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='10a) V µ −→ V µ α = Uα V µ U † α , δαV µ = i[α, V µ] , (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='10b) S −→ Sα = U ∗ α S U † α , δαS = −i(αTS + Sα) , (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='10c) T µν −→ T µν α = U ∗ α T µν U † α , δαT µν = −i(αTT µν + T µνα) , (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='10d) LG,φ −→ LG,φ[Gα, φα] = LG,φ[G, φ] , δαLG,φ = 0 , (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='10e) – 5 – where δα denotes the first order (in α) gauge variation, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' δαP µ ≡ (P µ α − P µ)|O(α).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' The Lagrangian in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='4) incorporates the most general scalar, vector, and tensor couplings to fermion bilinears.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' For example, in SMEFT, the vector interac- tions V µ ij cover current-current operators such as � H†i←→ D µH �� ¯ψγµψ � , |H|2� H†i←→ D µH �� ¯ψγµψ � , · · (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='11) where H is the Higgs doublet and ψ may represent any of the SM fermions ψ ∈ {q, u, d, ℓ, e}, written in four-component notation here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' The scalar interactions Sij cover Yukawa-type operators such as ¯ℓeH , |H|2 ¯ℓeH , · · (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='12) The tensor interactions T µν ij cover dipole operators like ¯ℓσµνeBµνH , |H|2 ¯ℓσµνeBµνH , · · (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='13) where σµν ≡ i 2[γµ, γν].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' At dimension six, these include all but the four-fermion operators in the Warsaw basis [22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' In fact, all operators in SMEFT involving up to two powers of fermions and no derivatives acting on them, up to arbitrarily high dimensions, are captured by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Furthermore, as argued in Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' [4, 9], four- fermion operators can be captured by introducing auxiliary fields, and we believe this argument may be extended to operators with six and more fermions by perturbatively including interactions among such auxiliary fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Therefore, our calculation in what follows should apply quite generally to all higher-dimensional SMEFT (as well as other relativistic EFT) operators1 with no derivatives acting on the fermions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' 3 Regularizing and Evaluating the Anomaly with CDE To facilitate the calculation of anomalies, we first recast the fermionic interactions in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='4) into the following matrix form L = LG,φ + 1 2 � χ† χT (−iσ2) � � P � χ iσ2χ∗ � , (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='1) where � P ≡ � � σµ(i∂µ + Gµ + Vµ) S† − i σνσµ T † µν S + iσµσν Tµν σµ(i∂µ − GT µ − V T µ ) � � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='2) 1Throughout this paper we use the term ‘higher-dimensional operators’ to emphasize the rel- evance of our analysis for the infinite series of EFT operators, though technically the operators considered here include also renormalizable ones like dimension-four Yukawa interactions (as part of S – see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='12)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' – 6 – For the Lagrangian to be real and symmetry preserving, the matrix � P needs to be hermitian, � P † = � P , and transform as � P −→ � Pα = eiα � P e−iα , δα � P = i � α, � P � with α ≡ � α 0 0 −αT � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='3) Clearly, these properties of � P can be verified using its explicit expression in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='2) together with the transformation properties given in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' As reviewed in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' [11] (see also Refs [1, 2]), anomalies can be derived from the gauge variation of the bosonic effective action obtained by integrating out the fermion fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' In the present case, the bosonic effective action depends on both gauge and scalar fields (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=', we integrate out the fermions in the path integral while treating all bosonic fields as classical backgrounds).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Formally, we have eiW[G,φ] = � DχDχ† eiS[χ,χ†,G,φ] = eiSG,φ� det � P �1/2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='4) Following Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='3), a gauge transformation yields eiW[Gα,φα] = eiSG,φ� det � Pα �1/2 = eiSG,φ � det � eiα � P e−iα��1/2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='5) As in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='4), the anomaly functional (or simply the anomaly) is defined by the first-order gauge variation of the bosonic effective action: A[α] ≡ δαW[G, φ] = � W[Gα, φα] − W[G, φ] ���� O(α) ≃ − i 2 Tr log � 1 + 1 � P � iα � P − � P iα ������ O(α) ≃ 1 2 Tr � 1 � P � α � P − � P α �� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='6) As explained in detail in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' [11], we use the notation ‘≃’ to emphasize that the expressions are not exactly equal unless they are regularized in the same way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' To proceed further, we need to introduce a regulator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Following similar steps as in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' 3 of Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' [11], we see that in the present case, each term in the expansion is proportional to tr � �σµ1σν1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' σµnσνn σµ1σν1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' σµnσνn � � = tr � γµ1γν1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' γµnγνn � � 1−γ5 2 1+γ5 2 � � � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='7) We can therefore replace all the 2×2 Pauli matrices by 4×4 gamma matrices while freely inserting chirality projection factors 1∓γ5 2 +β 1±γ5 2 , such that terms proportional to β will hit the opposite chirality projection operator when anti-commuted to the – 7 – right and vanish.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' To this end, let us define � Pβ ≡ � i/∂+/G � 1−γ5 2 +βG 1+γ5 2 � + /V � 1−γ5 2 +βV 1+γ5 2 � S†� 1+γ5 2 +βS 1−γ5 2 � +σµνT † µν � 1+γ5 2 +βT 1−γ5 2 � S � 1−γ5 2 +βS 1+γ5 2 � +σµνTµν � 1−γ5 2 +βT 1+γ5 2 � i/∂−/GT� 1+γ5 2 +βG 1−γ5 2 � − /V T � 1+γ5 2 +βV 1−γ5 2 � � , (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='8) We clarify that /G T, /V T are defined as /G T ≡ γµGT µ , /V T ≡ γµV T µ , (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='9) in which the gamma matrices are not transposed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Here βG, βS, βV , βT can all be different in principle, and we denote them collectively as β in the subscript of � Pβ (and also Aβ below).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Replacing � P → � Pβ in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='6), we see that similarly to Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' [11], a damping factor f � − � P 2 β /Λ2� emerges as a natural regulator, with any function f(u) that satisfies the following conditions f(0) = 1 ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' f(+∞) = 0 ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' � ∞ 0 duf(u) well defined , (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='10a) undnf dun ���� u=0 = undnf dun ���� u→+∞ = 0 for n ≥ 1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='10b) The regularized anomaly is then defined by AΛ β[α] ≡ 1 2 Tr � f � − � P 2 β Λ2 � � P −1 β � α � Pβ − � Pβα � 1 − Γ5 2 � , (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='11) where we have introduced the notation Γ5 ≡ � γ5 0 0 −γ5 � satisfying � PβΓ5 = −Γ5 � Pβ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='12) Now using the cyclicity of the trace and commuting � Pβ through f � − � P 2 β Λ2 � , we obtain AΛ β[α] = 1 2 Tr � f � − � P 2 β Λ2 � Γ5 α � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='13) The renormalized anomaly is then defined by Aβ[α] ≡ lim Λ→∞ � AΛ β[α] + δα � d4x LΛ ct � , (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='14) where LΛ ct is the local counterterm Lagrangian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Since AΛ β[α] may be quadratically divergent, we must include appropriate O(Λ2) counterterms to make the renormalized anomaly finite in the limit Λ → ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Meanwhile, the finite part of LΛ ct defines the renormalization scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Generically AΛ β[α] also contains O(1/Λ) terms, which we – 8 – will suppress throughout the paper since they vanish when Λ → ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='13) is a generalization of the minimal coupling (mc) case formula in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' To see the connection explicitly, we note that when S = Vµ = Tµν = 0, � Pβ becomes block diagonal with the two blocks related by charge conjugation:2 � P mc β = � �Pβ 0 0 �P β � = � i/∂+γµGµ � 1−γ5 2 +βG 1+γ5 2 � 0 0 −i/∂T−γµGT µ � 1+γ5 2 +βG 1−γ5 2 � � , (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='15) where ‘charge conjugation’ is the operation �P β ≡ γ0γ2 �P T β γ0γ2 , (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='16) under which the gamma matrices transform as γµ = −γµ , σµν = −σµν , γ5 = γ5 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='17) It satisfies the expected properties: A = A , tr � ABC · · · � = tr � · · C B A � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='18) Therefore, the two blocks in � P mc β contribute equally, and Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='13) reduces to the result derived in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' [11]: AΛ,mc β [α] = Tr � f � − �P 2 β Λ2 � γ5 α � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='19) It is useful to introduce an extended version of this charge conjugation operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' For a matrix A acting on the field multiplet space, we define A ≡ γ0γ2� 0 1 1 0 � AT γ0γ2� 0 1 1 0 � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='20) Clearly, the properties in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='18) hold for this extended version as well, and one can also check that � P β = � Pβ , α = −α , Γ5 = −Γ5 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='21) The CDE evaluation of the functional trace in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='13) proceeds in a similar way to the minimal coupling case detailed in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' After performing the loop integrals, we obtain AΛ β[α] = i 32π2 � d4x � − Λ2 �� ∞ 0 duf(u) � tr0 + 1 6 � tr1 + tr2 + tr3 �� , (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='22) 2Note that (∂µ)T = ←−∂ µ = −∂µ upon integration by parts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' – 9 – with a few (non-functional) traces over the field multiplet and internal indices (de- noted by lowercase ‘tr’): tr0 = tr � � P 2 β Γ5α � , (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='23a) tr1 = tr � � P 4 β Γ5α � , (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='23b) tr2 = − 1 2 tr �� � P 2 β γµ � Pβγµ � Pβ + � Pβγµ � Pβγµ � P 2 β � Γ5α � , (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='23c) tr3 = − 1 2 tr � � Pβγµ � P 2 β γµ � Pβ Γ5α � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='23d) These are generalizations of tr0–tr3 (unbolded) in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' [11], although (obviously) their evaluation result is twice as large, tri = 2 tri, in the minimal coupling case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' It is also useful to note that the two terms in tr2 are related by charge conjugation and therefore equal,3 which simplifies its calculation later on.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' 4 Higher-dimensional Operators Yield Irrelevant Anomalies In this section, we complete the evaluation of the regularized anomaly AΛ β[α] by com- puting the traces in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='23).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' For general values of βG, βS, βV , βT, the calculation is very tedious and does not give new insights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' The reason is that most β choices lead to results that do not satisfy the Wess-Zumino consistency condition [23], which means they do not correspond to consistent regularization schemes of the effective action and there is no meaningful notion of relevant vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' irrelevant anomalies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' This point has been discussed in detail in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' [11] in the minimal coupling case where only βG is present;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' for example, βG = 0 is the only choice that satisfies the Wess-Zumino consistency condition for the case of a nontrivial non-Abelian anomaly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Motivated by the results in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' [11], we will set all the β’s to zero in the present analysis: βG = βS = βV = βT = 0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='1) With this regularization scheme choice, we will show that all the additional contri- butions to the anomaly are irrelevant, namely: AΛ β=0[α] = AΛ,mc β=0 [α] − δα � d4x ∆LΛ ct .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='2) This means that by appropriately adjusting the local counterterms (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' choosing the renormalization scheme), the renormalized anomaly defined in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='14) is the same 3Note that we need to use cyclic permutation inside the internal trace ‘tr’ for this argument.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' See App.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' A of Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' [11] for a detailed discussion about the legitimacy of such operations, which will be assumed throughout this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' – 10 – as that in the minimal coupling case: Aβ=0[α] = Amc β=0[α] .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='3) Setting β = 0 significantly simplifies the presentation;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' we now have � Pβ=0 ≡ i/∂ + � /G+ /V S†+σµνT † µν S+σµνTµν −/GT− /V T � 1 − Γ5 2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='4) Nevertheless, the calculation including S, Vµ, Tµν all at once is still quite lengthy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' So in what follows, we will work up to the full results gradually, adding one type of interactions at each step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='1 Vector Interactions We begin with the case of having vector interactions Vµ only, while setting S and Tµν to zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' In this case, there is actually a shortcut.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' From the expression of � Pβ=0 in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='4) we see that, instead of directly calculating the traces in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='23), we can simply take the minimal coupling result and replace Gµ → Gµ + Vµ: AΛ β=0[α] ��� S=Tµν=0 = AΛ,mc β=0 [α] ��� Gµ→Gµ+Vµ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='5) In Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' [11], we obtained the result for the minimal coupling case AΛ,mc β=0 [α] = � d4x � 1 48π2 εµνρσ tr � (∂µα) (GνFρσ + iGνGρGσ) � − δαLΛ ct,0 � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='6) The first term is the standard result for the consistent anomaly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' The second term, being the gauge variation of a local counterterm LΛ ct,0 = 1 16π2 � Λ2 � ∞ 0 duf(u) � tr � GµGµ � + 1 96π2 tr � (∂µGµ)2 − 2i F µνGµGν + 1 2 GµGνGµGν � , (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='7) is an irrelevant anomaly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Upon making the substitution Gµ → Gµ + Vµ, we first note that the irrelevant term in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='6) remains irrelevant, because the two operations ‘taking the gauge variation’ and ‘substituting Gµ → Gµ + Vµ’ commute with each other: � δαLΛ ct,0 ���� Gµ→Gµ+Vµ = δα � LΛ ct,0 ��� Gµ→Gµ+Vµ � , (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='8) – 11 – due to the fact δα(Gµ + Vµ) = (∂µα) + i [α, Gµ] + i [α, Vµ] = (∂µα) + i [α, Gµ + Vµ] .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='9) For the relevant part of AΛ,mc β=0 (first term in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='6)), the substitution Gµ → Gµ + Vµ produces additional terms that we need to track carefully.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Using Fµν �� Gµ→Gµ+Vµ = Fµν + (DµVν) − (DνVµ) − i [Vµ, Vν] , (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='10) where (DµVν) ≡ (∂µVν) − i [Gµ, Vν], we get AΛ β=0[α] �� S=Tµν=0 = AΛ,mc β=0 [α] − δα � d4x � LΛ ct,0 ��� Gµ→Gµ+Vµ − LΛ ct,0 � − � d4x 1 48π2 εµνρσ tr � (∂µα) � − (VνGρσ + GρσVν) − i (GνGρVσ + VνGρGσ − GνVρGσ) − 2Vν (DρVσ) − iVνGρVσ + i (GνVρVσ − VνVρGσ) + iVνVρVσ �� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='11) Using the gauge transformation properties of the various quantities: δαGµ = (∂µα) + i [α, Gµ] , δαGµν = i [α, Gµν] , (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='12a) δαVµ = i [α, Vµ] , δα(DµVν) = i [α, (DµVν)] , (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='12b) we can organize the terms beyond the first line in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='11) into the gauge variation of the following local counterterm: ∆L(V ) ct = 1 48π2 εµνρσ tr � − Gµ (VνFρσ + FρσVν) − iGµGνGρVσ − 2GµVν (DρVσ) − i 2 GµVνGρVσ + iGµGνVρVσ + iGµVνVρVσ � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='13) Note that when taking the gauge variation of the expression above, all the commuta- tor terms generated through Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='12) cancel out, which leaves us only with terms proportional to (∂µα), reproducing the expression in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='11).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' In summary, we have shown that AΛ β=0[α] ��� S=Tµν=0 = AΛ,mc β=0 [α] − δα � d4x � LΛ ct,0 ��� Gµ→Gµ+Vµ − LΛ ct,0 + ∆L(V ) ct � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='14) We conclude that all additional contributions to the anomaly due to the vector interactions Vµ are irrelevant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' – 12 – 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='2 Vector and Scalar Interactions In this subsection, we turn on both the scalar interactions S and vector interactions Vµ while keeping Tµν = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' We will further include the tensor interactions Tµν in the next subsection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' To calculate the traces in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='23) in the presence of S and/or Tµν, it is useful to decompose � Pβ=0 in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='4) as � Pβ=0 = (SL + γµV µ L + σµνT µν L ) 1 − γ5 2 + (SR + γµV µ R + σµνT µν R ) 1 + γ5 2 ≡ (SL + VL + TL) 1 − γ5 2 + (SR + VR + TR) 1 + γ5 2 , (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='15) where we have introduced the notation: VL = � i/∂+/G+ /V 0 0 i/∂ � , SL = � 0 0 S 0 � , TL = σµν � 0 0 T µν 0 � , (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='16a) VR = � i/∂ 0 0 i/∂−/GT− /V T � , SR = � 0 S† 0 0 � , TR = σµν � 0 T †µν 0 0 � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='16b) These components satisfy the following relations under the (extended) charge conju- gation defined in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='20): V L/R = VR/L , SL/R = SL/R , T L/R = TL/R .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='17) With the decomposition in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='15), we can expand the traces in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='23) into a set of terms, each being a product of the components VL/R 1 ∓ γ5 2 , SL/R 1 ∓ γ5 2 , TL/R 1 ∓ γ5 2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='18) The matrix structures of these components, their chiralities, and charge conjugation properties lead to simplifications of the calculation: For the Dirac trace to be nonzero, each term must have an even power of γµ matrices in total.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Given the structures of the traces in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='23), this implies that only terms with an even power of VL/R will contribute.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' The matrix structure of SL/R tells us that SL � · · VL/R · · · � SL = SR � · · VL/R · · · � SR = 0 , (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='19) where � · · VL/R · · · � does not contain any SL/R or TL/R factors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' The same is true if we replace any of the SL/R in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='19) with TL/R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' – 13 – The product of the chirality projection factors 1∓γ5 2 will impose further selection rules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Finally, one can make use of the charge conjugation properties in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='17) to merge terms and simplify the result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Now we apply these constraints to the case of this subsection, where S, Vµ ̸= 0 but Tµν = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' It is easy to see that tr0 does not contain any S-dependent terms, while the nonzero terms in tr1, tr2, tr3 must have two powers of S and two powers of V with appropriate chirality combinations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Starting with tr1, we get tr(S2V 2) 1 = 1 2 tr �� SRVLSLVR − VLSLVRSR + SLVRSRVL − VRSRVLSL � α � , (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='20) where terms containing one power of γ5 have been dropped since tr(γµγνγ5) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' We can use charge conjugation to further simplify this trace.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Upon cyclic permutation the four terms in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='20) combine in pairs and give tr(S2V 2) 1 = tr �� SRVLSLVR − VRSRVLSL � α � = tr � SRVLSL [VR, α] � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='21) The other two traces tr2 and tr3 admit similar simplifications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' The general rule we follow is to rewrite half of the terms using charge conjugation such that the entire expression is proportional to the commutator [VR, α].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' After contracting the gamma matrices using γµγµ = 4, γµγνγµ = −2γν, we find tr(S2V 2) 2 = tr �� SRVRSL − 2VLSRSL − 2SRSLVL � [VR, α] � , (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='22a) tr(S2V 2) 3 = tr � SRSL [VR, α] � = tr �� SRSLVR + VRSRSL � [VR, α] � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='22b) Combining the three traces above and substituting in the expressions for SL,R , VL,R from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='16), we find that the additional contribution to the anomaly from scalar couplings is AΛ β=0[α] ��� O(S2V 2) = − 1 192π2 � d4x tr �� S†(/G T + /V T)S − S†S (/G + /V ) − (/G + /V ) S†S + i � S†←→ /DV S �� (/∂α) � , (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='23) where � S†←→ /DV S � ≡ γµ � S†(Dµ V S)−(Dµ V S†)S � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Here we have defined a shifted covariant derivative Dµ V that also contains the vector interactions V µ: Dµ V ≡ Dµ�� Gµ→Gµ+V µ = ∂µ − i (Gµ + V µ) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='24) – 14 – Its action on S, S† follows the same substitution: (Dµ V S) ≡ (DµS) �� Gµ→Gµ+V µ , � Dµ V S†� ≡ � DµS†��� Gµ→Gµ+V µ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='25) If desired, one could easily evaluate the Dirac trace tr(γµγν) = 4ηµν in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='23), but this is unnecessary for showing that it is an irrelevant anomaly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' To find the corresponding counterterm, we recall the gauge transformation of the scalar interactions S[Gµ, φ] from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='10): S −→ Sα = U ∗ αSU † α , (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='26) which leads to S†S −→ UαS†SU † α , δα � S†S � = i � α, S†S � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='27) Their covariant derivatives by definition transform in the same way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' This remains true for the shifted covariant derivative Dµ V defined in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='24), and therefore we have δα � S†←→ /DV S � = i � α, � S†←→ /DV S �� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='28) From the gauge transformation properties discussed above, together with those of Gµ, Vµ in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='12), we can identify AΛ β=0[α] ��� O(S2V 2) = −δα � d4x ∆L(S2V 2) ct , (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='29) where ∆L(S2V 2) ct = 1 192π2 � d4x tr �1 2 S†(/G T + /V T) S (/G + /V ) − S†S(/G + /V )(/G + /V ) + i � S†←→ /DV S � /G � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='30) We therefore conclude that when both vector and scalar interactions are present, the additional contributions to the anomaly beyond the minimal coupling case are all irrelevant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='3 Vector, Scalar, and Tensor Interactions Finally, we also include the tensor interactions Tµν alongside vector and scalar inter- actions in this subsection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' The calculation proceeds in a similar way to the vector and scalar interactions case in the previous subsection;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' the gamma matrix algebra is slightly more tedious but it is straightforward.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Using the decomposition in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='15), we immediately see that again, tr0 does – 15 – not contain any Tµν-dependent terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' For tr1, tr2, tr3, the additional nonzero terms are of the form TSV 2 and T 2V 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' We examine them in turn below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' T SV 2 terms: Upon contraction of gamma matrices using γµγµ = 4, γµγνγµ = −2γν, and noting γµTL,Rγµ = 0 (since γµγνγργµ = 4ηνρ while TL,R involves the antisymmetric σµν), we find tr(TSV 2) 1 = tr �� TRVLSL + SRVLTL � [VR, α] (1 + γ5) � , (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='31a) tr(TSV 2) 2 = tr �� TRVRSL + SRVRTL − 2VLSRTL − 2TRSLVL � [VR, α] (1 + γ5) � , (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='31b) tr(TSV 2) 3 = tr � TRSL � V 2 R, α � (1 + γ5) + SRTL � V 2 R, α � (1 − γ5) � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='31c) To arrive at these equations we have combined terms that are related by charge conjugation and used cyclic permutation as in the previous subsection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' We can further show that tr(TSV 2) 3 = 0 because � V 2 R, α � = � V µ R [V ν R, α] + [V µ R , α] V ν R � γµγν = �� V µ R , [V ν R, α] � + [V ν R, α] V µ R + [V µ R , α] V ν R � γµγν .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='32) The expression in parentheses is symmetric in µ ↔ ν (note that for � V µ R , [V ν R, α] � , only its upper-left block (−∂µ∂να) will eventually feed into the expressions), whereas the Dirac traces are antisymmetric: tr � γµγνσρτ � = − tr � γνγµσρτ � , (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='33a) tr � γµγνσρτγ5� = − tr � γνγµσρτγ5� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='33b) Adding up tr1 and tr2 and substituting in the expressions for SL,R, VL,R, TL,R from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='16), we obtain AΛ β=0[α] ��� O(TSV 2) = − 1 192π2 � d4x tr �� (σ · T †)(/G T + /V T)S + S†(/G T + /V T)(σ · T) + 2i � (σ · T †)( /DV S) − ( /DV S†)(σ · T) �� (/∂α)(1 + γ5) � , (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='34) where we have introduced the shorthand notation σ · T ≡ σµνT µν , σ · T † ≡ σµνT †µν .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='35) – 16 – From the gauge transformation properties discussed earlier we see that AΛ β=0[α] ��� O(TSV 2) = −δα � d4x ∆L(TSV 2) ct (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='36) is an irrelevant anomaly corresponding to the following local counterterm: ∆L(TSV 2) ct = 1 192π2 � d4x tr ��1 2 � (σ · T †)(/G T + /V T)S(/G + /V ) + S†(/G T + /V T)(σ · T)(/G + /V ) � + 2i � (σ · T †)( /DV S) − ( /DV S†)(σ · T) � /G � (1 + γ5) � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='37) T 2V 2 terms: Finally, for the T 2V 2 terms, we find tr(T 2V 2) 1 = tr � TRVLTL [VR, α] (1 + γ5) � , (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='38a) tr(T 2V 2) 2 = tr � TRVRTL [VR, α] (1 + γ5) � , (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='38b) tr(T 2V 2) 3 = − tr � TRγµTLγν [V µ R V ν R, α] (1 + γ5) � , (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='38c) where we have used γµTLVRγµ = 2γµTLV µ R to simplify tr3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Further, since the Dirac traces involved are symmetric under the exchange of γµ and γν: tr � γµσρτγνσκλ � = tr � γνσρτγµσκλ � , (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='39a) tr � γµσρτγνσκλγ5� = tr � γνσρτγµσκλγ5� , (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='39b) we can freely interchange µ and ν in tr3 and obtain tr(T 2V 2) 3 = − tr �� TRγµTLV µ R + V µ R TRγµTL � [VR, α] (1 + γ5) � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='40) Adding up all three traces and substituting in the expressions for VL,R , TL,R from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='16), we get AΛ β=0[α] ��� O(T 2V 2) = − 1 192π2 � d4x tr �� (σ · T †)(/G T + /V T)(σ · T) + (σ · T †)γµ(σ · T)(Gµ + V µ) + (Gµ + V µ)(σ · T †)γµ(σ · T) + i � (σ · T †) ←→ /DV (σ · T) �� (/∂α)(1 + γ5) � , (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='41) where � (σ · T †) ←→ /DV (σ · T) � = σρτγµσκλ � T †ρτ(Dµ V T κλ) − (Dµ V T †ρτ)T κλ� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' This again – 17 – can be identified with the gauge variation of a local counterterm: AΛ β=0[α] ��� O(T 2V 2) = −δα � d4x ∆L(T 2V 2) ct , (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='42) where ∆L(T 2V 2) ct = 1 192π2 � d4x tr ��1 2 (σ · T †)(/G T + /V T)(σ · T)(/G + /V ) + (σ · T †)γµ(σ · T)γν(Gµ + V µ)(Gν + V ν) + i � (σ · T †) ←→ /DV (σ · T) �/G � (1 + γ5) � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='43) We therefore conclude that additional contributions to AΛ β=0[α] remain irrelevant when tensor couplings are included.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='4 Summary To summarize, in this section we have completed the calculation of the regularized anomaly AΛ β[α] in the presence of scalar, vector, and tensor couplings to fermion bilinears and found that, with the Wess-Zumino consistent scheme choice β = 0, the difference with respect to the minimal coupling case is an irrelevant anomaly: AΛ β=0[α] = AΛ,mc β=0 [α] − δα � d4x ∆LΛ ct .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='44) The corresponding local counterterm is ∆LΛ ct = LΛ ct,0 ��� Gµ→Gµ+Vµ −LΛ ct,0 +∆L(V ) ct +∆L(S2V 2) ct +∆L(TSV 2) ct +∆L(T 2V 2) ct , (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='45) with LΛ ct,0, ∆L(V ) ct , ∆L(S2V 2) ct , ∆L(TSV 2) ct and ∆L(T 2V 2) ct given by Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='7), (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='13), (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='30), (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='37) and (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='43), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' This means that for the renormalized anomaly Aβ[α] defined in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='14): There exists a renormalization scheme where Aβ=0[α] = Amc β=0[α] .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='46) 5 Discussion and Future Directions In this paper, we generalized the CDE framework for computing anomalies in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' [11] to the case of relativistic EFTs with a general class of higher-dimensional operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' We systematically calculated the anomaly in this formalism, and demonstrated ex- plicitly that the additional contributions from higher-dimensional operators are irrel- evant anomalies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' This means, in particular, that the (relevant) anomaly cancellation – 18 – condition in SMEFT including the aforementioned higher-dimensional operators is the same as that in the Standard Model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Our calculation did not include higher-dimensional operators which involve deriva- tives acting on the fermions (beyond the kinetic term), such as ϵikϵjl (HiDµHj) � ℓT k iγ0γ2Dµℓl � , � H†DµDνH � �¯ℓγµDνℓ � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='1) While there is no essential obstacle to incorporate them in our present formalism, the CDE calculation becomes more and more tedious with the inclusion of each derivative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Nevertheless, noting that the counterterms we found in Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='30), (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='37) and (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='43) share similar structures, we are hopeful that there could be a more efficient framework that would make such a calculation more manageable and potentially also shed new light on the underlying structures of CDE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' We plan to pursue this intriguing possibility in future work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' The master functional trace evaluated in this paper, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='13), can also be relevant for certain EFT matching calculations, such as when integrating out heavy fermions that acquire masses from a Yukawa interaction via spontaneous symmetry breaking [24, 25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Modern EFT matching calculations are typically performed with dimensional regularization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' However, we anticipate our regularization prescription, applied in exclusively d = 4 spacetime dimensions, should produce the same anomaly- related non-decoupling effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' We leave the exploration of this interesting question for future study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Acknowledgments We thank Quentin Bonnefoy, Nathaniel Craig, Sungwoo Hong, Markus Luty and Aneesh Manohar for useful discussions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' is supported by the U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Department of Energy under grant number DE-SC0011640.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' is supported by the U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' De- partment of Energy under grant numbers DE-SC0009919 and DE-SC0011640.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' is supported by the U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Department of Energy under grant number DE-SC0011702.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' This work was performed in part at Aspen Center for Physics, which is supported by National Science Foundation grant PHY-1607611.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' References [1] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Bertlmann, Anomalies in quantum field theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' 1996.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' [2] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Bilal, “Lectures on Anomalies,” arXiv:0802.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='0634 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' [3] Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Bonnefoy, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Di Luzio, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Grojean, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Paul, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Rossia, “Comments on gauge anomalies at dimension-six in the Standard Model Effective Field Theory,” JHEP 05 (2021) 153, arXiv:2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='07740 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' – 19 – [4] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Feruglio, “A Note on Gauge Anomaly Cancellation in Effective Field Theories,” JHEP 03 (2021) 128, arXiv:2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='13989 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' [5] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Marculescu and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Mezincescu, “Axial Anomaly in Nonrenormalizable Theories,”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' [6] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Manohar and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Moore, “Anomalous Inequivalence of Phenomenological Theories,” Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' B 243 (1984) 55–64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' [7] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Minn, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Kim, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='-k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Lee, “Spinor Loop Anomalies With Very General Local Fermion Lagrangians,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' D 35 (1987) 1872.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' [8] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Kim, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Pac, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Shin, “Spinor Loop Anomalies in Higher Derivative Theories,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' D 39 (1989) 1251.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' [9] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Soto, “Anomaly cancellation at finite cutoff,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' D 45 (1992) 4621–4631.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' [10] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Dixon, “Anomalies, BRS cohomology and effective theories,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' 67 (1991) 797–800.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' [11] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Cohen, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Lu, and Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Zhang, “Anomalies From the Covariant Derivative Expansion,” (2023) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' [12] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Gaillard, “The Effective One Loop Lagrangian With Derivative Couplings,” Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' B268 (1986) 669–692.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' [13] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Chan, “Derivative Expansion for the One Loop Effective Actions With Internal Symmetry,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' 57 (1986) 1199.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' [14] O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Cheyette, “Effective Action for the Standard Model With Large Higgs Mass,” Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' B297 (1988) 183–204.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' [15] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Henning, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Lu, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Murayama, “How to use the Standard Model effective field theory,” JHEP 01 (2016) 023, arXiv:1412.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='1837 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' [16] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Henning, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Lu, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Murayama, “One-loop Matching and Running with Covariant Derivative Expansion,” JHEP 01 (2018) 123, arXiv:1604.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='01019 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' [17] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Cornella, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Feruglio, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Vecchi, “Gauge Invariance and Finite Counterterms in Chiral Gauge Theories,” arXiv:2205.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='10381 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' [18] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Fujikawa, “Path Integral Measure for Gauge Invariant Fermion Theories,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' 42 (1979) 1195–1198.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' [19] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Fujikawa, “Path Integral for Gauge Theories with Fermions,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' D 21 (1980) 2848.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' [Erratum: Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='D 22, 1499 (1980)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' [20] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Fujikawa, “On the Evaluation of Chiral Anomaly in Gauge Theories with Gamma(5) Couplings,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' D 29 (1984) 285.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' [21] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Fujikawa and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Suzuki, Path integrals and quantum anomalies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' [22] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Grzadkowski, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Iskrzynski, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Misiak, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Rosiek, “Dimension-Six Terms in the Standard Model Lagrangian,” JHEP 10 (2010) 085, arXiv:1008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content='4884 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' – 20 – [23] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Wess and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Zumino, “Consequences of anomalous Ward identities,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' B 37 (1971) 95–97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' [24] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' D’Hoker and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Farhi, “Decoupling a Fermion Whose Mass Is Generated by a Yukawa Coupling: The General Case,” Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' B 248 (1984) 59–76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' [25] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' D’Hoker and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Farhi, “Decoupling a Fermion in the Standard Electroweak Theory,” Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' B 248 (1984) 77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} +page_content=' – 21 –' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/MdAyT4oBgHgl3EQf6vqH/content/2301.00827v1.pdf'} diff --git a/NdE3T4oBgHgl3EQfwwth/content/tmp_files/2301.04705v1.pdf.txt b/NdE3T4oBgHgl3EQfwwth/content/tmp_files/2301.04705v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..0ca13ab8b3a1e6dfeca9fdc2239bea9857afcb61 --- /dev/null +++ b/NdE3T4oBgHgl3EQfwwth/content/tmp_files/2301.04705v1.pdf.txt @@ -0,0 +1,1133 @@ +Inverse Quantum Fourier Transform Inspired +Algorithm for Unsupervised Image Segmentation +†Taoreed Akinola, †Xiangfang Li, †Richard Wilkins, †Pamela Obiomon, †‡Lijun Qian +†Department of Electrical and Computer Engineering, Prairie View A&M University +Prairie View, Texas 77446, USA +Email: takinola2@pvamu.edu, xili@pvamu.edu, rtwilkins@pvamu.edu, phobiomon@pvamu.edu, liqian@pvamu.edu +‡ corresponding author +Abstract—Image segmentation is a very popular and important +task in computer vision. In this paper, inverse quantum Fourier +transform (IQFT) for image segmentation has been explored and +a novel IQFT-inspired algorithm is proposed and implemented by +leveraging the underlying mathematical structure of the IQFT. +Specifically, the proposed method takes advantage of the phase +information of the pixels in the image by encoding the pixels’ +intensity into qubit relative phases and applying IQFT to classify +the pixels into different segments automatically and efficiently. To +the best of our knowledge, this is the first attempt of using IQFT +for unsupervised image segmentation. The proposed method has +low computational cost comparing to the deep learning based +methods and more importantly it does not require training, thus +make it suitable for real-time applications. The performance +of the proposed method is compared with K-means and Otsu- +thresholding. The proposed method outperform both of them +on the PASCAL VOC 2012 segmentation benchmark and the +xVIEW2 challenge dataset by as much as 50% in terms of mean +Intersection-Over-Union (mIOU). +Index Terms—Inverse Quantum Fourier Transform, Computer +Vision, Image Segmentation +I. INTRODUCTION +Image segmentation is defined as the separation of an +image dataset into non-intersecting, homogeneous subsections +in terms of certain properties such as color intensities and +textures [1]. In image processing and computer vision, seg- +mentation is generally applied to separate the regions of inter- +est from the other part of the image (called the background) +for further analysis [2]. Segmentation is a crucial and difficult +problem in many fields such as digital image processing, object +or pattern recognition, enhanced object features extraction +and artificial intelligence [3], [4]. It is a very important tool +for solving image semantic problems which involves predict- +ing the categories of the pixels contained in an image [5]. +The applications of image segmentation span many different +fields, such as in medical diagnostic imaging applications +for automatic detection of anomalies, treatment monitoring +and disease diagnosis [6], [7], in image-based remote sensing +technology [8], and in additive manufacturing processes for +in-situ monitoring and detection of shifts in product quality +during production [9]. +In the classical computing domain, Fourier transform is +one of the popular techniques that have been researched and +developed extensively for image segmentation [10]–[12]. For +instance, the auto-registration property of the magnitude spec- +tra has been exploited for texture identification [10]. Similarly, +structural texture in the satellite images have been extracted +using Fourier transform for agriculture applications [12]. Seg- +menting foreground to track spontaneous changes in the shape +of objects embedded in a template image using total variation +and fast Fourier transform has been studied in [11]. On +the other hand, several image segmentation algorithms have +emerged in the quantum computing domain. For instance, the +authors of [13] provided a quantum circuit for gray image +encoding and a proof-of-concept quantum circuit of dual- +threshold segmentation algorithm, and simulated it on an 8×8 +image. However, inverse quantum Fourier transform (IQFT) +for image segmentation has not been studied. +In this work, we seek to leverage the unique properties of +IQFT and provide an IQFT-inspired approach for unsupervised +image segmentation. Specifically, the proposed method takes +advantage of the phase information of the pixels in the image +by encoding the pixels’ intensity into qubit relative phases and +applying IQFT to classify the pixels into different segments +automatically and efficiently. The contributions of this paper +are: +1) An IQFT-inspired algorithm is proposed for unsuper- +vised image segmentation. To the best of our knowledge, +this is the first unsupervised image segmentation algo- +rithm using IQFT. +2) Comparing to many deep learning based image seg- +mentation methods, the proposed approach has much +less computational cost. More importantly, the proposed +method does not require training, thus make it suitable +for real-time applications. +3) We demonstrate the potential of IQFT in solving image +segmentation problem, and compare its effectiveness +with two popular unsupervised segmentation techniques: +Otsu thresholding [14], and K-means Clustering [15]. +The proposed method outperform both of them on the +PASCAL VOC 2012 segmentation benchmark [16], and +the xVIEW2 challenge dataset [17] by as much as 50% +in terms of mIOU. +The remainder of this paper is structured as follows: Related +works are reviewed in Section II. Section III introduces inverse +quantum Fourier transform. Section ?? provides the details of +the proposed approach. The experimental results are given in +arXiv:2301.04705v1 [cs.CV] 11 Jan 2023 + +Section V and observations and insights from the results are +discussed. Section VI concludes the paper. +II. RELATED WORKS +A. Image Segmentation in Classical Computing +As a key process in image processing and analysis, image +segmentation has been well studied in the classical comput- +ing domain. Many methods for solving image segmentation +problems have emerged over the years. These methods vary +widely depending on the specific application since a single +method is not sufficient for different images with varying char- +acteristics in terms of sharpness, texture, noise presence, and +the degree of overlapping objects [4]. Traditional techniques +used for image segmentation are categorized as thresholding- +based technique [18], region-based technique [19], edge-based +technique [20], clustering-based technique [21], and watershed +technique [22]. These methods vary widely depending on +the specific application since they all have their limitations +based on the underlying principles. For instance, employing an +unsupervised method like the K-means for image segmentation +has a major drawback which is the requirement for the optimal +number of clusters to be specified before the algorithm is +applied [23]. The segmentation error decreases as the number +of clusters increases and there is no theoretical means of +obtaining the optimal number of clusters to be used. Similarly, +Otsu’s thresholding technique does not consider the spatial +information of image, and this makes it sensitive to the +unevenness and noise in a grayscale image [24]. +Although the advent of deep learning has brought about +new classes of image segmentation techniques that have +become widely available [25], usually they have very high +computational complexity. Furthermore, most of them are +supervised methods that require training and probably re- +training when applied to a new dataset. On the contrary, the +proposed method has low computational cost comparing to +the deep learning based methods and more importantly it +does not require training, thus make it suitable for real-time +applications. In our analysis, we will compare the performance +of our proposed technique with two popular unsupervised +segmentation techniques that do not require training: Otsu +thresholding [14], and K-means Clustering [15]. +B. Image Segmentation in Quantum Computing +In recent years, several image segmentation algorithms have +emerged in the quantum domain to exploit the properties of +quantum computing to improve the performance of classical +techniques and, subsequently, their applications. Some com- +mon algorithms are thresholding segmentation [26] and quan- +tum search algorithm [27]. Most of these proposed methods +involve implementation of some oracle operators which are +either fully theoretical or hard to simulate due to the number +of qubits required. +Most of the well-known quantum algorithms such as quan- +tum phase estimation, Grover’s algorithm and Shor’s algorithm +utilize QFT (or IQFT) as part of their major subroutines [28]. +Similarly, in applications such as quantum image processing, +error-correction, and encryption [29], [30], QFT (or IQFT) +is embedded. Consequently, QFT is undoubtedly a valuable +transformation in the quantum domain, and itas applications +are not yet fully studied [31]. +III. INVERSE QUANTUM FOURIER TRANSFORM +QFT transforms a computational basis state |x⟩ into a +superposition of all the computational basis states with the +inclusion of relative phases. This is defined mathematically +in equation (1) [28], where N = 2n, n is the number of +qubits; ω = ei 2π +N , the +nth root of unity. In tensor product +form, equation (1) becomes equation (2) [28]. Considering a +three qubit system, for example, n = 3, equation (2) can be +expanded to equation (3). +QFT(|x⟩) = +1 +√ +N +N−1 +� +k=0 +ωxk|k⟩ +(1) +QFT(|x⟩n) = +1 +√ +N +⊗n +k=1 +� +|0⟩ + ei 2πx +2k |1⟩ +� +(2) +QFT(|x⟩3) = +1 +√ +8 +� +|0⟩ + ei 2πx +2 |1⟩ +� +⊗ +� +|0⟩ + ei 2πx +4 |1⟩ +� +⊗ +� +|0⟩ + ei 2πx +8 |1⟩ +� +(3) +For example, the QFT of a quantum state |x⟩ = |100⟩ +is determined from equation (3) by substituting x = 4, +the decimal equivalent of 1002. This operation is shown in +equation (4). The result suggests that a superposition of states, +with some phase information, can be transformed into a single +state representation by employing the inverse operation of the +QFT. +QFT(|x = 100⟩3) = +1 +√ +8(|000⟩ − |001⟩ + |010⟩ − |011⟩ ++|100⟩ − |101⟩ + |110⟩ − |111⟩) +(4) +The inverse quantum Fourier transform (IQFT) performs the +reverse operation of the QFT. It transforms from a phase +representation into the computational basis. From equation (2), +the inverse operation, IQFT, can be written as equation (5), +where |k⟩ is the state of a quantum system with some phase +information [28]. Equation (6) presents a case of three qubits, +n = 3. +IQFT +� 1 +√ +N +⊗n +k=1 +� +|0⟩ + ei 2πx +2k |1⟩ +� � += |k⟩n +(5) +IQFT +� 1 +√ +8 +� +|0⟩ + ei 2πx +2 |1⟩ +� +⊗ +� +|0⟩ + ei 2πx +4 |1⟩ +� +⊗ +� +|0⟩ + ei 2πx +8 |1⟩ +� � += |k⟩3 +(6) + +IQFT +� 1 +√ +8 +� +|0⟩ + eiα|1⟩ +� +⊗ +� +|0⟩ + eiβ|1⟩ +� +⊗ +� +|0⟩ + eiγ|1⟩ +� � += |k⟩3 +(7) +IQFT +� 1 +√ +8 +� +|0⟩ + eiα|1⟩ +� +⊗ +� +|0⟩ + eiβ|1⟩ +� +⊗ +� +|0⟩ + eiγ|1⟩ +�� += +1 +√ +8 × +� +IQFT|000⟩ + eiγIQFT|001⟩ + eiβIQFT|010⟩ + ei(β+γ)IQFT|011⟩ ++eiαIQFT|100⟩ + ei(α+γ)IQFT|101⟩ + ei(α+β)IQFT|110⟩ +ei(α+β+γ)IQFT|111⟩ +� +(8) +IQFT(|000⟩) = +1 +√ +8 +7 +� +x=0 +ω−x(0)|x⟩ = +1 +√ +8(|000⟩ + |001⟩ + |010⟩ + |011⟩ + |100⟩ + |101⟩ + |110⟩ + |111⟩) +(9) +IQFT +� 1 +√ +8 +� +|0⟩ + eiα|1⟩ +� +⊗ +� +|0⟩ + eiβ|1⟩ +� +⊗ +� +|0⟩ + eiγ|1⟩ +�� += P|000⟩ + Q|001⟩ + R|010⟩ + S|011⟩ + T|100⟩ + U|101⟩ + V |110⟩ + W|111⟩ +(10) +� +����������� +P +Q +R +S +T +U +V +W +� +����������� +≡ 1 +8 × +� +����������� +1 +1 +1 +1 +1 +1 +1 +1 +1 +ω−1 +ω−2 +ω−3 +ω−4 +ω−5 +ω−6 +ω−7 +1 +ω−2 +ω−4 +ω−6 +1 +ω−2 +ω−4 +ω−6 +1 +ω−3 +ω−6 +ω−1 +ω−4 +ω−7 +ω−2 +ω−5 +1 +ω−4 +1 +ω−4 +1 +ω−4 +1 +ω−4 +1 +ω−5 +ω−2 +ω−7 +ω−4 +ω−1 +ω−6 +ω−3 +1 +ω−6 +ω−4 +ω−2 +1 +ω−6 +ω−4 +ω−2 +1 +ω−7 +ω−6 +ω−5 +ω−4 +ω−3 +ω−2 +ω−1 +� +����������� +� +����������� +1 +eiγ +eiβ +ei(β+γ) +eiα +ei(α+γ) +ei(α+β) +ei(α+β+γ) +� +����������� +(11) +B. Proposed IQFT-Inspired Algorithm +The proposed algorithm is developed from equation (11). +Firstly, eight state basis vectors are given by the rows of the +8 by 8 matrix. These basis vectors are visualized as a set +of points on a unit circle as shown in Figure 1. Secondly, +a 3-dimensional input vector, [α, β, γ], is transformed into +an eight-dimensional vector given by the column matrix on +the right-hand side of equation (11). This vector also can be +represented by a set of eight points on a unit circle. A random +example for which α = 2.464 , β = 0.025, and γ = 0.246 is +shown in Figure 2. By visual inspection, the input pattern has +two obvious clusters similar to basis state vector |100⟩. Lastly, +the probability that the pattern generated by the input vector +is similar to each of the characteristic patterns of the basis +vectors is determined. This is given by the modulus squared +of the probability amplitudes (P, Q, R, S, T, U, V, W ). The +input vector is then classified based on the basis state vector +that gives the highest probability value. Figure 3 shows the +probabilities associated with the random input in Figure 2. It +is obvious that this input is most similar to state basis vector +|100⟩ as previously observed. +Subject to this insight, the proposed IQFT-inspired algo- +rithm for RGB image segmentation is presented in Algorithm1, +where the input Pm is a 3D vector of RGB intensities of the +mth pixel, T is the total number of pixels, W is a complex 8 by +8 matrix in equation (11), θ1, θ2, and θ3 are angle parameters +for transforming pixel intensities into phase values, and the +output is the required pixel label lm∈{0, 1, 2, ..., 7}. The seg- +mentation algorithm involves a normalization process in Line +1, linear transformation in Line 2, dimensional transformation +from 3D to 8D vector in Line 3, and probability measure in +Line 4. A pixel is classified according to the basis vector with +the highest probability. +C. Proposed IQFT-inspired Algorithm for Grayscale Image +Segmentation +Since our approach in Section IV-B is not limited by the +image color space, it can be adapted for segmentation of +grayscale images. In this case, the governing mathematical +equation is given by equation (12), where the probability +amplitudes, P and Q, are determined from equation (13). For +a normalized pixel intensity I, and chosen angle parameter θ, +γ = Iθ. +IQFT +� 1 +√ +2 +� +|0⟩ + eiγ|1⟩ +�� +≡ P|0⟩ + Q|1⟩ +(12) +� P +Q +� +≡ 1 +2 × +� 1 +1 +1 +−1 +� � +1 +eiγ +� +(13) +In this grayscale implementation, a pixel can be classified +into one of two classes based on the probabilities given by + +Fig. 1: Visualization of the eight state basis vectors +Fig. 2: Transformed input pattern on the unit circle for a +random case of α = 2.464 , β = 0.025, and γ = 0.246. +Some points are coincident. +Fig. 3: Probability distribution for input pattern of a random +case of α = 2.464 , β = 0.025, and γ = 0.246 +equation (14). For P(class1) = P(class2), I = Ith, where +Ith is a threshold value given by equation (15), where k ∈ Z. +p (class1) = +(1+cos(Iθ))2 + (sin(Iθ))2 +4 +p (class2) = +(1−cos(Iθ))2 + (sin(Iθ))2 +4 +(14) +Algorithm 1 : IQFT-inspired algorithm for RGB image seg- +mentation +Input: +I = { Pm ∈ R3}, m = [1, T] +θ1, θ2, θ3 ∈ R +W ∈ C8×8 +Output: L = {lm ∈ Z} +for m=1to T do +1. {Pm} ←− {Pm/255} , {Pm} = {Rm, Gm, Bm} +2. {γm, βm, αm} ←− {Rm × θ1, Gm × θ2, Bm × θ3} +3. {Fm} = +� +� +� +� +� +� +� +� +� +� +� +� +� +� +� +� +� +� +� +� +� +� +� +1 +eiγ +eiβ +ei(β+γ) +eiα +ei(α+γ) +ei(α+β) +ei(α+β+γ) +� +� +� +� +� +� +� +� +� +� +� +� +� +� +� +� +� +� +� +� +� +� +� +←− +� +� +� +γm +βm +αm +� +� +� +4. {Sm} ←− [abs (Dot Product (Fm, W) /8)]2 +5. {lm} ←− {argmax{Sm} } +cosIthθ = 0 =⇒ Ithθ = (4k ± 1) π +2θ ≤ 1 +(15) +Therefore, selecting a particular value of θ is equivalent to +setting a threshold value, and the network behaves like a +thresholding technique. Table I shows some θ values and +the corresponding threshold using equation (15). Considering +equation (15), with a single selection of θ, it is possible to +establish multiple thresholds. For instance, choosing θ = 4π +results in four thresholds as shown in equation (16) for +k = 0, 1, 2, respectively. The advantage of these multiple +thresholds is captured in the following example. Consider the +task of separating red , green, and lemon balls from the others +of lower and higher intensities in Figure 4. To achieve the + +1000)State +1.0 +0.5 +imaginary +54 +0.0 +0.5 +1.0 +-1 +0 +1 +real1.00 +0.880 +0.75 +Probabilities +0.50 +0.25 +0.103 +0.004 +0 +0.008 +0.00 +0.005 +0 +0100)State +1.0 +0.5 +imaginary +7: 5 +6 +4 +0.0 +4 +04 +13 +2 +0.5 +1.0 +-1 +0 +1 +real001)State +1.0 +3s +0.5 +imaginary +0.0 +0.5 +50 +78 +1.0 +6 +-1 +0 +1 +real101)State +1.0 +5° +0.5 +imaginary +0.0 +0.5 +30 +1.0 +6 +-1 +0 +1 +real1010)State +1.0 +0.5 +imaginary +0.0 +246 +0.5 +1.0 +-1 +0 +1 +real[110)State +1.0 +0.5 +imaginary +0.0 +16 +0.5 +1.0 +-1 +0 +1 +real011)State +1.0 +0.5 +imaginary +0.0 +0.5 +70 +50 +1.0 +-1 +0 +1 +real[111)State +1.0 +5, +0.5 +imaginary +0.0 +0.5 +37 +1.0 +-1 +0 +1 +real1.0 +5g +0.5 +imaginary +4 +60 +0.0 +0.5 +-1.0 +-1 +0 +1 +realdesired goal, θ is simply set to 4π. However, Otsu-thresholding +would require two clearly defined thresholds to achieve the set +goal. +Ith = (4k ± 1) π +2θ = 1 +8, 3 +8, 5 +8, 7 +8 +(16) +Image +K-means +Otsu +IQFT +Fig. 4: Application of multiple thresholding +TABLE I: Parameter θ and the corresponding threshold value +using equation 15. +Parameter, θ +Threshold value, Ith +3π/4 +0.667 +π +0.500 +5π/4 +0.400 +3π/2 +0.333 +7π/4 +0.285, 0.857 (multiple) +2π +0.25, 0.75 (multiple) +V. RESULTS AND ANALYSIS +A. Dataset +Considering that most image dataset exist in the classical +domain, we have performed simulations of the proposed +method in the classical domain. To demonstrate the effec- +tiveness of our proposed method for Image segmentation, we +conduct several experiments on two datasets: (1) the training +and validation dataset of PASCAL VOC 2012 segmentation +benchmark [16], focusing only on the segmentation category +which contains 2913 labeled set; (2) the xVIEW2 challenge +dataset [17] focussing on the 148 RGB satellite pre-disaster +images for a “joplin-tornado” disaster. +B. Experimental Setup +All images are RGB, and the corresponding grayscale +images are prepared by calculating the weighted sum of the +corresponding red, green and blue pixels according to Scikit- +image [32], using equation (17). +Y = R × 0.2125 + G × 0.7154 + B × 0.0721 +(17) +K-means [15] and Otsu-thresholding [14] are selected as +the baseline methods for performance comparison with our +method. To implement the baseline methods, we used the +scikit-learn library [33] with default settings for K-means, +and scikit-image library [32] for Otsu-thresholding. All the +algorithms used in this study are coded using Python on +MacBook Pro with 8-Core Intel Core i9 running at 2.3 GHz. +C. Evaluation Metric +The segmentation accuracies of the methods used in this +study are assessed by the mean intersection over union (mIOU) +score defined in equation (18) and equation (19), where +TP, FP, FN, T, and P are true positive, false positive, false +negative, ground truth and prediction, respectively. TensorFlow +function [34], utilizing equation (18), is used for all mIOU cal- +culations. Pixels around the border of an object that are marked +‘void’ in the ground truth are not used in our calculations [35]. +mIOU = IOU(foreground) + IOU(background) +2 +(18) +IOU = +TP +TP + FP + FN = T ∪ P +T ∩ P +(19) +D. Experimental Results +For the purpose of evaluating the effects of design choices +on performance, different experiments are conducted on stan- +dard datasets and the results obtained are presented in this +section. +1) Effect of the normalization process: Here, the effect of +the normalization process of Section IV-B on the quality of +the segmentation pattern is investigated. The results obtained +in Figure 5 show that, for a smooth segmentation pattern, +normalized image intensities are required to avoid “noisy” +segments. +Fig. 5: Effect of the normalization process. First row con- +tains two different images, second rows contains segmentation +patterns when the normalization process is included, and the +last row shows segmentation patterns when the normalization +process is not included +2) Effects of angle parameter (θ1, θ2, θ3) on the number of +segments: To study the effects of the angular parameter, θ, on +the segmentation pattern, we generated 100, 000 × 3 random +numbers between 0 and 1 as normalized RGB values and +determined the maximum number of segments using all the +combinations for different values of θ. The results are shown + +in Table II. It is evident that the number of segments varies +with the angular parameter. This is due to the modification +of the transformed input pattern as the angular parameters +are varied. This effect is observed on real images shown in +Figure 6. For θ1 = θ2 = θ3 = π/4, the six arguments from +the complex representation of each pixel are located between 0 +and 3π/4 radian. This tends to produce a pattern most similar +to the |000⟩ state. Therefore, all pixels are classified into one +segment. For θ1 = θ2 = θ3 = π/2, the segmentation process +is biased towards the low-luminous pixels, as pixels (objects) +with strong brightness are visible in Figure 6. Using different +angles can result in some peculiar segmentation effects. This is +shown by θ1 = π/4, θ2 = π/2, θ3 = π which usually outputs +two segments. +TABLE II: Parameter θ and the possible number of segments +Parameter, θ +max. number of segments +θ1 = θ2 = θ3 = π/4 +1 +θ1 = θ2 = θ3 = π/2 +3 +θ1 = θ2 = θ3 = 3π/4 +5 +θ1 = θ2 = θ3 = π +6 +θ1 = θ2 = θ3 = 5π/4 +8 +θ1 = θ2 = θ3 = 3π/2 +8 +θ1 = θ2 = θ3 = 7π/4 +8 +θ1 = θ2 = θ3 = 2π +8 +θ1 = π/4, θ2 = π/2, θ3 = π +2 (constant) +Image +Image +Image +θ = π/4, 1-seg +θ = π/4, 1-seg. +θ = π/4, 1-seg. +θ = π/2, 2-seg. +θ = π/2, 3-seg. +θ = π/2, 1-seg. +θ = π, 4-seg. +θ = π, 6-seg. +θ = π, 5-seg. +mixed, 2-seg. +mixed, 2-seg. +mixed, 2-seg. +Fig. 6: Effects of θ on the number of segments and the +segmentation quality–where ’mixed’ in the last row represents +θ1 = π/4, θ2 = π/2, θ3 = π +E. Performance comparison +1) A performance comparison of the IQFT-inspired al- +gorithm for grayscale Images and Otsu-threshold method: +As pointed out in Section IV-C, setting a value of θ is +equivalent to a threshold value in equation (15). To support this +conclusion, Figure 7 shows two examples of the segmentation +results observed from using Otsu-thresholding and IQFT- +inspired algorithm for grayscale images with equivalent angle +parameters using equation (15). Therefore, setting θ according +to equation (15) results in identical segmentation pattern and +equal mIOU values (not shown) for both methods. +Ith = 0.4465 +θ = 1.1197π +Ith = 0.4911 +θ = 1.0180π +Fig. 7: Performance comparison of the IQFT-inspired al- +gorithm for grayscale images and Otsu-thresholding. If the +threshold from Otsu method is converted to parameter θ +according to equation (15), the outputs of the two methods +are identical +2) A performance comparison of the proposed method and +the baseline methods: The effectiveness of the proposed +algorithm for image segmentation was validated by performing +foreground-background segmentation on PASCAL VOC2012 +and xVIEW2 challenge datasets. The resulting performance +values are compared with K-means and Otsu-thresholding in +Table III. Based on the average mIOU values, the IQFT- +inspired algorithm for RGB image segmentation was observed +to outperform K-means and Otsu-thresholding in, respectively, +53.24% and 52.32% of the images in PASCAL VOC 2012. +Similarly, the IQFT-inspired algorithm outperformed K-means +and Otsu-thresholding in 95.94% and 97.97% of the pre- +disaster images for ”joplin-tornado” in the xVIEW2 chal- +lenge dataset. Figure 8 shows some segmentation outputs +of PASCAL VOC 2012 images for which the IQFT-inspired +algorithm outperformed the baseline techniques. Similar out- +puts are shown for xVIEW2 challenge dataset in Figure 9. +However, the IQFT-inspired algorithm also showed poor +performance(mIOU < 0.1) for about 1.4% of the PASCAL +VOC 2012 images. This value doubles the observed values for +K-means and Otsu thresholding because the performance of +the proposed algorithm depends on the chosen value of angle +parameter θ which was set to π in this experiment. Adjusting +the value of θ for each image will result in an observable +performance improvement as shown in Figure 10. + +TABLE III: Comparing the mIOU, computation time, and computational complexity. +Image segmentation methods +Datasets +Metrics +K-means +OTSU +IQFT +IQFT +(RGB) +(Grayscale) +Pascal +Average mIOU +0.4318 +0.4331 +0.4354 +0.4172 +VOC 2012 +Runtime (sec.) +0.25 +0.01 +3.06 +1.76 +xVIEW2 +Average mIOU +0.3375 +0.4008 +0.5070 +0.478 +Runtime (sec.) +1.74 +0.10 +17.5 +9.67 +mIOU=0.3197 +mIOU=0.2080 mIOU=0.2036 +mIOU=0.3179 +mIOU=0.2052 mIOU=0.2036 +mIOU=0.9762 +mIOU=0.9187 mIOU=0.9697 +Fig. 8: Results of segmentation with reference images on +PASCAL VOC 2012. The IQFT-inspired algorithm for RGB +images shows better foreground-background segmentation re- +sults as shown by the mIOU scores +VI. CONCLUSIONS +In this work, a novel method for unsupervised image +segmentation based on the inverse quantum Fourier transform +(IQFT) is proposed. Specifically, the proposed method takes +advantage of the phase information of the pixels in the image +by encoding the pixels’ intensity into qubit relative phases and +applying IQFT to classify the pixels into different segments +automatically and efficiently. To the best of our knowledge, +this is the first attempt of using IQFT for unsupervised image +segmentation. The proposed method has low computational +cost comparing to the deep learning based methods and more +importantly it does not require training, thus make it suitable +for real-time applications. Supported by the segmentation +patterns obtained for image samples from xView2 and Pascal +VOC datasets, this quantum-inspired method shows a promis- +ing performance when compared to the classical K-means +clustering and Otsu-thresholding methods. One of the appeals +of the proposed method is that it automatically adapts to the +characteristics of the image such that the number of segments +mIOU=0.1175 +mIOU=0.5243 +mIOU=0.2394 +mIOU=0.3597 +mIOU=0.5226 +mIOU=0.3390 +mIOU=0.51295 +mIOU=0.5683 +mIOU=0.5453 +Fig. 9: Segmentation result using xVIEW2 challenge dataset. +Measured by the mIOU scores, the IQFT-inspired algorithm +for RGB images shows better foreground-background segmen- +tation results. +is not a required parameter like in K-means. +Note that the proposed method can be implemented in both +classical computing domain and the quantum computing do- +main. Considering most of the datasets of image segmentation +benchmark is in the classical computing domain, we have +performed experiments to validate the proposed approach in +the classical computing domain as well. We are working on + +ImageGround-Truth(-means +KOtsu. +iif 74 +117TImage +Ground truth +K-means +mIOU=0.8892 +Otsu +mIOU=0.8663 +IQFT +mIOU=π,0.0084 +IQFT +mIOU=3π/4,0.8327 +Fig. 10: Performance improvement through θ adjustment. +Using θ = 3π/4, rather than θ = π, can improve the +segmentation quality of these images, as shown by increase +in the mIOU score +the quantum domain implementation and the results will be +shared in a future paper. +VII. ACKNOWLEDGMENT +This research work is supported by the IBM-HBCU Quan- +tum Center. +REFERENCES +[1] H.-D. Cheng, X. H. Jiang, Y. Sun, and J. Wang, “Color image segmen- +tation: advances and prospects,” Pattern recognition, vol. 34, no. 12, +pp. 2259–2281, 2001. +[2] E. Goceri, A comparative evaluation for liver segmentation from spir +images and a novel level set method using signed pressure force function. +Izmir Institute of Technology (Turkey), 2013. +[3] Z. Wang, E. Wang, and Y. Zhu, “Image segmentation evaluation: +a survey of methods,” Artificial Intelligence Review, vol. 53, no. 8, +pp. 5637–5674, 2020. +[4] R. Pandey and R. Lalchhanhima, “Segmentation techniques for complex +image,” in 2020 International Conference on Computational Perfor- +mance Evaluation (ComPE), pp. 804–808, IEEE, 2020. +[5] D. Ye and R. Han, “Image semantic segmentation method based on +improved erfnet model,” The Journal of Engineering, vol. 2022, no. 2, +pp. 180–190, 2022. +[6] S. Zhou, D. Nie, E. Adeli, J. Yin, J. Lian, and D. Shen, “High-resolution +encoder–decoder networks for low-contrast medical image segmenta- +tion,” IEEE Transactions on Image Processing, vol. 29, pp. 461–475, +2019. +[7] E. Goceri and C. Songul, “Biomedical information technology: image +based computer aided diagnosis systems,” in International Conference +on Advanced Technologies, Antalaya, Turkey, 2018. +[8] Y. Wang, Q. Qi, L. Jiang, and Y. Liu, “Hybrid remote sensing image +segmentation considering intrasegment homogeneity and intersegment +heterogeneity,” IEEE Geoscience and Remote Sensing Letters, vol. 17, +no. 1, pp. 22–26, 2019. +[9] O. Aworunse, H. Zhou, J. Deng, and C. Cheng, “Image decomposition +accelerates dynamic network modeling for in situ monitoring of bio- +mimic wing printing processes,” Procedia Manufacturing, vol. 39, +pp. 178–184, 2019. +[10] M. Zou and D. Wang, “Texture identification and image segmentation via +fourier transform,” in Image Extraction, Segmentation, and Recognition, +vol. 4550, pp. 34–39, SPIE, 2001. +[11] T. Atta-Fosu and W. Guo, “Joint segmentation and nonlinear registration +using fast fourier transform and total variation,” in Research in Shape +Analysis, pp. 111–132, Springer, 2018. +[12] D.-M. Tsai and W.-L. Chen, “Coffee plantation area recognition in +satellite images using fourier transform,” Computers and electronics in +agriculture, vol. 135, pp. 115–127, 2017. +[13] S. Yuan, C. Wen, B. Hang, and Y. Gong, “The dual-threshold quantum +image segmentation algorithm and its simulation,” Quantum Information +Processing, vol. 19, no. 12, pp. 1–21, 2020. +[14] N. Otsu, “A threshold selection method from gray-level histograms,” +IEEE transactions on systems, man, and cybernetics, vol. 9, no. 1, +pp. 62–66, 1979. +[15] J. MacQueen, “Classification and analysis of multivariate observations,” +in 5th Berkeley Symp. Math. Statist. Probability, pp. 281–297, 1967. +[16] W. Kim, A. Kanezaki, and M. Tanaka, “Unsupervised learning of +image segmentation based on differentiable feature clustering,” IEEE +Transactions on Image Processing, vol. 29, pp. 8055–8068, 2020. +[17] R. Gupta, R. Hosfelt, S. Sajeev, N. Patel, B. Goodman, J. Doshi, +E. Heim, H. Choset, and M. Gaston, “xbd: A dataset for assessing build- +ing damage from satellite imagery,” arXiv preprint arXiv:1911.09296, +2019. +[18] S. U. Lee, S. Y. Chung, and R. H. Park, “A comparative performance +study of several global thresholding techniques for segmentation,” Com- +puter Vision, Graphics, and Image Processing, vol. 52, no. 2, pp. 171– +190, 1990. +[19] H. G. Kaganami and Z. Beiji, “Region-based segmentation versus +edge detection,” in 2009 Fifth International Conference on Intelligent +Information Hiding and Multimedia Signal Processing, pp. 1217–1221, +IEEE, 2009. +[20] M. A. Wani and B. G. Batchelor, “Edge-region-based segmentation of +range images,” IEEE Transactions on Pattern Analysis and Machine +Intelligence, vol. 16, no. 3, pp. 314–319, 1994. +[21] Y. Zou and B. Liu, “Survey on clustering-based image segmentation +techniques,” in 2016 IEEE 20th International Conference on Computer +Supported Cooperative Work in Design (CSCWD), pp. 106–110, IEEE, +2016. +[22] N. Salman, “Image segmentation based on watershed and edge detection +techniques,” Int. Arab J. Inf. Technol., vol. 3, no. 2, pp. 104–110, 2006. +[23] D. T. Pham, S. S. Dimov, and C. D. Nguyen, “Selection of k in k-means +clustering,” Proceedings of the Institution of Mechanical Engineers, Part +C: Journal of Mechanical Engineering Science, vol. 219, no. 1, pp. 103– +119, 2005. +[24] N. R. Pal and S. K. Pal, “A review on image segmentation techniques,” +Pattern recognition, vol. 26, no. 9, pp. 1277–1294, 1993. +[25] A. Garcia-Garcia, S. Orts-Escolano, S. Oprea, V. Villena-Martinez, and +J. Garcia-Rodriguez, “A review on deep learning techniques applied to +semantic segmentation,” arXiv preprint arXiv:1704.06857, 2017. +[26] P. Li, T. Shi, Y. Zhao, and A. Lu, “Design of threshold segmenta- +tion method for quantum image,” International Journal of Theoretical +Physics, vol. 59, no. 2, pp. 514–538, 2020. +[27] H.-S. Li, Z. Qingxin, S. Lan, C.-Y. Shen, R. Zhou, and J. Mo, “Image +storage, retrieval, compression and segmentation in a quantum system,” +Quantum information processing, vol. 12, no. 6, pp. 2269–2290, 2013. +[28] M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum +Information. Cambridge University Press, 2011. +[29] C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and W. K. Wootters, +“Mixed-state entanglement and quantum error correction,” Physical +Review A, vol. 54, no. 5, p. 3824, 1996. +[30] P. D. Townsend, “System and method for key distribution using quantum +cryptography,” Oct. 7 1997. US Patent 5,675,648. +[31] O. Al-Ta’ani1a, A. M. Alqudah, and M. Al-Bzoor, “Implementation and +analysis of quantum fourier transform in image processing,” +[32] S. Van der Walt, et. al., “scikit-image: image processing in python,” +PeerJ, vol. 2, p. e453, 2014. +[33] F. Pedregosa, et. al., “Scikit-learn: Machine learning in python,” Journal +of Machine Learning Research, vol. 12, pp. 2825–2830, 2011. +[34] M. Abadi, et. al., “TensorFlow: Large-scale machine learning on hetero- +geneous systems,” 2015. Software available from tensorflow.org. +[35] M. Everingham, S. Eslami, L. Van Gool, C. K. Williams, J. Winn, +and A. Zisserman, “The pascal visual object classes challenge: A +retrospective,” International journal of computer vision, vol. 111, no. 1, +pp. 98–136, 2015. + +XX +Ertlar !! \ No newline at end of file diff --git a/NdE3T4oBgHgl3EQfwwth/content/tmp_files/load_file.txt b/NdE3T4oBgHgl3EQfwwth/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..679f6350b564661a9b347359beccadb0ca07eaab --- /dev/null +++ b/NdE3T4oBgHgl3EQfwwth/content/tmp_files/load_file.txt @@ -0,0 +1,781 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf,len=780 +page_content='Inverse Quantum Fourier Transform Inspired Algorithm for Unsupervised Image Segmentation †Taoreed Akinola, †Xiangfang Li, †Richard Wilkins, †Pamela Obiomon, †‡Lijun Qian †Department of Electrical and Computer Engineering, Prairie View A&M University Prairie View, Texas 77446, USA Email: takinola2@pvamu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='edu, xili@pvamu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='edu, rtwilkins@pvamu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='edu, phobiomon@pvamu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='edu, liqian@pvamu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='edu ‡ corresponding author Abstract—Image segmentation is a very popular and important task in computer vision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' In this paper, inverse quantum Fourier transform (IQFT) for image segmentation has been explored and a novel IQFT-inspired algorithm is proposed and implemented by leveraging the underlying mathematical structure of the IQFT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Specifically, the proposed method takes advantage of the phase information of the pixels in the image by encoding the pixels’ intensity into qubit relative phases and applying IQFT to classify the pixels into different segments automatically and efficiently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' To the best of our knowledge, this is the first attempt of using IQFT for unsupervised image segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' The proposed method has low computational cost comparing to the deep learning based methods and more importantly it does not require training, thus make it suitable for real-time applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' The performance of the proposed method is compared with K-means and Otsu- thresholding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' The proposed method outperform both of them on the PASCAL VOC 2012 segmentation benchmark and the xVIEW2 challenge dataset by as much as 50% in terms of mean Intersection-Over-Union (mIOU).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Index Terms—Inverse Quantum Fourier Transform, Computer Vision, Image Segmentation I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' INTRODUCTION Image segmentation is defined as the separation of an image dataset into non-intersecting, homogeneous subsections in terms of certain properties such as color intensities and textures [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' In image processing and computer vision, seg- mentation is generally applied to separate the regions of inter- est from the other part of the image (called the background) for further analysis [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Segmentation is a crucial and difficult problem in many fields such as digital image processing, object or pattern recognition, enhanced object features extraction and artificial intelligence [3], [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' It is a very important tool for solving image semantic problems which involves predict- ing the categories of the pixels contained in an image [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' The applications of image segmentation span many different fields, such as in medical diagnostic imaging applications for automatic detection of anomalies, treatment monitoring and disease diagnosis [6], [7], in image-based remote sensing technology [8], and in additive manufacturing processes for in-situ monitoring and detection of shifts in product quality during production [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' In the classical computing domain, Fourier transform is one of the popular techniques that have been researched and developed extensively for image segmentation [10]–[12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' For instance, the auto-registration property of the magnitude spec- tra has been exploited for texture identification [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Similarly, structural texture in the satellite images have been extracted using Fourier transform for agriculture applications [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Seg- menting foreground to track spontaneous changes in the shape of objects embedded in a template image using total variation and fast Fourier transform has been studied in [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' On the other hand, several image segmentation algorithms have emerged in the quantum computing domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' For instance, the authors of [13] provided a quantum circuit for gray image encoding and a proof-of-concept quantum circuit of dual- threshold segmentation algorithm, and simulated it on an 8×8 image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' However, inverse quantum Fourier transform (IQFT) for image segmentation has not been studied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' In this work, we seek to leverage the unique properties of IQFT and provide an IQFT-inspired approach for unsupervised image segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Specifically, the proposed method takes advantage of the phase information of the pixels in the image by encoding the pixels’ intensity into qubit relative phases and applying IQFT to classify the pixels into different segments automatically and efficiently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' The contributions of this paper are: 1) An IQFT-inspired algorithm is proposed for unsuper- vised image segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' To the best of our knowledge, this is the first unsupervised image segmentation algo- rithm using IQFT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 2) Comparing to many deep learning based image seg- mentation methods, the proposed approach has much less computational cost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' More importantly, the proposed method does not require training, thus make it suitable for real-time applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 3) We demonstrate the potential of IQFT in solving image segmentation problem, and compare its effectiveness with two popular unsupervised segmentation techniques: Otsu thresholding [14], and K-means Clustering [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' The proposed method outperform both of them on the PASCAL VOC 2012 segmentation benchmark [16], and the xVIEW2 challenge dataset [17] by as much as 50% in terms of mIOU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' The remainder of this paper is structured as follows: Related works are reviewed in Section II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Section III introduces inverse quantum Fourier transform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Section ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' provides the details of the proposed approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' The experimental results are given in arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='04705v1 [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='CV] 11 Jan 2023 Section V and observations and insights from the results are discussed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Section VI concludes the paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' RELATED WORKS A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Image Segmentation in Classical Computing As a key process in image processing and analysis, image segmentation has been well studied in the classical comput- ing domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Many methods for solving image segmentation problems have emerged over the years.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' These methods vary widely depending on the specific application since a single method is not sufficient for different images with varying char- acteristics in terms of sharpness, texture, noise presence, and the degree of overlapping objects [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Traditional techniques used for image segmentation are categorized as thresholding- based technique [18], region-based technique [19], edge-based technique [20], clustering-based technique [21], and watershed technique [22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' These methods vary widely depending on the specific application since they all have their limitations based on the underlying principles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' For instance, employing an unsupervised method like the K-means for image segmentation has a major drawback which is the requirement for the optimal number of clusters to be specified before the algorithm is applied [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' The segmentation error decreases as the number of clusters increases and there is no theoretical means of obtaining the optimal number of clusters to be used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Similarly, Otsu’s thresholding technique does not consider the spatial information of image, and this makes it sensitive to the unevenness and noise in a grayscale image [24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Although the advent of deep learning has brought about new classes of image segmentation techniques that have become widely available [25], usually they have very high computational complexity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Furthermore, most of them are supervised methods that require training and probably re- training when applied to a new dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' On the contrary, the proposed method has low computational cost comparing to the deep learning based methods and more importantly it does not require training, thus make it suitable for real-time applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' In our analysis, we will compare the performance of our proposed technique with two popular unsupervised segmentation techniques that do not require training: Otsu thresholding [14], and K-means Clustering [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Image Segmentation in Quantum Computing In recent years, several image segmentation algorithms have emerged in the quantum domain to exploit the properties of quantum computing to improve the performance of classical techniques and, subsequently, their applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Some com- mon algorithms are thresholding segmentation [26] and quan- tum search algorithm [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Most of these proposed methods involve implementation of some oracle operators which are either fully theoretical or hard to simulate due to the number of qubits required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Most of the well-known quantum algorithms such as quan- tum phase estimation, Grover’s algorithm and Shor’s algorithm utilize QFT (or IQFT) as part of their major subroutines [28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Similarly, in applications such as quantum image processing, error-correction, and encryption [29], [30], QFT (or IQFT) is embedded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Consequently, QFT is undoubtedly a valuable transformation in the quantum domain, and itas applications are not yet fully studied [31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' INVERSE QUANTUM FOURIER TRANSFORM QFT transforms a computational basis state |x⟩ into a superposition of all the computational basis states with the inclusion of relative phases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' This is defined mathematically in equation (1) [28], where N = 2n, n is the number of qubits;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' ω = ei 2π N , the nth root of unity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' In tensor product form, equation (1) becomes equation (2) [28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Considering a three qubit system, for example, n = 3, equation (2) can be expanded to equation (3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' QFT(|x⟩) = 1 √ N N−1 � k=0 ωxk|k⟩ (1) QFT(|x⟩n) = 1 √ N ⊗n k=1 � |0⟩ + ei 2πx 2k |1⟩ � (2) QFT(|x⟩3) = 1 √ 8 � |0⟩ + ei 2πx 2 |1⟩ � ⊗ � |0⟩ + ei 2πx 4 |1⟩ � ⊗ � |0⟩ + ei 2πx 8 |1⟩ � (3) For example, the QFT of a quantum state |x⟩ = |100⟩ is determined from equation (3) by substituting x = 4, the decimal equivalent of 1002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' This operation is shown in equation (4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' The result suggests that a superposition of states, with some phase information, can be transformed into a single state representation by employing the inverse operation of the QFT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' QFT(|x = 100⟩3) = 1 √ 8(|000⟩ − |001⟩ + |010⟩ − |011⟩ +|100⟩ − |101⟩ + |110⟩ − |111⟩) (4) The inverse quantum Fourier transform (IQFT) performs the reverse operation of the QFT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' It transforms from a phase representation into the computational basis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' From equation (2), the inverse operation, IQFT, can be written as equation (5), where |k⟩ is the state of a quantum system with some phase information [28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Equation (6) presents a case of three qubits, n = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='IQFT ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='� 1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='√ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='N ' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='ω−4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='ω−3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='ω−2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='ω−1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='����������� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='����������� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='eiγ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='eiβ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='ei(β+γ) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='eiα ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='ei(α+γ) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='ei(α+β) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='ei(α+β+γ) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='����������� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='(11) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Proposed IQFT-Inspired Algorithm The proposed algorithm is developed from equation (11).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Firstly, eight state basis vectors are given by the rows of the 8 by 8 matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' These basis vectors are visualized as a set of points on a unit circle as shown in Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Secondly, a 3-dimensional input vector, [α, β, γ], is transformed into an eight-dimensional vector given by the column matrix on the right-hand side of equation (11).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' This vector also can be represented by a set of eight points on a unit circle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' A random example for which α = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='464 , β = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='025, and γ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='246 is shown in Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' By visual inspection, the input pattern has two obvious clusters similar to basis state vector |100⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Lastly, the probability that the pattern generated by the input vector is similar to each of the characteristic patterns of the basis vectors is determined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' This is given by the modulus squared of the probability amplitudes (P, Q, R, S, T, U, V, W ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' The input vector is then classified based on the basis state vector that gives the highest probability value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Figure 3 shows the probabilities associated with the random input in Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' It is obvious that this input is most similar to state basis vector |100⟩ as previously observed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Subject to this insight, the proposed IQFT-inspired algo- rithm for RGB image segmentation is presented in Algorithm1, where the input Pm is a 3D vector of RGB intensities of the mth pixel, T is the total number of pixels, W is a complex 8 by 8 matrix in equation (11), θ1, θ2, and θ3 are angle parameters for transforming pixel intensities into phase values, and the output is the required pixel label lm∈{0, 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=', 7}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' The seg- mentation algorithm involves a normalization process in Line 1, linear transformation in Line 2, dimensional transformation from 3D to 8D vector in Line 3, and probability measure in Line 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' A pixel is classified according to the basis vector with the highest probability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Proposed IQFT-inspired Algorithm for Grayscale Image Segmentation Since our approach in Section IV-B is not limited by the image color space, it can be adapted for segmentation of grayscale images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' In this case, the governing mathematical equation is given by equation (12), where the probability amplitudes, P and Q, are determined from equation (13).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' For a normalized pixel intensity I, and chosen angle parameter θ, γ = Iθ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' IQFT � 1 √ 2 � |0⟩ + eiγ|1⟩ �� ≡ P|0⟩ + Q|1⟩ (12) � P Q � ≡ 1 2 × � 1 1 1 −1 � � 1 eiγ � (13) In this grayscale implementation, a pixel can be classified into one of two classes based on the probabilities given by Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 1: Visualization of the eight state basis vectors Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 2: Transformed input pattern on the unit circle for a random case of α = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='464 , β = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='025, and γ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='246.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Some points are coincident.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 3: Probability distribution for input pattern of a random case of α = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='464 , β = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='025, and γ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='246 equation (14).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' For P(class1) = P(class2), I = Ith, where Ith is a threshold value given by equation (15), where k ∈ Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' p (class1) = (1+cos(Iθ))2 + (sin(Iθ))2 4 p (class2) = (1−cos(Iθ))2 + (sin(Iθ))2 4 (14) Algorithm 1 : IQFT-inspired algorithm for RGB image seg- mentation Input: I = { Pm ∈ R3}, m = [1, T] θ1, θ2, θ3 ∈ R W ∈ C8×8 Output: L = {lm ∈ Z} for m=1to T do 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' {Pm} ←− {Pm/255} , {Pm} = {Rm, Gm, Bm} 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' {γm, βm, αm} ←− {Rm × θ1, Gm × θ2, Bm × θ3} 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' {Fm} = � � � � � � � � � � � � � � � � � � � � � � � 1 eiγ eiβ ei(β+γ) eiα ei(α+γ) ei(α+β) ei(α+β+γ) � � � � � � � � � � � � � � � � � � � � � � � ←− � � � γm βm αm � � � 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' {Sm} ←− [abs (Dot Product (Fm, W) /8)]2 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' {lm} ←− {argmax{Sm} } cosIthθ = 0 =⇒ Ithθ = (4k ± 1) π 2θ ≤ 1 (15) Therefore, selecting a particular value of θ is equivalent to setting a threshold value, and the network behaves like a thresholding technique.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Table I shows some θ values and the corresponding threshold using equation (15).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Considering equation (15), with a single selection of θ, it is possible to establish multiple thresholds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' For instance, choosing θ = 4π results in four thresholds as shown in equation (16) for k = 0, 1, 2, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' The advantage of these multiple thresholds is captured in the following example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Consider the task of separating red , green, and lemon balls from the others of lower and higher intensities in Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' To achieve the 1000)State 1.' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='0 1 0 1 realdesired goal, θ is simply set to 4π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' However, Otsu-thresholding would require two clearly defined thresholds to achieve the set goal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Ith = (4k ± 1) π 2θ = 1 8, 3 8, 5 8, 7 8 (16) Image K-means Otsu IQFT Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 4: Application of multiple thresholding TABLE I: Parameter θ and the corresponding threshold value using equation 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Parameter, θ Threshold value, Ith 3π/4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='667 π 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='500 5π/4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='400 3π/2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='333 7π/4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='285, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='857 (multiple) 2π 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='25, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='75 (multiple) V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' RESULTS AND ANALYSIS A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Dataset Considering that most image dataset exist in the classical domain, we have performed simulations of the proposed method in the classical domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' To demonstrate the effec- tiveness of our proposed method for Image segmentation, we conduct several experiments on two datasets: (1) the training and validation dataset of PASCAL VOC 2012 segmentation benchmark [16], focusing only on the segmentation category which contains 2913 labeled set;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' (2) the xVIEW2 challenge dataset [17] focussing on the 148 RGB satellite pre-disaster images for a “joplin-tornado” disaster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Experimental Setup All images are RGB, and the corresponding grayscale images are prepared by calculating the weighted sum of the corresponding red, green and blue pixels according to Scikit- image [32], using equation (17).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Y = R × 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='2125 + G × 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='7154 + B × 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='0721 (17) K-means [15] and Otsu-thresholding [14] are selected as the baseline methods for performance comparison with our method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' To implement the baseline methods, we used the scikit-learn library [33] with default settings for K-means, and scikit-image library [32] for Otsu-thresholding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' All the algorithms used in this study are coded using Python on MacBook Pro with 8-Core Intel Core i9 running at 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='3 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Evaluation Metric The segmentation accuracies of the methods used in this study are assessed by the mean intersection over union (mIOU) score defined in equation (18) and equation (19), where TP, FP, FN, T, and P are true positive, false positive, false negative, ground truth and prediction, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' TensorFlow function [34], utilizing equation (18), is used for all mIOU cal- culations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Pixels around the border of an object that are marked ‘void’ in the ground truth are not used in our calculations [35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' mIOU = IOU(foreground) + IOU(background) 2 (18) IOU = TP TP + FP + FN = T ∪ P T ∩ P (19) D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Experimental Results For the purpose of evaluating the effects of design choices on performance, different experiments are conducted on stan- dard datasets and the results obtained are presented in this section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 1) Effect of the normalization process: Here, the effect of the normalization process of Section IV-B on the quality of the segmentation pattern is investigated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' The results obtained in Figure 5 show that, for a smooth segmentation pattern, normalized image intensities are required to avoid “noisy” segments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 5: Effect of the normalization process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' First row con- tains two different images,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' second rows contains segmentation patterns when the normalization process is included,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' and the last row shows segmentation patterns when the normalization process is not included 2) Effects of angle parameter (θ1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' θ2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' θ3) on the number of segments: To study the effects of the angular parameter,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' θ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' on the segmentation pattern,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' we generated 100,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 000 × 3 random numbers between 0 and 1 as normalized RGB values and determined the maximum number of segments using all the combinations for different values of θ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' The results are shown in Table II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' It is evident that the number of segments varies with the angular parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' This is due to the modification of the transformed input pattern as the angular parameters are varied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' This effect is observed on real images shown in Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' For θ1 = θ2 = θ3 = π/4, the six arguments from the complex representation of each pixel are located between 0 and 3π/4 radian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' This tends to produce a pattern most similar to the |000⟩ state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Therefore, all pixels are classified into one segment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' For θ1 = θ2 = θ3 = π/2, the segmentation process is biased towards the low-luminous pixels, as pixels (objects) with strong brightness are visible in Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Using different angles can result in some peculiar segmentation effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' This is shown by θ1 = π/4, θ2 = π/2, θ3 = π which usually outputs two segments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' TABLE II: Parameter θ and the possible number of segments Parameter, θ max.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' number of segments θ1 = θ2 = θ3 = π/4 1 θ1 = θ2 = θ3 = π/2 3 θ1 = θ2 = θ3 = 3π/4 5 θ1 = θ2 = θ3 = π 6 θ1 = θ2 = θ3 = 5π/4 8 θ1 = θ2 = θ3 = 3π/2 8 θ1 = θ2 = θ3 = 7π/4 8 θ1 = θ2 = θ3 = 2π 8 θ1 = π/4, θ2 = π/2, θ3 = π 2 (constant) Image Image Image θ = π/4, 1-seg θ = π/4, 1-seg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' θ = π/4, 1-seg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' θ = π/2, 2-seg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' θ = π/2, 3-seg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' θ = π/2, 1-seg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' θ = π, 4-seg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' θ = π, 6-seg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' θ = π, 5-seg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' mixed, 2-seg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' mixed, 2-seg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' mixed, 2-seg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 6: Effects of θ on the number of segments and the segmentation quality–where ’mixed’ in the last row represents θ1 = π/4, θ2 = π/2, θ3 = π E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Performance comparison 1) A performance comparison of the IQFT-inspired al- gorithm for grayscale Images and Otsu-threshold method: As pointed out in Section IV-C, setting a value of θ is equivalent to a threshold value in equation (15).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' To support this conclusion, Figure 7 shows two examples of the segmentation results observed from using Otsu-thresholding and IQFT- inspired algorithm for grayscale images with equivalent angle parameters using equation (15).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Therefore, setting θ according to equation (15) results in identical segmentation pattern and equal mIOU values (not shown) for both methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Ith = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='4465 θ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='1197π Ith = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='4911 θ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='0180π Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 7: Performance comparison of the IQFT-inspired al- gorithm for grayscale images and Otsu-thresholding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' If the threshold from Otsu method is converted to parameter θ according to equation (15), the outputs of the two methods are identical 2) A performance comparison of the proposed method and the baseline methods: The effectiveness of the proposed algorithm for image segmentation was validated by performing foreground-background segmentation on PASCAL VOC2012 and xVIEW2 challenge datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' The resulting performance values are compared with K-means and Otsu-thresholding in Table III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Based on the average mIOU values, the IQFT- inspired algorithm for RGB image segmentation was observed to outperform K-means and Otsu-thresholding in, respectively, 53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='24% and 52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='32% of the images in PASCAL VOC 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Similarly, the IQFT-inspired algorithm outperformed K-means and Otsu-thresholding in 95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='94% and 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='97% of the pre- disaster images for ”joplin-tornado” in the xVIEW2 chal- lenge dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Figure 8 shows some segmentation outputs of PASCAL VOC 2012 images for which the IQFT-inspired algorithm outperformed the baseline techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Similar out- puts are shown for xVIEW2 challenge dataset in Figure 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' However, the IQFT-inspired algorithm also showed poor performance(mIOU < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='1) for about 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='4% of the PASCAL VOC 2012 images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' This value doubles the observed values for K-means and Otsu thresholding because the performance of the proposed algorithm depends on the chosen value of angle parameter θ which was set to π in this experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Adjusting the value of θ for each image will result in an observable performance improvement as shown in Figure 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' TABLE III: Comparing the mIOU, computation time, and computational complexity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Image segmentation methods Datasets Metrics K-means OTSU IQFT IQFT (RGB) (Grayscale) Pascal Average mIOU 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='4318 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='4331 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='4354 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='4172 VOC 2012 Runtime (sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=') 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='01 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='06 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='76 xVIEW2 Average mIOU 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='3375 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='4008 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='5070 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='478 Runtime (sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=') 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='74 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='10 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='5 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='67 mIOU=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='3197 mIOU=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='2080 mIOU=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='2036 mIOU=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='3179 mIOU=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='2052 mIOU=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='2036 mIOU=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='9762 mIOU=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='9187 mIOU=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='9697 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 8: Results of segmentation with reference images on PASCAL VOC 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' The IQFT-inspired algorithm for RGB images shows better foreground-background segmentation re- sults as shown by the mIOU scores VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' CONCLUSIONS In this work, a novel method for unsupervised image segmentation based on the inverse quantum Fourier transform (IQFT) is proposed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Specifically, the proposed method takes advantage of the phase information of the pixels in the image by encoding the pixels’ intensity into qubit relative phases and applying IQFT to classify the pixels into different segments automatically and efficiently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' To the best of our knowledge, this is the first attempt of using IQFT for unsupervised image segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' The proposed method has low computational cost comparing to the deep learning based methods and more importantly it does not require training, thus make it suitable for real-time applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Supported by the segmentation patterns obtained for image samples from xView2 and Pascal VOC datasets, this quantum-inspired method shows a promis- ing performance when compared to the classical K-means clustering and Otsu-thresholding methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' One of the appeals of the proposed method is that it automatically adapts to the characteristics of the image such that the number of segments mIOU=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='1175 mIOU=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='5243 mIOU=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='2394 mIOU=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='3597 mIOU=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='5226 mIOU=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='3390 mIOU=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='51295 mIOU=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='5683 mIOU=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='5453 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 9: Segmentation result using xVIEW2 challenge dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Measured by the mIOU scores, the IQFT-inspired algorithm for RGB images shows better foreground-background segmen- tation results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' is not a required parameter like in K-means.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Note that the proposed method can be implemented in both classical computing domain and the quantum computing do- main.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Considering most of the datasets of image segmentation benchmark is in the classical computing domain, we have performed experiments to validate the proposed approach in the classical computing domain as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' We are working on ImageGround-Truth(-means KOtsu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' iif 74 117TImage Ground truth K-means mIOU=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='8892 Otsu mIOU=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='8663 IQFT mIOU=π,0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='0084 IQFT mIOU=3π/4,0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='8327 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 10: Performance improvement through θ adjustment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Using θ = 3π/4, rather than θ = π, can improve the segmentation quality of these images, as shown by increase in the mIOU score the quantum domain implementation and the results will be shared in a future paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' VII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' ACKNOWLEDGMENT This research work is supported by the IBM-HBCU Quan- tum Center.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' REFERENCES [1] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='-D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Cheng, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Jiang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Sun, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Wang, “Color image segmen- tation: advances and prospects,” Pattern recognition, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 34, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 12, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 2259–2281, 2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' [2] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Goceri, A comparative evaluation for liver segmentation from spir images and a novel level set method using signed pressure force function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Izmir Institute of Technology (Turkey), 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' [3] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Wang, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Wang, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Zhu, “Image segmentation evaluation: a survey of methods,” Artificial Intelligence Review, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 53, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 8, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 5637–5674, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' [4] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Pandey and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Lalchhanhima, “Segmentation techniques for complex image,” in 2020 International Conference on Computational Perfor- mance Evaluation (ComPE), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 804–808, IEEE, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' [5] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Ye and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Han, “Image semantic segmentation method based on improved erfnet model,” The Journal of Engineering, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 2022, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 180–190, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' [6] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Zhou, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Nie, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Adeli, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Yin, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Lian, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Shen, “High-resolution encoder–decoder networks for low-contrast medical image segmenta- tion,” IEEE Transactions on Image Processing, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 29, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 461–475, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' [7] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Goceri and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Songul, “Biomedical information technology: image based computer aided diagnosis systems,” in International Conference on Advanced Technologies, Antalaya, Turkey, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' [8] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Wang, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Qi, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Jiang, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Liu, “Hybrid remote sensing image segmentation considering intrasegment homogeneity and intersegment heterogeneity,” IEEE Geoscience and Remote Sensing Letters, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 17, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 22–26, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' [9] O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Aworunse, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Zhou, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Deng, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Cheng, “Image decomposition accelerates dynamic network modeling for in situ monitoring of bio- mimic wing printing processes,” Procedia Manufacturing, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 39, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 178–184, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' [10] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Zou and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Wang, “Texture identification and image segmentation via fourier transform,” in Image Extraction, Segmentation, and Recognition, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 4550, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 34–39, SPIE, 2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' [11] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Atta-Fosu and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Guo, “Joint segmentation and nonlinear registration using fast fourier transform and total variation,” in Research in Shape Analysis, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 111–132, Springer, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' [12] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='-M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Tsai and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Chen, “Coffee plantation area recognition in satellite images using fourier transform,” Computers and electronics in agriculture, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 135, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 115–127, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' [13] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Yuan, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Wen, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Hang, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Gong, “The dual-threshold quantum image segmentation algorithm and its simulation,” Quantum Information Processing, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 19, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 12, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 1–21, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' [14] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Otsu, “A threshold selection method from gray-level histograms,” IEEE transactions on systems, man, and cybernetics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 9, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 62–66, 1979.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' [15] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' MacQueen, “Classification and analysis of multivariate observations,” in 5th Berkeley Symp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Statist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Probability, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 281–297, 1967.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' [16] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Kim, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Kanezaki, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Tanaka, “Unsupervised learning of image segmentation based on differentiable feature clustering,” IEEE Transactions on Image Processing, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 29, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 8055–8068, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' [17] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Gupta, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Hosfelt, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Sajeev, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Patel, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Goodman, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Doshi, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Heim, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Choset, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Gaston, “xbd: A dataset for assessing build- ing damage from satellite imagery,” arXiv preprint arXiv:1911.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='09296, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' [18] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Lee, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Chung, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Park, “A comparative performance study of several global thresholding techniques for segmentation,” Com- puter Vision, Graphics, and Image Processing, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 52, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 171– 190, 1990.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' [19] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Kaganami and Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Beiji, “Region-based segmentation versus edge detection,” in 2009 Fifth International Conference on Intelligent Information Hiding and Multimedia Signal Processing, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 1217–1221, IEEE, 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' [20] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Wani and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Batchelor, “Edge-region-based segmentation of range images,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 16, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 314–319, 1994.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' [21] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Zou and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Liu, “Survey on clustering-based image segmentation techniques,” in 2016 IEEE 20th International Conference on Computer Supported Cooperative Work in Design (CSCWD), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 106–110, IEEE, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' [22] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Salman, “Image segmentation based on watershed and edge detection techniques,” Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Arab J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Inf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Technol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 3, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 104–110, 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' [23] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Pham, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Dimov, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Nguyen, “Selection of k in k-means clustering,” Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 219, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 103– 119, 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' [24] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Pal and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Pal, “A review on image segmentation techniques,” Pattern recognition, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 26, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 9, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 1277–1294, 1993.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' [25] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Garcia-Garcia, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Orts-Escolano, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Oprea, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Villena-Martinez, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Garcia-Rodriguez, “A review on deep learning techniques applied to semantic segmentation,” arXiv preprint arXiv:1704.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='06857, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' [26] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Li, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Shi, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Zhao, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Lu, “Design of threshold segmenta- tion method for quantum image,” International Journal of Theoretical Physics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 59, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 514–538, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' [27] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Li, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Qingxin, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Lan, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Shen, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Zhou, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Mo, “Image storage, retrieval, compression and segmentation in a quantum system,” Quantum information processing, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 12, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 6, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 2269–2290, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' [28] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Nielsen and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Chuang, Quantum Computation and Quantum Information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Cambridge University Press, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' [29] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Bennett, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' DiVincenzo, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Smolin, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Wootters, “Mixed-state entanglement and quantum error correction,” Physical Review A, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 54, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 5, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 3824, 1996.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' [30] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Townsend, “System and method for key distribution using quantum cryptography,” Oct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 7 1997.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' US Patent 5,675,648.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' [31] O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Al-Ta’ani1a, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Alqudah, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Al-Bzoor, “Implementation and analysis of quantum fourier transform in image processing,” [32] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Van der Walt, et.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=', “scikit-image: image processing in python,” PeerJ, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 2, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' e453, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' [33] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Pedregosa, et.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=', “Scikit-learn: Machine learning in python,” Journal of Machine Learning Research, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 12, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 2825–2830, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' [34] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Abadi, et.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=', “TensorFlow: Large-scale machine learning on hetero- geneous systems,” 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Software available from tensorflow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content='org.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' [35] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Everingham, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Eslami, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Van Gool, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Williams, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Winn, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' Zisserman, “The pascal visual object classes challenge: A retrospective,” International journal of computer vision, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 111, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' 98–136, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' XX Ertlar !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} +page_content=' !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/NdE3T4oBgHgl3EQfwwth/content/2301.04705v1.pdf'} diff --git a/O9E3T4oBgHgl3EQfxgsc/vector_store/index.faiss b/O9E3T4oBgHgl3EQfxgsc/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..1f1658cbba594a16f0e15c2ccbb70ff792872172 --- /dev/null +++ b/O9E3T4oBgHgl3EQfxgsc/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:3d8cfc69fe751c191d45568e8d58ab74b2bb090ea606cd12af34adcc723d90d1 +size 6094893 diff --git a/QdAzT4oBgHgl3EQfz_5Y/content/2301.01777v1.pdf b/QdAzT4oBgHgl3EQfz_5Y/content/2301.01777v1.pdf new file mode 100644 index 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+Millimetre-waves to Terahertz SISO and MIMO +Continuous Variable Quantum Key Distribution +Mingqi Zhang1, Stefano Pirandola2, and Kaveh Delfanazari1,* +1 Electronics and Nanoscale Engineering Division, James Watt School of Engineering, University of Glasgow, Glasgow G12 8QQ, UK +2 Department of Computer Science, University of York, York YO10 5GH, UK + *Corresponding author: kaveh.delfanazari@glasgow.ac.uk +Dated:25122022 +Abstract—With the exponentially increased demands for +large bandwidth, it is important to think about the best network +platform as well as the security and privacy of the information +in communication networks. Millimetre (mm)-waves and +terahertz (THz) with high carrier frequency are proposed as the +enabling technologies to overcome Shannon’s channel capacity +limit of existing communication systems by providing +ultrawide bandwidth signals. Mm-waves and THz are also able +to build wireless links compatible with optical communication +systems. However, most solid-state components that can +operate reasonably efficiently at these frequency ranges +(100GHz-10THz), especially sources and detectors, require +cryogenic cooling, as is a requirement for most quantum +systems. Here, we show that secure mm-waves and THz QKD +can be achieved when the sources and detectors operate at +cryogenic temperatures down to T= 4K. We compare single- +input single-output (SISO) and multiple-input multiple-output +(MIMO) Continuous Variable THz Quantum Key Distribution +(CVQKD) schemes and find the positive secret key rate in the +frequency ranges between f=100 GHz and 1 THz. Moreover, +we find that the maximum transmission distance could be +extended, the secret key rate could be improved in lower +temperatures, and achieve a maximum secrete communication +distance of more than 5Km at f=100GHz and T=4K by using +1024×1024 antennas. Our results may contribute to the efforts +to develop next-generation secure wireless communication +systems and quantum internet for applications from inter- +satellite and deep space, to indoor and short-distance +communications. + +Index Terms— Millimetre (mm)-waves, terahertz (THz) waves, 6G +communication, +quantum +key +distribution +(QKD), +quantum +communication, cryogenic system, MIMO, SISO, +I. INTRODUCTION +With the extension of wireless communication and the fast +development of information security, higher carrier frequencies +and more spectral resources are required [1, 2]. Millimetre +(mm)- and terahertz (THz)- waves [3-6] offer ultrawide +bandwidth and high-speed data rate communication and are +considered to build next-generation (6G) communication +systems [7-11]. Mm-waves and THz bands lie between the +mature microwave and optical bands as less explored area [12- +16]. A gap in the electromagnetic spectrum exists at these + +C +frequency ranges due to the inefficient and unpractical of the +devices and circuit [1-19]. However, the recent development of +electronic, photonic and plasmonic-based mm-waves and THz +technologies help close this gap with the demonstration of +power-efficient sources [20-26], antennas [27-31], filters [32- +34], waveguides [29, 35-39], modulators [40-49], and detectors +[3, 49-52]. Demands for 6G are including, but are not limited +to, Terabit per second (Tb/s), mm-precision sensing and +positioning, seamless connectivity, and ultrafast wireless +communications [7-11]. Moreover, practical implementation of +quantum processors and quantum computers operating at low +temperatures (cryogenics) [53-55], requires massive open air +and free space data transfer from and to high-performance +classical processors, computers, and communication systems. +Therefore, to realise a robust building block for practical +quantum information processing attention should be on both +security and low-temperature operation. Compared with the +free-space optical link, the THz link is more stable under harsh +environments such as fog conditions [56]. The limit of mm- +waves [57] and THz links [58, 59] in long distances is mainly +caused by the absorption of the air [60]. So it is important to +find the window with low atmospheric absorption through this +band. High-level security is also an important aspect of +realising mm-waves and THz communications which is quite +challenging to maintain with classical cryptography schemes. +Quantum key distribution (QKD) can help to achieve the goal +of high-level unconditional security with the power of the +quantum physics [61-64]. QKD could be divided into discrete +variables (DVQKD based on single photon sources and +detectors) and continuous variables (CVQKD based on +standard communication systems) [62-75]. CVQKD uses +coherent homodyne detection instead of single photon detection +[65] +and +could +be +integrated +with +next-generation +communication systems [66]. +Single-input single-output (SISO) is a kind of classical +communication system where the transmitter and receiver don’t +have several antennas. To meet the explosion of data +transmission, +multiple-input +multiple-output +(MIMO) +technology has been widely used in wireless communication +nowadays. MIMO system with multiple antennas at both the +transmitter and receiver side brings benefits on data throughout +and communication range with limited bandwidth and transmit +power [67]. THz QKD with SISO and MIMO systems was +introduced in Refs [61] and [68], with the main focus on mid- + +2 + +and far-infrared frequency ranges (10THz-40THz) at room +temperature (T= 296 K). +Motivated by the works of [61] and [68], this work focuses +on SISO and MIMO QKD at the temperature of T< 50 K. We +investigate CVQKD at frequency ranges of mm-waves and +THz, from f=100 GHz to 1 THz, with antennas and detectors +both operating in the cryogenic environment (T< 50 K). +Moreover, we compare the performance of both the SISO and +MIMO CVQKD systems at this frequency range. +II. SYSTEM MODEL +For +the +proposed +mm-waves +and +THz +quantum +communication scheme, the cryogenic antennas generate +electromagnetic (EM) fields that oscillate at an angular +frequency ꞷ. This EM field is quantized and the system gets a +Hamiltonian 𝐻 = ℎ𝜔(𝑎̂†𝑎̂ + +1 +2) . The H is similar to the +Hamiltonian of a quantum harmonic oscillator with h as +Planck’s constant, 𝑎̂ as the annihilation operator, and 𝑎̂† as the +creation operator. Moreover, the quadrature field operators q̂ = +𝑎̂+𝑎̂† +√2 and p̂ = +i(𝑎̂+𝑎̂†) +√2 + are dimensionless canonical observables +of the system (similar to the position and momentum of the +quantum harmonic oscillator) [69]. Finally, coherent states of +the system are the eigenstates of the annihilation operator 𝑎̂, +provided by 𝑎̂|𝛼⟩ = α|𝛼⟩. Here, α = q + ip ∈ C indicates the +coherent state amplitude [68], taken from a two-dimensional +Gaussian distribution. Two independent continuous variables q +and p are used to create a secret key between Alice and Bob +[61]. +Notation: Boldface and italic capital letters such as A denote +matrices. 𝑨† is the conjugate transpose of matrix A while 𝑨𝑇 is +the transpose. 𝟎𝑀×𝑁 ∈ ℂ𝑀×𝑁 is a zero complex matrix and +𝟏𝑀×𝑁 ∈ ℂ𝑀×𝑁 is a complex matrix of ones. 𝑰𝑀 represents a +𝑀 × 𝑀 identity matrix. A 𝑀 × 𝑀 diagonal matrix described by +𝑑𝑖𝑎𝑔(𝒂) with 𝒂 ∈ ℂ𝑀 shows 𝒂 on its diagonal. And 𝒩(𝜇, 𝜮) +is a real multivariate Gaussian distribution in which the vector +is 𝜇 and the covariance matrix (CM) is 𝜮. +A. Channel model +We consider a one-way communication channel to build a +secret key between Alice and Bob as shown in Fig.1 (a). A +MIMO mm-waves and THz communication channel between +Alice and Bob include a transmitter with 𝑁𝑡 antennas at Alice's +side and a receiver with 𝑁𝑟 antennas at Bob's side. We assume +the antennas at both sides are distributed in a one-dimensional +uniform linear array (ULA) with each antenna element’s gain +𝐺𝑎. So the antenna gains of Alice and Bob are 𝐺𝑡 = 𝑁𝑡𝐺𝑎 and +𝐺𝑟 = 𝑁𝑟𝐺𝑎 [68]. The Gaussian modulation of the thermal state +is a widely used encoding protocol for several frequencies [61]. +Alice begins with a vacuum state |0⟩ and generates 𝑁𝑡 coherent +states |𝑎𝑖⟩ with amplitudes 𝑎𝑖 = 𝑄𝐴,𝑖 + 𝑗𝑃𝐴,𝑖, 𝑖 = 1,2, … , 𝑁𝑡 +from the 𝑁𝑡 antennas with quadratures being chosen from two +independent random vectors 𝑸, 𝑷~𝒩(𝟎𝑁𝑡×1, 𝑉𝑠𝑰𝑁𝑡) where 𝑉𝑠 +is the variance of the initial signal encoding [68]. Two +quadratures 𝑄̂𝐴,𝑖 and 𝑃̂𝐴,𝑖 of a quantum THz source (thermal) +state are randomly sent by the i-th antenna element of Alice and +described by 𝑋̂𝐴,𝑖 ∈ {𝑄̂𝐴,𝑖, 𝑃̂𝐴,𝑖}. So the i-th mode of Alice can be +considered as 𝑋̂𝐴,𝑖 = 𝑎𝑖 + 0̂ , where 0̂ is the thermal mode +(quadrature operator) due to the background thermal noise at +mm-waves and THz and XAi denotes the classical modulated +variable [61, 76]. The total variance of Alice’s mode is +𝑉𝑎 = 𝑉𝑠 + 𝑉0 +(1) +where 𝑉0 is the variance of thermal state (contains variance of +vacuum mode and variance of preparation noise) [61]. 𝑉0 is +defined as +Fig. 1. (a) The system model of the proposed mm-waves and THz QKD. Alice prepares thermal states at the source which +denotes a generator. The transmitter and receiver are antennas distributed in a one-dimensional uniform linear array (ULA). +Alice, Bob, and Eve do their job at cryogenic ambient (low temperature). The channel loss through the open-air environment +contains atmospheric absorption and free-space loss. Eve’s output modes are stored in a quantum memory (QM). Bob uses a +homodyne detector to measure quadrature. (b) The schematic of the phase shifters model described for a 2×2 MIMO system. +The channel is modelled by 4 beam splitters. Alice generates 2 coherent states 𝑎̂𝐴,1 and 𝑎̂𝐴,2 based on random vectors and send +them out from her 2 antennas as thermal states. These two states are mixed by the first beam-splitter 𝑽†. Then Eve operates +collective Gaussian attack. She prepares two two-mode squeezed vacuum states and uses beam-splitter B1 and B2 to combine +the input and her states. The output and one of the original modes are saved in quantum memory (QM). Before Bob detects the +input, the signals are mixed by beam-splitter 𝑼. At last, Bob uses his two antennas to receive the modes 𝑎̂𝐵,1 and 𝑎̂𝐵,2. + +(a) +(b) +Eve +Eve +BI +QM +ae,1- +OM +Alice +Bob +agr, +Cryogenic +Homodyne +aA,1 +ag,1 +agi,2 +U +Cryogenic +Open air +Cryogenic +Alice +B2 +Bob +background +loss +source +transmitter +attacker +receiver +detector +ab,2 +photons3 + +𝑉0 = 1 + 2𝑛̅ +(2) +Here, 1 is the vacuum shot noise unit (SNU) and +𝑛̅ = [exp ( ℎ𝑓𝑐 +𝑘𝐵𝑇) − 1] +−1 +(3) +is the mean thermal photon number, ℎ is Planck’s constant, 𝑘𝐵 +denotes Boltzmann’s constant, T is the environment +temperature, and 𝑓𝑐 is the carrier frequency. Now, let’s consider +Alice sends her states to Bob (receiver) over an insecure +quantum channel. Bob uses a noisy homodyne detection +technique, which is based on mm-waves and THz shot-noise +limited quantum detector that randomly switches between +quadrature 𝑄̂ and 𝑃̂, to measure the incoming thermal states. +The channel matrix between Alice and Bob could be +modelled as [68, 70, 71] +𝑯 = ∑ √𝛾𝑙𝑒𝑗2𝜋𝑓𝑐𝜏𝑙𝜓𝑁𝑟(𝜙𝑟,𝐿𝑂𝑆)𝜓𝑁𝑡 +† (𝜙𝑡,𝐿𝑂𝑆) +𝐿 +𝑙=1 +(4) +where, 𝑯 ∈ ℂ𝑁𝑟×𝑁𝑡 , L is the full number of multipath +components, 𝜏𝑙 is the propagation delay of the l-th multipath. +We only consider the line-of-sight (LOS) path with L=1 in this +work. So the path loss 𝛾𝑙 is given by [68] +𝛾𝑙=1 = 𝐺𝑡𝐺𝑟 ( 𝜆 +4𝜋𝑑) +2 +10−𝛿𝑑 +10 +(5) +where d is the distance (km) between Alice and Bob and 𝛿 is +the atmospheric loss and is defined as dB/km [61, 70]. It +contains both the free space path and the atmospheric +absorption losses of mm-waves and THz waves. 𝜙𝑟,𝐿𝑂𝑆 and +𝜙𝑡,𝐿𝑂𝑆 is the angle of arrival seen by Bob, and the angle of +departure from Alice, respectively. 𝜓𝐾(𝜃) represents the array +response vector of a ULA which contains K number of +antennas. +The derivation details of the channel model are described by a +singular-value decomposition (SVD) scheme introduced by +Ref. [68] are presented in Appendix A. +Although the coherent attack is the general attack, the works +reported in Refs. [72, 73] proved that once the system is secure +against collective attacks, it is also secure against general +attacks with the long secret key. In CVQKD, the most realistic +and studied collective attack against Gaussian protocols is the +entangling cloner attack [61]. So, we assume the channel are +totally under Eve’s control and she uses entangling cloners to +steal information. Fig.1 (b) shows a 2 × 2 MIMO system built +by 4 beam-splitters as an example [69]. After the two +transmitted modes from Alice are combined by beam-splitter +𝑽†, Eve will pick up two produced output modes. Eve should +prepare two pairs of entangled Einstein-Podolsky-Rosen +{𝑒̂1, 𝐸̂1} and {𝑒̂2, 𝐸̂2} (known also as two-mode squeezed +vacuum states) in advance. Once received the input, Eve uses +𝑩1 and 𝑩2 to combine them with 𝐸̂1 and 𝐸̂2. The relationship +of input and output of 𝑩𝑖 can be written as [68, 69] +[𝑎̂𝑜𝑢𝑡,1 +𝑎̂𝑜𝑢𝑡,2] = [ +√𝜂𝑖 +√1 − 𝜂𝑖 +−√1 − 𝜂𝑖 +√𝜂𝑖 +] [𝑎̂𝑖𝑛,1 +𝑎̂𝑖𝑛,2] +(6) +Here, 𝜂𝑖 is the round trip transmissivity of two port beam- +splitter 𝑩𝑖 . Then Eve will save one of the outputs from every +beam-splitters (𝐸̂′1, 𝐸̂′2) and the original modes (𝑒̂1, 𝑒̂2) in her +quantum memory (QM) and measure the ancilla modes to +exploit information when Alice and Bob completed their +classical communication. The other two output modes will be +combined by the beam-splitter 𝑼 and sent to Bob. We assume +Alice applies 𝑽 as the base of beamforming at her end, and Bob +employs 𝑼† as the base of decoding at his side. The whole +model could be described by [68, 69] +𝒂̂𝐵 = 𝑼†𝑯𝑽𝒂̂𝐴 + 𝑼†𝑼𝑺𝒂̂𝐸 +(7) +where 𝒂̂𝐵 = [𝑎̂𝐵,1, … , 𝑎̂𝐵,𝑁𝑟]𝑇 is the received mode of Bob, +𝒂̂𝐴 = [𝑎̂𝐴,1, … , 𝑎̂𝐴,𝑁𝑡]𝑇 is the transmitted mode of Alice, 𝒂̂𝐸 = +[𝑎̂𝐸,1, … , 𝑎̂𝐸,𝑁𝑡]𝑇 is the injected Gaussian mode of Eve. +𝑺 = 𝑑𝑖𝑎𝑔{√1 − 𝜂1, … , √1 − 𝜂𝑟, 𝟏(𝑀−𝑟)×1} +(8) +is a diagonal matrix with 𝑀 = min(𝑁𝑡, 𝑁𝑟). The calculation +details could be found in Appendix A. The efficient channel +between Alice and Bob can be disintegrated into r parallel SISO +channels by utilizing the SVD of H (r is the rank of 𝑯). In this +case, the relation between channels' input and output can be +written as [68] +𝒂̂𝐵,𝑖 = √𝑇𝑖𝒂̂𝐴,𝑖 + √1 − 𝑇𝑖𝒂̂𝐸,𝑖, +𝑖 = 1,2, … , 𝑟 +(9) +Here, 𝑇𝑖 is the i-th non-zero eigenvalue of 𝑯†𝑯 and could also +be considered as the i-th transmissivity of the channel. +Homodyne experiments on one of the randomly selected +quadratures will be performed by Bob for every r-received +mode and get the result detailed in Appendix A. +We set W to the variance of the thermal noise introduced by +Eve. So, Bob will receive the i-th mode with the shot-noise level +𝑉 (𝑋̂𝐵,𝑖) = 𝑇𝑖𝑉0 + (1 − 𝑇𝑖)𝑊 [61]. 𝑋̂𝐵,𝑖 is Bob’s received +quadrature described by Eq. (22) in Appendix A. If Eve wants +to completely hide in the background noise, she can use 𝑊 = +𝑉0. Then Bob will receive the shot-noise level 𝑉 (𝑋̂𝐵,𝑖) = 𝑉0 +which is the same as what Alice sent. Although the value of 𝑉0 +could be enlarged by frequencies below 1THz, we could gain +𝑉0 ≈ 1 𝑆𝑁𝑈 by cooling down the system to low temperatures. +B. Secret key rate +In this mm-waves and THz CVQKD scheme, Alice and Bob +replicate the previous quantum communication protocol several +times to generate a string. Then they correct errors in their string +by using reconciliation protocol. Direct reconciliation (DR) is +the scheme in which Bob uses Alice’s encoding string to +prepare the key while reverse reconciliation (RR) is when Alice +prepares the key based on Bob’s decoding result. Alice and Bob +use a reconciliation protocol to achieve privacy amplification to +reduce the knowledge stole by Eve [68]. In this work, we use +an asymptotic secret key rate to study the performance of RR +protocol in mm-waves and THz QKD. In RR it is possible to +achieve a positive secret key rate when the channel +transmissivity is almost 0 while in DR it required a channel +transmissivity larger than 0.5 [76], and is impractical in mm- +waves and THz because of the high losses (both atmospheric +absorption and path). +According to [68], the secret key rate of the MIMO system +could be divided into r SISO channels. So we first analyse the +secret key rate of a SISO channel. In the RR scheme, Alice and +Bob use the decoding outcomes from Bob's side to generate +their secret key [74]. Alice and Bob could estimate the mutual +information they shared, described as 𝐼(𝑎: 𝑏) , and the +accessible information of Eve, described as 𝐼(𝐸: 𝑏) . The +asymptotic secret key rate 𝑅◄ could be described by the surplus +information shared by Alice and Bob and is given by [62] +𝑅◄ = 𝐼(𝑎: 𝑏) − 𝐼(𝐸: 𝑏) +(10) + +4 + +The mutual information between Alice and Bob is +I(a: b) = 1 +2 𝑙𝑜𝑔2[1 + +𝑇𝑉𝑠 +Λ(𝑉0, 𝑊)] +(11) +Λ(x, y) = Tx + (1 − T)y +(12) +while 𝑉𝑠 ≫ 𝑉0, 𝑊, and Eve’s information is bounded by the +Holevo information I(E: b) which is defined as +I(E: b) = 𝐻𝐸 − 𝐻𝐸|𝑏 +(13) +where 𝐻𝐸 and 𝐻𝐸|𝑏 are the von Neumann entropy of Eve’s total +and conditional state given by Eq. (25) and Eq. (26) in +Appendix A respectively [68, 75]. +The total secret key rate is finally given by the sum of r +SISO links’ secret key rate [68] assuming 𝑇𝑖 → 0 +𝑅𝑀𝐼𝑀𝑂 +◄ += ∑ 𝑅𝑖 +◄ +𝑟 +𝑖=1 +≈ 𝜁𝑡𝑟(𝑯†𝑯) − 𝑟ℎ(𝑊) +(14) +where +𝜁 = 0.72 [𝑉𝑠 +𝑊 − ln (𝑉𝑎 + 1 +𝑉𝑎 − 1) (𝑉𝑎 +2 − 𝑊2 +2𝑊 +− 𝑉𝑎)] +(15) +and 𝑡𝑟(𝑯†𝑯) = ∑ +𝑇𝑖 +𝑟 +𝑖=1 +. ℎ(𝑊) is a function given by +h(x) = 𝑥 + 1 +2 +𝑙𝑜𝑔2 (𝑥 + 1 +2 +) − 𝑥 − 1 +2 +𝑙𝑜𝑔2 (𝑥 − 1 +2 +) +(16) +C. System conditions +To achieve a positive secret key rate, 𝜁𝑡𝑟(𝑯†𝑯) > 𝑟ℎ(𝑊) is +required. Verified from Eq. (1)-(4), only 𝜁𝑡𝑟(𝑯†𝑯) in Eq. (14) +depends on frequency and 𝜁 also depends on temperature. With +a given frequency, lower temperature could decrease 𝑉0 and +increase 𝜁 in Eq. (15). This also happens with a given +temperature and increasing frequency. But higher frequency +normally brings higher path loss which may decrease 𝑡𝑟(𝑯†𝑯). +Since 𝑡𝑟(𝑯†𝑯)>0, the limit of 𝜁 > 𝛼 = +𝑟ℎ(𝑊) +𝑡𝑟(𝑯†𝑯) is equal to 𝜁 > +𝛼 = 0 while W=1. This condition helps us find the balance +between 𝜁 and 𝑡𝑟(𝑯†𝑯) and get a positive secret key rate. +Figure 2 shows ζ as a function of temperature for different +frequencies in a MIMO THz QKD system [68]. According to +the simulation results, we achieved secure transmission for +frequencies between f=100GHz and 1THz, at temperatures T< +43K. The detail of the maximum operating temperature for each +frequency is shown in Table 1. +III. SIMULATION RESULT +We use the secret key rate (R) to define whether the system +is safe or not. A positive secret key rate reflects a safe +transmission. As R of the MIMO system is the sum of the SISO +system, we also compared the different performances of the +MIMO and SISO systems at the same conditions. +TABLE I + +A. Simulation of the MIMO system +According to [60], [77], [78], the atmospheric absorption for +each frequency is shown in Table 1. We assume the target of +the secret key rate is 10−5 𝑏𝑖𝑡/𝑢𝑠𝑒 [68]. Table 1 also shows the +distance of 32×32 MIMO system at maximum temperature for +each frequency. While f=700GHz and f=800GHz could reach +Frequency +Atmospheric +absorption 𝛿 +Maximum +temperature Tmax (K) +Distance of 32×32 +MIMO system at Tmax (m) +100GHz +0.4dB/km +4 +700 +200GHz +3dB/km +8 +320 +300GHz +4dB/km +13 +75 +400GHz +20dB/km +17 +86 +500GHz +50dB/km +21 +68 +600GHz +150dB/km +26 +26 +700GHz +70dB/km +30 +38 +800GHz +100dB/km +35 +36 +900GHz +100dB/km +39 +25 +1THz +100dB/km +43 +21 + +Fig. 2. The curves show ζ as a function of temperature for +different frequencies. To achieve secure transmission, ζ should +keep above line 𝛼 (locate in the secure range). +Fig. 3. (a) The transmission distance of a 32×32 MIMO +system for f=100GHz to 500GHz at T=4K. (b) The +transmission distance of a 32×32 MIMO system for +f=600GHz to 1THz at T=4K. Here, parameters are Ga =30, +W=1, Va=1000. + +Temperature bound +0.8 +secure +0.7 +100GHz +200GHz +0.6 +300GHz +400GHz +0.5 +500GHz +600GHz +0.4 +700GHz +800GHz +S0.3 +900GHz +1THz +0.2 +0 +0.1 +0 +-0.1 +-0.2 +0 +5 +10 +15 +20 +25 +30 +35 +40 +45 +50 +T(K)32x32MIMOatT=4K +100 +100GHz +Secret Key Rate (bits/use) +(a) +200GHz +10-1 +300GHz +400GHz +500GHz +10-2 +10-3 +10-4 +10-5 +0 +100 +200 +300 +400 +500 +600 +700 +Distance (m) +32x32MIMOatT=4K +100 +600GHz +Secret Key Rate (bits/use) +(b) +700GHz +10-1 +800GHz +900GHz +-1THZ +102 +10-3 +10-4 +10-5 +0 +20 +40 +60 +80 +100 +120 +Distance (m)5 + +more than 35m at T>30K, f=600GHz could only get to 26m at +a lower temperature because of higher absorption at this +frequency. Figure 3 shows the secret key rate as a function of +secure transmission distance for frequencies from f=100GHz to +1THz at T=4K in a 32×32 MIMO system. The distance of +f=100GHz and f=200GHz could achieve d=700m at T=4K +which is the maximum through all frequencies. The secure +distance for f=300GHz could get to d=500m but it will drop to +under d=160m for frequencies above f=500GHz. If the number +of antennas reduces to 8×8, the maximum distance could still +reach d=200m for f=200GHz as shown in Fig. 4 (a). But for +frequencies above f=600GHz in Fig. 4 (b), the distances are all +below 50m because of the high absorption. +High MIMO configuration could enhance the maximum +secure distance as shown in Fig.5. While the maximum distance +is d=700m for a 32×32 MIMO system, the secure transmission +could achieve much more than d=8000m for a 1024×1024 +MIMO at f=100GHz at T=4K as shown in Fig. 5 (a). The same +trend could be found for f=200GHz at T=8K and f=1THz at +T=43K. For f=200GHz, the maximum distance is more than +d=3000m for 1024×1024 MIMO at T=8K. But secure distances +for f=1THz at T=43K are not as much shorter because of the +high channel loss caused by atmospheric absorption and +thermal noise. It could only get to 160m with a 1024×1024 +MIMO antenna system at T=43K. And compared with Fig. 3 +(b), the distance for f=1THz at T=43K is just one-fifth of T=4K, +with 32×32 antennas. +B. Simulation of the SISO system +Compared with a large MIMO scheme, the maximum +distance of a SISO scheme is shorter at frequency ranges +between f=100 GHz and f=1THz. We assume the target secret +key rate is 10−5 𝑏𝑖𝑡/𝑢𝑠𝑒 [68]. Figure 6 (a) shows that the +maximum distance in the SISO system is less than 12m for +f=200GHz at T=8K, which is much less than what is observed +in a MIMO system shown in Fig. 5 (b). Figure 6 (b) shows the +distance for f=100GHz-1THz in a SISO scheme at T= 4K. We +could find that the maximum distance decrease with higher +frequency at 200GHz-1THz range caused by the path loss. +Comparing Figs. 6 (a) and (b), it is obverse that lower +temperature increases the maximum distance for the same +frequency. +Comparing Fig.6 (b) with Fig. 4 we find that at the same +temperature, the MIMO scheme could achieve a longer distance +than the SISO scheme. So it is necessary to use multiple +antennas in mm-waves and THz QKD system. As frequencies +f=800GHz, f=900GHz, and f=1THz have the same atmospheric +absorption, Fig.6 (b) shows that the transmission distance +improved by the lower frequency. This may cause by the +increase of 𝑡𝑟(𝑯†𝑯) as lower frequencies have less free-space +path loss and matter more than the increase of 𝑉0 (which in turn +Fig. 4. (a) The transmission distance of an 8×8 MIMO +system for f=100GHz to 500GHz under T=4K. (b) The +transmission distance of an 8×8 MIMO system for +f=600GHz to 1THz under T=4K. Here, parameters are +Ga=30, W=1, Va=1000. + + +Fig. 5. The curves show the secret key rate as a function of transmission distance for the different numbers of antennas in MIMO +systems. (a) is the result for f=100GHz, at T=4K. (b) is the result for f=200GHz, at T=8K. and (c) is the result for f=1THz, at +T=43K. +(a) +(b) +(c) + +8x8MIMOatT=4K +100 +100GHz +(a) +200GHz +10-1 +300GHz +400GHz +500GHz +102 +104 +10-5 +0 +50 +100 +150 +200 +Distance (m) +8x8MIMOatT=4K +100 +600GHz +700GHz +10-1 +(b) +800GHz +900GHz +·1THz +10-2 +10-3 +10-4 +10-5 +0 +10 +20 +30 +40 +50 +Distance (m)f=1THzatT=43K +100 +32*32 +Secret Key Rate (bits/use) +64*64 +128*128 +256*256 +-2 +512*512 +10 +1024*1024 +-3 +10-5 +0 +50 +100 +150 +Distance (m)f=200GHzatT=8K +100 +32*32 +Secret Key Rate (bits/use) +64*64 +10-7 +128*128 +256*256 +512*512 +102 +1024*1024 +10-3 +10-4 +10-5 +0 +500 +1000 +1500 +2000 +2500 +3000 +Distance(m)f=100GHz at T=4K +100 +32*32 +10-1 +64*64 +128*128 +256*256 +512*512 +10-2 +1024*1024 +10-5 +0 +2000 +4000 +6000 +8000 +Distance (m)6 + +decreases 𝜁) at this range. As a result, to enhance the secure +distance, we could use more antennas, cool down the +temperature or choose lower frequencies. +IV. CONCLUSION +In this work, we studied the SISO, and MIMO QKD schemes +in mm-waves and THz frequency ranges, from f= 0.1 to f= 1 +THz, with the cryogenic operation of sources and detectors. We +found that a positive secret key rate can be observed at the +targeted frequency range. MIMO technology could improve the +secure transmission distance compared with the SISO scheme. +Moreover, we showed that the more antennas are in the system +the longer transmission distance could be achieved. To build a +long-way secure communication channel, more antennas, low- +temperature operation and lower frequencies are required. We +assumed the perfect quality of the beam-splitter and +communication channel in this study, however, there are still +many research efforts to be performed to accomplish the whole +scheme in practical hardware. +REFERENCES +[1] +T. Nagatsuma et al., "Terahertz wireless communications based on +photonics technologies," Optics Express, vol. 21, no. 20, pp. 23736- +23747, 2013. +[2] +D. +M. +M. +Thomas +Kürner, +Tadao +Nagatsuma, +THz +Communications: Paving the Way Towards Wireless Tbps. Springer +ISBN: 978-3-030-73738-2. +[3] +K. Delfanazari, R. A. Klemm, H. J. Joyce, D. A. Ritchie, and K. +Kadowaki, "Integrated, Portable, Tunable, and Coherent Terahertz +Sources +and +Sensitive +Detectors +Based +on +Layered +Superconductors," Proceedings of the IEEE, vol. 108, no. 5, pp. +721-734, 2020. +[4] + H. Elayan, O. Amin, R. M. Shubair, and M. S. Alouini, "Terahertz +communication: The opportunities of wireless technology beyond +5G," +in +2018 +International +Conference +on +Advanced +Communication Technologies and Networking (CommNet), 2-4 +April 2018 2018, pp. 1-5, doi: 10.1109/COMMNET.2018.8360286. +[5] +K. Kadowaki et al., "Quantum terahertz electronics (QTE) using +coherent radiation from high temperature superconducting +Bi2Sr2CaCu2O8+δ intrinsic Josephson junctions," Physica C: +Superconductivity, vol. 491, pp. 2-6, 2013. +[6] +M. J. Fitch and R. Osiander, "Terahertz waves for communications +and sensing," JOHNS HOPKINS APL TECHNICAL DIGEST, vol. +25, no. 4, pp. 348-355, 2004. +[7] +Z. T. Ma, Z. X. Geng, Z. Y. Fan, J. Liu, and H. D. Chen, "Modulators +for Terahertz Communication: The Current State of the Art," +Research, vol. 2019, 2019. +[8] +Z. Chen et al., "A survey on terahertz communications," China +Communications, vol. 16, no. 2, pp. 1-35, 2019. +[9] +Z. Chen et al., "Terahertz Wireless Communications for 2030 and +Beyond: A Cutting-Edge Frontier," IEEE Communications +Magazine, vol. 59, no. 11, pp. 66-72, 2021. +[10] +H. Sarieddeen, M. S. Alouini, and T. Y. Al-Naffouri, "An Overview +of Signal Processing Techniques for Terahertz Communications," +Proceedings of the IEEE, vol. 109, no. 10, pp. 1628-1665, 2021. +[11] +H. J. Song and T. Nagatsuma, "Present and Future of Terahertz +Communications," IEEE Transactions on Terahertz Science and +Technology, vol. 1, no. 1, pp. 256-263, 2011. +[12] +M. Tsujimoto et al., "Broadly Tunable Subterahertz Emission from +Internal Branches of the Current-Voltage Characteristics of +Superconducting Bi2Sr2CaCu2O8+δ Single Crystals," Physical +Review Letters, vol. 108, no. 10, 2012. +[13] +K. Delfanazari et al., "Terahertz Oscillating Devices Based Upon +the Intrinsic Josephson Junctions in a High Temperature +Superconductor," Journal of Infrared Millimeter and Terahertz +Waves, vol. 35, no. 1, pp. 131-146, 2014. +[14] +I. F. Akyildiz, C. Han, Z. Hu, S. Nie, and J. M. Jornet, "Terahertz +Band Communication: An Old Problem Revisited and Research +Directions for the Next Decade," IEEE Transactions on +Communications, vol. 70, no. 6, pp. 4250-4285, 2022. +[15] + K. Delfanazari et al., "Experimental and Theoretical Studies of +Mesas of Several Geometries for Terahertz Wave Radiation from +the +Intrinsic +Josephson +Junctions +in +Superconducting +Bi2Sr2CaCu2O8+δ " in 37th International Conference on Infrared, +Millimeter, +and +Terahertz +Waves +(IRMMW-THz), +Univ +Wollongong, Wollongong, AUSTRALIA, Sep 23-28 2012, in +International Conference on Infrared Millimeter and Terahertz +Waves, 2012. +[16] +R. H. Caverly, "Breakthroughs in Microwaves: Programmable +Terahertz Chip-Scale Surfaces and Systems—An Interview With +Dr. Kaushik Sengupta," IEEE Journal of Microwaves, vol. 1, no. 4, +pp. 853-863, 2021. +[17] +K. Delfanazari et al., "Tunable terahertz emission from the intrinsic +Josephson junctions in acute isosceles triangular Bi2Sr2CaCu2O8+δ +mesas," Optics Express, vol. 21, no. 2, pp. 2171-2184, 2013. +[18] +T. Kashiwagi et al., "High Temperature Superconductor Terahertz +Emitters: Fundamental Physics and Its Applications," Japanese +Journal of Applied Physics, vol. 51, no. 1, 2012. +[19] +T. Kashiwagi et al., "Efficient Fabrication of Intrinsic-Josephson- +Junction Terahertz Oscillators with Greatly Reduced Self-Heating +Effects," Physical Review Applied, vol. 4, no. 5, 2015. +[20] +T. Kashiwagi et al., "Study of Radiation Characteristics of Intrinsic +Josephson Junction Terahertz Emitters with Different Thickness of +Bi2Sr2CaCu2O8+δ Crystals," Materials, vol. 14, no. 5, doi: +10.3390/ma14051135. +[21] +K. Delfanazari et al., "Effect of Bias Electrode Position on Terahertz +Radiation +From +Pentagonal +Mesas +of +Superconducting +Bi2Sr2CaCu2O8+δ," IEEE Transactions on Terahertz Science and +Technology, vol. 5, no. 3, pp. 505-511, 2015. +[22] + Y. Xiong, T. Kashiwagi, R. A. Klemm, K. Kadowaki, and K. +Delfanazari, "Engineering the Cavity modes and Polarization in +Integrated Superconducting Coherent Terahertz Emitters," in 2020 +Fig. 6. (a) The secret key rate R as a function of transmission +distance for SISO for frequency ranges between f=100GHz +and f=500GHz at the highest operational temperature. +Atmospheric absorptions in the channel are shown in table 1. +(b) The secret key rate R as a function of transmission distance +for SISO for frequency ranges between f=100GHz and f=1THz +at T=4K. + +SISO +100 +(a) +f=100GHzT=4K +Secret Key Rate (bits/use) +10-1 +f=200GHzT=8K +f=300GHzT=13K +-·f=400GHzT=17K +f=500GHzT=21K +10-2 +10-3 +10-4 +10-5 +0 +5 +10 +15 +20 +Distance(m) +SISOatT=4K +100 +100GHz +Secret Key Rate (bits/use) +(b) +200GHz +10-1 +300GHz +400GHZ +500GHZ +102 +600GHZ +700GHz +10-3 +800GHZ +900GHz +1THz +10-4 +10-5 +0 +5 +10 +15 +20 +25 +Distance (m)7 + +45th International Conference on Infrared, Millimeter, and +Terahertz Waves (IRMMW-THz), 8-13 Nov. 2020 2020, pp. 1-2, doi: +10.1109/IRMMW-THz46771.2020.9370587. +[23] +K. Delfanazari et al., "Study of coherent and continuous terahertz +wave emission in equilateral triangular mesas of superconducting +Bi2Sr2CaCu2O8+δ intrinsic Josephson junctions," Physica C- +Superconductivity and Its Applications, vol. 491, pp. 16-19, 2013. +[24] +Y. Saiwai et al., "Liquid helium-free high-Tc superconducting +terahertz emission system and its applications," Japanese Journal of +Applied Physics, vol. 59, no. 10, p. 105004, 2020. +[25] +K. A. Fedorova et al., "Widely Tunable Terahertz-Generating +Semiconductor Disk Laser," physica status solidi (RRL) – Rapid +Research Letters, vol. 14, no. 10, p. 2000204, 2020. +[26] +R. Cattaneo, E. A. Borodianskyi, A. A. Kalenyuk, and V. M. +Krasnov, "Superconducting Terahertz Sources with 12% Power +Efficiency," Physical Review Applied, vol. 16, no. 6, 2021. +[27] +J. R. Rain et al., "Wave functions for high-symmetry, thin microstrip +antennas, and two-dimensional quantum boxes," Physical Review A, +vol. 104, no. 6, p. 062205, 2021. +[28] + Y. Xiong and K. Delfanazari, "Engineering Circular Polarization in +Chip-integrated High-Tc Superconducting THz Antennas," in 2021 +Photonics & Electromagnetics Research Symposium (PIERS), 21- +25 +Nov. +2021 +2021, +pp. +1016-1019, +doi: +10.1109/PIERS53385.2021.9694960. +[29] +Y. Xie, N. Bai, W. Hong, and X. Sun, "Study of a hexagonal lattice +defect photonic crystal waveguide slow wave structure for G-band +traveling wave tube," Journal of Electromagnetic Waves and +Applications, vol. 36, no. 6, pp. 843-855, 2022. +[30] +D. P. Cerkoney et al., "Cavity mode enhancement of terahertz +emission from equilateral triangular microstrip antennas of the high- +Tc superconductor Bi2Sr2CaCu2O8+δ," Journal of Physics: +Condensed Matter, vol. 29, no. 1, p. 015601, 2017. +[31] +R. A. Klemm et al., "Modeling the electromagnetic cavity mode +contributions to the THz emission from triangular Bi2Sr2CaCu2O8+δ +mesas," Physica C: Superconductivity, vol. 491, pp. 30-34, 2013. +[32] + S. Kalhor, M. Ghanaatshoar, and K. Delfanazari, "On-chip +Superconducting THz Metamaterial Bandpass Filter," in 2020 45th +International Conference on Infrared, Millimeter, and Terahertz +Waves (IRMMW-THz), 8-13 Nov. 2020 2020, pp. 1-2, doi: +10.1109/IRMMW-THz46771.2020.9370663. +[33] +K. Yang, S. Liu, S. Arezoomandan, A. Nahata, and B. Sensale- +Rodriguez, "Graphene-based tunable metamaterial terahertz filters," +Applied Physics Letters, vol. 105, no. 9, p. 093105, 2014. +[34] +I. J. H. McCrindle, J. Grant, T. D. Drysdale, and D. R. S. Cumming, +"Multi-Spectral Materials: Hybridisation of Optical Plasmonic +Filters and a Terahertz Metamaterial Absorber," Advanced Optical +Materials, vol. 2, no. 2, pp. 149-153, 2014. +[35] +S. Kalhor, M. Ghanaatshoar, H. J. Joyce, D. A. Ritchie, K. +Kadowaki, and K. Delfanazari, "Millimeter-Wave-to-Terahertz +Superconducting +Plasmonic +Waveguides +for +Integrated +Nanophotonics at Cryogenic Temperatures," Materials, vol. 14, no. +15, 2021. +[36] +S. Atakaramians, S. Afshar V, T. M. Monro, and D. Abbott, +"Terahertz dielectric waveguides," Advances in Optics and +Photonics, vol. 5, no. 2, pp. 169-215, 2013. +[37] + S. Kalhor, M. Ghanaatshoar, and K. Delfanazari, "Guiding of +terahertz photons in superconducting nano-circuits," in 2020 +International Conference on UK-China Emerging Technologies +(UCET), +20-21 +Aug. +2020 +2020, +pp. +1-3, +doi: +10.1109/UCET51115.2020.9205480. +[38] +G. Gallot, S. P. Jamison, R. W. McGowan, and D. Grischkowsky, +"Terahertz waveguides," J. Opt. Soc. Am. B, vol. 17, no. 5, pp. 851- +863, 2000. +[39] +K. Wang and D. M. Mittleman, "Metal wires for terahertz wave +guiding," Nature, vol. 432, no. 7015, pp. 376-379, 2004. +[40] +S. Kalhor, M. Ghanaatshoar, T. Kashiwagi, K. Kadowaki, M. J. +Kelly, and K. Delfanazari, "Thermal Tuning of High-T-c +Superconducting Bi2Sr2CaCu2O8+δ Terahertz Metamaterial," IEEE +Photonics Journal, vol. 9, no. 5, 2017. +[41] +R. Degl’Innocenti, H. Lin, and M. Navarro-Cía, "Recent progress in +terahertz metamaterial modulators," vol. 11, no. 8, pp. 1485-1514, +2022. +[42] +V. Savinov, K. Delfanazari, V. A. Fedotov, and N. I. Zheludev, +"Giant +nonlinearity +in +a +superconducting +sub-terahertz +metamaterial," Applied Physics Letters, vol. 108, no. 10, p. 101107, +2016. +[43] +A. S. Malishevskii and S. A. Uryupin, "On Cherenkov excitation of +electromagnetic waves by vortex travelling in Josephson sandwich," +Physica Scripta, vol. 97, no. 5, p. 055817, 2022. +[44] +S. Kalhor et al., "Active Terahertz Modulator and Slow Light +Metamaterial Devices with Hybrid Graphene-Superconductor +Photonic Integrated Circuits," Nanomaterials, vol. 11, no. 11, 2021. +[45] +A. Squires, X. Gao, T. van der Laan, Z. Han, and J. Du, "Adding a +Tuneable Response to a Terahertz Metasurface Using a Graphene +Thin Film," Journal of Infrared, Millimeter, and Terahertz Waves, +vol. 43, no. 9, pp. 806-818, 2022. +[46] + S. Kalhor et al., "Active Terahertz Modulator and Slow Light +Metamaterial Devices with Hybrid Graphene-superconductor +Coupled Split-ring Resonator Arrays," in 2022 Photonics & +Electromagnetics Research Symposium (PIERS), 25-29 April 2022, +pp. 967-971, doi: 10.1109/PIERS55526.2022.9792980. +[47] +S. J. Kindness et al., "A Terahertz Chiral Metamaterial Modulator," +Advanced Optical Materials, vol. 8, no. 21, p. 2000581, 2020. +[48] +C. Li et al., "Electrically terahertz switchable device based on +superconducting composite structure metamaterial," Applied +Physics Letters, vol. 121, no. 3, p. 031702, 2022. +[49] +S. J. Kindness et al., "Graphene-Integrated Metamaterial Device for +All-Electrical Polarization Control of Terahertz Quantum Cascade +Lasers," ACS Photonics, vol. 6, no. 6, pp. 1547-1555, 2019. +[50] +F. Sizov and A. Rogalski, "THz detectors," Progress in Quantum +Electronics, vol. 34, no. 5, pp. 278-347, 2010. +[51] +S. Castilla et al., "Fast and Sensitive Terahertz Detection Using an +Antenna-Integrated Graphene pn Junction," Nano Letters, vol. 19, +no. 5, pp. 2765-2773, 2019. +[52] +R. A. Lewis, "A review of terahertz detectors," Journal of Physics +D: Applied Physics, vol. 52, no. 43, p. 433001, 2019. +[53] +M. Zhang, Foshat, P., Poorgholam Khanjari, S., Imran, M. , Weides, +M. and Delfanazari, K, "Microwave Quantum Key Distribution with +Cryogenic Microwave Components for Superconducting Quantum +Computing," presented at the 2022 International Symposium on +Quantum +Computing: +Circuits +Systems +Automation +and +Applications (QC-CSAA), Knoxville, TN, USA, 18-19 July 2022. +[54] +P. Magnard et al., "Microwave Quantum Link between +Superconducting Circuits Housed in Spatially Separated Cryogenic +Systems," Physical Review Letters, vol. 125, no. 26, p. 260502, +2020. +[55] +F. K. Florian Fesquet, Michael Renger, Qiming Chen, Kedar +Honasoge, Oscar Gargiulo, Yuki Nojiri, Achim Marx, Frank Deppe, +Rudolf Gross, Kirill G. Fedorov, "Perspectives of microwave +quantum key distribution in open-air," arXiv:2203.05530. +[56] +Y. H. Yang, M. Mandehgar, and D. R. Grischkowsky, "Broadband +THz Signals Propagate Through Dense Fog," IEEE Photonics +Technology Letters, vol. 27, no. 4, pp. 383-386, 2015. +[57] +M. Karmoose, C. Fragouli, S. Diggavi, R. Misoczki, L. L. Yang, and +Z. L. Zhang, "Using mm-Waves for Secret Key Establishment," +IEEE Communications Letters, vol. 23, no. 6, pp. 1077-1080, 2019. +[58] + Z. Q. Wang, R. Malaney, and J. Green, "Inter-satellite Quantum +Key Distribution at Terahertz Frequencies," in IEEE International +Conference on Communications (IEEE ICC), Shanghai, PEOPLES +R CHINA, May 20-24 2019, in IEEE International Conference on +Communications, 2019. +[59] +Y. Q. He, Y. Y. Mao, D. Huang, Q. Liao, and Y. Guo, "Indoor +channel modeling for continuous variable quantum key distribution +in the terahertz band," Optics Express, vol. 28, no. 22, pp. 32386- +32402, 2020. +[60] +T. Schneider, A. Wiatrek, S. Preussler, M. Grigat, and R. P. Braun, +"Link Budget Analysis for Terahertz Fixed Wireless Links," IEEE +Transactions on Terahertz Science and Technology, vol. 2, no. 2, +pp. 250-256, 2012. +[61] +C. Ottaviani et al., "Terahertz Quantum Cryptography," IEEE +Journal on Selected Areas in Communications, vol. 38, no. 3, pp. +483-495, 2020. +[62] +S. Pirandola et al., "Advances in quantum cryptography," Advances +in Optics and Photonics, vol. 12, no. 4, pp. 1012-1236, 2020. +[63] +S. Pirandola, R. Laurenza, C. Ottaviani, and L. Banchi, +"Fundamental limits of repeaterless quantum communications," +Nature Communications, vol. 8, 2017. +[64] +S. Pirandola, "Composable security for continuous variable +quantum key distribution: Trust levels and practical key rates in + +8 + +wired and wireless networks," Physical Review Research, vol. 3, no. +4, p. 043014, 2021. +[65] +I. H. L. Grande, S. Etcheverry, J. Aldama, S. Ghasemi, D. Nolan, +and V. Pruneri, "Adaptable transmitter for discrete and continuous +variable quantum key distribution," Optics Express, vol. 29, no. 10, +pp. 14815-14827, 2021. +[66] +C. J. Liu, C. H. Zhu, X. Liu, M. Nie, H. Yang, and C. X. Pei, +"Multicarrier Multiplexing Continuous-Variable Quantum Key +Distribution at Terahertz Bands Under Indoor Environment and in +Inter-Satellite Links Communication," IEEE Photonics Journal, +vol. 13, no. 4, 2021. +[67] +R. H. Shi, J. J. Shi, Y. Guo, X. Q. Peng, and M. H. Lee, "Quantum +MIMO Communication Scheme Based on Quantum Teleportation +with Triplet States," International Journal of Theoretical Physics, +vol. 50, no. 8, pp. 2334-2346, 2011. +[68] +N. K. Kundu, S. P. Dash, M. R. McKay, and R. K. Mallik, "MIMO +Terahertz Quantum Key Distribution," IEEE Communications +Letters, vol. 25, no. 10, pp. 3345-3349, 2021. +[69] + R. Jantti, R. Di Candia, R. F. Duan, and K. Ruttik, "Multiantenna +Quantum Backscatter Communications," in 36th IEEE Global +Communications +Conference +(GLOBECOM), +Singapore, +SINGAPORE, Dec 04-08 2017, in IEEE Globecom Workshops, +2017. +[70] + H. Deng and A. Sayeed, "Mm-Wave MIMO Channel Modeling and +User Localization Using Sparse Beamspace Signatures," in IEEE +15th International Workshop on Signal Processing Advances in +Wireless Communications (SPAWC), Toronto, CANADA, Jun 22- +25 2014, in IEEE International Workshop on Signal Processing +Advances in Wireless Communications, 2014, pp. 130-134. +[71] + S. A. Busari, K. M. S. Huq, S. Mumtaz, and J. Rodriguez, +"Terahertz +Massive +MIMO +for +Beyond-5G +Wireless +Communication," +in +IEEE +International +Conference +on +Communications (IEEE ICC), Shanghai, PEOPLES R CHINA, May +20-24 2019, in IEEE International Conference on Communications, +2019. +[72] +B. Kraus, N. Gisin, and R. Renner, "Lower and Upper Bounds on +the Secret-Key Rate for Quantum Key Distribution Protocols Using +One-Way Classical Communication," Physical Review Letters, vol. +95, no. 8, p. 080501, 2005. +[73] +R. Renner and J. I. Cirac, "de Finetti Representation Theorem for +Infinite-Dimensional Quantum Systems and Applications to +Quantum Cryptography," Physical Review Letters, vol. 102, no. 11, +p. 110504, 2009. +[74] +F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, and +P. Grangier, "Quantum key distribution using gaussian-modulated +coherent states," Nature, vol. 421, no. 6920, pp. 238-241, 2003. +[75] +C. Weedbrook et al., "Gaussian quantum information," Reviews of +Modern Physics, vol. 84, no. 2, pp. 621-669, 2012. +[76] +C. Weedbrook, S. Pirandola, S. Lloyd, and T. C. Ralph, "Quantum +Cryptography Approaching the Classical Limit," Physical Review +Letters, vol. 105, no. 11, 2010. +[77] +J. Y. Sun, F. J. Hu, and S. Lucyszyn, "Predicting Atmospheric +Attenuation Under Pristine Conditions Between 0.1 and 100 THz," +IEEE Access, vol. 4, pp. 9377-9399, 2016. +[78] +Y. H. Yang, A. Shutler, and D. Grischkowsky, "Measurement of the +transmission of the atmosphere from 0.2 to 2 THz," Optics Express, +vol. 19, no. 9, pp. 8830-8838, 2011. + APPENDIX A +A. Computation of channel model +The channel matrix between Alice and Bob could be +modelled as Eq. (4) +𝑯 = ∑ √𝛾𝑙𝑒𝑗2𝜋𝑓𝑐𝜏𝑙𝜓𝑁𝑟(𝜙𝑟,𝐿𝑂𝑆)𝜓𝑁𝑡 +† (𝜙𝑡,𝐿𝑂𝑆) +𝐿 +𝑙=1 + +where, 𝑯 ∈ ℂ𝑁𝑟×𝑁𝑡 , L is the full number of multipath +components, 𝜏𝑙 is the propagation delay of the l-th multipath. +The path loss 𝛾𝑙 for the line-of-sight (LOS) path (L=1) is given +by Eq. (5) +𝛾𝑙=1 = 𝐺𝑡𝐺𝑟 ( 𝜆 +4𝜋𝑑) +2 +10−𝛿𝑑 +10 + +where d is the distance (km) between Alice and Bob and 𝛿 is +the atmospheric loss. 𝜙𝑟,𝐿𝑂𝑆 and 𝜙𝑡,𝐿𝑂𝑆 is the angle of arrival +seen by Bob, and the angle of departure from Alice, +respectively. 𝜓𝐾(𝜃) represents the array response vector of a +ULA which contains K number of antennas [68]: +𝜓𝐾(𝜃) = 1 +√𝐾 +[1, 𝑒𝑗2𝜋𝑑𝑎 +𝜆 𝑠𝑖𝑛𝜃, … , 𝑒𝑗2𝜋𝑑𝑎 +𝜆 (𝐾−1)𝑠𝑖𝑛𝜃] +𝑇 +(17) +Here, 𝑑𝑎 and 𝜆 denote the inter-antenna spacing and +wavelength of the carrier signal, respectively. We assume 𝑑𝑎 = +𝜆 +4 in this work. The channel model could be described by a +singular-value decomposition (SVD) scheme introduced by +Ref. [68]: +𝑯 = 𝑼𝜮𝑽† +(18) +Here, 𝑼 ∈ ℂ𝑁𝑟×𝑁𝑟 and 𝑽 ∈ ℂ𝑁𝑡×𝑁𝑡 are unitary matrices +represent K phase shifters [69], and 𝜮 is given as +𝜮 = [𝑑𝑖𝑎𝑔{√𝜂1, … , √𝜂𝑟} +𝟎𝑟×(𝑁𝑡−𝑟) +𝟎(𝑁𝑟−𝑟)×𝑟 +𝟎(𝑁𝑟−𝑟)×(𝑁𝑡−𝑟) +] +(19) +where r is the rank of 𝑯 and √𝜂1, … , √𝜂𝑟 are the r non-zero +singular values of 𝑯 generated by the transmissivity of beam- +splitters in the system [69]. +As shown in Fig.1 (b), the whole model of a MIMO system +could be described by [68, 69] +𝒂̂𝐵 = 𝑼†𝑯𝑽𝒂̂𝐴 + 𝑼†𝑼𝑺𝒂̂𝐸 +(20) +where 𝒂̂𝐵 = [𝑎̂𝐵,1, … , 𝑎̂𝐵,𝑁𝑟]𝑇 is the received mode of Bob, +𝒂̂𝐴 = [𝑎̂𝐴,1, … , 𝑎̂𝐴,𝑁𝑡]𝑇 is the transmitted mode of Alice, 𝒂̂𝐸 = +[𝑎̂𝐸,1, … , 𝑎̂𝐸,𝑁𝑡]𝑇 is the injected Gaussian mode of Eve. +𝑺 = 𝑑𝑖𝑎𝑔{√1 − 𝜂1, … , √1 − 𝜂𝑟, 𝟏(𝑀−𝑟)×1} +(21) +is a diagonal matrix with 𝑀 = min(𝑁𝑡, 𝑁𝑟). We get 𝑼†𝑼 = 𝑰𝑁𝑟 +and 𝑽†𝑽 = 𝑰𝑁𝑡 as 𝑼 and 𝑽 are unitary matrices. Considering +Eq. (18) 𝑯 = 𝑼𝜮𝑽†, diagonal matrix 𝜮 and 𝑺, Eq. (20) would +turn to 𝒂̂𝐵 = 𝑼†𝑼𝜮𝑽†𝑽𝒂̂𝐴 + 𝑼†𝑼𝑺𝒂̂𝐸 = 𝜮𝒂̂𝐴 + 𝑺𝒂̂𝐸 . So the +efficient channel between Alice and Bob can be disintegrated +into r parallel SISO channels. +Bob randomly chooses quadratures for his input and operates +homodyne measurements. Then the input-output relationship of +i-th parallel channel between Bob’s received quadrature 𝑋̂𝐵,𝑖, +and Alice’s transmitted quadrature 𝑋̂𝐴,𝑖, can be written by a +generic quantum channel as [68] +𝑋̂𝐵,𝑖 = √𝑇𝑖𝑋̂𝐴,𝑖 + √1 − 𝑇𝑖𝑋̂𝐸,𝑖, +𝑖 = 1,2, … , 𝑟 +(22) +with Ti and 𝑋̂𝐸,𝑖 as transmittance, and Eve’s excess noise +quadrature, respectively. We can write for Eve’s ancilla mode: +𝑋̂𝐸′,𝑖 = −√1 − 𝑇𝑖𝑋̂𝐴,𝑖 + √𝑇𝑖𝑋̂𝐸,𝑖, +𝑖 = 1,2, … , 𝑟 +(23) +B. Computation of the secret key rate +The secret key rate 𝑅◄ = 𝐼(𝑎: 𝑏) − 𝐼(𝐸: 𝑏) is given defined +by mutual information. Assuming Gaussian statistic for +simulating purposes, the mutual information between Alice and +Bob is +I(a: b) = 1 +2 𝑙𝑜𝑔2[1 + +𝑇𝑉𝑠 +Λ(𝑉0, 𝑊)] + +Λ(x, y) = Tx + (1 − T)y + +And Eve’s information is bounded by the Holevo information +I(E: b) which is defined as + +9 + +I(E: b) = 𝐻𝐸 − 𝐻𝐸|𝑏 +(24) +𝐻𝐸 = ℎ(𝑣1) + ℎ(𝑣2) +(25) +𝐻𝐸|𝑏 = ℎ(𝑣3) + ℎ(𝑣4) +(26) + +where 𝐻𝐸 and 𝐻𝐸|𝑏 are the von Neumann entropy of Eve’s total +and conditional state respectively [68, 75]. The von Neumann +entropy depends on symplectic eigenvalues is given by [68] +𝑣1 = Λ(W, 𝑉𝑎), 𝑣2 = W, +(27) +𝑣3, 𝑣4 = √1 +2 (Δ ± √Δ2 − 4Υ), +(28) +and +Δ = 𝑉𝑎𝑊Λ(𝑊, 𝑉𝑎) + 𝑊Λ(𝑊𝑉𝑎, 1) +Λ(𝑉𝑎, 𝑊) +(29) +Υ = 𝑉𝑎𝑊2Λ(𝑊, 𝑉𝑎)Λ(𝑊𝑉𝑎, 1) +Λ2(𝑉𝑎, 𝑊) +(30) +The function h(x) is defined as +h(x) = 𝑥 + 1 +2 +𝑙𝑜𝑔2 (𝑥 + 1 +2 +) − 𝑥 − 1 +2 +𝑙𝑜𝑔2 (𝑥 − 1 +2 +) +(31) + + diff --git a/R9E3T4oBgHgl3EQfywu5/content/tmp_files/load_file.txt b/R9E3T4oBgHgl3EQfywu5/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..f2c9f10990d1589afba4dcb5e48ba52ee962bdc7 --- /dev/null +++ b/R9E3T4oBgHgl3EQfywu5/content/tmp_files/load_file.txt @@ -0,0 +1,965 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf,len=964 +page_content='1 Millimetre-waves to Terahertz SISO and MIMO Continuous Variable Quantum Key Distribution Mingqi Zhang1, Stefano Pirandola2, and Kaveh Delfanazari1,* 1 Electronics and Nanoscale Engineering Division, James Watt School of Engineering, University of Glasgow, Glasgow G12 8QQ, UK 2 Department of Computer Science, University of York, York YO10 5GH, UK Corresponding author: kaveh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='delfanazari@glasgow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='uk Dated:25122022 Abstract—With the exponentially increased demands for large bandwidth, it is important to think about the best network platform as well as the security and privacy of the information in communication networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Millimetre (mm)-waves and terahertz (THz) with high carrier frequency are proposed as the enabling technologies to overcome Shannon’s channel capacity limit of existing communication systems by providing ultrawide bandwidth signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Mm-waves and THz are also able to build wireless links compatible with optical communication systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' However, most solid-state components that can operate reasonably efficiently at these frequency ranges (100GHz-10THz), especially sources and detectors, require cryogenic cooling, as is a requirement for most quantum systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Here, we show that secure mm-waves and THz QKD can be achieved when the sources and detectors operate at cryogenic temperatures down to T= 4K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' We compare single- input single-output (SISO) and multiple-input multiple-output (MIMO) Continuous Variable THz Quantum Key Distribution (CVQKD) schemes and find the positive secret key rate in the frequency ranges between f=100 GHz and 1 THz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Moreover, we find that the maximum transmission distance could be extended, the secret key rate could be improved in lower temperatures, and achieve a maximum secrete communication distance of more than 5Km at f=100GHz and T=4K by using 1024×1024 antennas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Our results may contribute to the efforts to develop next-generation secure wireless communication systems and quantum internet for applications from inter- satellite and deep space, to indoor and short-distance communications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Index Terms— Millimetre (mm)-waves, terahertz (THz) waves, 6G communication, quantum key distribution (QKD), quantum communication, cryogenic system, MIMO, SISO, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' INTRODUCTION With the extension of wireless communication and the fast development of information security, higher carrier frequencies and more spectral resources are required [1, 2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Millimetre (mm)- and terahertz (THz)- waves [3-6] offer ultrawide bandwidth and high-speed data rate communication and are considered to build next-generation (6G) communication systems [7-11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Mm-waves and THz bands lie between the mature microwave and optical bands as less explored area [12- 16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' A gap in the electromagnetic spectrum exists at these C frequency ranges due to the inefficient and unpractical of the devices and circuit [1-19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' However, the recent development of electronic, photonic and plasmonic-based mm-waves and THz technologies help close this gap with the demonstration of power-efficient sources [20-26], antennas [27-31], filters [32- 34], waveguides [29, 35-39], modulators [40-49], and detectors [3, 49-52].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Demands for 6G are including, but are not limited to, Terabit per second (Tb/s), mm-precision sensing and positioning, seamless connectivity, and ultrafast wireless communications [7-11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Moreover, practical implementation of quantum processors and quantum computers operating at low temperatures (cryogenics) [53-55], requires massive open air and free space data transfer from and to high-performance classical processors, computers, and communication systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Therefore, to realise a robust building block for practical quantum information processing attention should be on both security and low-temperature operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Compared with the free-space optical link, the THz link is more stable under harsh environments such as fog conditions [56].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' The limit of mm- waves [57] and THz links [58, 59] in long distances is mainly caused by the absorption of the air [60].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' So it is important to find the window with low atmospheric absorption through this band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' High-level security is also an important aspect of realising mm-waves and THz communications which is quite challenging to maintain with classical cryptography schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Quantum key distribution (QKD) can help to achieve the goal of high-level unconditional security with the power of the quantum physics [61-64].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' QKD could be divided into discrete variables (DVQKD based on single photon sources and detectors) and continuous variables (CVQKD based on standard communication systems) [62-75].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' CVQKD uses coherent homodyne detection instead of single photon detection [65] and could be integrated with next-generation communication systems [66].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Single-input single-output (SISO) is a kind of classical communication system where the transmitter and receiver don’t have several antennas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' To meet the explosion of data transmission, multiple-input multiple-output (MIMO) technology has been widely used in wireless communication nowadays.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' MIMO system with multiple antennas at both the transmitter and receiver side brings benefits on data throughout and communication range with limited bandwidth and transmit power [67].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' THz QKD with SISO and MIMO systems was introduced in Refs [61] and [68], with the main focus on mid- 2 and far-infrared frequency ranges (10THz-40THz) at room temperature (T= 296 K).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Motivated by the works of [61] and [68], this work focuses on SISO and MIMO QKD at the temperature of T< 50 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' We investigate CVQKD at frequency ranges of mm-waves and THz, from f=100 GHz to 1 THz, with antennas and detectors both operating in the cryogenic environment (T< 50 K).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Moreover, we compare the performance of both the SISO and MIMO CVQKD systems at this frequency range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' SYSTEM MODEL For the proposed mm-waves and THz quantum communication scheme, the cryogenic antennas generate electromagnetic (EM) fields that oscillate at an angular frequency ꞷ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' This EM field is quantized and the system gets a Hamiltonian 𝐻 = ℎ𝜔(𝑎̂†𝑎̂ + 1 2) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' The H is similar to the Hamiltonian of a quantum harmonic oscillator with h as Planck’s constant, 𝑎̂ as the annihilation operator, and 𝑎̂† as the creation operator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Moreover, the quadrature field operators q̂ = 𝑎̂+𝑎̂† √2 and p̂ = i(𝑎̂+𝑎̂†) √2 are dimensionless canonical observables of the system (similar to the position and momentum of the quantum harmonic oscillator) [69].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Finally, coherent states of the system are the eigenstates of the annihilation operator 𝑎̂, provided by 𝑎̂|𝛼⟩ = α|𝛼⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Here, α = q + ip ∈ C indicates the coherent state amplitude [68], taken from a two-dimensional Gaussian distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Two independent continuous variables q and p are used to create a secret key between Alice and Bob [61].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Notation: Boldface and italic capital letters such as A denote matrices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 𝑨† is the conjugate transpose of matrix A while 𝑨𝑇 is the transpose.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 𝟎𝑀×𝑁 ∈ ℂ𝑀×𝑁 is a zero complex matrix and 𝟏𝑀×𝑁 ∈ ℂ𝑀×𝑁 is a complex matrix of ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 𝑰𝑀 represents a 𝑀 × 𝑀 identity matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' A 𝑀 × 𝑀 diagonal matrix described by 𝑑𝑖𝑎𝑔(𝒂) with 𝒂 ∈ ℂ𝑀 shows 𝒂 on its diagonal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' And 𝒩(𝜇, 𝜮) is a real multivariate Gaussian distribution in which the vector is 𝜇 and the covariance matrix (CM) is 𝜮.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Channel model We consider a one-way communication channel to build a secret key between Alice and Bob as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='1 (a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=" A MIMO mm-waves and THz communication channel between Alice and Bob include a transmitter with 𝑁𝑡 antennas at Alice's side and a receiver with 𝑁𝑟 antennas at Bob's side." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' We assume the antennas at both sides are distributed in a one-dimensional uniform linear array (ULA) with each antenna element’s gain 𝐺𝑎.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' So the antenna gains of Alice and Bob are 𝐺𝑡 = 𝑁𝑡𝐺𝑎 and 𝐺𝑟 = 𝑁𝑟𝐺𝑎 [68].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' The Gaussian modulation of the thermal state is a widely used encoding protocol for several frequencies [61].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Alice begins with a vacuum state |0⟩ and generates 𝑁𝑡 coherent states |𝑎𝑖⟩ with amplitudes 𝑎𝑖 = 𝑄𝐴,𝑖 + 𝑗𝑃𝐴,𝑖, 𝑖 = 1,2, … , 𝑁𝑡 from the 𝑁𝑡 antennas with quadratures being chosen from two independent random vectors 𝑸, 𝑷~𝒩(𝟎𝑁𝑡×1, 𝑉𝑠𝑰𝑁𝑡) where 𝑉𝑠 is the variance of the initial signal encoding [68].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Two quadratures 𝑄̂𝐴,𝑖 and 𝑃̂𝐴,𝑖 of a quantum THz source (thermal) state are randomly sent by the i-th antenna element of Alice and described by 𝑋̂𝐴,𝑖 ∈ {𝑄̂𝐴,𝑖, 𝑃̂𝐴,𝑖}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' So the i-th mode of Alice can be considered as 𝑋̂𝐴,𝑖 = 𝑎𝑖 + 0̂ , where 0̂ is the thermal mode (quadrature operator) due to the background thermal noise at mm-waves and THz and XAi denotes the classical modulated variable [61, 76].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' The total variance of Alice’s mode is 𝑉𝑎 = 𝑉𝑠 + 𝑉0 (1) where 𝑉0 is the variance of thermal state (contains variance of vacuum mode and variance of preparation noise) [61].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 𝑉0 is defined as Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' (a) The system model of the proposed mm-waves and THz QKD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Alice prepares thermal states at the source which denotes a generator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' The transmitter and receiver are antennas distributed in a one-dimensional uniform linear array (ULA).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Alice, Bob, and Eve do their job at cryogenic ambient (low temperature).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' The channel loss through the open-air environment contains atmospheric absorption and free-space loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Eve’s output modes are stored in a quantum memory (QM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Bob uses a homodyne detector to measure quadrature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' (b) The schematic of the phase shifters model described for a 2×2 MIMO system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' The channel is modelled by 4 beam splitters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Alice generates 2 coherent states 𝑎̂𝐴,1 and 𝑎̂𝐴,2 based on random vectors and send them out from her 2 antennas as thermal states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' These two states are mixed by the first beam-splitter 𝑽†.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Then Eve operates collective Gaussian attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' She prepares two two-mode squeezed vacuum states and uses beam-splitter B1 and B2 to combine the input and her states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' The output and one of the original modes are saved in quantum memory (QM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Before Bob detects the input, the signals are mixed by beam-splitter 𝑼.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' At last, Bob uses his two antennas to receive the modes 𝑎̂𝐵,1 and 𝑎̂𝐵,2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' (a) (b) Eve Eve BI QM ae,1- OM Alice Bob agr, Cryogenic Homodyne aA,1 ag,1 agi,2 U Cryogenic Open air Cryogenic Alice B2 Bob background loss source transmitter attacker receiver detector ab,2 photons3 𝑉0 = 1 + 2𝑛̅ (2) Here, 1 is the vacuum shot noise unit (SNU) and 𝑛̅ = [exp ( ℎ𝑓𝑐 𝑘𝐵𝑇) − 1] −1 (3) is the mean thermal photon number, ℎ is Planck’s constant, 𝑘𝐵 denotes Boltzmann’s constant, T is the environment temperature, and 𝑓𝑐 is the carrier frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Now, let’s consider Alice sends her states to Bob (receiver) over an insecure quantum channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Bob uses a noisy homodyne detection technique, which is based on mm-waves and THz shot-noise limited quantum detector that randomly switches between quadrature 𝑄̂ and 𝑃̂, to measure the incoming thermal states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' The channel matrix between Alice and Bob could be modelled as [68, 70, 71] 𝑯 = ∑ √𝛾𝑙𝑒𝑗2𝜋𝑓𝑐𝜏𝑙𝜓𝑁𝑟(𝜙𝑟,𝐿𝑂𝑆)𝜓𝑁𝑡 † (𝜙𝑡,𝐿𝑂𝑆) 𝐿 𝑙=1 (4) where, 𝑯 ∈ ℂ𝑁𝑟×𝑁𝑡 , L is the full number of multipath components, 𝜏𝑙 is the propagation delay of the l-th multipath.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' We only consider the line-of-sight (LOS) path with L=1 in this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' So the path loss 𝛾𝑙 is given by [68] 𝛾𝑙=1 = 𝐺𝑡𝐺𝑟 ( 𝜆 4𝜋𝑑) 2 10−𝛿𝑑 10 (5) where d is the distance (km) between Alice and Bob and 𝛿 is the atmospheric loss and is defined as dB/km [61, 70].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' It contains both the free space path and the atmospheric absorption losses of mm-waves and THz waves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 𝜙𝑟,𝐿𝑂𝑆 and 𝜙𝑡,𝐿𝑂𝑆 is the angle of arrival seen by Bob, and the angle of departure from Alice, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 𝜓𝐾(𝜃) represents the array response vector of a ULA which contains K number of antennas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' The derivation details of the channel model are described by a singular-value decomposition (SVD) scheme introduced by Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [68] are presented in Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Although the coherent attack is the general attack, the works reported in Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [72, 73] proved that once the system is secure against collective attacks, it is also secure against general attacks with the long secret key.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' In CVQKD, the most realistic and studied collective attack against Gaussian protocols is the entangling cloner attack [61].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' So, we assume the channel are totally under Eve’s control and she uses entangling cloners to steal information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='1 (b) shows a 2 × 2 MIMO system built by 4 beam-splitters as an example [69].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' After the two transmitted modes from Alice are combined by beam-splitter 𝑽†, Eve will pick up two produced output modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Eve should prepare two pairs of entangled Einstein-Podolsky-Rosen {𝑒̂1, 𝐸̂1} and {𝑒̂2, 𝐸̂2} (known also as two-mode squeezed vacuum states) in advance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Once received the input, Eve uses 𝑩1 and 𝑩2 to combine them with 𝐸̂1 and 𝐸̂2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' The relationship of input and output of 𝑩𝑖 can be written as [68, 69] [𝑎̂𝑜𝑢𝑡,1 𝑎̂𝑜𝑢𝑡,2] = [ √𝜂𝑖 √1 − 𝜂𝑖 −√1 − 𝜂𝑖 √𝜂𝑖 ] [𝑎̂𝑖𝑛,1 𝑎̂𝑖𝑛,2] (6) Here, 𝜂𝑖 is the round trip transmissivity of two port beam- splitter 𝑩𝑖 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Then Eve will save one of the outputs from every beam-splitters (𝐸̂′1, 𝐸̂′2) and the original modes (𝑒̂1, 𝑒̂2) in her quantum memory (QM) and measure the ancilla modes to exploit information when Alice and Bob completed their classical communication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' The other two output modes will be combined by the beam-splitter 𝑼 and sent to Bob.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' We assume Alice applies 𝑽 as the base of beamforming at her end, and Bob employs 𝑼† as the base of decoding at his side.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' The whole model could be described by [68, 69] 𝒂̂𝐵 = 𝑼†𝑯𝑽𝒂̂𝐴 + 𝑼†𝑼𝑺𝒂̂𝐸 (7) where 𝒂̂𝐵 = [𝑎̂𝐵,1, … , 𝑎̂𝐵,𝑁𝑟]𝑇 is the received mode of Bob, 𝒂̂𝐴 = [𝑎̂𝐴,1, … , 𝑎̂𝐴,𝑁𝑡]𝑇 is the transmitted mode of Alice, 𝒂̂𝐸 = [𝑎̂𝐸,1, … , 𝑎̂𝐸,𝑁𝑡]𝑇 is the injected Gaussian mode of Eve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 𝑺 = 𝑑𝑖𝑎𝑔{√1 − 𝜂1, … , √1 − 𝜂𝑟, 𝟏(𝑀−𝑟)×1} (8) is a diagonal matrix with 𝑀 = min(𝑁𝑡, 𝑁𝑟).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' The calculation details could be found in Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' The efficient channel between Alice and Bob can be disintegrated into r parallel SISO channels by utilizing the SVD of H (r is the rank of 𝑯).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=" In this case, the relation between channels' input and output can be written as [68] 𝒂̂𝐵,𝑖 = √𝑇𝑖𝒂̂𝐴,𝑖 + √1 − 𝑇𝑖𝒂̂𝐸,𝑖, 𝑖 = 1,2, … , 𝑟 (9) Here, 𝑇𝑖 is the i-th non-zero eigenvalue of 𝑯†𝑯 and could also be considered as the i-th transmissivity of the channel." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Homodyne experiments on one of the randomly selected quadratures will be performed by Bob for every r-received mode and get the result detailed in Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' We set W to the variance of the thermal noise introduced by Eve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' So, Bob will receive the i-th mode with the shot-noise level 𝑉 (𝑋̂𝐵,𝑖) = 𝑇𝑖𝑉0 + (1 − 𝑇𝑖)𝑊 [61].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 𝑋̂𝐵,𝑖 is Bob’s received quadrature described by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' (22) in Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' If Eve wants to completely hide in the background noise, she can use 𝑊 = 𝑉0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Then Bob will receive the shot-noise level 𝑉 (𝑋̂𝐵,𝑖) = 𝑉0 which is the same as what Alice sent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Although the value of 𝑉0 could be enlarged by frequencies below 1THz, we could gain 𝑉0 ≈ 1 𝑆𝑁𝑈 by cooling down the system to low temperatures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Secret key rate In this mm-waves and THz CVQKD scheme, Alice and Bob replicate the previous quantum communication protocol several times to generate a string.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Then they correct errors in their string by using reconciliation protocol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Direct reconciliation (DR) is the scheme in which Bob uses Alice’s encoding string to prepare the key while reverse reconciliation (RR) is when Alice prepares the key based on Bob’s decoding result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Alice and Bob use a reconciliation protocol to achieve privacy amplification to reduce the knowledge stole by Eve [68].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' In this work, we use an asymptotic secret key rate to study the performance of RR protocol in mm-waves and THz QKD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' In RR it is possible to achieve a positive secret key rate when the channel transmissivity is almost 0 while in DR it required a channel transmissivity larger than 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='5 [76], and is impractical in mm- waves and THz because of the high losses (both atmospheric absorption and path).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' According to [68], the secret key rate of the MIMO system could be divided into r SISO channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' So we first analyse the secret key rate of a SISO channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=" In the RR scheme, Alice and Bob use the decoding outcomes from Bob's side to generate their secret key [74]." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Alice and Bob could estimate the mutual information they shared, described as 𝐼(𝑎: 𝑏) , and the accessible information of Eve, described as 𝐼(𝐸: 𝑏) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' The asymptotic secret key rate 𝑅◄ could be described by the surplus information shared by Alice and Bob and is given by [62] 𝑅◄ = 𝐼(𝑎: 𝑏) − 𝐼(𝐸: 𝑏) (10) 4 The mutual information between Alice and Bob is I(a: b) = 1 2 𝑙𝑜𝑔2[1 + 𝑇𝑉𝑠 Λ(𝑉0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 𝑊)] (11) Λ(x,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' y) = Tx + (1 − T)y (12) while 𝑉𝑠 ≫ 𝑉0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 𝑊,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' and Eve’s information is bounded by the Holevo information I(E: b) which is defined as I(E: b) = 𝐻𝐸 − 𝐻𝐸|𝑏 (13) where 𝐻𝐸 and 𝐻𝐸|𝑏 are the von Neumann entropy of Eve’s total and conditional state given by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' (25) and Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' (26) in Appendix A respectively [68, 75].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' The total secret key rate is finally given by the sum of r SISO links’ secret key rate [68] assuming 𝑇𝑖 → 0 𝑅𝑀𝐼𝑀𝑂 ◄ = ∑ 𝑅𝑖 ◄ 𝑟 𝑖=1 ≈ 𝜁𝑡𝑟(𝑯†𝑯) − 𝑟ℎ(𝑊) (14) where 𝜁 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='72 [𝑉𝑠 𝑊 − ln (𝑉𝑎 + 1 𝑉𝑎 − 1) (𝑉𝑎 2 − 𝑊2 2𝑊 − 𝑉𝑎)] (15) and 𝑡𝑟(𝑯†𝑯) = ∑ 𝑇𝑖 𝑟 𝑖=1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' ℎ(𝑊) is a function given by h(x) = 𝑥 + 1 2 𝑙𝑜𝑔2 (𝑥 + 1 2 ) − 𝑥 − 1 2 𝑙𝑜𝑔2 (𝑥 − 1 2 ) (16) C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' System conditions To achieve a positive secret key rate, 𝜁𝑡𝑟(𝑯†𝑯) > 𝑟ℎ(𝑊) is required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Verified from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' (1)-(4), only 𝜁𝑡𝑟(𝑯†𝑯) in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' (14) depends on frequency and 𝜁 also depends on temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' With a given frequency, lower temperature could decrease 𝑉0 and increase 𝜁 in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' (15).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' This also happens with a given temperature and increasing frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' But higher frequency normally brings higher path loss which may decrease 𝑡𝑟(𝑯†𝑯).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Since 𝑡𝑟(𝑯†𝑯)>0, the limit of 𝜁 > 𝛼 = 𝑟ℎ(𝑊) 𝑡𝑟(𝑯†𝑯) is equal to 𝜁 > 𝛼 = 0 while W=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' This condition helps us find the balance between 𝜁 and 𝑡𝑟(𝑯†𝑯) and get a positive secret key rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Figure 2 shows ζ as a function of temperature for different frequencies in a MIMO THz QKD system [68].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' According to the simulation results, we achieved secure transmission for frequencies between f=100GHz and 1THz, at temperatures T< 43K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' The detail of the maximum operating temperature for each frequency is shown in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' SIMULATION RESULT We use the secret key rate (R) to define whether the system is safe or not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' A positive secret key rate reflects a safe transmission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' As R of the MIMO system is the sum of the SISO system, we also compared the different performances of the MIMO and SISO systems at the same conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' TABLE I A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Simulation of the MIMO system According to [60], [77], [78], the atmospheric absorption for each frequency is shown in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' We assume the target of the secret key rate is 10−5 𝑏𝑖𝑡/𝑢𝑠𝑒 [68].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Table 1 also shows the distance of 32×32 MIMO system at maximum temperature for each frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' While f=700GHz and f=800GHz could reach Frequency Atmospheric absorption 𝛿 Maximum temperature Tmax (K) Distance of 32×32 MIMO system at Tmax (m) 100GHz 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='4dB/km 4 700 200GHz 3dB/km 8 320 300GHz 4dB/km 13 75 400GHz 20dB/km 17 86 500GHz 50dB/km 21 68 600GHz 150dB/km 26 26 700GHz 70dB/km 30 38 800GHz 100dB/km 35 36 900GHz 100dB/km 39 25 1THz 100dB/km 43 21 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' The curves show ζ as a function of temperature for different frequencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' To achieve secure transmission, ζ should keep above line 𝛼 (locate in the secure range).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' (a) The transmission distance of a 32×32 MIMO system for f=100GHz to 500GHz at T=4K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' (b) The transmission distance of a 32×32 MIMO system for f=600GHz to 1THz at T=4K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Here, parameters are Ga =30, W=1, Va=1000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Temperature bound 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='8 secure 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='7 100GHz 200GHz 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='6 300GHz 400GHz 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='5 500GHz 600GHz 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='4 700GHz 800GHz S0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='3 900GHz 1THz 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='2 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='1 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='2 0 5 10 15 20 25 30 35 40 45 50 T(K)32x32MIMOatT=4K 100 100GHz Secret Key Rate (bits/use) (a) 200GHz 10-1 300GHz 400GHz 500GHz 10-2 10-3 10-4 10-5 0 100 200 300 400 500 600 700 Distance (m) 32x32MIMOatT=4K 100 600GHz Secret Key Rate (bits/use) (b) 700GHz 10-1 800GHz 900GHz 1THZ 102 10-3 10-4 10-5 0 20 40 60 80 100 120 Distance (m)5 more than 35m at T>30K,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' f=600GHz could only get to 26m at a lower temperature because of higher absorption at this frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Figure 3 shows the secret key rate as a function of secure transmission distance for frequencies from f=100GHz to 1THz at T=4K in a 32×32 MIMO system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' The distance of f=100GHz and f=200GHz could achieve d=700m at T=4K which is the maximum through all frequencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' The secure distance for f=300GHz could get to d=500m but it will drop to under d=160m for frequencies above f=500GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' If the number of antennas reduces to 8×8, the maximum distance could still reach d=200m for f=200GHz as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 4 (a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' But for frequencies above f=600GHz in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 4 (b), the distances are all below 50m because of the high absorption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' High MIMO configuration could enhance the maximum secure distance as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' While the maximum distance is d=700m for a 32×32 MIMO system, the secure transmission could achieve much more than d=8000m for a 1024×1024 MIMO at f=100GHz at T=4K as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 5 (a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' The same trend could be found for f=200GHz at T=8K and f=1THz at T=43K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' For f=200GHz, the maximum distance is more than d=3000m for 1024×1024 MIMO at T=8K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' But secure distances for f=1THz at T=43K are not as much shorter because of the high channel loss caused by atmospheric absorption and thermal noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' It could only get to 160m with a 1024×1024 MIMO antenna system at T=43K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' And compared with Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 3 (b), the distance for f=1THz at T=43K is just one-fifth of T=4K, with 32×32 antennas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Simulation of the SISO system Compared with a large MIMO scheme, the maximum distance of a SISO scheme is shorter at frequency ranges between f=100 GHz and f=1THz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' We assume the target secret key rate is 10−5 𝑏𝑖𝑡/𝑢𝑠𝑒 [68].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Figure 6 (a) shows that the maximum distance in the SISO system is less than 12m for f=200GHz at T=8K, which is much less than what is observed in a MIMO system shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 5 (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Figure 6 (b) shows the distance for f=100GHz-1THz in a SISO scheme at T= 4K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' We could find that the maximum distance decrease with higher frequency at 200GHz-1THz range caused by the path loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Comparing Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 6 (a) and (b), it is obverse that lower temperature increases the maximum distance for the same frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Comparing Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='6 (b) with Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 4 we find that at the same temperature, the MIMO scheme could achieve a longer distance than the SISO scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' So it is necessary to use multiple antennas in mm-waves and THz QKD system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' As frequencies f=800GHz, f=900GHz, and f=1THz have the same atmospheric absorption, Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='6 (b) shows that the transmission distance improved by the lower frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' This may cause by the increase of 𝑡𝑟(𝑯†𝑯) as lower frequencies have less free-space path loss and matter more than the increase of 𝑉0 (which in turn Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' (a) The transmission distance of an 8×8 MIMO system for f=100GHz to 500GHz under T=4K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' (b) The transmission distance of an 8×8 MIMO system for f=600GHz to 1THz under T=4K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Here, parameters are Ga=30, W=1, Va=1000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' The curves show the secret key rate as a function of transmission distance for the different numbers of antennas in MIMO systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' (a) is the result for f=100GHz, at T=4K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' (b) is the result for f=200GHz, at T=8K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' and (c) is the result for f=1THz, at T=43K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='(a) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='(b) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='(c) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='8x8MIMOatT=4K ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='100 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='100GHz ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='(a) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='200GHz ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='10-1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='300GHz ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='400GHz ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='500GHz ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='102 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='104 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='10-5 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='50 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='100 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='150 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='200 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='Distance (m) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='8x8MIMOatT=4K ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='100 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='600GHz ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='700GHz ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='10-1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='(b) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='800GHz ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='900GHz ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='1THz ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='10-2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='10-3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='10-4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='10-5 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='20 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='30 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='40 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='50 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='Distance (m)f=1THzatT=43K ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='100 ' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='150 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='Distance (m)f=200GHzatT=8K ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='100 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='32*32 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='Secret Key Rate (bits/use) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='64*64 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='10-7 ' 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='4000 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='6000 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='8000 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='Distance (m)6 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='decreases 𝜁) at this range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' As a result, to enhance the secure distance, we could use more antennas, cool down the temperature or choose lower frequencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' CONCLUSION In this work, we studied the SISO, and MIMO QKD schemes in mm-waves and THz frequency ranges, from f= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='1 to f= 1 THz, with the cryogenic operation of sources and detectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' We found that a positive secret key rate can be observed at the targeted frequency range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' MIMO technology could improve the secure transmission distance compared with the SISO scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Moreover, we showed that the more antennas are in the system the longer transmission distance could be achieved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' To build a long-way secure communication channel, more antennas, low- temperature operation and lower frequencies are required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' We assumed the perfect quality of the beam-splitter and communication channel in this study, however, there are still many research efforts to be performed to accomplish the whole scheme in practical hardware.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' REFERENCES [1] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Nagatsuma et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=', "Terahertz wireless communications based on photonics technologies," Optics Express, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 21, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 20, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 23736- 23747, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [2] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Thomas Kürner, Tadao Nagatsuma, THz Communications: Paving the Way Towards Wireless Tbps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Springer ISBN: 978-3-030-73738-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [3] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Delfanazari, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Klemm, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Joyce, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Ritchie, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Kadowaki, "Integrated, Portable, Tunable, and Coherent Terahertz Sources and Sensitive Detectors Based on Layered Superconductors," Proceedings of the IEEE, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 108, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 5, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 721-734, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [4] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Elayan, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Amin, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Shubair, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Alouini, "Terahertz communication: The opportunities of wireless technology beyond 5G," in 2018 International Conference on Advanced Communication Technologies and Networking (CommNet), 2-4 April 2018 2018, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 1-5, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='1109/COMMNET.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='8360286.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [5] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Kadowaki et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=', "Quantum terahertz electronics (QTE) using coherent radiation from high temperature superconducting Bi2Sr2CaCu2O8+δ intrinsic Josephson junctions," Physica C: Superconductivity, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 491, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 2-6, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [6] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Fitch and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Osiander, "Terahertz waves for communications and sensing," JOHNS HOPKINS APL TECHNICAL DIGEST, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 25, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 4, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 348-355, 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [7] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Ma, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Geng, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Fan, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Liu, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Chen, "Modulators for Terahertz Communication: The Current State of the Art," Research, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 2019, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [8] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=', "A survey on terahertz communications," China Communications, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 16, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 1-35, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [9] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=', "Terahertz Wireless Communications for 2030 and Beyond: A Cutting-Edge Frontier," IEEE Communications Magazine, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 59, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 11, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 66-72, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [10] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Sarieddeen, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Alouini, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Al-Naffouri, "An Overview of Signal Processing Techniques for Terahertz Communications," Proceedings of the IEEE, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 109, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 10, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 1628-1665, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [11] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Song and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Nagatsuma, "Present and Future of Terahertz Communications," IEEE Transactions on Terahertz Science and Technology, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 1, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 256-263, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [12] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Tsujimoto et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=', "Broadly Tunable Subterahertz Emission from Internal Branches of the Current-Voltage Characteristics of Superconducting Bi2Sr2CaCu2O8+δ Single Crystals," Physical Review Letters, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 108, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 10, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [13] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Delfanazari et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=', "Terahertz Oscillating Devices Based Upon the Intrinsic Josephson Junctions in a High Temperature Superconductor," Journal of Infrared Millimeter and Terahertz Waves, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 35, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 131-146, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [14] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Akyildiz, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Han, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Hu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Nie, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Jornet, "Terahertz Band Communication: An Old Problem Revisited and Research Directions for the Next Decade," IEEE Transactions on Communications, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 70, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 6, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 4250-4285, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [15] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Delfanazari et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=', "Experimental and Theoretical Studies of Mesas of Several Geometries for Terahertz Wave Radiation from the Intrinsic Josephson Junctions in Superconducting Bi2Sr2CaCu2O8+δ " in 37th International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz), Univ Wollongong, Wollongong, AUSTRALIA, Sep 23-28 2012, in International Conference on Infrared Millimeter and Terahertz Waves, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [16] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Caverly, "Breakthroughs in Microwaves: Programmable Terahertz Chip-Scale Surfaces and Systems—An Interview With Dr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Kaushik Sengupta," IEEE Journal of Microwaves, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 1, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 4, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 853-863, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [17] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Delfanazari et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=', "Tunable terahertz emission from the intrinsic Josephson junctions in acute isosceles triangular Bi2Sr2CaCu2O8+δ mesas," Optics Express, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 21, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 2171-2184, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [18] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Kashiwagi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=', "High Temperature Superconductor Terahertz Emitters: Fundamental Physics and Its Applications," Japanese Journal of Applied Physics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 51, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 1, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [19] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Kashiwagi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=', "Efficient Fabrication of Intrinsic-Josephson- Junction Terahertz Oscillators with Greatly Reduced Self-Heating Effects," Physical Review Applied, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 4, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 5, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [20] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Kashiwagi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=', "Study of Radiation Characteristics of Intrinsic Josephson Junction Terahertz Emitters with Different Thickness of Bi2Sr2CaCu2O8+δ Crystals," Materials, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 14, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 5, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='3390/ma14051135.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [21] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Delfanazari et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=', "Effect of Bias Electrode Position on Terahertz Radiation From Pentagonal Mesas of Superconducting Bi2Sr2CaCu2O8+δ," IEEE Transactions on Terahertz Science and Technology, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 5, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 505-511, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [22] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Xiong, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Kashiwagi, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Klemm, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Kadowaki, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Delfanazari, "Engineering the Cavity modes and Polarization in Integrated Superconducting Coherent Terahertz Emitters," in 2020 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' (a) The secret key rate R as a function of transmission distance for SISO for frequency ranges between f=100GHz and f=500GHz at the highest operational temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Atmospheric absorptions in the channel are shown in table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' (b) The secret key rate R as a function of transmission distance for SISO for frequency ranges between f=100GHz and f=1THz at T=4K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' SISO 100 (a) f=100GHzT=4K Secret Key Rate (bits/use) 10-1 f=200GHzT=8K f=300GHzT=13K -·f=400GHzT=17K f=500GHzT=21K 10-2 10-3 10-4 10-5 0 5 10 15 20 Distance(m) SISOatT=4K 100 100GHz Secret Key Rate (bits/use) (b) 200GHz 10-1 300GHz 400GHZ 500GHZ 102 600GHZ 700GHz 10-3 800GHZ 900GHz 1THz 10-4 10-5 0 5 10 15 20 25 Distance (m)7 45th International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz), 8-13 Nov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 2020 2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 1-2, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='1109/IRMMW-THz46771.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='9370587.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [23] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Delfanazari et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=', "Study of coherent and continuous terahertz wave emission in equilateral triangular mesas of superconducting Bi2Sr2CaCu2O8+δ intrinsic Josephson junctions," Physica C- Superconductivity and Its Applications, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 491, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 16-19, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [24] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Saiwai et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=', "Liquid helium-free high-Tc superconducting terahertz emission system and its applications," Japanese Journal of Applied Physics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 59, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 10, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 105004, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [25] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Fedorova et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=', "Widely Tunable Terahertz-Generating Semiconductor Disk Laser," physica status solidi (RRL) – Rapid Research Letters, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 14, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 10, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 2000204, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [26] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Cattaneo, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Borodianskyi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Kalenyuk, and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Krasnov, "Superconducting Terahertz Sources with 12% Power Efficiency," Physical Review Applied, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 16, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 6, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [27] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Rain et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=', "Wave functions for high-symmetry, thin microstrip antennas, and two-dimensional quantum boxes," Physical Review A, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 104, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 6, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 062205, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [28] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Xiong and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Delfanazari, "Engineering Circular Polarization in Chip-integrated High-Tc Superconducting THz Antennas," in 2021 Photonics & Electromagnetics Research Symposium (PIERS), 21- 25 Nov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 2021 2021, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 1016-1019, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='1109/PIERS53385.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='9694960.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [29] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Xie, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Bai, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Hong, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Sun, "Study of a hexagonal lattice defect photonic crystal waveguide slow wave structure for G-band traveling wave tube," Journal of Electromagnetic Waves and Applications, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 36, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 6, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 843-855, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [30] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Cerkoney et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=', "Cavity mode enhancement of terahertz emission from equilateral triangular microstrip antennas of the high- Tc superconductor Bi2Sr2CaCu2O8+δ," Journal of Physics: Condensed Matter, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 29, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 1, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 015601, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [31] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Klemm et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=', "Modeling the electromagnetic cavity mode contributions to the THz emission from triangular Bi2Sr2CaCu2O8+δ mesas," Physica C: Superconductivity, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 491, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 30-34, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [32] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Kalhor, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Ghanaatshoar, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Delfanazari, "On-chip Superconducting THz Metamaterial Bandpass Filter," in 2020 45th International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz), 8-13 Nov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 2020 2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 1-2, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='1109/IRMMW-THz46771.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='9370663.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [33] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Yang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Liu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Arezoomandan, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Nahata, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Sensale- Rodriguez, "Graphene-based tunable metamaterial terahertz filters," Applied Physics Letters, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 105, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 9, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 093105, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [34] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' McCrindle, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Grant, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Drysdale, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Cumming, "Multi-Spectral Materials: Hybridisation of Optical Plasmonic Filters and a Terahertz Metamaterial Absorber," Advanced Optical Materials, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 2, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 149-153, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [35] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Kalhor, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Ghanaatshoar, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Joyce, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Ritchie, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Kadowaki, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Delfanazari, "Millimeter-Wave-to-Terahertz Superconducting Plasmonic Waveguides for Integrated Nanophotonics at Cryogenic Temperatures," Materials, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 14, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 15, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [36] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Atakaramians, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Afshar V, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Monro, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Abbott, "Terahertz dielectric waveguides," Advances in Optics and Photonics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 5, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 169-215, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [37] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Kalhor, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Ghanaatshoar, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Delfanazari, "Guiding of terahertz photons in superconducting nano-circuits," in 2020 International Conference on UK-China Emerging Technologies (UCET), 20-21 Aug.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 2020 2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 1-3, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='1109/UCET51115.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='9205480.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [38] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Gallot, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Jamison, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' McGowan, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Grischkowsky, "Terahertz waveguides," J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Am.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' B, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 17, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 5, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 851- 863, 2000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [39] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Wang and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Mittleman, "Metal wires for terahertz wave guiding," Nature, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 432, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 7015, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 376-379, 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [40] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Kalhor, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Ghanaatshoar, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Kashiwagi, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Kadowaki, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Kelly, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Delfanazari, "Thermal Tuning of High-T-c Superconducting Bi2Sr2CaCu2O8+δ Terahertz Metamaterial," IEEE Photonics Journal, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 9, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 5, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [41] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Degl’Innocenti, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Lin, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Navarro-Cía, "Recent progress in terahertz metamaterial modulators," vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 11, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 8, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 1485-1514, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [42] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Savinov, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Delfanazari, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Fedotov, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Zheludev, "Giant nonlinearity in a superconducting sub-terahertz metamaterial," Applied Physics Letters, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 108, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 10, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 101107, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [43] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Malishevskii and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Uryupin, "On Cherenkov excitation of electromagnetic waves by vortex travelling in Josephson sandwich," Physica Scripta, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 97, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 5, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 055817, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [44] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Kalhor et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=', "Active Terahertz Modulator and Slow Light Metamaterial Devices with Hybrid Graphene-Superconductor Photonic Integrated Circuits," Nanomaterials, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 11, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 11, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [45] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Squires, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Gao, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' van der Laan, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Han, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Du, "Adding a Tuneable Response to a Terahertz Metasurface Using a Graphene Thin Film," Journal of Infrared, Millimeter, and Terahertz Waves, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 43, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 9, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 806-818, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [46] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Kalhor et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=', "Active Terahertz Modulator and Slow Light Metamaterial Devices with Hybrid Graphene-superconductor Coupled Split-ring Resonator Arrays," in 2022 Photonics & Electromagnetics Research Symposium (PIERS), 25-29 April 2022, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 967-971, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='1109/PIERS55526.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='9792980.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [47] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Kindness et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=', "A Terahertz Chiral Metamaterial Modulator," Advanced Optical Materials, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 8, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 21, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 2000581, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [48] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=', "Electrically terahertz switchable device based on superconducting composite structure metamaterial," Applied Physics Letters, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 121, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 3, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 031702, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [49] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Kindness et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=', "Graphene-Integrated Metamaterial Device for All-Electrical Polarization Control of Terahertz Quantum Cascade Lasers," ACS Photonics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 6, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 6, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 1547-1555, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [50] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Sizov and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Rogalski, "THz detectors," Progress in Quantum Electronics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 34, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 5, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 278-347, 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [51] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Castilla et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=', "Fast and Sensitive Terahertz Detection Using an Antenna-Integrated Graphene pn Junction," Nano Letters, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 19, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 5, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 2765-2773, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [52] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Lewis, "A review of terahertz detectors," Journal of Physics D: Applied Physics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 52, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 43, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 433001, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [53] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Zhang, Foshat, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=', Poorgholam Khanjari, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=', Imran, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' , Weides, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' and Delfanazari, K, "Microwave Quantum Key Distribution with Cryogenic Microwave Components for Superconducting Quantum Computing," presented at the 2022 International Symposium on Quantum Computing: Circuits Systems Automation and Applications (QC-CSAA), Knoxville, TN, USA, 18-19 July 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [54] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Magnard et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=', "Microwave Quantum Link between Superconducting Circuits Housed in Spatially Separated Cryogenic Systems," Physical Review Letters, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 125, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 26, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 260502, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [55] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Florian Fesquet, Michael Renger, Qiming Chen, Kedar Honasoge, Oscar Gargiulo, Yuki Nojiri, Achim Marx, Frank Deppe, Rudolf Gross, Kirill G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Fedorov, "Perspectives of microwave quantum key distribution in open-air," arXiv:2203.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='05530.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [56] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Yang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Mandehgar, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Grischkowsky, "Broadband THz Signals Propagate Through Dense Fog," IEEE Photonics Technology Letters, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 27, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 4, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 383-386, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [57] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Karmoose, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Fragouli, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Diggavi, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Misoczki, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Yang, and Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Zhang, "Using mm-Waves for Secret Key Establishment," IEEE Communications Letters, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 23, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 6, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 1077-1080, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [58] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Wang, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Malaney, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Green, "Inter-satellite Quantum Key Distribution at Terahertz Frequencies," in IEEE International Conference on Communications (IEEE ICC), Shanghai, PEOPLES R CHINA, May 20-24 2019, in IEEE International Conference on Communications, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [59] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' He, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Mao, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Huang, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Liao, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Guo, "Indoor channel modeling for continuous variable quantum key distribution in the terahertz band," Optics Express, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 28, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 22, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 32386- 32402, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [60] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Schneider, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Wiatrek, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Preussler, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Grigat, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Braun, "Link Budget Analysis for Terahertz Fixed Wireless Links," IEEE Transactions on Terahertz Science and Technology, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 2, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 250-256, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [61] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Ottaviani et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=', "Terahertz Quantum Cryptography," IEEE Journal on Selected Areas in Communications, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 38, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 483-495, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [62] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Pirandola et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=', "Advances in quantum cryptography," Advances in Optics and Photonics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 12, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 4, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 1012-1236, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [63] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Pirandola, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Laurenza, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Ottaviani, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Banchi, "Fundamental limits of repeaterless quantum communications," Nature Communications, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 8, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [64] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Pirandola, "Composable security for continuous variable quantum key distribution: Trust levels and practical key rates in 8 wired and wireless networks," Physical Review Research, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 3, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 4, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 043014, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [65] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Grande, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Etcheverry, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Aldama, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Ghasemi, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Nolan, and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Pruneri, "Adaptable transmitter for discrete and continuous variable quantum key distribution," Optics Express, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 29, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 10, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 14815-14827, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [66] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Liu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Zhu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Liu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Nie, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Yang, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Pei, "Multicarrier Multiplexing Continuous-Variable Quantum Key Distribution at Terahertz Bands Under Indoor Environment and in Inter-Satellite Links Communication," IEEE Photonics Journal, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 13, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 4, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [67] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Shi, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Shi, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Guo, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Peng, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Lee, "Quantum MIMO Communication Scheme Based on Quantum Teleportation with Triplet States," International Journal of Theoretical Physics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 50, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 8, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 2334-2346, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [68] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Kundu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Dash, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' McKay, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Mallik, "MIMO Terahertz Quantum Key Distribution," IEEE Communications Letters, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 25, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 10, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 3345-3349, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [69] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Jantti, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Di Candia, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Duan, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Ruttik, "Multiantenna Quantum Backscatter Communications," in 36th IEEE Global Communications Conference (GLOBECOM), Singapore, SINGAPORE, Dec 04-08 2017, in IEEE Globecom Workshops, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [70] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Deng and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Sayeed, "Mm-Wave MIMO Channel Modeling and User Localization Using Sparse Beamspace Signatures," in IEEE 15th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC), Toronto, CANADA, Jun 22- 25 2014, in IEEE International Workshop on Signal Processing Advances in Wireless Communications, 2014, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 130-134.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [71] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Busari, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Huq, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Mumtaz, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Rodriguez, "Terahertz Massive MIMO for Beyond-5G Wireless Communication," in IEEE International Conference on Communications (IEEE ICC), Shanghai, PEOPLES R CHINA, May 20-24 2019, in IEEE International Conference on Communications, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [72] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Kraus, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Gisin, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Renner, "Lower and Upper Bounds on the Secret-Key Rate for Quantum Key Distribution Protocols Using One-Way Classical Communication," Physical Review Letters, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 95, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 8, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 080501, 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [73] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Renner and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Cirac, "de Finetti Representation Theorem for Infinite-Dimensional Quantum Systems and Applications to Quantum Cryptography," Physical Review Letters, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 102, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 11, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 110504, 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [74] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Grosshans, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Van Assche, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Wenger, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Brouri, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Cerf, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Grangier, "Quantum key distribution using gaussian-modulated coherent states," Nature, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 421, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 6920, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 238-241, 2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [75] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Weedbrook et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=', "Gaussian quantum information," Reviews of Modern Physics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 84, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 621-669, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [76] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Weedbrook, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Pirandola, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Lloyd, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Ralph, "Quantum Cryptography Approaching the Classical Limit," Physical Review Letters, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 105, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 11, 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [77] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Sun, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Hu, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Lucyszyn, "Predicting Atmospheric Attenuation Under Pristine Conditions Between 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='1 and 100 THz," IEEE Access, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 4, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 9377-9399, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [78] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Yang, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Shutler, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Grischkowsky, "Measurement of the transmission of the atmosphere from 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='2 to 2 THz," Optics Express, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 19, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 9, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 8830-8838, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' APPENDIX A A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Computation of channel model The channel matrix between Alice and Bob could be modelled as Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' (4) 𝑯 = ∑ √𝛾𝑙𝑒𝑗2𝜋𝑓𝑐𝜏𝑙𝜓𝑁𝑟(𝜙𝑟,𝐿𝑂𝑆)𝜓𝑁𝑡 † (𝜙𝑡,𝐿𝑂𝑆) 𝐿 𝑙=1 where, 𝑯 ∈ ℂ𝑁𝑟×𝑁𝑡 , L is the full number of multipath components, 𝜏𝑙 is the propagation delay of the l-th multipath.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' The path loss 𝛾𝑙 for the line-of-sight (LOS) path (L=1) is given by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' (5) 𝛾𝑙=1 = 𝐺𝑡𝐺𝑟 ( 𝜆 4𝜋𝑑) 2 10−𝛿𝑑 10 where d is the distance (km) between Alice and Bob and 𝛿 is the atmospheric loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 𝜙𝑟,𝐿𝑂𝑆 and 𝜙𝑡,𝐿𝑂𝑆 is the angle of arrival seen by Bob, and the angle of departure from Alice, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 𝜓𝐾(𝜃) represents the array response vector of a ULA which contains K number of antennas [68]: 𝜓𝐾(𝜃) = 1 √𝐾 [1, 𝑒𝑗2𝜋𝑑𝑎 𝜆 𝑠𝑖𝑛𝜃, … , 𝑒𝑗2𝜋𝑑𝑎 𝜆 (𝐾−1)𝑠𝑖𝑛𝜃] 𝑇 (17) Here, 𝑑𝑎 and 𝜆 denote the inter-antenna spacing and wavelength of the carrier signal, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' We assume 𝑑𝑎 = 𝜆 4 in this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' The channel model could be described by a singular-value decomposition (SVD) scheme introduced by Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' [68]: 𝑯 = 𝑼𝜮𝑽† (18) Here, 𝑼 ∈ ℂ𝑁𝑟×𝑁𝑟 and 𝑽 ∈ ℂ𝑁𝑡×𝑁𝑡 are unitary matrices represent K phase shifters [69], and 𝜮 is given as 𝜮 = [𝑑𝑖𝑎𝑔{√𝜂1, … , √𝜂𝑟} 𝟎𝑟×(𝑁𝑡−𝑟) 𝟎(𝑁𝑟−𝑟)×𝑟 𝟎(𝑁𝑟−𝑟)×(𝑁𝑡−𝑟) ] (19) where r is the rank of 𝑯 and √𝜂1, … , √𝜂𝑟 are the r non-zero singular values of 𝑯 generated by the transmissivity of beam- splitters in the system [69].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content='1 (b), the whole model of a MIMO system could be described by [68, 69] 𝒂̂𝐵 = 𝑼†𝑯𝑽𝒂̂𝐴 + 𝑼†𝑼𝑺𝒂̂𝐸 (20) where 𝒂̂𝐵 = [𝑎̂𝐵,1, … , 𝑎̂𝐵,𝑁𝑟]𝑇 is the received mode of Bob, 𝒂̂𝐴 = [𝑎̂𝐴,1, … , 𝑎̂𝐴,𝑁𝑡]𝑇 is the transmitted mode of Alice, 𝒂̂𝐸 = [𝑎̂𝐸,1, … , 𝑎̂𝐸,𝑁𝑡]𝑇 is the injected Gaussian mode of Eve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' 𝑺 = 𝑑𝑖𝑎𝑔{√1 − 𝜂1, … , √1 − 𝜂𝑟, 𝟏(𝑀−𝑟)×1} (21) is a diagonal matrix with 𝑀 = min(𝑁𝑡, 𝑁𝑟).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' We get 𝑼†𝑼 = 𝑰𝑁𝑟 and 𝑽†𝑽 = 𝑰𝑁𝑡 as 𝑼 and 𝑽 are unitary matrices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Considering Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' (18) 𝑯 = 𝑼𝜮𝑽†, diagonal matrix 𝜮 and 𝑺, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' (20) would turn to 𝒂̂𝐵 = 𝑼†𝑼𝜮𝑽†𝑽𝒂̂𝐴 + 𝑼†𝑼𝑺𝒂̂𝐸 = 𝜮𝒂̂𝐴 + 𝑺𝒂̂𝐸 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' So the efficient channel between Alice and Bob can be disintegrated into r parallel SISO channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Bob randomly chooses quadratures for his input and operates homodyne measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Then the input-output relationship of i-th parallel channel between Bob’s received quadrature 𝑋̂𝐵,𝑖, and Alice’s transmitted quadrature 𝑋̂𝐴,𝑖, can be written by a generic quantum channel as [68] 𝑋̂𝐵,𝑖 = √𝑇𝑖𝑋̂𝐴,𝑖 + √1 − 𝑇𝑖𝑋̂𝐸,𝑖, 𝑖 = 1,2, … , 𝑟 (22) with Ti and 𝑋̂𝐸,𝑖 as transmittance, and Eve’s excess noise quadrature, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' We can write for Eve’s ancilla mode: 𝑋̂𝐸′,𝑖 = −√1 − 𝑇𝑖𝑋̂𝐴,𝑖 + √𝑇𝑖𝑋̂𝐸,𝑖, 𝑖 = 1,2, … , 𝑟 (23) B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Computation of the secret key rate The secret key rate 𝑅◄ = 𝐼(𝑎: 𝑏) − 𝐼(𝐸: 𝑏) is given defined by mutual information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' Assuming Gaussian statistic for simulating purposes, the mutual information between Alice and Bob is I(a: b) = 1 2 𝑙𝑜𝑔2[1 + 𝑇𝑉𝑠 Λ(𝑉0, 𝑊)] Λ(x, y) = Tx + (1 − T)y And Eve’s information is bounded by the Holevo information I(E: b) which is defined as 9 I(E: b) = 𝐻𝐸 − 𝐻𝐸|𝑏 (24) 𝐻𝐸 = ℎ(𝑣1) + ℎ(𝑣2) (25) 𝐻𝐸|𝑏 = ℎ(𝑣3) + ℎ(𝑣4) (26) where 𝐻𝐸 and 𝐻𝐸|𝑏 are the von Neumann entropy of Eve’s total and conditional state respectively [68, 75].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} +page_content=' The von Neumann entropy depends on symplectic eigenvalues is given by [68] 𝑣1 = Λ(W, 𝑉𝑎), 𝑣2 = W, (27) 𝑣3, 𝑣4 = √1 2 (Δ ± √Δ2 − 4Υ), (28) and Δ = 𝑉𝑎𝑊Λ(𝑊, 𝑉𝑎) + 𝑊Λ(𝑊𝑉𝑎, 1) Λ(𝑉𝑎, 𝑊) (29) Υ = 𝑉𝑎𝑊2Λ(𝑊, 𝑉𝑎)Λ(𝑊𝑉𝑎, 1) Λ2(𝑉𝑎, 𝑊) (30) The function h(x) is defined as h(x) = 𝑥 + 1 2 𝑙𝑜𝑔2 (𝑥 + 1 2 ) − 𝑥 − 1 2 𝑙𝑜𝑔2 (𝑥 − 1 2 ) (31)' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfywu5/content/2301.04723v1.pdf'} diff --git a/S9AzT4oBgHgl3EQf0v4t/content/tmp_files/2301.01787v1.pdf.txt b/S9AzT4oBgHgl3EQf0v4t/content/tmp_files/2301.01787v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..8ba54af23e9ca9c4fa69d446923cba6803f02321 --- /dev/null +++ b/S9AzT4oBgHgl3EQf0v4t/content/tmp_files/2301.01787v1.pdf.txt @@ -0,0 +1,1852 @@ +Measuring out quasi-local integrals of motion from entanglement +B. Lu,1, ∗ C. Bertoni,1, ∗ S. J. Thomson,1, † and J. Eisert1, 2, ‡ +1Dahlem Centre for Complex Quantum Systems, Freie Universit¨at, 14195 Berlin, Germany +2Helmholtz Center Berlin, 14109 Berlin, Germany +(Dated: January 6, 2023) +Quasi-local integrals of motion are a key concept underpinning the modern understanding of many-body +localisation, an intriguing phenomenon in which interactions and disorder come together. Despite the existence +of several numerical ways to compute them—and astoundingly in the light of the observation that much of the +phenomenology of many properties can be derived from them—it is not obvious how to directly measure aspects +of them in real quantum simulations; in fact, the smoking gun of their experimental observation is arguably +still missing. In this work, we propose a way to extract the real-space properties of such quasi-local integrals +of motion based on a spatially-resolved entanglement probe able to distinguish Anderson from many-body +localisation from non-equilibrium dynamics. We complement these findings with a new rigorous entanglement +bound and compute the relevant quantities using tensor networks. We demonstrate that the entanglement gives +rise to a well-defined length scale that can be measured in experiments. +It is widely believed that generic quantum systems iso- +lated from their environments will evolve under their own +dynamics until they reach an apparent equilibrium state that +locally resembles the expectations of a thermal equilibrium +state [1, 2]. This expectation is seen as a stepping stone to +reconcile predictions from statistical mechanics and those of +basic quantum mechanics. One major exception to this rule +is the case of low-dimensional quantum systems in the pres- +ence of random disorder. Non-interacting quantum systems +in one dimension will entirely fail to thermalise due to any +finite concentration of disorder [3], and in recent decades it +has been shown that interacting many-body systems appear +to suffer the same fate [4, 5], leading to the phenomenon +now known as many-body localisation (MBL) [6–12]. From +a theoretical standpoint, MBL is now fairly well understood +in terms of the emergence of an extensive number of con- +served quantities known as (quasi-)local integrals of motion +(LIOMs, also known as localised bits or l-bits) which can +prevent many-body systems from reaching thermal equilib- +rium [7, 13]. While phenomenological models based around +the concept of l-bits have seen great success [14, 15], and +there are several approaches that can map microscopic mod- +els onto effective l-bit models [16–26], the l-bits themselves +remain a strictly theoretical construct, inaccessible to any ex- +perimental probes. This is in contrast with the case of An- +derson localised systems, where the exponentially localised +l-bits can be straightforwardly related to the real-space decay +of the single-particle states, which has been experimentally +observed [27]. +In this work, we propose an experimentally feasible ap- +proach to measuring the actual real-space properties of local +integrals of motion in many-body quantum systems using the +entanglement negativity, a sensitive entanglement monotone +that allows for the recovery of spatially resolved entangle- +ment information. In this way, we accommodate the above +missing link. Various quantities capturing correlations and +entanglement, including the negativity, have been measured +in recent experiments with ultra-cold bosons: Ref. [28] has +measured the configurational entanglement and number en- +FIG. 1. a) A sketch showing how a one-dimensional spin chain is +partitioned into three subsystems. We are interested in computing +the entanglement between subsystems A and B after subsystem C +has been traced out, giving rise to a spatially-resolved entanglement +measure. b) Sketch of the initial quantum state in matrix product op- +erator (MPO) form, made by taking the outer product of two matrix +product state vectors. c) Sketch of how the negativity is computed: +the partial transpose of subsystem A corresponds to ‘twisting’ the +MPO legs while tracing out subsystem C corresponds to contracting +the relevant MPO indices. +tanglement for a system subject to a quasi-periodic potential +and has provided evidence for an exponentially decaying cor- +relation length, while Ref. [29] has studied a disordered sys- +tem and has shown that the entanglement negativity can be +directly measured. In a first experiment, the authors of the +latter work prepared the system in a product state and mea- +sured the two-qubit entanglement of formation as they vary +the separation between the qubits. While this setting is close +in spirit to our approach, they have chosen a two-qubit setting, +which is the only setting in which one can compute this quan- +tity, so that the diagnostic time scale that allows observation +of any spatial dependence is short. In a second experiment, +the preservation of entanglement has been studied, departing +from the approach taken here. Here, we demonstrate that the +negativity itself gives direct access to a unique length scale +that characterises the l-bits. +Quasi-local operators. +While the question of whether +many-body localisation is a well-defined stable phase in the +thermodynamic limit remains unsettled, for our purposes we +shall define many-body localisation in the following way. +arXiv:2301.01787v1 [cond-mat.dis-nn] 4 Jan 2023 + +A +B2 +Definition 1 (Quasi-local operators). An operator O on the +lattice Λ is said to be quasi-local around a region R with lo- +calisation length ξ if for any region X ⊂ Λ containing R +���� +����O − +1 +2|Xc| trXc(O) ⊗ IXc +���� +���� +2 +≤ ∥O∥2 Ke−d(R,Xc)/ξ (1) +where C +> +0 is a universal constant, d(Xc, R) += +min x∈Xc,r∈Rd(x, r), and ∥ · ∥ is the normalized 2-norm, +∥O∥2 = trOO†/trI. +Interestingly, the relatively loose sense of decay in 2-norm +seems crucial, an insight that is often under-appreciated [30, +31]. It is important to note that this is an abstract definition: +it does not give operational advice on how to find those l- +bits. What is more, even if they exist, they are by no means +unique [32]. There could be “more local” l-bits than those +given that still give rise to a complete set of l-bits. Either way, +as is common, such l-bits serve as our definition for many- +body localisation. +Definition 2 (Many-body localisation). A Hamiltonian +H = +n +� +j=1 +ω(1) +j hj + +n +� +j,k=1 +ω(2) +j,khjhk + . . . +(2) +with real weights {ω(1) +j } and {ω(2) +j,k}, is called many-body lo- +calised if it can be written as a sum of mutually commuting +([hj, hk] = 0 for all j, k) quasi-local terms hj, each cen- +tred around site j, and if ωi1,...,in ≤ ωe−|i1−in|/κ, where +i1 < i2 · · · < in. +Premise of the approach. When written in the basis that +diagonalises the Hamiltonian, as in Eq. (2), these l-bits are +strictly local objects, but in real-space they are quasi-local +with exponentially decaying tails. In order to extract proper- +ties of l-bits from experiments, we shall consider the evolution +of an arbitrary initial state under the following Hamiltonian +dynamics as +ρ(t) = e−itHρeitH, +(3) +for times t ≥ 0. To simplify the notation, we will suppress the +time argument for time t = 0. How can this time evolution +be exploited to measure out real-space properties of the l-bits? +Some intuition can be attained in the situation when the {hj} +are strictly local. The terms that do not overlap do not con- +tribute to the entanglement evolution at all. So in the end, it is +the overlapping tails that will lead to entanglement growth. +Model. We will demonstrate our scheme numerically using +the ‘standard model’ of MBL, namely the XXZ spin-1/2 chain +with random on-site fields, while it should be clear that the ap- +proach taken would be applicable to any many-body localised +model. Its Hamiltonian is given by +H = J0 +� +i +� +Sx +i Sx +i+1 + Sy +i Sy +i+1 + ∆Sz +i Sz +i+1 +� ++ +� +i +hiSz +i , +(4) +with hi ∈ [−d, d]. We shall set J0 = 1 as the unit of en- +ergy throughout, with ∆ = 1.0 unless otherwise stated, and +will use open boundary conditions. This model has been thor- +oughly studied and shown to exhibit a phase with anoma- +lous thermalisation properties above a disorder strength of +d ≳ 3.7 [9], although recent work has suggested that the true +phase transition in the thermodynamic limit could be at much +larger values of d if it exists at all [33–37]. +The characteristic growth in time of the von Neumann en- +tanglement entropy +[38, 39] (or its correlation-based ana- +logues [40]) has been shown to be a good indicator of many- +body localisation, able to distinguish it from single-particle +Anderson localisation via the late-time logarithmic growth. +Motivated by this, our aim in this work is to show that other +entanglement measures which provide spatially-resolved in- +formation can not only distinguish many-body localisation +from Anderson localisation, but can also allow direct quan- +titative measurement of the properties of many-body local in- +tegrals of motion. +Diagnostic entanglement quantity. The main quantity of +interest in this work is the logarithmic negativity, a measure of +the entanglement between two subsystems of the spin chain, +denoted A and B, separated by a distance r, which together +with C constitutes the entire system (sketched in Fig. 1). It is +defined as [41–44] +EN(ρA,B(t)) := log2(∥ρTA +A,B(t)∥1), +(5) +where ∥O∥1 = tr|O| denotes the trace norm, ρA,B(t) = +tr\{A,B}[ρ(t)] is the time-dependent quantum state of sub- +systems A and B after tracing out all other lattice sites, and +the superscript TA indicates the partial transpose with respect +to subsystem A. +This has been shown to be an entangle- +ment monotone meaningfully quantifying entanglement [43– +45]. In the following, we shall refer to this quantity simply +as ‘negativity’. By contrast to the more commonly studied bi- +partite von Neumann or R`enyi entanglement entropies which +consider a single bi-partition between two connected subsys- +tems, the entanglement negativity allows for a meaningful +spatially resolved measure of mixed-state entanglement, as +the two subsystems can be separated by an arbitrary distance +r := dist(A, B), a feature the von Neumann entropy cannot +capture as a pure state entanglement measure. This measure +can also be used to study the entanglement between subsys- +tems of arbitrary size. However, for conceptual clarity, we +shall mainly consider A and B to cover the entire chain ex- +cept for a piece C with |C| = r + 1 separating A and B, +as shown in Fig. 1. +That said, the concept works as well +for small regions A and B, as they are accessible in experi- +ments and are discussed in the rigorous bounds. Numerical +evidence is shown [46]. The negativity has previously been +investigated in the context of ground states of disordered spin +chains [47], the many-body localisation transition [48], and +quench dynamics in the presence of a defect [49]. For clarity, +in the following, we shall drop the explicit dependence of EN +on the quantum state and instead use the notation EN(r, t) + +3 +to represent the negativity associated to two subsystems sepa- +rated by a distance r and a time t following a quench from an +initial product state, emphasizing that this is indeed a spatially +resolving entanglement measure. +A heuristic argument for why this quantity is relevant in +our case can be given in the following manner. +Ref. [13] +has shown that the von Neumann entanglement entropy grows +in time following a quench according to Sent ∝ ln(J0t/ℏ), +once the system enters the late-time dephasing regime. +If +we wish to consider the entanglement negativity between two +subsystems separated by a distance r, a reasonable starting +assumption is that the negativity will vary in time accord- +ing to the same ∼ ln(t) growth but will be exponentially +suppressed in magnitude due to the spatial separation of the +two subsystems, leading to an overall behaviour of EN ∝ +exp(−r/ξ) ln(J0t/ℏ). +We shall show that this ansatz is a +good match for the numerical results. We also wish to empha- +sise that this logarithmic growth is characteristic of the inter- +acting system and is entirely absent from Anderson-localised +systems, meaning that the existence of this length scale is a +distinct fingerprint of a many-body localised system. +Corroborating the reasoning with rigorous bounds. We see +that Hamiltonians that are many-body localised in the sense +of Definition 2 create entanglement at a rate that decays expo- +nentially in the distance r = dist(A, B) between parts A and +B, reflecting the exponential decay of the tails in quasi-local +l-bits. In fact, not only this intuition can be made entirely +rigorous, but, at the cost of slightly weakening the definition +of quasi-locality, we are in the position to state precise upper +bounds for the negativity for all times and distances. +Theorem 1 (Rigorous entanglement bounds). Let ρ be an ini- +tial product state. Let H be a many-body localised Hamil- +tonian as per Definition 2 with localisation length ξ +< +1/(4 log(2)) and 2(1/κ − log(2)) > 1/ξ, consider three +blocks A, C, B such that C divides A from B, with |C| = r + +1. The growth of the negativity of the state ρ(t) = e−itHρeitH +restricted to the regions A, B is bounded as +EN(r, t) ≤ min{t O(e−r/(2ξ)), 8ξ log2(t)−2r}+O(1), (6) +for times t ≥ er/(4ξ), while for t < er/(4ξ), +EN(r, t) ≤ t O(e−r/(4ξ)). +(7) +We hence find a short time behaviour signifying a linear +growth in time, a cross-over regime governed by the correla- +tion length, and a logarithmic growth for long times. These +bounds—interesting in their own right and complementing +and refining those of Ref. [50]—are perfectly compatible with +the above numerical assessment. In the Supplemental Mate- +rial, we state details of the proof of the bound that makes ex- +tensive use of the precise form of the tails of the l-bits. Based +on our numerical results, we expect that our assumptions on +the localisation length and the definition of quasi-locality can +be relaxed without affecting the result. We also note that the +10−1 +100 +101 +102 +t +0.0 +0.2 +0.4 +0.6 +EN(r, t) +(a) +(b) +(c) +r = 1 +r = 2 +r = 3 +r = 4 +r = 5 +r = 6 +0 +10 +r +−1 +0 +1 +2 +log10(t) +log10(EN) +ε = 0.005 +ε = 0.001 +ε = 0.0001 +0 +5 +10 +r +−10 +−5 +0 +log(EN(r, t∗)) +t∗ = 46 +t∗ = 115 +t∗ = 288 +t∗ = 391 +t∗ = 500 +−4 +−2 +0 +FIG. 2. Results showing the growth of the negativity EN(r, t) with +time for different distances r. Data is shown for a system size L = 24 +and a disorder strength d = 8.0, averaged over Ns = 100 disor- +der realisations. a) The dynamics of EN(r, t) following a quench +from a N`eel state, showing the logarithmic growth at late times. +The circular markers are the raw data points, while the solid lines +are a smoothed guide to the eye. The error bars indicate the stan- +dard error in the mean. b) The full dynamics of EN(r, t), reflect- +ing the logarithmic ‘light cone’. c) By extracting the behaviour of +EN(r, t∗) ∝ exp(−r/ξ) at fixed times t∗ [dashed vertical lines in +panel (a), horizontal lines in panel (b)], we can extract a well-defined +length scale ξ(t), which depends only weakly on time. The solid +lines indicate the fits to the data points which are used to extract the +l-bit length scale, demonstrating convergence at late times. +observed ξ−dependence of the late time decay of the entan- +glement with the size of C is not visible in this bound, though +we expect that it can be refined to show this. +Extraction of the l-bits. +We compute the negativity us- +ing time-dependent matrix product state simulations – an in- +stance of a tensor network method [51] – implemented in the +Quimb package [52] using the time-evolving block decima- +tion (TEBD) algorithm to perform the evolution [53, 54], with +the system initially prepared in a N´eel state. We use system +size L = 24 with a maximum bond dimension of χ = 192. +We perform the time evolution using a maximum time step +dt = 0.05, at each step discarding singular values smaller +than ϵ = 10−10. We have checked that the results are well- +converged. Detailed benchmarks are shown in Ref. [46]. Our +TEBD results are compared against l-bit length scales ob- +tained using exact diagonalisation, following Ref. [30]. +The negativity can be computed straightforwardly from a +matrix product state (MPS) representation [55]. +The state +vector can be turned into a matrix product operator (MPO) +(sketched in Fig. 1) representing the quantum state by consid- +ering vectors and dual vectors represented as MPS. The partial +transpose can be computed by ‘twisting’ the legs of the MPO +tensors, while the partial trace over the subsystem C can be +performed by contracting the free indices of the MPO tensors + +4 +in this subsystem. At long times, the negativity should satu- +rate at a value controlled by the size of the subsystems, and +at any time t < ts (where ts is the saturation time), the nega- +tivity should satisfy the hierarchy EN(r1, t) < EN(r2, t) for +any two distances r1 > r2. +We first discuss qualitatively the results for the growth +of the entanglement negativity with time for various differ- +ent distances r, as shown in Fig. 2a) for a disorder strength +d = 8.0 (deep in the localised phase), where we find that +indeed the negativity grows logarithmically with time at late +times. Results for further disorder strengths, system sizes, and +subsystem sizes are available in Ref. [46]. At short times, +the negativity is dominated by diffusive transport on length +scales shorter than the localisation length. At large distances +r, the negativity remains close to zero until a time exponen- +tially large in r, which can be used to define a ‘light cone’ +that characterises the spreading of the entanglement negativ- +ity, shown in Fig. 2b). The three lines indicate when the neg- +ativity grows above a threshold ε ∈ {0.0001, 0.001, 0.005}, +mapping out an approximately logarithmic light cone. As the +negativity outside of this length cone is exponentially small, +in the following analysis, we restrict ourselves to space-time +coordinates (r, t), which are within the light cone. The exis- +tence of this light cone means that we gain only diminishing +returns by going to larger system sizes: although we are able +to separate the subsystems by a larger value of r, the evolu- +tion time required to obtain meaningful entanglement scales +exponentially in r, which incurs a large computational cost +for large systems and quickly becomes prohibitive. +In the late-time logarithmic growth regime, where the dy- +namics are dominated by the quasi-local nature of the l-bits, +we extract the value of the negativity at a given time t∗ follow- +ing the quench from an initial N´eel state and plot it versus the +subsystem separation r. We show this in Fig. 2c) for several +different choices of time t∗ [indicated by the dashed lines in +Fig. 2a)]. The data points form a straight line (on a logarith- +mic scale), and at late times the gradient of the line does not +strongly change with the choice of time t∗, appearing to satu- +rate at a fixed value (although the y-axis offset will, of course, +continue to increase in time). Further details are available in +Ref. [46]. Under the assumption that the negativity decays +exponentially with distance like EN(r, t∗) ∝ exp(−r/ξ), we +can perform a linear fit to the data shown in Fig. 2c) and ex- +tract a well-defined length scale ξ which characterises the spa- +tial extent of the l-bits. The results are shown in Fig. 3, where +we find that the length scale ξ exhibits monotonic decay with +increasing disorder strength, as expected. Note that no as- +sumptions are involved other than the exponential decay of the +negativity with distance at some fixed time t∗: the resulting +length scale is an emergent property of the many-body sys- +tem. This assumption does not hold in the delocalised phase, +where the entanglement does not enter a regime of logarithmic +growth. We can further compare the length scale extracted +from our procedure with the l-bit decay lengths computed us- +ing the established numerically exact method of Ref. [30], +using the definition of quasi-locality from Eq. (1). We find +2 +4 +6 +8 +10 +d +0 +2 +4 +6 +ξ +L = 24 +L = 14 (ED) +L = 12 (ED) +L = 128 (∆ = 0) +FIG. 3. The characteristic l-bit length scale ξ extracted from the +entanglement negativity at time t∗ = 500, shown for L = 24 +with Ns ∈ [50, 100] disorder realisations and various values of +the disorder strength d. +Error bars indicate the fit error and are +roughly the same size as the plot markers. +The black line indi- +cates the localisation length of the corresponding Anderson-localised +system, obtained by directly diagonalising the Hamiltonian in the +non-interacting limit (∆ = 0), for a system of size L = 128 with +Ns = 10000. +excellent agreement between the entanglement-based length +scale and the l-bit localisation length obtained independently +from this method, confirming that the length scale probed by +the negativity is the localisation length of the l-bits. +For comparison, we also indicate the corresponding locali- +sation length of an Anderson localised system, here obtained +by directly diagonalising the Hamiltonian with ∆ = 0 (fol- +lowing a Jordan-Wigner transform into the fermionic repre- +sentation). We compute the eigenvectors of the Hamiltonian +in the non-interacting setting, which decay in real space as +exp(−r/ξ) [56], average over disorder realisations and ex- +tract the localisation length ξ from a least-squares fit. The +length scale extracted from the TEBD data behaves in a +qualitatively similar manner to the single-particle localisation +length but is always larger, confirming that we are not measur- +ing single-particle properties but are indeed extracting a gen- +uinely many-body feature of the system. In the delocalised +phase, our assumed form of the negativity is no longer valid, +and as such, the method cannot extract a reliable length scale. +We also note that the entanglement negativity is not the +only entanglement measure which may be used in this way: +any spatially-resolved entanglement probe should behave sim- +ilarly. In the Supplemental Material [46], we demonstrate that +the mutual information also gives consistent results. +Conclusion. In this work, we have outlined a new exper- +imentally feasible procedure for measuring local integrals of +motion based on their contribution to the slow growth of the +negativity at long times following a quench from an arbitrary +initial state. We have demonstrated that the length scale which +we obtain from this procedure, which characterises the l-bits, +is in good agreement with that obtained using other theoreti- +cal methods in the literature. The crucial advantage is that our +scheme is experimentally tractable, unlike other purely the- +oretical/numerical methods, which cannot be verified in real +experiments. It would be extremely interesting to apply this +method to other scenarios where many-body localisation is + +5 +believed to exist, such as in disorder-free systems and two- +dimensional models, in order to see if well-defined length +scales based on the spreading of entanglement may still be +extracted in these situations. This work paves the way for +the application of spatially-resolved entanglement probes to +phenomena in quantum simulation beyond many-body local- +isation, where such methods may be able to provide valuable +insight into emergent length scales associated with other types +of quasi-particles. +Acknowledgements. This project has been inspired by dis- +cussions with P. Roushan and B. Chiaro of Google AI. We +also thank A. Kshetrimayum, S. Sotiriadis, S. Qasim, and +J. Gray for discussions. B. Lu is grateful for feedback from +D. Abanin, M. Fleischhauer, and M. Kiefer-Emmanouilidis at +the CRC 183 summer school “Many-body physics with Ryd- +berg atoms”. This project has received funding from the Eu- +ropean Union’s Horizon 2020 research and innovation pro- +gramme under the Marie Skłodowska-Curie grant agreement +No. 101031489 (Ergodicity Breaking in Quantum Matter), +grant agreement No. 817482 (PASQuanS), and the Deutsche +Forschungsgemeinschaft (CRC 183 and FOR 2724). +We +also acknowledge funding from the BMBF (FermiQP and +MUNIQC-ATOMS). The full code and data for this work are +available at Refs. [57, 58]. +∗ These two authors contributed equally +† steven.thomson@fu-berlin.de (he/him/his) +‡ jense@zedat.fu-berlin.de +[1] A. Polkovnikov, K. Sengupta, A. Silva, and M. Vengalattore, +Rev. Mod. Phys. 83, 863 (2011). +[2] C. Gogolin and J. Eisert, Rep. Prog. Phys. 79, 56001 (2016). +[3] P. W. Anderson, Phys. Rev. 109, 1492 (1958). +[4] L. Fleishman and P. W. Anderson, Phys. Rev. B 21, 2366 +(1980). +[5] D. M. Basko, I. Aleiner, and B. Altshuler, Ann. Phys. 321, 1126 +(2006). +[6] D. A. Huse, R. Nandkishore, V. Oganesyan, A. Pal, and S. L. +Sondhi, Phys. Rev. B 88, 014206 (2013). +[7] D. A. Huse, R. Nandkishore, and V. Oganesyan, Phys. Rev. B +90, 174202 (2014). +[8] E. Altman and R. Vosk, Ann. Rev. Cond. Matt. Phys. 6, 383 +(2015). +[9] D. J. Luitz, N. Laflorencie, +and F. Alet, Phys. Rev. B 91, +081103 (2015). +[10] F. Alet and N. Laflorencie, Compt. Rend. Phys. 19, 498 (2018). +[11] D. A. Abanin, E. Altman, I. Bloch, and M. Serbyn, Rev. Mod. +Phys. 91, 021001 (2019). +[12] M. Friesdorf, A. H. Werner, W. Brown, V. B. Scholz, and J. Eis- +ert, Phys. Rev. Lett. 114, 170505 (2015). +[13] M. Serbyn, Z. Papi´c, and D. A. Abanin, Phys. Rev. Lett. 111, +127201 (2013). +[14] V. Ros, M. M¨uller, and A. Scardicchio, Nucl. Phys. B 891, 420 +(2015). +[15] J. Z. Imbrie, V. Ros, +and A. Scardicchio, Ann. Phys. 529, +1600278 (2017). +[16] L. Rademaker and M. Ortu˜no, Phys. Rev. Lett. 116, 010404 +(2016). +[17] L. Rademaker, M. Ortu˜no, and A. M. Somoza, Ann. Phys. , +1600322 (2017). +[18] D. Pekker, B. K. Clark, V. Oganesyan, and G. Refael, Phys. +Rev. Lett. 119, 075701 (2017). +[19] M. Goihl, M. Gluza, C. Krumnow, and J. Eisert, Phys. Rev. B +97, 134202 (2018). +[20] S. J. Thomson and M. Schir´o, Phys. Rev. B 97, 060201 (2018). +[21] A. K. Kulshreshtha, A. Pal, T. B. Wahl, and S. H. Simon, Phys. +Rev. B 99, 104201 (2019). +[22] S. J. Thomson and M. Schir´o, Phys. Rev. Research 2, 043368 +(2020). +[23] S. J. Thomson, D. Magano, and M. Schir´o, SciPost Phys. 11, +28 (2021). +[24] S. J. Thomson and M. Schir´o, arXiv:2110.02906 (2021). +[25] S. J. Thomson, arXiv:2208.11731 (2022). +[26] C. Bertoni, J. Eisert, A. Kshetrimayum, A. Nietner, and S. J. +Thomson, arXiv:2208.14432 (2022). +[27] J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, +D. Cl´ement, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, +Nature 453, 891 (2008). +[28] A. Lukin, M. Rispoli, R. Schittko, M. E. Tai, A. M. Kaufman, +S. Choi, V. Khemani, J. L´eonard, and M. Greiner, Science 364, +256 (2019). +[29] B. Chiaro, C. Neill, A. Bohrdt, M. Filippone, F. Arute, +K. Arya, R. Babbush, D. Bacon, J. Bardin, R. Barends, +S. Boixo, D. Buell, B. Burkett, Y. Chen, Z. Chen, R. Collins, +A. Dunsworth, E. Farhi, A. Fowler, B. Foxen, C. Gidney, +M. Giustina, M. Harrigan, T. Huang, S. Isakov, E. Jeffrey, +Z. Jiang, D. Kafri, K. Kechedzhi, J. Kelly, P. Klimov, A. Ko- +rotkov, F. Kostritsa, D. Landhuis, E. Lucero, J. McClean, X. Mi, +A. Megrant, M. Mohseni, J. Mutus, M. McEwen, O. Naa- +man, M. Neeley, M. Niu, A. Petukhov, C. Quintana, N. Rubin, +D. Sank, K. Satzinger, T. White, Z. Yao, P. Yeh, A. Zalcman, +V. Smelyanskiy, H. Neven, S. Gopalakrishnan, D. Abanin, +M. Knap, J. Martinis, and P. Roushan, Phys. Rev. Research +4, 013148 (2022). +[30] M. Goihl, M. Gluza, C. Krumnow, and J. Eisert, Phys. Rev. B +97, 134202 (2018). +[31] E. Ilievski, M. Medenjak, T. Prosen, and L. Zadnik, J. Stat. +Mech. , 064008 (2016). +[32] A. Chandran, I. H. Kim, G. Vidal, and D. A. Abanin, Phys. +Rev. B 91, 085425 (2015). +[33] E. V. H. Doggen, F. Schindler, K. S. Tikhonov, A. D. Mirlin, +T. Neupert, D. G. Polyakov, and I. V. Gornyi, Phys. Rev. B 98, +174202 (2018). +[34] J. ˇSuntajs, J. Bonˇca, T. Prosen, and L. Vidmar, Phys. Rev. E +102, 062144 (2020). +[35] J. ˇSuntajs, J. Bonˇca, T. Prosen, and L. Vidmar, Phys. Rev. B +102, 064207 (2020). +[36] D. Sels and A. Polkovnikov, arXiv:2105.09348 (2021). +[37] D. Sels and A. Polkovnikov, Phys. Rev. E 104, 054105 (2021). +[38] J. H. Bardarson, F. Pollmann, and J. E. Moore, Phys. Rev. Lett. +109, 017202 (2012). +[39] M. Znidaric, T. Prosen, +and P. Prelovsek, Phys. Rev. B 77, +064426 (2008). +[40] M. Goihl, M. Friesdorf, A. H. Werner, W. Brown, and J. Eisert, +Quantum Rep. 1, 50 (2019). +[41] K. ˙Zyczkowski, P. Horodecki, A. Sanpera, and M. Lewenstein, +Phys. Rev. A 58, 883 (1998). +[42] J. Eisert and M. B. Plenio, J. Mod. Opt. 46, 145 (1999). +[43] G. Vidal and R. F. Werner, Phys. Rev. A 65, 032314 (2002). +[44] M. B. Plenio, Phys. Rev. Lett. 95, 090503 (2005). +[45] J. Eisert, “Entanglement in quantum information theory,” +(2001), PhD thesis, University of Potsdam, arXiv:quant- + +6 +ph/0610253. +[46] See Supplemental Material for details. The Supplemental Ma- +terial contains Refs. [59–64]. +[47] P. Ruggiero, V. Alba, and P. Calabrese, Phys. Rev. B 94, 035152 +(2016). +[48] J. Gray, A. Bayat, A. Pal, +and S. Bose, arXiv:1908.02761 +(2019). +[49] M. Gruber and V. Eisler, J. Phys. A 53, 205301 (2020). +[50] I. H. Kim, A. Chandran, and D. A. Abanin, arXiv:1412.3073 +(2014). +[51] R. Or´us, Ann. Phys. 349, 117 (2014). +[52] J. Gray, Journal of Open Source Software 3, 819 (2018). +[53] G. Vidal, Phys. Rev. Lett. 93, 040502 (2004). +[54] U. Schollw¨ock, Ann. Phys. 326, 96 (2011). +[55] J. Gray, arXiv:1809.01685 (2018). +[56] P. A. Lee and T. V. Ramakrishnan, Rev. Mod. Phys. 57, 287 +(1985). +[57] S. J. Thomson, https://github.com/sjt48/EntanglementDynamics +(2022). +[58] B. +Lu, +C. +Bertoni, +S. +J. +Thomson, +and +J. +Eisert, +https://doi.org/10.5281/zenodo.7322988 (2022). +[59] A. K. Kulshreshtha, A. Pal, T. B. Wahl, and S. H. Simon, Phys. +Rev. B 98, 184201 (2018). +[60] M. Mari¨en, K. M. R. Audenaert, K. V. Acoleyen, and F. Ver- +straete, Commun. Math. Phys. 346, 35–73 (2016). +[61] J. Eisert and T. J. Osborne, Phys. Rev. Lett. 97, 150404 (2006). +[62] J. Eisert, Phys. Rev. Lett. 127, 020501 (2021). +[63] A. E. Rastegin, J. Stat. Phys. 148, 1040 (2012). +[64] A. Tsuyoshi and T. Sano, Positivity 12 (2008), 10.1007/s11117- +007-2121-7. + +7 +Supplemental Material to “Measuring local integrals of motion from entanglement” +TEBD accuracy benchmarks +As TEBD does not precisely conserve the energy of the initial state, as a benchmark of the accuracy of our numerics we +compute the relative error in the energy of the time-evolved state vector, E(t) = ⟨ψ(t)|H|ψ(t)⟩, computed with respect to its +energy at time t = 0. The relative error is defined as +δE(t) := +���� +E(t) − E(t = 0) +E(t = 0) +���� . +(8) +Fig. 4 shows the relative error versus time for a variety of different disorder strengths. We find that in most cases, the relative error +remains close to δE ≈ 0.001, i.e., the energy is conserved up to an error of approximately one-tenth of a percent, confirming +that our simulations are reliable. +100 +102 +0.000 +0.002 +0.004 +δE(t) +(a) +(b) +(c) +(d) +d = 1.0 +100 +102 +0.000 +0.002 +0.004 +d = 2.0 +100 +102 +0.000 +0.002 +0.004 +d = 3.0 +100 +102 +0.000 +0.002 +0.004 +d = 4.0 +100 +102 +t +0.000 +0.002 +0.004 +δE(t) +(e) +(f) +(g) +(h) +d = 6.0 +100 +102 +t +0.000 +0.002 +0.004 +d = 7.0 +100 +102 +t +0.000 +0.002 +0.004 +d = 8.0 +100 +102 +t +0.000 +0.002 +0.004 +d = 9.0 +L = 14 +L = 24 +FIG. 4. A comparison of the relative error in the energy of the time-evolved state for different values of the disorder strength d, shown for +system sizes L = 14 (χ = 128, averaged over Ns = 240 disorder realisations) and - at strong disorder only - L = 24 (χ = 192, averaged +over Ns = 100 disorder realisations). The relative error remains below 1% for all disorder strengths. Error bars indicate the variance over +disorder distributions and in most cases, are of comparable size to the plot markers. +Comparison of disorder strengths +In addition to the data presented in the main text, here we show the behaviou of the entanglement negativity over a range +of different disorder strengths, demonstrating the logarithmic growth at late times in the localised phase, and the qualitatively +different behaviour seen in the delocalised phase. The results are shown in Fig. 5, for a system of size L = 14, bond dimension +χ = 128, and averaged over Ns = 240 disorder realisations. The circle markers represent the data points, while the solid lines +are smoothed guides to the eye. Deep in the delocalised phase (d = 1.0), we see that the negativity saturates for all values of r at +relatively early times, making it difficult to pinpoint a regime where the growth of the negativity can be associated with a length +scale. In contrast, the negativity in the localised phase increases much more slowly with time, and the spacing of the curves is +consistent with an exponential suppression of the negativity with distance, as demonstrated in the main text. + +8 +100 +102 +0 +2 +4 +EN(r, t) +(a) +(b) +(c) +(d) +d = 1.0 +100 +102 +0 +2 +4 +d = 2.0 +100 +102 +0 +1 +2 +3 +d = 3.0 +100 +102 +0 +1 +2 +d = 4.0 +100 +102 +t +0.0 +0.5 +1.0 +EN(r, t) +(e) +(f) +(g) +(h) +d = 6.0 +100 +102 +t +0.0 +0.5 +1.0 +d = 7.0 +100 +102 +t +0.0 +0.5 +1.0 +d = 8.0 +100 +102 +t +0.0 +0.5 +d = 9.0 +r = 0 +r = 1 +r = 2 +r = 3 +r = 4 +r = 5 +r = 6 +FIG. 5. A comparison of the dynamics of the entanglement negativity EN(r, t) for different values of the disorder strength d, shown for +L = 14 with bond dimension χ = 128 and averaged over Ns = 240 disorder realisations. In the delocalised phase, the negativity saturates to +a value determined by the size of the subsystems A and B, while in the localised phase the negativity displays a slow ∝ log(t) growth even at +late times. In this dephasing regime, we are able to use the data shown here to extract a length scale that characterises the localised phase, as +detailed in the main text. +Bond dimension +In Fig. 6, we show the negativity dynamics for system size L = 24 and varying bond dimension χ, demonstrating that for +χ = 192 (the choice used in the main text) the results are well-converged. The crucial factor for our work is the rate of growth +of the negativity, which appears largely unaffected by the choice of bond dimension, although deviations can be seen for the +smallest value shown in Fig. 6. +10−1 +100 +101 +102 +0 +1 +EN(r, t) +d = 6 +10−1 +100 +101 +102 +0.5 +1.0 +d = 7 +10−1 +100 +101 +102 +t +0.5 +1.0 +EN(r, t) +d = 8 +10−1 +100 +101 +102 +t +0.5 +1.0 +d = 9 +χ = 32 +χ = 128 +χ = 192 +FIG. 6. The dynamics of the negativity EN(r, t) with r = 0, for different bond dimensions and disorder strengths. Data shown is for L = 24, +averaged over Ns = 100 disorder realisations. Error bars show the standard error. + +9 +Comparison of different measurement times +In the main text, all results for the length scale ξ ≡ ξ(t∗) are taken with t∗ = 500, i.e., the maximum evolution time of our +simulations, however, it is clear from the negativity dynamics that there should be a weak dependence of ξ on the measurement +time t∗. Here we demonstrate this effect. Fig. 7 shows how the linear fit used to extract the decay of EN(r, t) against r depends +on the choice of time t∗ for a variety of different disorder strengths, and Fig. 9 shows how the resulting values of ξ(t∗) change +as t∗ and d are varied. At short times there is a visible change in the length scale ξ(t), however, at longer times we see that +it appears to saturate towards a well-defined length scale with only a weak dependence on time. It is possible that simulations +which extend to longer times may be able to improve upon the results presented here, but our results suggest this will be a meagre +quantitative improvement in exchange for a great deal of computational effort. +0 +2 +4 +3 +4 +5 +log EN(r, t∗) +(a) +(b) +(c) +(d) +d = 1.0 +0 +2 +4 +2 +4 +d = 2.0 +0 +2 +4 +0 +2 +4 +d = 3.0 +0 +2 +4 +0 +2 +d = 4.0 +0 +2 +4 +r +−4 +−2 +0 +2 +log EN(r, t∗) +(e) +(f) +(g) +(h) +d = 6.0 +0 +2 +4 +r +−4 +−2 +0 +2 +d = 7.0 +0 +2 +4 +r +−4 +−2 +0 +2 +d = 8.0 +0 +2 +4 +t +−4 +−2 +0 +2 +d = 9.0 +t∗ = 19 +t∗ = 33 +t∗ = 72 +t∗ = 157 +t∗ = 251 +FIG. 7. A comparison of the fits to the entanglement negativity EN(r, t∗) at different times t∗ and for different values of the disorder strength +d, shown for L = 14 and averaged over Ns = 240 disorder realisations. The circular markers show the data, while the solid lines indicate the +linear fits used to extract the l-bit localisation length. Error bars showing the standard error in the mean are typically smaller than the marker +size. At large disorder strengths (i.e., in the localised phase), the linear fit is very good, confirming that the negativity does indeed decrease +exponentially with distance in this phase. After a time of t∗ ≈ 100, the gradient of the decay (and hence the corresponding l-bit localisation +length) does not strongly change with time in the localised phase. +0 +5 +10 +−10 +−5 +0 +log EN(r, t∗) +(a) +(b) +(c) +(d) +d = 6.0 +0 +5 +10 +−10 +−5 +0 +d = 7.0 +0 +5 +10 +−15 +−10 +−5 +0 +d = 8.0 +0 +5 +10 +t +−15 +−10 +−5 +0 +d = 9.0 +t∗ = 25 +t∗ = 46 +t∗ = 115 +t∗ = 288 +t∗ = 500 +FIG. 8. The same as in Fig. 7, but for L = 24, χ = 192 and averaged over Ns = 100 disorder realisations, shown only in the localised phase. +The solid lines indicate the range of points over which the exponential fits were performed in order to extract the length scale shown in Fig. 3 +of the main text. + +10 +2 +3 +4 +5 +6 +7 +8 +9 +10 +d +1 +2 +3 +ξ(t∗) +t∗ = 13 +t∗ = 25 +t∗ = 46 +t∗ = 115 +t∗ = 288 +t∗ = 391 +t∗ = 442 +t∗ = 470 +t∗ = 500 +FIG. 9. A comparison of how the length scale ξ(t∗) changes as the measurement time t∗ is varied. The results here are extracted from the fits +shown in Fig. 8. At short times, the value of ξ(t∗) changes rapidly, however, at longer times, the dependence of t∗ weakens significantly. The +black line is the Anderson localisation length for comparison, as discussed in the main text. For clarity, error bars are not shown except on the +Anderson localisation length. (Note that error bars are shown in the data presented in the main text.) +Negativity between subsystems of fixed size +It is also possible to compute the entanglement negativity on a more general interval between two subsystems of fixed size +Rb separated by a distance r, as sketched in Fig. 10. In this case, a very similar procedure to that proposed in the main text is +possible, with the caveat that one must carefully choose both the block size Rb and the distance r to ensure that the extraction of +the l-bit length scale is done during the dephasing regime. +To be specific, if the block size Rb is small and the subsystems are close together (i.e., r is small), then the entanglement +negativity will rapidly saturate (as the maximum entanglement is controlled by the size of the subsystems under consideration). +On the other hand, if the blocks are widely separated (i.e., large r), then the negativity will remain zero until times exponentially +large in r. If one were to consider a small subsystem of Rb = 2, for example, then the entanglement negativity for small values +of r would saturate well before widely separated subsystems have time to become entangled, this meaning that the data points +for both small r and large r would have to be discarded when performing the fit. This can be ameliorated by using blocks of +intermediate size, such that they are large enough that the subsystem entanglement does not saturate too rapidly and the data +at small values of r remains reliable. Representative results for this case are shown in Fig. 11, where it is clear that for block +size Rb = 2, the curves for small values of r saturate too quickly to be used in extracting the l-bit length scale. Block size +Rb = 3 is better, and here Rb = 4 offers the best compromise, with a clearly identifiable region where the curves for all values +of 1 ≤ r < 5 are in a regime of logarithmic growth with approximately the same rate, and a length scale may be extracted. On +the other hand, for block size Rb = 5, with a system size of L = 16 it is not possible to separate the blocks widely enough to +extract enough data to perform a reliable fit. (Note that in these computations, we avoid subsystems that contain the two sites on +each end of the chain in order to reduce finite-size effects. In addition, we average over all possible positions of the blocks with +size Rb separated by a distance r within our system of size L.) +FIG. 10. A sketch of how the entanglement negativity can be used to quantify the entanglement between subsystems of fixed size Rb separated +by a distance r. a) A sketch of the spin chain, identifying the subsystems A and B and the relevant distances Rb and r. b) A sketch of the +corresponding density matrix in MPO form, identifying the subsystems. c) A sketch of how the negativity is computed in this case, tracing out +the complement of A and B while still applying the same ‘twist’ to the MPO legs in order to compute the partial transpose, as in Fig. 1 of the +main text. + +A +B +HHOO11 +101 +102 +103 +t +0.00 +0.05 +0.10 +EN +Rb = 2 +101 +102 +103 +t +0.0 +0.2 +Rb = 3 +101 +102 +103 +t +0.0 +0.2 +0.4 +Rb = 4 +101 +102 +103 +t +0.0 +0.5 +Rb = 5 +r = 1 +r = 2 +r = 3 +r = 4 +r = 5 +r = 6 +FIG. 11. Entanglement negativity following a quench from a N´eel state, shown for disorder strength d = 6.0 with system size L = 16, +averaged over Ns = 96 disorder realisations. Here we compute the negativity for a subsystem of fixed size Rb := |A| = |B|, as sketched in +Fig. 10. We can see that for small values of Rb, the negativity at small separations r saturates quickly and that only for larger values of Rb +does the negativity increase in a manner that allows extraction of the relevant l-bit length scale. Error bars show the standard error in the mean, +and the solid lines are a smoothed guide to the eye. +Mutual information +In the main text and in our analytical results, we specified the logarithmic negativity as our chosen spatially-resolved entan- +glement probe. Here we briefly demonstrate that another spatially-resolved entanglement measure, the mutual information, also +exhibits qualitatively similar behaviour. The mutual information between subsystems A and B is defined as +I(A : B) := S(ρA) + S(ρB) − S(ρAB) +(9) +where S(ρ) := −trρ log(ρ) represents the von Neumann entropy of a quantum state ρ, and ρA is the reduced quantum state +of subsystem A. Fig. 12 shows the results for a small system of size L = 12 with bond dimension χ = 128, averaged over +Ns = 100 disorder realisations. The mutual information is qualitatively – and even quantitatively, in many cases – similar to the +entanglement negativity, strongly suggesting that it would be a more than acceptable substitute and that much of the intuition +developed in the main text should also apply to the mutual information. +0 +5 +10 +0 +2 +4 +I(A : B) +d = 2.0 +0 +5 +10 +0 +1 +2 +d = 3.0 +0 +5 +10 +0.0 +0.5 +1.0 +1.5 +d = 4.0 +0 +5 +10 +0.0 +0.5 +1.0 +d = 5.0 +0 +5 +10 +t +0.0 +0.5 +I(A : B) +d = 6.0 +0 +5 +10 +t +0.00 +0.25 +0.50 +0.75 +d = 7.0 +0 +5 +10 +t +0.0 +0.2 +0.4 +0.6 +d = 8.0 +0 +5 +10 +t +0.0 +0.2 +0.4 +0.6 +d = 9.0 +r = 0 +r = 1 +r = 2 +r = 3 +r = 4 +FIG. 12. A comparison of mutual information (solid lines) and entanglement negativity (dashed lines) between subsystems A and B separated +by a distance r, for a system of size L = 12 with bond dimension χ = 128, averaged over Ns = 100 disorder realisations. + +12 +Computation of the l-bits and the quasi-locality measure +The l-bits in this work are calculated using the method described in Ref. [30]. For completeness, we offer a brief explanation +of the method: A system in the fully many-body localised phase can be fully characterized by a complete set of l-bits. Let H +be the MBL Hamiltonian of a system of size N and τi, i = 1, . . . , N, be the l-bits, then they need to satisfy the following +properties: +1. [H, τ z +i ] = 0, +2. [τ z +i , τ z +j ] = 0 for all i and j, +3. τi is quasi-local in real space (will be elaborated in the next section). +A simple prescription in Ref. [50] has been given to construct the l-bits out of infinite time averages of terms that the Hamiltonian +contains. The infinite-time average of a term hj is +E(hj) = lim +T →∞ +1 +T +� T +0 +e−iHt hj eiHt dt = +� +k +⟨Ek| hj |Ek⟩ |Ek⟩ ⟨Ek| , +(10) +assuming a non-degenerate spectrum {Ek} of H. Therefore, E(hj), being sums of projectors onto the eigenstates of H, +automatically fulfill properties 1 and 2. The authors have also demonstrated the quasi-locality of the resulting operator, showing +that the non-local contributions from the off-diagonal elements, i.e., contributions from τ x and τ y will be removed through the +infinite-time averaging procedure. The downside with this approach is that the resulting operator has a degenerate spectrum that +is distinct from what the Pauli algebra mandates. Thus, we can no longer associate this operator with the picture of having ladder +operators that help us transverse through the different modes/eigenstates. +The authors in Ref. [30] have computed E(σz +j ) from (10) and re-arranged the order of the eigenstates in Ud to minimize the +pair-wise differences between the spectrum of E(σz +j ) and that of +τ z +j = U † +dσz +j Ud, +(11) +starting with j = 1 and sequentially optimising the eigenstate order with larger j while keeping the already optimized partial +ordering from smaller j intact. The resulting operators will preserve the Pauli algebra by construction while becoming quasi-local +in real space. For simplicity, we only deal with trace-less and Hermitian operators for the moment. Operators with non-vanishing +traces require special procedures to meet the orthonormality of the Hilbert-Schmidt inner product. +Definition 3 (Quasi-locality). Let τ be a trace-less Hermitian operator, normalized with respect to the Frobenius norm, and Li +its orthogonal trace-less Hermitian basis. Consider the decomposition +τ = +� +i +aiLi. +(12) +Let S(Li) be the support of Li in real-space. τ is quasi-local around site j, if and only if for any connected region B containing +j, we have +� +S(Li)⊈B +|ai|2 ≤ k exp(−dist(j, B)/ξ). +(13) +This definition, although rigorous, can be cumbersome, and it is not easy to compute the relevant quantities. Let us consider +the partial trace of the operator τ, +trBC(τ) = 2|BC| +� +S(Li)⊆B +ai ˜Li, +(14) +where ˜Li are now defined on a smaller Hilbert space contained in B and the extra identity operators outside B become the +pre-factor 2|BC| after the partial trace. Then, we can compute the square of the Frobenius norm of this truncated operator to get +∥trBC(τ)∥2 +2 = 22|BC|tr( +� +S(Li)⊆B +a∗ +i ˜Li +� +S(Lj)⊆B +aj ˜Lj) = 22|BC|+|B| +� +S(Li)⊆B +|ai|2, +(15) + +13 +due to the orthogonality of the basis operators Li and their restrictions to any region B. Finally, we leverage the normalisation +of τ to observe that +� +S(Li)⊆B +|ai|2 + +� +S(Li)⊈B +|ai|2 = ∥τ∥2 +2 = 1. +(16) +Therefore, +� +S(Li)⊈B +|ai|2 = 1 − +1 +2|B|+2|BC| ∥trBC(τ)∥2 +2 ≤ k exp(−dist(j, B)/ξ). +(17) +This is exactly the quasi-locality measure proposed in Refs. [30, 32]. The spatial decay of the l-bits can also be computed +using the weight measure in Eq. (6) from Ref. [59]. This notion of quasi-locality is agnostic to operator content and where it is +quasi-local around because one only needs to compute the weight of the operator filtered at each site. +Entanglement growth bound +In this section, we prove an entanglement growth bound that has been tailored for the case at hand. Generic entanglement +growth bounds for the entanglement entropy have been proven for local Hamiltonians [50, 60–62]. Here, we prove novel +bounds for the negativity, ones that are tailored to be applicable to many-body localised systems and the geometry at hand. +We now look at the specific setting of having two regions, A and B separated by a region C that has been traced out, and +ask how much entanglement can be generated by a many-body localised Hamiltonian. We consider states evolving in time as +ρ(t) := e−itHρeitH. For the purpose of this proof, we will consider a slightly relaxed definition of quasi-locality with respect to +Definition 17, namely, instead of the normalized Frobenius norm, we will assume the l-bits are localised in the operator norm, +i.e., the following. +Definition 4 (Weak quasi-locality). An operator is said to be quasi-local around a region R, if for any region X ⊂ R, it holds +that +����O − +1 +2|Xc| trXc(O) ⊗ IXc +���� +2 +∞ +≤ ∥O∥2 +∞Ke−d(R,Xc)/ξ +(18) +for some constant K > 0. +This definition is weaker than Definition 17, in the sense that if an operator is localised in the sense above, it is also localised +in the sense of Definition 17. The following is the central statement from which the entanglement bound easily follows: +Theorem 2 (Entanglement growth bound for sums of quasi-local operators). Let ρ be any initial state. Let H be a many-body +localised Hamiltonian as per Definition 2 with localisation length ξ ≤ 1/(4 log(2)) and 2(1/κ − log(2)) > 1/ξ, consider three +blocks A, C, B such that C divides A from B the growth of the negativity of the state ρ(t) = e−itHρeitH restricted to the regions +A, B for times t ≥ 0 and for any r ≥ |C|/2 +EN(t) = log2(∥ρTA +A,B(t)∥1) ≤ min{t O(e−|C|/(2ξ)), 4r − 2|C|} + tO(e−r/(2ξ)). +(19) +Notice the the r in the above is a parameter one can choose freely. We obtain the following statement simply by picking +r = 2ξ log(t) in the above bound if t > e|C|/(4ξ) and r = |C|/2 otherwise. +Corollary 1 (Logarithmic growth of the negativity). If t ≥ e|C|/4ξ, under the assumptions of Theorem 2, we have +EN(t) ≤ min{t O(e−|C|/(2ξ)), 8ξ log2(t) − 2|C|} + O(1), +(20) +while for t < e|C|/4ξ, +EN(t) ≤ t O(e−|C|/(4ξ)) +(21) +To turn this result into a proper bound for many-body localised Hamiltonians, we need to reduce such Hamiltonians to the +form considered in Theorem 2. For this purpose, we will assume a slightly stronger definition of the many-body localised +Hamiltonian. We call a unitary quasi-local with localisation length ξ if it maps any local operator on a region R to a quasi-local +operator around R with localisation length ξ. We will assume that the Hamiltonian is diagonalised by a quasi-local unitary, + +14 +which means that the l-bits are simply dressed Pauli Z operators, hi = Uσi +zU †. In particular this implies that a product of l-bits +hi1hi2 . . . hin, with i1 < i2 < · · · < in is quasi-local around {i1, . . . , in}. For the purposes of the subsequent discussion, it will +be useful to define the projector +PX(O) = trXc(O) ⊗ +I +2|Xc| , +(22) +for any region X of the lattice. It is easy to verify that PX is a projector and that it is self-adjoint in the Hilbert Schmidt inner +product. In what follows, ∥ · ∥ denotes the operator norm. +Lemma 1 (Quasi-local sums). Let H be a many-body localised Hamiltonian in the sense described above with localisation +length ξ, and in addition, assume 2(1/κ − log(2)) > 1/ξ, where κ has been defined in Definition 2. Then the Hamiltonian can +be written as +H = +N +� +i=1 +Hi +(23) +where Hi is quasi-local around the site i with localisation length 2ξ. +We note that, a quasi-local operator with localisation length ξ is quasi-local for any localisation length ξ′ > ξ, if 2(1/κ − +log(2)) ≤ 1/ξ, it suffices to relax the quasi-locality of the l-bits by increasing the localisation length until this condition is +satisfied, i.e., chooses +ξ′ = +1 +2(1κ − log(2)) + ϵ > ξ +(24) +for some constant ϵ. This will result in faster (∼ r/ξ′), but still exponentially slow, growth of entanglement in the bound. +Proof. Define Hi as +Hi = ωihi + +� +l≥1 +2l+1 +� +k=2 +� +Ik∩{i−l,i+l} +Ik⊂[i−l,i+l] +ωIkhIk +(25) +where Ik = {i1, . . . , ik} are collections of k sites contained in i − l . . . i + l and such that they contain at least one of the two +boundaries i−l, i+l. In the above, we have defined hIk = hi1 . . . hik. We have then ω2 +Ik ≤ ω2e−2l/κ and that hIk is quasi-local +around [i − l, i + l] with localisation length ξ. Clearly, H = � +i Hi, it remains to show that the Hi are quasi-local as claimed. +Let R = [i − r, i + r] be a stretch of sites of radius r around i. We have by the triangle inequality +∥Hi − PR(Hi)∥ = ωi∥hi − PR(hi)∥ + +� +l≥1 +2l+1 +� +k=2 +� +Ik∩{i−l,i+l} +Ik⊂[i−l,i+l] +ωIk∥hi − PR(hi)∥ +≤ ωKe−r/ξ + K +r−1 +� +l=1 +� +Ik∩{i−l,i+l} +Ik⊂[i−l,i+l] +ωe−2l/κe−(r−l)/(2ξ) + 2 +� +l≥r +� +Ik∩{i−l,i+l} +Ik⊂[i−l,i+l] +ωe−2l/κ, +(26) +where we have used quasi-locality and in the l ≥ r part of the sum, that ∥hi − PR(hi)∥ ≤ 2. Now notice that +� +Ik∩{i−l,i+l} +Ik⊂[i−l,i+l] += 22l−1 + 22l−2 + 22l−2 = 22l +(27) +we then have that +∥Hi − PR(Hi)∥ ≤ ωKe−r/(2ξ) + K +r−1 +� +l=1 +22lωe−2l/κe−(r−l)/(2ξ) + 2 +� +l≥r +22lωe−2l/κ += ωKe−r/(2ξ) + K +r−1 +� +l=1 +ωe−2l(1/κ−log(2))e−(r−l)/(2ξ) + 2ω +� +l≥r +e−2l(1/κ−log(2)). +(28) + +15 +The first term is already bounded as needed, and for the third term, we use 2(1/κ − log(2)) > 1/(2ξ) to get +� +l≥r +e−2l(1/κ−log(2)) ≤ +� +l≥r +e−l/(2ξ) = +1 +1 − e−1/(2ξ) e−r/(2ξ). +(29) +For the second term, let δ = 2(1/κ − log(2)) − 1/(2ξ) > 0. Then +r−1 +� +l=1 +e−2l(1/κ−log(2))e−(r−l)/(2ξ) = e−r/(2ξ) +r−1 +� +l=1 +e−δl ≤ +e−δ +1 − e−δ e−r/(2ξ). +(30) +We note in passing that if δ = 0, the bound does not diverge, but an additional linear term is added to get a bound of the form +re−rξ. In conclusion, +∥Hi − PR(Hi)∥ ≤ K′e−r/(2ξ) +(31) +with +K′ := ω +� +K + K +e−δ +1 − e−δ + +2 +1 − e−1/ξ +� +, +(32) +that is, +∥Hi − PR(Hi)∥2 ≤ K′2e−r/ξ +(33) +which is the definition of quasi-locality noticing ||hi|| = 1. +The rest of this section is dedicated to proving Theorem 2. The technique used for the proof is analogous to that of Ref. [50], +where an analogous bound was derived for the entanglement entropy in the case |C| = 0, the properties of the negativity, which +is a meaningful entanglement measure for mixed states, allow the generalisation to disconnected regions. The following two +properties of the 1-norm and the partial transpose will be used repeatedly: +• The 1−norm contracts under the partial trace, i.e., ||ρA||1 ≤ ||ρA,B|| for any bipartite state ρA,B [63], +• ||ρTB +A,B||1 ≤ dB||ρA,B||1 [64]. +First, we need to understand how local Hamiltonians affect the entanglement negativity. +Lemma 2 (Local Hamiltonians affecting the entanglement negativity). Let ρA,B be an arbitrary bipartite state and let H = +� +I HI(t) be a local time-dependent Hamiltonian, where I are regions of the lattice. Assume the norm of the derivative of HI +is bounded by ||H′ +I(t)|| ≤ hI where hI is independent of time, then the bound +||(eiHtρe−iHt)TB||1 ≤ ||ρTB||1 exp +� +t +� +I +hId2 +I∩B +� +(34) +holds. +Proof. Let ρ(t) = eiH(t)ρe−iH(t). We have +||ρ(t + δ)TB||1 = ||ρ(t)TB + δρ′(t)TB + O(δ2)||1 ≤ ||ρ(t)TB|| + δ||[H′(t), ρ(t)]|| + O(δ2), +(35) +and hence +d +dt||(eiH(t)ρe−iH(t))TB||1 ≤ +� +I +||[H′ +I(t), ρ]TB||1 ≤ 2 +� +I +||(H′ +I(t)ρ)TB||1 = 2 +� +I +||(H′ +I(t)(ρ)TB/I)TI∩B||1 +(36) +≤ 2 +� +I +dI∩BhI||ρTB/I||1, +now use +||ρTB/I||1 = ||(ρTB)I∩B||1 ≤ dI∩B||ρTB||1 +(37) + +16 +to get +d +dt||ρ(t)TB||1 ≤ +� +I +hId2 +I∩B||ρ(t)TB||1. +(38) +We now just need to see that for any strictly positive differentiable function f : R+ → R+, f ′(x) ≤ cf(x) implies f(x) ≤ +f(0)ecx. To see this, define g : R+ → R+ as g(x) := log f(x), then +g′(x) = +1 +f(x)f ′(x) ≤ c, +(39) +and therefore +g(x) = +� x +0 +dsg′(s) + g(0) ≤ cx + g(0) +(40) +which by monotonicity of the log function implies the claim. +We note in passing that a much stronger bound can be proven in the same way for time-independent Hamiltonians. In this +case, it suffices to write ρ(t + δ) = eiδHρ(t)e−iδH, then the term in the Hamiltonian which has no intersection with B simply +vanish and do not contribute to the bound. We will now prove Theorem 2. From now on we will assume that |C| is even, the +odd case is analogous. We will label the two central sites of C as ±1, all the sites to the right of the center of C have positive +integer labels, and to the left negative integer labels (notice that there is no site 0). In addition, we will use the standard notation +[a, b) denoting real intervals to denote intervals in the chain, so from now on [a, b) is understood to mean [a, b) ∩ Z/{0}. +Divide the chain into the following regions (see Figure 13), recall that r is an arbitrary integer greater than |C|/2. +¯L = (−∞, −r + |C|/2), +L = (−∞, |C|/2), +(41) +¯∂ = [−r + |C|/2, r − |C|/2], +∂ = [−2r + |C|/2, 2r − |C|/2], +(42) +¯R = (r − |C|/2, ∞), +R = (−|C|/2, ∞), +(43) +and divide the terms in the Hamiltonian accordingly as +H = h¯L + h ¯ +R + h¯∂ +(44) +where h ¯S = � +i∈S hi for S ∈ L, ∂, R. We will now split the term h ¯S into a main local part acting on S and a tail whose norm +is exponentially small in r. +@ +ACDXicdVDLSgNBEJyNrxhfUY9eBoPgaZlNoia3gBePEYwJCH0Tjo6OPtgpleQxW8QvOpveBOv +foN/4Se4GyOoaJ2Kqu6pnvJjrSwJ8eYU5uYXFpeKy6WV1bX1jfLm1rmNEiOxIyMdmZ4PFrUKsUOKNPZigxD4G +rv+1XHud6/RWBWFZ3QT4zCAi1BNlATKpN4gBkMK9KhcEa4PGiKJhfugfAaUyLEYaNa415GclTYDO1R+X0wj +mQSYEhSg7V9T8Q0TPXpMb0iCxGIO8gvsZzSEAO0wnd57y/cSCxTxGA1Xmk9F/L6RQmDtTeBnkwHQpf3t5e +Kfnu9HevwrnCaNYarCOCEMZ5NSuM020qjsm6Qj5VBIsg/g1yFXIBIjSKg5SZmGRlbKvnrg/5PzquvV3Op +pvdKqz8oqsh2y/aZx45Yi52wNuswyTS7Zw/s0blznpxn5+VztODMdrbZDzivH1LDnME= +¯@ +ACEnicdVDLSgNBEJz1bXxFPXoZDIKnMJuXyS3gxaOC0YC7hN5Jq0NmH870CiHkLwSv+hvexKs/ +4F/4Ce7GCpap6Kqe6qngkQrS0K8OTOzc/MLi0vLhZXVtfWN4ubWmY1TI7EjYx2bgAWtYqwQ4o0dhODEAYaz +4PBYe6f36KxKo5OaZigH8JVpC6VBMok3wvAcC8BQwp0r1gSZdGot0SLi3JduM0JEaLRrFS5m5EcJTbFca/47 +vVjmYkdRg7YUrEvJH+WtS47jgpRYTkAO4wouMRhCi9UeTo8d8L7VAMU/QcKX5RMTvGyMIrR2GQTYZAl3b31 +4u/ukFQaz7v8LpsumPVJSkhJHMs0lpnGRbaVRWEPK+MkgE+WeQq4hLMECERnGQMhPTrLFCVtFXD/x/clYpu9V +y5aRWatemZS2xHbL9pnLDlibHbFj1mGS3bB79sAenTvnyXl2Xj5HZ5zpzjb7Aef1A+ConqQ= +L +ACBnicdVDL +SgNBEJyNrxhfUY9eBoPgadndxCTeAl48eEjAPCBZwuy +kEwdnH8z0CmHJXfCqv+FNvPob/oWf4G6MoEHrVFR1U +93lRVJotKx3I7eyura+kd8sbG3v7O4V9w86OowVhzY +PZah6HtMgRQBtFCihFylgvieh691eZH73DpQWYXCN0w +hcn0CMRacYSq1robFkmWe16vOmUMt07JqTrmaEadW +crUTpUMJbJAc1j8GIxCHvsQIJdM675tRegmTKHgEma +FQawhYvyWTaCf0oD5oN1kfuiMnsSaYUgjUFRIOhfh5 +0bCfK2nvpdO+gxv9LKXiX96nhfK0VI4jutuIoIoRgh4 +lo1CwjxbcyXSUoCOhAJElj0DVASUM8UQnKOE/FOG +2pkFb03QP9n3Qc0y6bTqtSalQWZeXJETkmp8QmNdIg +l6RJ2oQTIA/kTwZ98az8WK8fo3mjMXOIfkF4+0TXlO +Zew= +R +ACBnicdVDLSgNBEJz1GeMr6tHLYBA8hd0YnILePGYiHlAsoTZScOmX0w0yuEJXfBq/6GN/Hq +b/gXfoKzawQNWqeiqpvqLi+SQqNtv1srq2vrG5u5rfz2zu7efuHgsKPDWHFo81CGqucxDVIE0EaBEnqRAuZ7E +re9DL1u3egtAiDG5xF4PpsEoix4AyN1LoeFop2yTaoVmlKnJrtGFKv18rlOnUy7aLZIHmsPAxGIU89iFAL +pnWfceO0E2YQsElzPODWEPE+JRNoG9owHzQbpIdOqensWY0gUFZJmIvzcSJiv9cz3zKTP8FYve6n4p+d5oR +wtheO45iYiGKEgKfZKCRk2ZorYUoBOhIKEFn6DFARUM4UQwQlKOPciLFpKW8q+u6B/k865ZJzXiq3KsVGZVF +WjhyTE3JGHJBGuSKNEmbcALkgTySJ+verZerNev0RVrsXNEfsF6+wRbqZl6 +¯R +AC3icdVDLSgNBEJyNrxhfUY9eBoPgKezGoMlN8OIxiokBs4TeSatjZh/M9Aqy+AmCV/0Nb+LV +j/Av/ARn1wgqWqeiqpvqriBR0pDrvjmlqemZ2bnyfGVhcWl5pbq61jNxqgV2Raxi3Q/AoJIRdkmSwn6iEcJA4 +WkwPsj902vURsbRCd0k6IdwEclzKYCs1BsEoPnxsFpz67F7i7PidyPUva7Vaj0eZeYblujU3QGVbfB6NYp +CFGJBQYc+a5CfkZaJC4W1lkBpMQIzhAs8sjSBE42fFtbd8KzVAMU9Qc6l4IeL3jQxCY27CwE6GQJfmt5eLf3 +pBEKvRr3A6b/mZjJKUMBJ5NkmFRbYRWtpmkI+kRiLIn0EuIy5AxFqyUEIK6a2qoqt6KsH/j/pNereTr1x1Kz +tNydldkG2TbzGN7bJ8dsg7rMsGu2D17YI/OnfPkPDsvn6MlZ7Kzn7Aef0A3XGbXQ= +¯L +AC3icdVDL +TgJBEJzF+IL9ehlIjHxRJYFAW8kXjx4wETABAjpHRo +cmX1kpteED7BxKv+hjfj1Y/wL/wEdxETJVqnSlV3q +rvcUElDtv1upZaWV1bX0uZjc2t7Z3s7l7TBJEW2BC +BCvS1CwaV9LFBkhRehxrBcxW23NFZ4rfuUBsZ+Fc0Dr +HrwdCXAymAYqnZcUHzi142Z+dPq2XnxOF23rYrTrGc +EKdScoq8ECsJcmyOei/70ekHIvLQJ6HAmHbBDqk7AU1 +SKJxmOpHBEMQIhtiOqQ8emu5kdu2UH0UGKOAhai4Vn +4n4c2MCnjFjz40nPaAbs+gl4p+e6waqvxBOg2p3Iv0w +IvRFk1S4SzbC3jZpD3pUYiSJ5BLn0uQAMRaslBiF +iM4qoycUXfPfD/SdPJF4p57KUq5XmZaXZATtkx6zA +KqzGzlmdNZhgt+yBPbIn6956tl6s16/RlDXf2We/YL1 +9AuAbm14= +r +ACBnicbVDLSgNBEJyNrxhfUY9eBoPgKexGQY8BLx4TMA9IltA76cQhsw9meoWw5C541d/wJl79 +Df/CT3B3YMm1qmo6qa6y4uUNGTbn1ZpbX1jc6u8XdnZ3ds/qB4edU0Ya4EdEapQ9z0wqGSAHZKksB9pBN9T2 +PNmN5nfe0BtZBjc0TxC14dpICdSAKVSW4+qNbtu5+CrxClIjRVojapfw3EoYh8DEgqMGTh2RG4CmqRQuKgMY +4MRiBlMcZDSAHw0bpIfuBnsQEKeYSaS8VzEX9vJOAbM/e9dNIHujfLXib+63leqMZL4TS5dhMZRDFhILJskg +rzbCO0TEtBPpYaiSB7BrkMuANRKglByFSMU5bqQVOcuFrJuo+5c1Bvty1rTLsoqsxN2ys6Zw65Yk92yFus +wZA9sWf2Yj1ar9ab9f4zWrKnWP2B9bHNzBKmVk= +r +ACBnicbVDLSgNBEJyNrxhfUY9eBoPgKexGQY8BLx4TMA9IltA76cQhsw9meoWw5C541d/wJl79 +Df/CT3B3YMm1qmo6qa6y4uUNGTbn1ZpbX1jc6u8XdnZ3ds/qB4edU0Ya4EdEapQ9z0wqGSAHZKksB9pBN9T2 +PNmN5nfe0BtZBjc0TxC14dpICdSAKVSW4+qNbtu5+CrxClIjRVojapfw3EoYh8DEgqMGTh2RG4CmqRQuKgMY +4MRiBlMcZDSAHw0bpIfuBnsQEKeYSaS8VzEX9vJOAbM/e9dNIHujfLXib+63leqMZL4TS5dhMZRDFhILJskg +rzbCO0TEtBPpYaiSB7BrkMuANRKglByFSMU5bqQVOcuFrJuo+5c1Bvty1rTLsoqsxN2ys6Zw65Yk92yFus +wZA9sWf2Yj1ar9ab9f4zWrKnWP2B9bHNzBKmVk= +FIG. 13. Division of the chain into regions for the proof of Theorem 2. The central region bounded by the vertical lines is C, represented by +the dashed red and blue line. Note that C is contained in both L and R. +More specifically, define HS = PS(h ¯S) as the local part, then the remaining evolution is given by a generator δS(t) implicitly +defined as +eih ¯ +St = eiHSteiδS(t) +(45) +i.e., eiδS(t) = e−iHSteih ¯ +St, then +iδ′ +S(t) = +� d +dteiδS(t) +� +e−iδS(t) = −iHS + ieiHSth ¯Se−iHSt = ieiHStTSe−iHSt +(46) +where we have defined TS := h ¯S − HS as the tail of the l-bits in ¯S. Then, since δS(0) = 0, we find +δS(t) = +� t +0 +dxeiHSxTSe−iHSx. +(47) + +17 +For now, we have written the tail evolution as an operator acting globally on the lattice, it has an exponentially small norm, but +it could still, in principle, create an amount of entanglement extensive in the system size. To apply Lemma 2, we have to recast +it as a local Hamiltonian. For each S, define S + q as the region S extended to the left and the right (if possible) by q sites. We +can then write the tail TS as a telescopic sum, defining HS+q = PS+q(h ¯S) +TS = −HS + HS+1 − HS+1 + HS+2 − HS+2 · · · = − +∞ +� +q=0 +HS+q − HS+q+1. +(48) +Clearly h ¯S = limq→∞ PS+q(h ¯S), as this is simply the “truncation” where the whole lattice is kept. We then have that +δS(t) = +∞ +� +q=0 +ZS+q+1(t) +(49) +where ZS+q(t) := +� t +0 dxeiHSx(HS+q − HS+q+1)e−iHSx acts only on S + q + 1. Until now, we have claimed that these tail +operators have exponentially small norms in r. Before continuing, let us prove this. +Lemma 3 (Tail bounds). ||ZS+q(t)|| ≤ tO(e−(r+q)/(2ξ)). +Proof. We will prove that ||h ¯S − HS+q|| ≤ O(e−(r+q)/(2ξ)), the statement follows as +||ZS+q(t)|| ≤ t||HS+q − HS+q+1|| ≤ t(||HS+q − h ¯S|| + ||HS+q+1 − h ¯S||). +(50) +Let us start with S = ∂. The closest l-bits to the boundary of ∂ + q in ¯∂ are separated from it by r + q sites, and the furthest +ones by 2r + q. The sum is clearly symmetric around the centre of the chain, and we use that for any S, S is constructed such +that the distance from any site in ¯S to the edge of ¯S is at least r. Recall that h ¯S = � +i∈ ¯S hi, where the hi are quasi-local as in +Definition 4. +||h¯∂ − H∂+q|| ≤ +r−|C|/2 +� +k=−r+|C|/2 +||hk − P∂+q(hk)|| ≤ 2K +2r+q−|C|/2 +� +j=r+q +e−j/(2ξ) ≤ O(e−(r+q)/(2ξ)) +(51) +for some constant K > 0, by the definition of quasi-locality. Let us move to S = R, where again the closest l-bits in ¯R to the +boundary of R + q are separated from it by r + q sites, and the furthest has a distance unbounded in the system size. We have +||h ¯ +R − HR+q|| ≤ +� +k>r−|C|/2 +||hk − PR+q(hk)|| ≤ 2K +� +j≥r+q +e−j/(2ξ) ≤ O(e−(r+q)/(2ξ)). +(52) +S = L is entirely analogous. +We have completed the split into local terms and tails. The intuition is now that the entanglement in the system will be driven +on the one hand by the term H∂, which is the only local term connecting A and B, and on the other hand by the tail. The former +can only create entanglement locally around C, and the latter is weak. This split allows us to prove the first part of the bound: +We can write +eiHt = eiH∂teiδ∂(t)eiHLteiδL(t)eiHRteiδR(t) +(53) +Given a Hamiltonian h, define the time evolution operator Uh(ρ) := eihρe−ih. Consider a state σ, notice that the overlap +between B and ∂ is of length 2r − |C|, in particular, +||trC(UH∂t(σ))TB||1 ≤ ||trC(eiH∂t(σ)T(2r−|C|/2,∞)e−iH∂t)T[|C|/2,2r−|C|/2]||1 ≤ 22r−|C|||σT(2r−|C|/2,∞)||1 +(54) +Here we simply assume enough time has passed that H∂ has had time to saturate the entanglement in the region ∂, that is, +create a maximally entangled state between the sites on either side of C. We have then +||ρ(t)TB||1 = ||trC +� +UH∂t ◦ Uδ∂(t) ◦ UHLt ◦ UδL(t) ◦ UHRt ◦ UδR(t)(ρ) +�TB ||1 +≤ 22r−|C||| +� +Uδ∂(t) ◦ UHLt ◦ UδL(t) ◦ UHRt ◦ UδR(t)(ρ) +�T(2r−|C|/2,∞) ||1. +(55) +Next, recall that δ∂(t) = �∞ +q=0 Z∂+q+1, then by Lemma 2, we have +||ρ(t)TB||1 ≤ 22r−|C|E∂,t|| +� +UHLt ◦ UδL(t) ◦ UHRt ◦ UδR(t)(ρ) +�T(2r−|C|/2,∞) ||1 +(56) + +18 +where +E∂,t ≤ exp +� +tO +� +e−r/(2ξ) +∞ +� +q=0 +22(| ∂+q+1∩(2r−|C|/2,∞)|)e−q/(2ξ) +�� +≤ exp +� +tO +� +e−r/(2ξ) +∞ +� +q=0 +22qe−q/(2ξ) +�� +≤ exp +� +tO +� +e−r/(2ξ)�� +, +(57) +where we have used the assumption ξ < 1/(4 log(2)), so that the terms in the sum above are exponentially decaying and sum +to a constant. Since L has no overlap with (2r − |C|/2, ∞), we can just bring the partial transpose inside the L evolution and +eliminate it by unitarity. Afterwards, we eliminate UδR(t), exactly as we have eliminated Uδ∂(t), to get +||ρ(t)TB||1 = 22r−|C|E∂,tEL,t|| +� +UHRt ◦ UδR(t)(ρ) +�T(2r−|C|/2,∞) ||1 +(58) +and in the same way one can show that EL,t ≤ exp +� +t O +� +e−r/(2ξ)�� +. Finally, notice that for any region X and a state σ, +||σTX||1 = ||σTXc ||1, since σ is Hermitian. Then +|| +� +UHRt ◦ UδR(t)(ρ) +�T(2r−|C|/2,∞) ||1 = || +� +UHRt ◦ UδR(t)(ρ) +�T(−∞,2r−|C|/2) ||1 +≤ 22r−|C||| +� +UδR(t)(ρ) +�T(−∞,−|C|/2) ||1 ≤ 22r−|C|ER,t||ρT(−∞,−|C|/2)||1 += 22r−|C|ER,t, +(59) +where we have used that the initial state is a product state, ER,t can be bounded as in the previous cases. Overall, we have then +proven that +||ρ(t)TB||1 ≤ 24r−2|C| exp +� +t O +� +e−r/(2ξ)�� +(60) +holds true. To get the other part of the bound, we need to refine the bound on the entanglement generated by the central term +eiH∂t. While it is true that this operator is quasi-local around C, it is also true that it decays fast outside of the boundaries of C. +We can separate the part of H∂ acting inside C from the rest, which we can subsequently simply treat as a tail, +H∂ = HC − HC−1 + HC+1 − HC + HC+2 − HC+1 + · · · = +2r−|C| +� +q=0 +HC+q−1 − HC+q, +(61) +where now HS = PS(H∂) = PS(h¯∂) for S ⊇ ∂. Just like before, we write +eiH∂t = eiHCtei˜δ∂(t), +(62) +and we proceed in the same exact way as before, except that now the first term gets eliminated by the trace. For some state σ, +we have +||trC(eiHCteiδ(t)σe−iδ(t)eiHC)||1 = ||trC(ei˜δ∂(t)σe−i˜δ∂(t))||1 ≤ E˜∂,t||σ||1 +(63) +and we can bound E˜∂,t ≤ exp(tO(e−|C|/(2ξ))) just like earlier. Proceeding in the same way as earlier, we get the bound +||ρ(t)TB||1 ≤ exp(tO(e−|C|/(2ξ))) exp +� +t O +� +e−r/(2ξ)�� +. +(64) +The final result is obtained by taking the minimum of the two bounds and applying log2 on both sides. + diff --git a/S9AzT4oBgHgl3EQf0v4t/content/tmp_files/load_file.txt b/S9AzT4oBgHgl3EQf0v4t/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..8be79590d685e8c6db8b599e98a3bac0cc321b49 --- /dev/null +++ b/S9AzT4oBgHgl3EQf0v4t/content/tmp_files/load_file.txt @@ -0,0 +1,1169 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf,len=1168 +page_content='Measuring out quasi-local integrals of motion from entanglement B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Lu,1, ∗ C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Bertoni,1, ∗ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Thomson,1, † and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Eisert1, 2, ‡ 1Dahlem Centre for Complex Quantum Systems, Freie Universit¨at, 14195 Berlin, Germany 2Helmholtz Center Berlin, 14109 Berlin, Germany (Dated: January 6, 2023) Quasi-local integrals of motion are a key concept underpinning the modern understanding of many-body localisation, an intriguing phenomenon in which interactions and disorder come together.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Despite the existence of several numerical ways to compute them—and astoundingly in the light of the observation that much of the phenomenology of many properties can be derived from them—it is not obvious how to directly measure aspects of them in real quantum simulations;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' in fact, the smoking gun of their experimental observation is arguably still missing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' In this work, we propose a way to extract the real-space properties of such quasi-local integrals of motion based on a spatially-resolved entanglement probe able to distinguish Anderson from many-body localisation from non-equilibrium dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' We complement these findings with a new rigorous entanglement bound and compute the relevant quantities using tensor networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' We demonstrate that the entanglement gives rise to a well-defined length scale that can be measured in experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' It is widely believed that generic quantum systems iso- lated from their environments will evolve under their own dynamics until they reach an apparent equilibrium state that locally resembles the expectations of a thermal equilibrium state [1, 2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' This expectation is seen as a stepping stone to reconcile predictions from statistical mechanics and those of basic quantum mechanics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' One major exception to this rule is the case of low-dimensional quantum systems in the pres- ence of random disorder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Non-interacting quantum systems in one dimension will entirely fail to thermalise due to any finite concentration of disorder [3], and in recent decades it has been shown that interacting many-body systems appear to suffer the same fate [4, 5], leading to the phenomenon now known as many-body localisation (MBL) [6–12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' From a theoretical standpoint, MBL is now fairly well understood in terms of the emergence of an extensive number of con- served quantities known as (quasi-)local integrals of motion (LIOMs, also known as localised bits or l-bits) which can prevent many-body systems from reaching thermal equilib- rium [7, 13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' While phenomenological models based around the concept of l-bits have seen great success [14, 15], and there are several approaches that can map microscopic mod- els onto effective l-bit models [16–26], the l-bits themselves remain a strictly theoretical construct, inaccessible to any ex- perimental probes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' This is in contrast with the case of An- derson localised systems, where the exponentially localised l-bits can be straightforwardly related to the real-space decay of the single-particle states, which has been experimentally observed [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' In this work, we propose an experimentally feasible ap- proach to measuring the actual real-space properties of local integrals of motion in many-body quantum systems using the entanglement negativity, a sensitive entanglement monotone that allows for the recovery of spatially resolved entangle- ment information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' In this way, we accommodate the above missing link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Various quantities capturing correlations and entanglement, including the negativity, have been measured in recent experiments with ultra-cold bosons: Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [28] has measured the configurational entanglement and number en- FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' a) A sketch showing how a one-dimensional spin chain is partitioned into three subsystems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' We are interested in computing the entanglement between subsystems A and B after subsystem C has been traced out, giving rise to a spatially-resolved entanglement measure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' b) Sketch of the initial quantum state in matrix product op- erator (MPO) form, made by taking the outer product of two matrix product state vectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' c) Sketch of how the negativity is computed: the partial transpose of subsystem A corresponds to ‘twisting’ the MPO legs while tracing out subsystem C corresponds to contracting the relevant MPO indices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' tanglement for a system subject to a quasi-periodic potential and has provided evidence for an exponentially decaying cor- relation length, while Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [29] has studied a disordered sys- tem and has shown that the entanglement negativity can be directly measured.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' In a first experiment, the authors of the latter work prepared the system in a product state and mea- sured the two-qubit entanglement of formation as they vary the separation between the qubits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' While this setting is close in spirit to our approach, they have chosen a two-qubit setting, which is the only setting in which one can compute this quan- tity, so that the diagnostic time scale that allows observation of any spatial dependence is short.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' In a second experiment, the preservation of entanglement has been studied, departing from the approach taken here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Here, we demonstrate that the negativity itself gives direct access to a unique length scale that characterises the l-bits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Quasi-local operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' While the question of whether many-body localisation is a well-defined stable phase in the thermodynamic limit remains unsettled, for our purposes we shall define many-body localisation in the following way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='01787v1 [cond-mat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='dis-nn] 4 Jan 2023 A B2 Definition 1 (Quasi-local operators).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' An operator O on the lattice Λ is said to be quasi-local around a region R with lo- calisation length ξ if for any region X ⊂ Λ containing R ���� ����O − 1 2|Xc| trXc(O) ⊗ IXc ���� ���� 2 ≤ ∥O∥2 Ke−d(R,Xc)/ξ (1) where C > 0 is a universal constant, d(Xc, R) = min x∈Xc,r∈Rd(x, r), and ∥ · ∥ is the normalized 2-norm, ∥O∥2 = trOO†/trI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Interestingly, the relatively loose sense of decay in 2-norm seems crucial, an insight that is often under-appreciated [30, 31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' It is important to note that this is an abstract definition: it does not give operational advice on how to find those l- bits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' What is more, even if they exist, they are by no means unique [32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' There could be “more local” l-bits than those given that still give rise to a complete set of l-bits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Either way, as is common, such l-bits serve as our definition for many- body localisation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Definition 2 (Many-body localisation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' A Hamiltonian H = n � j=1 ω(1) j hj + n � j,k=1 ω(2) j,khjhk + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' (2) with real weights {ω(1) j } and {ω(2) j,k}, is called many-body lo- calised if it can be written as a sum of mutually commuting ([hj, hk] = 0 for all j, k) quasi-local terms hj, each cen- tred around site j, and if ωi1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=',in ≤ ωe−|i1−in|/κ, where i1 < i2 · · · < in.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Premise of the approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' When written in the basis that diagonalises the Hamiltonian, as in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' (2), these l-bits are strictly local objects, but in real-space they are quasi-local with exponentially decaying tails.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' In order to extract proper- ties of l-bits from experiments, we shall consider the evolution of an arbitrary initial state under the following Hamiltonian dynamics as ρ(t) = e−itHρeitH, (3) for times t ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' To simplify the notation, we will suppress the time argument for time t = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' How can this time evolution be exploited to measure out real-space properties of the l-bits?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Some intuition can be attained in the situation when the {hj} are strictly local.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' The terms that do not overlap do not con- tribute to the entanglement evolution at all.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' So in the end, it is the overlapping tails that will lead to entanglement growth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' We will demonstrate our scheme numerically using the ‘standard model’ of MBL, namely the XXZ spin-1/2 chain with random on-site fields, while it should be clear that the ap- proach taken would be applicable to any many-body localised model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Its Hamiltonian is given by H = J0 � i � Sx i Sx i+1 + Sy i Sy i+1 + ∆Sz i Sz i+1 � + � i hiSz i , (4) with hi ∈ [−d, d].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' We shall set J0 = 1 as the unit of en- ergy throughout, with ∆ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0 unless otherwise stated, and will use open boundary conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' This model has been thor- oughly studied and shown to exhibit a phase with anoma- lous thermalisation properties above a disorder strength of d ≳ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='7 [9], although recent work has suggested that the true phase transition in the thermodynamic limit could be at much larger values of d if it exists at all [33–37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' The characteristic growth in time of the von Neumann en- tanglement entropy [38, 39] (or its correlation-based ana- logues [40]) has been shown to be a good indicator of many- body localisation, able to distinguish it from single-particle Anderson localisation via the late-time logarithmic growth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Motivated by this, our aim in this work is to show that other entanglement measures which provide spatially-resolved in- formation can not only distinguish many-body localisation from Anderson localisation, but can also allow direct quan- titative measurement of the properties of many-body local in- tegrals of motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Diagnostic entanglement quantity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' The main quantity of interest in this work is the logarithmic negativity, a measure of the entanglement between two subsystems of the spin chain, denoted A and B, separated by a distance r, which together with C constitutes the entire system (sketched in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' It is defined as [41–44] EN(ρA,B(t)) := log2(∥ρTA A,B(t)∥1), (5) where ∥O∥1 = tr|O| denotes the trace norm, ρA,B(t) = tr\\{A,B}[ρ(t)] is the time-dependent quantum state of sub- systems A and B after tracing out all other lattice sites, and the superscript TA indicates the partial transpose with respect to subsystem A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' This has been shown to be an entangle- ment monotone meaningfully quantifying entanglement [43– 45].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' In the following, we shall refer to this quantity simply as ‘negativity’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' By contrast to the more commonly studied bi- partite von Neumann or R`enyi entanglement entropies which consider a single bi-partition between two connected subsys- tems, the entanglement negativity allows for a meaningful spatially resolved measure of mixed-state entanglement, as the two subsystems can be separated by an arbitrary distance r := dist(A, B), a feature the von Neumann entropy cannot capture as a pure state entanglement measure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' This measure can also be used to study the entanglement between subsys- tems of arbitrary size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' However, for conceptual clarity, we shall mainly consider A and B to cover the entire chain ex- cept for a piece C with |C| = r + 1 separating A and B, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' That said, the concept works as well for small regions A and B, as they are accessible in experi- ments and are discussed in the rigorous bounds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Numerical evidence is shown [46].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' The negativity has previously been investigated in the context of ground states of disordered spin chains [47], the many-body localisation transition [48], and quench dynamics in the presence of a defect [49].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' For clarity, in the following, we shall drop the explicit dependence of EN on the quantum state and instead use the notation EN(r, t) 3 to represent the negativity associated to two subsystems sepa- rated by a distance r and a time t following a quench from an initial product state, emphasizing that this is indeed a spatially resolving entanglement measure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' A heuristic argument for why this quantity is relevant in our case can be given in the following manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [13] has shown that the von Neumann entanglement entropy grows in time following a quench according to Sent ∝ ln(J0t/ℏ), once the system enters the late-time dephasing regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' If we wish to consider the entanglement negativity between two subsystems separated by a distance r, a reasonable starting assumption is that the negativity will vary in time accord- ing to the same ∼ ln(t) growth but will be exponentially suppressed in magnitude due to the spatial separation of the two subsystems, leading to an overall behaviour of EN ∝ exp(−r/ξ) ln(J0t/ℏ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' We shall show that this ansatz is a good match for the numerical results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' We also wish to empha- sise that this logarithmic growth is characteristic of the inter- acting system and is entirely absent from Anderson-localised systems, meaning that the existence of this length scale is a distinct fingerprint of a many-body localised system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Corroborating the reasoning with rigorous bounds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' We see that Hamiltonians that are many-body localised in the sense of Definition 2 create entanglement at a rate that decays expo- nentially in the distance r = dist(A, B) between parts A and B, reflecting the exponential decay of the tails in quasi-local l-bits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' In fact, not only this intuition can be made entirely rigorous, but, at the cost of slightly weakening the definition of quasi-locality, we are in the position to state precise upper bounds for the negativity for all times and distances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Theorem 1 (Rigorous entanglement bounds).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Let ρ be an ini- tial product state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Let H be a many-body localised Hamil- tonian as per Definition 2 with localisation length ξ < 1/(4 log(2)) and 2(1/κ − log(2)) > 1/ξ, consider three blocks A, C, B such that C divides A from B, with |C| = r + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' The growth of the negativity of the state ρ(t) = e−itHρeitH restricted to the regions A, B is bounded as EN(r, t) ≤ min{t O(e−r/(2ξ)), 8ξ log2(t)−2r}+O(1), (6) for times t ≥ er/(4ξ), while for t < er/(4ξ), EN(r, t) ≤ t O(e−r/(4ξ)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' (7) We hence find a short time behaviour signifying a linear growth in time, a cross-over regime governed by the correla- tion length, and a logarithmic growth for long times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' These bounds—interesting in their own right and complementing and refining those of Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [50]—are perfectly compatible with the above numerical assessment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' In the Supplemental Mate- rial, we state details of the proof of the bound that makes ex- tensive use of the precise form of the tails of the l-bits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Based on our numerical results, we expect that our assumptions on the localisation length and the definition of quasi-locality can be relaxed without affecting the result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' We also note that the 10−1 100 101 102 t 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='6 EN(r, t) (a) (b) (c) r = 1 r = 2 r = 3 r = 4 r = 5 r = 6 0 10 r −1 0 1 2 log10(t) log10(EN) ε = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='005 ε = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='001 ε = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0001 0 5 10 r −10 −5 0 log(EN(r, t∗)) t∗ = 46 t∗ = 115 t∗ = 288 t∗ = 391 t∗ = 500 −4 −2 0 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Results showing the growth of the negativity EN(r, t) with time for different distances r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Data is shown for a system size L = 24 and a disorder strength d = 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0, averaged over Ns = 100 disor- der realisations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' a) The dynamics of EN(r, t) following a quench from a N`eel state, showing the logarithmic growth at late times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' The circular markers are the raw data points, while the solid lines are a smoothed guide to the eye.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' The error bars indicate the stan- dard error in the mean.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' b) The full dynamics of EN(r, t), reflect- ing the logarithmic ‘light cone’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' c) By extracting the behaviour of EN(r, t∗) ∝ exp(−r/ξ) at fixed times t∗ [dashed vertical lines in panel (a), horizontal lines in panel (b)], we can extract a well-defined length scale ξ(t), which depends only weakly on time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' The solid lines indicate the fits to the data points which are used to extract the l-bit length scale, demonstrating convergence at late times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' observed ξ−dependence of the late time decay of the entan- glement with the size of C is not visible in this bound, though we expect that it can be refined to show this.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Extraction of the l-bits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' We compute the negativity us- ing time-dependent matrix product state simulations – an in- stance of a tensor network method [51] – implemented in the Quimb package [52] using the time-evolving block decima- tion (TEBD) algorithm to perform the evolution [53, 54], with the system initially prepared in a N´eel state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' We use system size L = 24 with a maximum bond dimension of χ = 192.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' We perform the time evolution using a maximum time step dt = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='05, at each step discarding singular values smaller than ϵ = 10−10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' We have checked that the results are well- converged.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Detailed benchmarks are shown in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [46].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Our TEBD results are compared against l-bit length scales ob- tained using exact diagonalisation, following Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' The negativity can be computed straightforwardly from a matrix product state (MPS) representation [55].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' The state vector can be turned into a matrix product operator (MPO) (sketched in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 1) representing the quantum state by consid- ering vectors and dual vectors represented as MPS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' The partial transpose can be computed by ‘twisting’ the legs of the MPO tensors, while the partial trace over the subsystem C can be performed by contracting the free indices of the MPO tensors 4 in this subsystem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' At long times, the negativity should satu- rate at a value controlled by the size of the subsystems, and at any time t < ts (where ts is the saturation time), the nega- tivity should satisfy the hierarchy EN(r1, t) < EN(r2, t) for any two distances r1 > r2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' We first discuss qualitatively the results for the growth of the entanglement negativity with time for various differ- ent distances r, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 2a) for a disorder strength d = 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0 (deep in the localised phase), where we find that indeed the negativity grows logarithmically with time at late times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Results for further disorder strengths, system sizes, and subsystem sizes are available in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [46].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' At short times, the negativity is dominated by diffusive transport on length scales shorter than the localisation length.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' At large distances r, the negativity remains close to zero until a time exponen- tially large in r, which can be used to define a ‘light cone’ that characterises the spreading of the entanglement negativ- ity, shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 2b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' The three lines indicate when the neg- ativity grows above a threshold ε ∈ {0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0001, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='001, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='005}, mapping out an approximately logarithmic light cone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' As the negativity outside of this length cone is exponentially small, in the following analysis, we restrict ourselves to space-time coordinates (r, t), which are within the light cone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' The exis- tence of this light cone means that we gain only diminishing returns by going to larger system sizes: although we are able to separate the subsystems by a larger value of r, the evolu- tion time required to obtain meaningful entanglement scales exponentially in r, which incurs a large computational cost for large systems and quickly becomes prohibitive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' In the late-time logarithmic growth regime, where the dy- namics are dominated by the quasi-local nature of the l-bits, we extract the value of the negativity at a given time t∗ follow- ing the quench from an initial N´eel state and plot it versus the subsystem separation r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' We show this in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 2c) for several different choices of time t∗ [indicated by the dashed lines in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 2a)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' The data points form a straight line (on a logarith- mic scale), and at late times the gradient of the line does not strongly change with the choice of time t∗, appearing to satu- rate at a fixed value (although the y-axis offset will, of course, continue to increase in time).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Further details are available in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [46].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Under the assumption that the negativity decays exponentially with distance like EN(r, t∗) ∝ exp(−r/ξ), we can perform a linear fit to the data shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 2c) and ex- tract a well-defined length scale ξ which characterises the spa- tial extent of the l-bits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' The results are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 3, where we find that the length scale ξ exhibits monotonic decay with increasing disorder strength, as expected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Note that no as- sumptions are involved other than the exponential decay of the negativity with distance at some fixed time t∗: the resulting length scale is an emergent property of the many-body sys- tem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' This assumption does not hold in the delocalised phase, where the entanglement does not enter a regime of logarithmic growth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' We can further compare the length scale extracted from our procedure with the l-bit decay lengths computed us- ing the established numerically exact method of Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [30], using the definition of quasi-locality from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' We find 2 4 6 8 10 d 0 2 4 6 ξ L = 24 L = 14 (ED) L = 12 (ED) L = 128 (∆ = 0) FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' The characteristic l-bit length scale ξ extracted from the entanglement negativity at time t∗ = 500, shown for L = 24 with Ns ∈ [50, 100] disorder realisations and various values of the disorder strength d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Error bars indicate the fit error and are roughly the same size as the plot markers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' The black line indi- cates the localisation length of the corresponding Anderson-localised system, obtained by directly diagonalising the Hamiltonian in the non-interacting limit (∆ = 0), for a system of size L = 128 with Ns = 10000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' excellent agreement between the entanglement-based length scale and the l-bit localisation length obtained independently from this method, confirming that the length scale probed by the negativity is the localisation length of the l-bits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' For comparison, we also indicate the corresponding locali- sation length of an Anderson localised system, here obtained by directly diagonalising the Hamiltonian with ∆ = 0 (fol- lowing a Jordan-Wigner transform into the fermionic repre- sentation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' We compute the eigenvectors of the Hamiltonian in the non-interacting setting, which decay in real space as exp(−r/ξ) [56], average over disorder realisations and ex- tract the localisation length ξ from a least-squares fit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' The length scale extracted from the TEBD data behaves in a qualitatively similar manner to the single-particle localisation length but is always larger, confirming that we are not measur- ing single-particle properties but are indeed extracting a gen- uinely many-body feature of the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' In the delocalised phase, our assumed form of the negativity is no longer valid, and as such, the method cannot extract a reliable length scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' We also note that the entanglement negativity is not the only entanglement measure which may be used in this way: any spatially-resolved entanglement probe should behave sim- ilarly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' In the Supplemental Material [46], we demonstrate that the mutual information also gives consistent results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Conclusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' In this work, we have outlined a new exper- imentally feasible procedure for measuring local integrals of motion based on their contribution to the slow growth of the negativity at long times following a quench from an arbitrary initial state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' We have demonstrated that the length scale which we obtain from this procedure, which characterises the l-bits, is in good agreement with that obtained using other theoreti- cal methods in the literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' The crucial advantage is that our scheme is experimentally tractable, unlike other purely the- oretical/numerical methods, which cannot be verified in real experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' It would be extremely interesting to apply this method to other scenarios where many-body localisation is 5 believed to exist, such as in disorder-free systems and two- dimensional models, in order to see if well-defined length scales based on the spreading of entanglement may still be extracted in these situations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' This work paves the way for the application of spatially-resolved entanglement probes to phenomena in quantum simulation beyond many-body local- isation, where such methods may be able to provide valuable insight into emergent length scales associated with other types of quasi-particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Acknowledgements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' This project has been inspired by dis- cussions with P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Roushan and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Chiaro of Google AI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' We also thank A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Kshetrimayum, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Sotiriadis, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Qasim, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Gray for discussions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Lu is grateful for feedback from D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Abanin, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Fleischhauer, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Kiefer-Emmanouilidis at the CRC 183 summer school “Many-body physics with Ryd- berg atoms”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' This project has received funding from the Eu- ropean Union’s Horizon 2020 research and innovation pro- gramme under the Marie Skłodowska-Curie grant agreement No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 101031489 (Ergodicity Breaking in Quantum Matter), grant agreement No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 817482 (PASQuanS), and the Deutsche Forschungsgemeinschaft (CRC 183 and FOR 2724).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' We also acknowledge funding from the BMBF (FermiQP and MUNIQC-ATOMS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' The full code and data for this work are available at Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [57, 58].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' ∗ These two authors contributed equally † steven.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='thomson@fu-berlin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='de (he/him/his) ‡ jense@zedat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='fu-berlin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='de [1] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Polkovnikov, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Sengupta, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Silva, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Vengalattore, Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 83, 863 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [2] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Gogolin and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Eisert, Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Prog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 79, 56001 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [3] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Anderson, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 109, 1492 (1958).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [4] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Fleishman and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Anderson, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' B 21, 2366 (1980).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [5] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Basko, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Aleiner, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Altshuler, Ann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 321, 1126 (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [6] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Huse, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Nandkishore, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Oganesyan, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Pal, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Sondhi, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' B 88, 014206 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [7] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Huse, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Nandkishore, and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Oganesyan, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' B 90, 174202 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [8] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Altman and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Vosk, Ann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Cond.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Matt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 6, 383 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [9] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Luitz, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Laflorencie, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Alet, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' B 91, 081103 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [10] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Alet and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Laflorencie, Compt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Rend.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 19, 498 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [11] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Abanin, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Altman, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Bloch, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Serbyn, Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 91, 021001 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [12] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Friesdorf, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Werner, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Brown, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Scholz, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Eis- ert, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 114, 170505 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [13] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Serbyn, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Papi´c, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Abanin, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 111, 127201 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [14] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Ros, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' M¨uller, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Scardicchio, Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' B 891, 420 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [15] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Imbrie, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Ros, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Scardicchio, Ann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 529, 1600278 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [16] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Rademaker and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Ortu˜no, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 116, 010404 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [17] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Rademaker, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Ortu˜no, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Somoza, Ann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' , 1600322 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [18] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Pekker, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Clark, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Oganesyan, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Refael, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 119, 075701 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [19] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Goihl, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Gluza, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Krumnow, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Eisert, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' B 97, 134202 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [20] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Thomson and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Schir´o, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' B 97, 060201 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [21] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Kulshreshtha, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Pal, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Wahl, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Simon, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' B 99, 104201 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [22] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Thomson and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Schir´o, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Research 2, 043368 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [23] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Thomson, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Magano, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Schir´o, SciPost Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 11, 28 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [24] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Thomson and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Schir´o, arXiv:2110.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='02906 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [25] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Thomson, arXiv:2208.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='11731 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [26] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Bertoni, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Eisert, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Kshetrimayum, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Nietner, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Thomson, arXiv:2208.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='14432 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [27] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Billy, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Josse, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Zuo, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Bernard, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Hambrecht, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Lugan, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Cl´ement, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Sanchez-Palencia, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Bouyer, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Aspect, Nature 453, 891 (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [28] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Lukin, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Rispoli, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Schittko, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Tai, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Kaufman, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Choi, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Khemani, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' L´eonard, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Greiner, Science 364, 256 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [29] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Chiaro, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Neill, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Bohrdt, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Filippone, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Arute, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Arya, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Babbush, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Bacon, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Bardin, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Barends, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Boixo, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Buell, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Mutus, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' McEwen, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Naa- man, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Neeley, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Niu, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Petukhov, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Quintana, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Rubin, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Sank, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Satzinger, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' White, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Yao, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Yeh, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Zalcman, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Smelyanskiy, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Neven, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Gopalakrishnan, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Abanin, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Knap, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Martinis, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Roushan, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Research 4, 013148 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [30] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Goihl, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Gluza, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Krumnow, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Eisert, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' B 97, 134202 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [31] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Ilievski, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Medenjak, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Prosen, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Zadnik, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Stat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Mech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' , 064008 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [32] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Chandran, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Kim, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Vidal, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Abanin, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' B 91, 085425 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [33] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Doggen, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Schindler, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Tikhonov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Mirlin, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Neupert, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Polyakov, and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Gornyi, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' B 98, 174202 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [34] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' ˇSuntajs, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Bonˇca, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Prosen, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Vidmar, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' E 102, 062144 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [35] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' ˇSuntajs, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Bonˇca, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Prosen, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Vidmar, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' B 102, 064207 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [36] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Sels and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Polkovnikov, arXiv:2105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='09348 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [37] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Sels and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Polkovnikov, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' E 104, 054105 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [38] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Bardarson, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Pollmann, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Moore, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 109, 017202 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [39] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Znidaric, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Prosen, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Prelovsek, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' B 77, 064426 (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [40] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Goihl, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Friesdorf, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Werner, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Brown, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Eisert, Quantum Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 1, 50 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [41] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' ˙Zyczkowski, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Horodecki, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Sanpera, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Lewenstein, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' A 58, 883 (1998).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [42] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Eisert and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Plenio, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 46, 145 (1999).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [43] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Vidal and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Werner, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' A 65, 032314 (2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [44] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Plenio, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 95, 090503 (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [45] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Eisert, “Entanglement in quantum information theory,” (2001), PhD thesis, University of Potsdam, arXiv:quant- 6 ph/0610253.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [46] See Supplemental Material for details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' The Supplemental Ma- terial contains Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [59–64].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [47] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Ruggiero, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Alba, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Calabrese, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' B 94, 035152 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [48] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Gray, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Bayat, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Pal, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Bose, arXiv:1908.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='02761 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [49] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Gruber and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Eisler, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' A 53, 205301 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [50] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Kim, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Chandran, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Abanin, arXiv:1412.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='3073 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [51] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Or´us, Ann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 349, 117 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [52] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Gray, Journal of Open Source Software 3, 819 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [53] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Vidal, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 93, 040502 (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [54] U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Schollw¨ock, Ann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 326, 96 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [55] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Gray, arXiv:1809.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='01685 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [56] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Lee and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Ramakrishnan, Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 57, 287 (1985).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [57] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Thomson, https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='com/sjt48/EntanglementDynamics (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [58] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Lu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Bertoni, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Thomson, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Eisert, https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='5281/zenodo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='7322988 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [59] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Kulshreshtha, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Pal, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Wahl, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Simon, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' B 98, 184201 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [60] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Mari¨en, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Audenaert, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Acoleyen, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Ver- straete, Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 346, 35–73 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [61] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Eisert and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Osborne, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 97, 150404 (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [62] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Eisert, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 127, 020501 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [63] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Rastegin, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Stat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 148, 1040 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [64] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Tsuyoshi and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Sano, Positivity 12 (2008), 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='1007/s11117- 007-2121-7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 7 Supplemental Material to “Measuring local integrals of motion from entanglement” TEBD accuracy benchmarks As TEBD does not precisely conserve the energy of the initial state, as a benchmark of the accuracy of our numerics we compute the relative error in the energy of the time-evolved state vector, E(t) = ⟨ψ(t)|H|ψ(t)⟩, computed with respect to its energy at time t = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' The relative error is defined as δE(t) := ���� E(t) − E(t = 0) E(t = 0) ���� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' (8) Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 4 shows the relative error versus time for a variety of different disorder strengths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' We find that in most cases, the relative error remains close to δE ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='001, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=', the energy is conserved up to an error of approximately one-tenth of a percent, confirming that our simulations are reliable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 100 102 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='000 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='002 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='004 δE(t) (a) (b) (c) (d) d = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0 100 102 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='000 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='002 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='004 d = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0 100 102 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='000 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='002 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='004 d = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0 100 102 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='000 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='002 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='004 d = 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0 100 102 t 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='000 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='002 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='004 δE(t) (e) (f) (g) (h) d = 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0 100 102 t 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='000 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='002 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='004 d = 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0 100 102 t 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='000 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='002 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='004 d = 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0 100 102 t 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='000 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='002 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='004 d = 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0 L = 14 L = 24 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' A comparison of the relative error in the energy of the time-evolved state for different values of the disorder strength d, shown for system sizes L = 14 (χ = 128, averaged over Ns = 240 disorder realisations) and - at strong disorder only - L = 24 (χ = 192, averaged over Ns = 100 disorder realisations).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' The relative error remains below 1% for all disorder strengths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Error bars indicate the variance over disorder distributions and in most cases, are of comparable size to the plot markers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Comparison of disorder strengths In addition to the data presented in the main text, here we show the behaviou of the entanglement negativity over a range of different disorder strengths, demonstrating the logarithmic growth at late times in the localised phase, and the qualitatively different behaviour seen in the delocalised phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' The results are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 5, for a system of size L = 14, bond dimension χ = 128, and averaged over Ns = 240 disorder realisations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' The circle markers represent the data points, while the solid lines are smoothed guides to the eye.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Deep in the delocalised phase (d = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0), we see that the negativity saturates for all values of r at relatively early times, making it difficult to pinpoint a regime where the growth of the negativity can be associated with a length scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' In contrast, the negativity in the localised phase increases much more slowly with time, and the spacing of the curves is consistent with an exponential suppression of the negativity with distance, as demonstrated in the main text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 8 100 102 0 2 4 EN(r, t) (a) (b) (c) (d) d = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0 100 102 0 2 4 d = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0 100 102 0 1 2 3 d = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0 100 102 0 1 2 d = 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0 100 102 t 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0 EN(r, t) (e) (f) (g) (h) d = 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0 100 102 t 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0 d = 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0 100 102 t 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0 d = 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0 100 102 t 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='5 d = 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0 r = 0 r = 1 r = 2 r = 3 r = 4 r = 5 r = 6 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' A comparison of the dynamics of the entanglement negativity EN(r, t) for different values of the disorder strength d, shown for L = 14 with bond dimension χ = 128 and averaged over Ns = 240 disorder realisations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' In the delocalised phase, the negativity saturates to a value determined by the size of the subsystems A and B, while in the localised phase the negativity displays a slow ∝ log(t) growth even at late times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' In this dephasing regime, we are able to use the data shown here to extract a length scale that characterises the localised phase, as detailed in the main text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Bond dimension In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 6, we show the negativity dynamics for system size L = 24 and varying bond dimension χ, demonstrating that for χ = 192 (the choice used in the main text) the results are well-converged.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' The crucial factor for our work is the rate of growth of the negativity, which appears largely unaffected by the choice of bond dimension, although deviations can be seen for the smallest value shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 10−1 100 101 102 0 1 EN(r, t) d = 6 10−1 100 101 102 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0 d = 7 10−1 100 101 102 t 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0 EN(r, t) d = 8 10−1 100 101 102 t 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0 d = 9 χ = 32 χ = 128 χ = 192 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' The dynamics of the negativity EN(r, t) with r = 0, for different bond dimensions and disorder strengths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Data shown is for L = 24, averaged over Ns = 100 disorder realisations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Error bars show the standard error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 9 Comparison of different measurement times In the main text, all results for the length scale ξ ≡ ξ(t∗) are taken with t∗ = 500, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=', the maximum evolution time of our simulations, however, it is clear from the negativity dynamics that there should be a weak dependence of ξ on the measurement time t∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Here we demonstrate this effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 7 shows how the linear fit used to extract the decay of EN(r, t) against r depends on the choice of time t∗ for a variety of different disorder strengths, and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 9 shows how the resulting values of ξ(t∗) change as t∗ and d are varied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' At short times there is a visible change in the length scale ξ(t), however, at longer times we see that it appears to saturate towards a well-defined length scale with only a weak dependence on time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' It is possible that simulations which extend to longer times may be able to improve upon the results presented here, but our results suggest this will be a meagre quantitative improvement in exchange for a great deal of computational effort.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 0 2 4 3 4 5 log EN(r, t∗) (a) (b) (c) (d) d = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0 0 2 4 2 4 d = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0 0 2 4 0 2 4 d = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0 0 2 4 0 2 d = 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0 0 2 4 r −4 −2 0 2 log EN(r, t∗) (e) (f) (g) (h) d = 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0 0 2 4 r −4 −2 0 2 d = 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0 0 2 4 r −4 −2 0 2 d = 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0 0 2 4 t −4 −2 0 2 d = 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0 t∗ = 19 t∗ = 33 t∗ = 72 t∗ = 157 t∗ = 251 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' A comparison of the fits to the entanglement negativity EN(r, t∗) at different times t∗ and for different values of the disorder strength d, shown for L = 14 and averaged over Ns = 240 disorder realisations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' The circular markers show the data, while the solid lines indicate the linear fits used to extract the l-bit localisation length.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Error bars showing the standard error in the mean are typically smaller than the marker size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' At large disorder strengths (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=', in the localised phase), the linear fit is very good, confirming that the negativity does indeed decrease exponentially with distance in this phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' After a time of t∗ ≈ 100, the gradient of the decay (and hence the corresponding l-bit localisation length) does not strongly change with time in the localised phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 0 5 10 −10 −5 0 log EN(r, t∗) (a) (b) (c) (d) d = 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0 0 5 10 −10 −5 0 d = 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0 0 5 10 −15 −10 −5 0 d = 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0 0 5 10 t −15 −10 −5 0 d = 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0 t∗ = 25 t∗ = 46 t∗ = 115 t∗ = 288 t∗ = 500 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' The same as in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 7, but for L = 24, χ = 192 and averaged over Ns = 100 disorder realisations, shown only in the localised phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' The solid lines indicate the range of points over which the exponential fits were performed in order to extract the length scale shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 3 of the main text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 10 2 3 4 5 6 7 8 9 10 d 1 2 3 ξ(t∗) t∗ = 13 t∗ = 25 t∗ = 46 t∗ = 115 t∗ = 288 t∗ = 391 t∗ = 442 t∗ = 470 t∗ = 500 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' A comparison of how the length scale ξ(t∗) changes as the measurement time t∗ is varied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' The results here are extracted from the fits shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' At short times, the value of ξ(t∗) changes rapidly, however, at longer times, the dependence of t∗ weakens significantly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' The black line is the Anderson localisation length for comparison, as discussed in the main text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' For clarity, error bars are not shown except on the Anderson localisation length.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' (Note that error bars are shown in the data presented in the main text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=') Negativity between subsystems of fixed size It is also possible to compute the entanglement negativity on a more general interval between two subsystems of fixed size Rb separated by a distance r, as sketched in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' In this case, a very similar procedure to that proposed in the main text is possible, with the caveat that one must carefully choose both the block size Rb and the distance r to ensure that the extraction of the l-bit length scale is done during the dephasing regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' To be specific, if the block size Rb is small and the subsystems are close together (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=', r is small), then the entanglement negativity will rapidly saturate (as the maximum entanglement is controlled by the size of the subsystems under consideration).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' On the other hand, if the blocks are widely separated (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=', large r), then the negativity will remain zero until times exponentially large in r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' If one were to consider a small subsystem of Rb = 2, for example, then the entanglement negativity for small values of r would saturate well before widely separated subsystems have time to become entangled, this meaning that the data points for both small r and large r would have to be discarded when performing the fit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' This can be ameliorated by using blocks of intermediate size, such that they are large enough that the subsystem entanglement does not saturate too rapidly and the data at small values of r remains reliable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Representative results for this case are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 11, where it is clear that for block size Rb = 2, the curves for small values of r saturate too quickly to be used in extracting the l-bit length scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Block size Rb = 3 is better, and here Rb = 4 offers the best compromise, with a clearly identifiable region where the curves for all values of 1 ≤ r < 5 are in a regime of logarithmic growth with approximately the same rate, and a length scale may be extracted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' On the other hand, for block size Rb = 5, with a system size of L = 16 it is not possible to separate the blocks widely enough to extract enough data to perform a reliable fit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' (Note that in these computations, we avoid subsystems that contain the two sites on each end of the chain in order to reduce finite-size effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' In addition, we average over all possible positions of the blocks with size Rb separated by a distance r within our system of size L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=') FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' A sketch of how the entanglement negativity can be used to quantify the entanglement between subsystems of fixed size Rb separated by a distance r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' a) A sketch of the spin chain, identifying the subsystems A and B and the relevant distances Rb and r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' b) A sketch of the corresponding density matrix in MPO form, identifying the subsystems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' c) A sketch of how the negativity is computed in this case, tracing out the complement of A and B while still applying the same ‘twist’ to the MPO legs in order to compute the partial transpose, as in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 1 of the main text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' A B HHOO11 101 102 103 t 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='10 EN Rb = 2 101 102 103 t 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='2 Rb = 3 101 102 103 t 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='4 Rb = 4 101 102 103 t 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='5 Rb = 5 r = 1 r = 2 r = 3 r = 4 r = 5 r = 6 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Entanglement negativity following a quench from a N´eel state, shown for disorder strength d = 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0 with system size L = 16, averaged over Ns = 96 disorder realisations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Here we compute the negativity for a subsystem of fixed size Rb := |A| = |B|, as sketched in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' We can see that for small values of Rb, the negativity at small separations r saturates quickly and that only for larger values of Rb does the negativity increase in a manner that allows extraction of the relevant l-bit length scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Error bars show the standard error in the mean, and the solid lines are a smoothed guide to the eye.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Mutual information In the main text and in our analytical results, we specified the logarithmic negativity as our chosen spatially-resolved entan- glement probe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Here we briefly demonstrate that another spatially-resolved entanglement measure, the mutual information, also exhibits qualitatively similar behaviour.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' The mutual information between subsystems A and B is defined as I(A : B) := S(ρA) + S(ρB) − S(ρAB) (9) where S(ρ) := −trρ log(ρ) represents the von Neumann entropy of a quantum state ρ, and ρA is the reduced quantum state of subsystem A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 12 shows the results for a small system of size L = 12 with bond dimension χ = 128, averaged over Ns = 100 disorder realisations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' The mutual information is qualitatively – and even quantitatively, in many cases – similar to the entanglement negativity, strongly suggesting that it would be a more than acceptable substitute and that much of the intuition developed in the main text should also apply to the mutual information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 0 5 10 0 2 4 I(A : B) d = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0 0 5 10 0 1 2 d = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0 0 5 10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='5 d = 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0 0 5 10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0 d = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0 0 5 10 t 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='5 I(A : B) d = 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0 0 5 10 t 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='75 d = 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0 0 5 10 t 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='6 d = 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0 0 5 10 t 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='6 d = 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='0 r = 0 r = 1 r = 2 r = 3 r = 4 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' A comparison of mutual information (solid lines) and entanglement negativity (dashed lines) between subsystems A and B separated by a distance r, for a system of size L = 12 with bond dimension χ = 128, averaged over Ns = 100 disorder realisations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' 12 Computation of the l-bits and the quasi-locality measure The l-bits in this work are calculated using the method described in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' For completeness, we offer a brief explanation of the method: A system in the fully many-body localised phase can be fully characterized by a complete set of l-bits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Let H be the MBL Hamiltonian of a system of size N and τi, i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' , N, be the l-bits, then they need to satisfy the following properties: 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [H, τ z i ] = 0, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [τ z i , τ z j ] = 0 for all i and j, 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' τi is quasi-local in real space (will be elaborated in the next section).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' A simple prescription in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [50] has been given to construct the l-bits out of infinite time averages of terms that the Hamiltonian contains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' The infinite-time average of a term hj is E(hj) = lim T →∞ 1 T � T 0 e−iHt hj eiHt dt = � k ⟨Ek| hj |Ek⟩ |Ek⟩ ⟨Ek| , (10) assuming a non-degenerate spectrum {Ek} of H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Therefore, E(hj), being sums of projectors onto the eigenstates of H, automatically fulfill properties 1 and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' The authors have also demonstrated the quasi-locality of the resulting operator, showing that the non-local contributions from the off-diagonal elements, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=', contributions from τ x and τ y will be removed through the infinite-time averaging procedure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' The downside with this approach is that the resulting operator has a degenerate spectrum that is distinct from what the Pauli algebra mandates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Thus, we can no longer associate this operator with the picture of having ladder operators that help us transverse through the different modes/eigenstates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' The authors in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [30] have computed E(σz j ) from (10) and re-arranged the order of the eigenstates in Ud to minimize the pair-wise differences between the spectrum of E(σz j ) and that of τ z j = U † dσz j Ud, (11) starting with j = 1 and sequentially optimising the eigenstate order with larger j while keeping the already optimized partial ordering from smaller j intact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' The resulting operators will preserve the Pauli algebra by construction while becoming quasi-local in real space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' For simplicity, we only deal with trace-less and Hermitian operators for the moment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Operators with non-vanishing traces require special procedures to meet the orthonormality of the Hilbert-Schmidt inner product.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Definition 3 (Quasi-locality).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Let τ be a trace-less Hermitian operator, normalized with respect to the Frobenius norm, and Li its orthogonal trace-less Hermitian basis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Consider the decomposition τ = � i aiLi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' (12) Let S(Li) be the support of Li in real-space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' τ is quasi-local around site j, if and only if for any connected region B containing j, we have � S(Li)⊈B |ai|2 ≤ k exp(−dist(j, B)/ξ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' (13) This definition, although rigorous, can be cumbersome, and it is not easy to compute the relevant quantities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Let us consider the partial trace of the operator τ, trBC(τ) = 2|BC| � S(Li)⊆B ai ˜Li, (14) where ˜Li are now defined on a smaller Hilbert space contained in B and the extra identity operators outside B become the pre-factor 2|BC| after the partial trace.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Then, we can compute the square of the Frobenius norm of this truncated operator to get ∥trBC(τ)∥2 2 = 22|BC|tr( � S(Li)⊆B a∗ i ˜Li � S(Lj)⊆B aj ˜Lj) = 22|BC|+|B| � S(Li)⊆B |ai|2, (15) 13 due to the orthogonality of the basis operators Li and their restrictions to any region B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Finally, we leverage the normalisation of τ to observe that � S(Li)⊆B |ai|2 + � S(Li)⊈B |ai|2 = ∥τ∥2 2 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' (16) Therefore, � S(Li)⊈B |ai|2 = 1 − 1 2|B|+2|BC| ∥trBC(τ)∥2 2 ≤ k exp(−dist(j, B)/ξ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' (17) This is exactly the quasi-locality measure proposed in Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [30, 32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' The spatial decay of the l-bits can also be computed using the weight measure in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' (6) from Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [59].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' This notion of quasi-locality is agnostic to operator content and where it is quasi-local around because one only needs to compute the weight of the operator filtered at each site.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Entanglement growth bound In this section, we prove an entanglement growth bound that has been tailored for the case at hand.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Generic entanglement growth bounds for the entanglement entropy have been proven for local Hamiltonians [50, 60–62].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Here, we prove novel bounds for the negativity, ones that are tailored to be applicable to many-body localised systems and the geometry at hand.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' We now look at the specific setting of having two regions, A and B separated by a region C that has been traced out, and ask how much entanglement can be generated by a many-body localised Hamiltonian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' We consider states evolving in time as ρ(t) := e−itHρeitH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' For the purpose of this proof, we will consider a slightly relaxed definition of quasi-locality with respect to Definition 17, namely, instead of the normalized Frobenius norm, we will assume the l-bits are localised in the operator norm, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=', the following.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Definition 4 (Weak quasi-locality).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' An operator is said to be quasi-local around a region R, if for any region X ⊂ R, it holds that ����O − 1 2|Xc| trXc(O) ⊗ IXc ���� 2 ∞ ≤ ∥O∥2 ∞Ke−d(R,Xc)/ξ (18) for some constant K > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' This definition is weaker than Definition 17, in the sense that if an operator is localised in the sense above, it is also localised in the sense of Definition 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' The following is the central statement from which the entanglement bound easily follows: Theorem 2 (Entanglement growth bound for sums of quasi-local operators).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Let ρ be any initial state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Let H be a many-body localised Hamiltonian as per Definition 2 with localisation length ξ ≤ 1/(4 log(2)) and 2(1/κ − log(2)) > 1/ξ, consider three blocks A, C, B such that C divides A from B the growth of the negativity of the state ρ(t) = e−itHρeitH restricted to the regions A, B for times t ≥ 0 and for any r ≥ |C|/2 EN(t) = log2(∥ρTA A,B(t)∥1) ≤ min{t O(e−|C|/(2ξ)), 4r − 2|C|} + tO(e−r/(2ξ)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' (19) Notice the the r in the above is a parameter one can choose freely.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' We obtain the following statement simply by picking r = 2ξ log(t) in the above bound if t > e|C|/(4ξ) and r = |C|/2 otherwise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Corollary 1 (Logarithmic growth of the negativity).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' If t ≥ e|C|/4ξ, under the assumptions of Theorem 2, we have EN(t) ≤ min{t O(e−|C|/(2ξ)), 8ξ log2(t) − 2|C|} + O(1), (20) while for t < e|C|/4ξ, EN(t) ≤ t O(e−|C|/(4ξ)) (21) To turn this result into a proper bound for many-body localised Hamiltonians, we need to reduce such Hamiltonians to the form considered in Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' For this purpose, we will assume a slightly stronger definition of the many-body localised Hamiltonian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' We call a unitary quasi-local with localisation length ξ if it maps any local operator on a region R to a quasi-local operator around R with localisation length ξ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' We will assume that the Hamiltonian is diagonalised by a quasi-local unitary, 14 which means that the l-bits are simply dressed Pauli Z operators, hi = Uσi zU †.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' In particular this implies that a product of l-bits hi1hi2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' hin, with i1 < i2 < · · · < in is quasi-local around {i1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' , in}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' For the purposes of the subsequent discussion, it will be useful to define the projector PX(O) = trXc(O) ⊗ I 2|Xc| , (22) for any region X of the lattice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' It is easy to verify that PX is a projector and that it is self-adjoint in the Hilbert Schmidt inner product.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' In what follows, ∥ · ∥ denotes the operator norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Lemma 1 (Quasi-local sums).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Let H be a many-body localised Hamiltonian in the sense described above with localisation length ξ, and in addition, assume 2(1/κ − log(2)) > 1/ξ, where κ has been defined in Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Then the Hamiltonian can be written as H = N � i=1 Hi (23) where Hi is quasi-local around the site i with localisation length 2ξ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' We note that, a quasi-local operator with localisation length ξ is quasi-local for any localisation length ξ′ > ξ, if 2(1/κ − log(2)) ≤ 1/ξ, it suffices to relax the quasi-locality of the l-bits by increasing the localisation length until this condition is satisfied, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=', chooses ξ′ = 1 2(1κ − log(2)) + ϵ > ξ (24) for some constant ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' This will result in faster (∼ r/ξ′), but still exponentially slow, growth of entanglement in the bound.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Define Hi as Hi = ωihi + � l≥1 2l+1 � k=2 � Ik∩{i−l,i+l} Ik⊂[i−l,i+l] ωIkhIk (25) where Ik = {i1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' , ik} are collections of k sites contained in i − l .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' i + l and such that they contain at least one of the two boundaries i−l, i+l.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' In the above, we have defined hIk = hi1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' hik.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' We have then ω2 Ik ≤ ω2e−2l/κ and that hIk is quasi-local around [i − l, i + l] with localisation length ξ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Clearly, H = � i Hi, it remains to show that the Hi are quasi-local as claimed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Let R = [i − r, i + r] be a stretch of sites of radius r around i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' We have by the triangle inequality ∥Hi − PR(Hi)∥ = ωi∥hi − PR(hi)∥ + � l≥1 2l+1 � k=2 � Ik∩{i−l,i+l} Ik⊂[i−l,i+l] ωIk∥hi − PR(hi)∥ ≤ ωKe−r/ξ + K r−1 � l=1 � Ik∩{i−l,i+l} Ik⊂[i−l,i+l] ωe−2l/κe−(r−l)/(2ξ) + 2 � l≥r � Ik∩{i−l,i+l} Ik⊂[i−l,i+l] ωe−2l/κ, (26) where we have used quasi-locality and in the l ≥ r part of the sum, that ∥hi − PR(hi)∥ ≤ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Now notice that � Ik∩{i−l,i+l} Ik⊂[i−l,i+l] = 22l−1 + 22l−2 + 22l−2 = 22l (27) we then have that ∥Hi − PR(Hi)∥ ≤ ωKe−r/(2ξ) + K r−1 � l=1 22lωe−2l/κe−(r−l)/(2ξ) + 2 � l≥r 22lωe−2l/κ = ωKe−r/(2ξ) + K r−1 � l=1 ωe−2l(1/κ−log(2))e−(r−l)/(2ξ) + 2ω � l≥r e−2l(1/κ−log(2)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' (28) 15 The first term is already bounded as needed, and for the third term, we use 2(1/κ − log(2)) > 1/(2ξ) to get � l≥r e−2l(1/κ−log(2)) ≤ � l≥r e−l/(2ξ) = 1 1 − e−1/(2ξ) e−r/(2ξ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' (29) For the second term, let δ = 2(1/κ − log(2)) − 1/(2ξ) > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Then r−1 � l=1 e−2l(1/κ−log(2))e−(r−l)/(2ξ) = e−r/(2ξ) r−1 � l=1 e−δl ≤ e−δ 1 − e−δ e−r/(2ξ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' (30) We note in passing that if δ = 0, the bound does not diverge, but an additional linear term is added to get a bound of the form re−rξ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' In conclusion, ∥Hi − PR(Hi)∥ ≤ K′e−r/(2ξ) (31) with K′ := ω � K + K e−δ 1 − e−δ + 2 1 − e−1/ξ � , (32) that is, ∥Hi − PR(Hi)∥2 ≤ K′2e−r/ξ (33) which is the definition of quasi-locality noticing ||hi|| = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' The rest of this section is dedicated to proving Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' The technique used for the proof is analogous to that of Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' [50], where an analogous bound was derived for the entanglement entropy in the case |C| = 0, the properties of the negativity, which is a meaningful entanglement measure for mixed states, allow the generalisation to disconnected regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' The following two properties of the 1-norm and the partial transpose will be used repeatedly: The 1−norm contracts under the partial trace, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=', ||ρA||1 ≤ ||ρA,B|| for any bipartite state ρA,B [63], ||ρTB A,B||1 ≤ dB||ρA,B||1 [64].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' First, we need to understand how local Hamiltonians affect the entanglement negativity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Lemma 2 (Local Hamiltonians affecting the entanglement negativity).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Let ρA,B be an arbitrary bipartite state and let H = � I HI(t) be a local time-dependent Hamiltonian, where I are regions of the lattice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Assume the norm of the derivative of HI is bounded by ||H′ I(t)|| ≤ hI where hI is independent of time, then the bound ||(eiHtρe−iHt)TB||1 ≤ ||ρTB||1 exp � t � I hId2 I∩B � (34) holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Let ρ(t) = eiH(t)ρe−iH(t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' We have ||ρ(t + δ)TB||1 = ||ρ(t)TB + δρ′(t)TB + O(δ2)||1 ≤ ||ρ(t)TB|| + δ||[H′(t), ρ(t)]|| + O(δ2), (35) and hence d dt||(eiH(t)ρe−iH(t))TB||1 ≤ � I ||[H′ I(t), ρ]TB||1 ≤ 2 � I ||(H′ I(t)ρ)TB||1 = 2 � I ||(H′ I(t)(ρ)TB/I)TI∩B||1 (36) ≤ 2 � I dI∩BhI||ρTB/I||1, now use ||ρTB/I||1 = ||(ρTB)I∩B||1 ≤ dI∩B||ρTB||1 (37) 16 to get d dt||ρ(t)TB||1 ≤ � I hId2 I∩B||ρ(t)TB||1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' (38) We now just need to see that for any strictly positive differentiable function f : R+ → R+, f ′(x) ≤ cf(x) implies f(x) ≤ f(0)ecx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' To see this, define g : R+ → R+ as g(x) := log f(x), then g′(x) = 1 f(x)f ′(x) ≤ c, (39) and therefore g(x) = � x 0 dsg′(s) + g(0) ≤ cx + g(0) (40) which by monotonicity of the log function implies the claim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' We note in passing that a much stronger bound can be proven in the same way for time-independent Hamiltonians.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' In this case, it suffices to write ρ(t + δ) = eiδHρ(t)e−iδH, then the term in the Hamiltonian which has no intersection with B simply vanish and do not contribute to the bound.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' We will now prove Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' From now on we will assume that |C| is even, the odd case is analogous.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' We will label the two central sites of C as ±1, all the sites to the right of the center of C have positive integer labels, and to the left negative integer labels (notice that there is no site 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' In addition, we will use the standard notation [a, b) denoting real intervals to denote intervals in the chain, so from now on [a, b) is understood to mean [a, b) ∩ Z/{0}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Divide the chain into the following regions (see Figure 13), recall that r is an arbitrary integer greater than |C|/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' ¯L = (−∞, −r + |C|/2), L = (−∞, |C|/2), (41) ¯∂ = [−r + |C|/2, r − |C|/2], ∂ = [−2r + |C|/2, 2r − |C|/2], (42) ¯R = (r − |C|/2, ∞), R = (−|C|/2, ∞), (43) and divide the terms in the Hamiltonian accordingly as H = h¯L + h ¯ R + h¯∂ (44) where h ¯S = � i∈S hi for S ∈ L, ∂, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' We will now split the term h ¯S into a main local part acting on S and a tail whose norm is exponentially small in r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='@ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='ACDXicdVDLSgNBEJyNrxhfUY9eBoPgaZlNoia3gBePEYwJCH0Tjo6OPtgpleQxW8QvOpveBOv ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='foN/4Se4GyOoaJ2Kqu6pnvJjrSwJ8eYU5uYXFpeKy6WV1bX1jfLm1rmNEiOxIyMdmZ4PFrUKsUOKNPZigxD4G ' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' More specifically, define HS = PS(h ¯S) as the local part, then the remaining evolution is given by a generator δS(t) implicitly defined as eih ¯ St = eiHSteiδS(t) (45) i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=', eiδS(t) = e−iHSteih ¯ St, then iδ′ S(t) = � d dteiδS(t) � e−iδS(t) = −iHS + ieiHSth ¯Se−iHSt = ieiHStTSe−iHSt (46) where we have defined TS := h ¯S − HS as the tail of the l-bits in ¯S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Then, since δS(0) = 0, we find δS(t) = � t 0 dxeiHSxTSe−iHSx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' (47) 17 For now, we have written the tail evolution as an operator acting globally on the lattice, it has an exponentially small norm, but it could still, in principle, create an amount of entanglement extensive in the system size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' To apply Lemma 2, we have to recast it as a local Hamiltonian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' For each S, define S + q as the region S extended to the left and the right (if possible) by q sites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' We can then write the tail TS as a telescopic sum, defining HS+q = PS+q(h ¯S) TS = −HS + HS+1 − HS+1 + HS+2 − HS+2 · · · = − ∞ � q=0 HS+q − HS+q+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' (48) Clearly h ¯S = limq→∞ PS+q(h ¯S), as this is simply the “truncation” where the whole lattice is kept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' We then have that δS(t) = ∞ � q=0 ZS+q+1(t) (49) where ZS+q(t) := � t 0 dxeiHSx(HS+q − HS+q+1)e−iHSx acts only on S + q + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Until now, we have claimed that these tail operators have exponentially small norms in r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Before continuing, let us prove this.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Lemma 3 (Tail bounds).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' ||ZS+q(t)|| ≤ tO(e−(r+q)/(2ξ)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' We will prove that ||h ¯S − HS+q|| ≤ O(e−(r+q)/(2ξ)), the statement follows as ||ZS+q(t)|| ≤ t||HS+q − HS+q+1|| ≤ t(||HS+q − h ¯S|| + ||HS+q+1 − h ¯S||).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' (50) Let us start with S = ∂.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' The closest l-bits to the boundary of ∂ + q in ¯∂ are separated from it by r + q sites, and the furthest ones by 2r + q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' The sum is clearly symmetric around the centre of the chain, and we use that for any S, S is constructed such that the distance from any site in ¯S to the edge of ¯S is at least r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Recall that h ¯S = � i∈ ¯S hi, where the hi are quasi-local as in Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' ||h¯∂ − H∂+q|| ≤ r−|C|/2 � k=−r+|C|/2 ||hk − P∂+q(hk)|| ≤ 2K 2r+q−|C|/2 � j=r+q e−j/(2ξ) ≤ O(e−(r+q)/(2ξ)) (51) for some constant K > 0, by the definition of quasi-locality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Let us move to S = R, where again the closest l-bits in ¯R to the boundary of R + q are separated from it by r + q sites, and the furthest has a distance unbounded in the system size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' We have ||h ¯ R − HR+q|| ≤ � k>r−|C|/2 ||hk − PR+q(hk)|| ≤ 2K � j≥r+q e−j/(2ξ) ≤ O(e−(r+q)/(2ξ)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' (52) S = L is entirely analogous.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' We have completed the split into local terms and tails.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' The intuition is now that the entanglement in the system will be driven on the one hand by the term H∂, which is the only local term connecting A and B, and on the other hand by the tail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' The former can only create entanglement locally around C, and the latter is weak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' This split allows us to prove the first part of the bound: We can write eiHt = eiH∂teiδ∂(t)eiHLteiδL(t)eiHRteiδR(t) (53) Given a Hamiltonian h, define the time evolution operator Uh(ρ) := eihρe−ih.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Consider a state σ, notice that the overlap between B and ∂ is of length 2r − |C|, in particular, ||trC(UH∂t(σ))TB||1 ≤ ||trC(eiH∂t(σ)T(2r−|C|/2,∞)e−iH∂t)T[|C|/2,2r−|C|/2]||1 ≤ 22r−|C|||σT(2r−|C|/2,∞)||1 (54) Here we simply assume enough time has passed that H∂ has had time to saturate the entanglement in the region ∂, that is, create a maximally entangled state between the sites on either side of C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' We have then ||ρ(t)TB||1 = ||trC � UH∂t ◦ Uδ∂(t) ◦ UHLt ◦ UδL(t) ◦ UHRt ◦ UδR(t)(ρ) �TB ||1 ≤ 22r−|C||| � Uδ∂(t) ◦ UHLt ◦ UδL(t) ◦ UHRt ◦ UδR(t)(ρ) �T(2r−|C|/2,∞) ||1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' (55) Next, recall that δ∂(t) = �∞ q=0 Z∂+q+1, then by Lemma 2, we have ||ρ(t)TB||1 ≤ 22r−|C|E∂,t|| � UHLt ◦ UδL(t) ◦ UHRt ◦ UδR(t)(ρ) �T(2r−|C|/2,∞) ||1 (56) 18 where E∂,t ≤ exp � tO � e−r/(2ξ) ∞ � q=0 22(| ∂+q+1∩(2r−|C|/2,∞)|)e−q/(2ξ) �� ≤ exp � tO � e−r/(2ξ) ∞ � q=0 22qe−q/(2ξ) �� ≤ exp � tO � e−r/(2ξ)�� , (57) where we have used the assumption ξ < 1/(4 log(2)), so that the terms in the sum above are exponentially decaying and sum to a constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Since L has no overlap with (2r − |C|/2, ∞), we can just bring the partial transpose inside the L evolution and eliminate it by unitarity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Afterwards, we eliminate UδR(t), exactly as we have eliminated Uδ∂(t), to get ||ρ(t)TB||1 = 22r−|C|E∂,tEL,t|| � UHRt ◦ UδR(t)(ρ) �T(2r−|C|/2,∞) ||1 (58) and in the same way one can show that EL,t ≤ exp � t O � e−r/(2ξ)�� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Finally, notice that for any region X and a state σ, ||σTX||1 = ||σTXc ||1, since σ is Hermitian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Then || � UHRt ◦ UδR(t)(ρ) �T(2r−|C|/2,∞) ||1 = || � UHRt ◦ UδR(t)(ρ) �T(−∞,2r−|C|/2) ||1 ≤ 22r−|C||| � UδR(t)(ρ) �T(−∞,−|C|/2) ||1 ≤ 22r−|C|ER,t||ρT(−∞,−|C|/2)||1 = 22r−|C|ER,t, (59) where we have used that the initial state is a product state, ER,t can be bounded as in the previous cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Overall, we have then proven that ||ρ(t)TB||1 ≤ 24r−2|C| exp � t O � e−r/(2ξ)�� (60) holds true.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' To get the other part of the bound, we need to refine the bound on the entanglement generated by the central term eiH∂t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' While it is true that this operator is quasi-local around C, it is also true that it decays fast outside of the boundaries of C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' We can separate the part of H∂ acting inside C from the rest, which we can subsequently simply treat as a tail, H∂ = HC − HC−1 + HC+1 − HC + HC+2 − HC+1 + · · · = 2r−|C| � q=0 HC+q−1 − HC+q, (61) where now HS = PS(H∂) = PS(h¯∂) for S ⊇ ∂.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Just like before, we write eiH∂t = eiHCtei˜δ∂(t), (62) and we proceed in the same exact way as before, except that now the first term gets eliminated by the trace.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' For some state σ, we have ||trC(eiHCteiδ(t)σe−iδ(t)eiHC)||1 = ||trC(ei˜δ∂(t)σe−i˜δ∂(t))||1 ≤ E˜∂,t||σ||1 (63) and we can bound E˜∂,t ≤ exp(tO(e−|C|/(2ξ))) just like earlier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' Proceeding in the same way as earlier, we get the bound ||ρ(t)TB||1 ≤ exp(tO(e−|C|/(2ξ))) exp � t O � e−r/(2ξ)�� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} +page_content=' (64) The final result is obtained by taking the minimum of the two bounds and applying log2 on both sides.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/S9AzT4oBgHgl3EQf0v4t/content/2301.01787v1.pdf'} diff --git a/StE2T4oBgHgl3EQfWwc0/content/tmp_files/2301.03836v1.pdf.txt b/StE2T4oBgHgl3EQfWwc0/content/tmp_files/2301.03836v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..8d139f6c7d396c5e8854f05075df410699bfab90 --- /dev/null +++ b/StE2T4oBgHgl3EQfWwc0/content/tmp_files/2301.03836v1.pdf.txt @@ -0,0 +1,1296 @@ +Multiple mechanisms in proton-induced nucleon removal at ∼100 MeV/nucleon +T. Pohl,1, ∗ Y. L. Sun,1, 2, 3, † A. Obertelli,1, 2 J. Lee,3 M. G´omez-Ramos,4 K. Ogata,5, 6 K. Yoshida,7 +B.S. Cai,8 C.X. Yuan,8 B. A. Brown,9 H. Baba,10 D. Beaumel,11 A. Corsi,2 J. Gao,10, 12 J. Gibelin,13 +A. Gillibert,2 K. I. Hahn,14, 15 T. Isobe,10 D. Kim,14, 15 Y. Kondo,16 T. Kobayashi,17 Y. Kubota,10, 18 +P. Li,3 P. Liang,3 H. N. Liu,1, 2, 19 J. Liu,3 T. Lokotko,3 F.M. Marqu´es,13 Y. Matsuda,20, 21 +T. Motobayashi,10 T. Nakamura,16 N.A. Orr,13 H. Otsu,10 V. Panin,10, 2 S. Y. Park,14, 10 +S. Sakaguchi,5 M. Sasano,10 H. Sato,10 H. Sakurai,10, 22 Y. Shimizu,10 L. Stuhl,10, 15 D. Suzuki,10 +Y. Togano,16, 10, 23 T. Uesaka,10 H. Wang,10 X. Xu,3 Z. H. Yang,10 K. Yoneda,10 and J. Zenihiro10 +1Institut f¨ur Kernphysik, Technische Universit¨at Darmstadt, 64289 Darmstadt, Germany +2IRFU, CEA, Universit´e Paris-Saclay, F-91191 Gif-sur-Yvette, France +3Department of Physics, The University of Hong Kong, Pokfulam, Hong Kong +4Departamento de F´ısica At´omica, Molecular y Nuclear, Facultad de +F´ısica, Universidad de Sevilla, Apartado 1065, E-41080 Sevilla, Spain +5Department of Physics, Kyushu University, Fukuoka 812-8581, Japan +6Research Center for Nuclear Physics (RCNP), Osaka University, Ibaraki 567-0047, Japan +7Advanced Science Research Center, Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195, Japan +8Sino-French Institute of Nuclear Engineering and Technology, Sun Yat-Sen University, Zhuhai, 519082, Guangdong, China +9Department of Physics and Astronomy and National Superconducting Cyclotron +Laboratory, Michigan State University, East Lansing, Michigan 48824-1321, USA +10RIKEN Nishina Center, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan +11Universit´e Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France +12State Key Laboratory of Nuclear Physics and Technology, School of Physics, Peking University, Beijing 100871, China +13LPC Caen, ENSICAEN, Universit´e de Caen, CNRS/IN2P3, F-14050 Caen, France +14Department of Physics, Ewha Womans University, Seoul, South Korea +15Center for Exotic Nuclear Studies, Institute for Basic Science, Daejeon 34126, Republic of Korea +16Department of Physics, Tokyo Institute of Technology, 2-12-1 O-Okayama, Meguro, Tokyo, 152-8551, Japan +17Department of Physics, Tohoku University, Sendai 980-8578, Japan +18Center for Nuclear Study, University of Tokyo, RIKEN campus, Wako, Saitama 351-0198, Japan +19Key Laboratory of Beam Technology and Material Modification of Ministry of Education, +College of Nuclear Science and Technology, Beijing Normal University, Beijing 100875, China +20Cyclotron and Radioisotope Center, Tohoku University, Sendai 980-8578, Japan +21Department of Physics, Konan University, Kobe 658-8501, Japan +22Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan +23Department of Physics, Rikkyo University, 3-34-1 Nishi-Ikebukuro, Toshima, Tokyo 172-8501, Japan +(Dated: January 11, 2023) +We report on the proton-induced one-nucleon removal reaction from the neutron-deficient 14O +nucleus with large proton-to-neutron separation energy asymmetry Sn − Sp = 18.6 MeV at +94 MeV/nucleon. +The measured inclusive cross sections and parallel momentum distributions +(PMDs) of the 13N and 13O residues are compared to the state-of-the-art reaction models. It is +shown that, in addition to the quasifree knockout, the inelastic scattering and nucleon transfer con- +tribute about 50% and 30% to the proton and neutron removal, respectively. These processes should +be considered in analyses of one-nucleon removal cross sections measured at intermediate energies +for quantitative nuclear-structure studies. +The nucleon single-particle (SP) motion is one of the +most important properties of nuclei [1]. The first success- +ful model for the description of the nuclear SP properties +is the Independent Particle Model (IPM) [2, 3], assuming +nucleons move freely in an effective mean-field potential. +It was revealed later by (e,e′p) experiments on stable nu- +clei that the SP strengths, quantified by the so called +spectroscopic factors (SFs), are reduced by (30–40)% rel- +ative to the IPM predictions [4, 5]. The “quenching” of +the SP strengths has been attributed to short- and long- +range correlations [5]. One main focus of today’s nuclear +physics is to extend these studies towards the proton and +neutron driplines to better understand nuclear structure +and many-body nuclear forces [6, 7]. +One-nucleon removal reactions at intermediate ener- +gies near and above 100 MeV/nucleon have been a pow- +erful tool to extract SP strengths of unstable nuclei [8]. +The quenching of the SP strengths has been connected +to the so-called reduction factor Rs [9], defined as the +ratio of the experimental to the theoretical cross sec- +tion that is usually computed using shell-model SFs +and an eikonal reaction model relying on the adiabatic +and eikonal approximations [8]. Systematic studies from +light-ion-induced one-nucleon removal reactions at ∼100 +MeV/nucleon [10–12] and higher incident beam ener- +gies [13] revealed that Rs has a strong dependence on the +arXiv:2301.03836v1 [nucl-ex] 10 Jan 2023 + +2 +proton-to-neutron asymmetry quantified as ∆S = Sn - Sp +or Sp - Sn for neutron or proton removal, respectively. +However, results from transfer reactions [14–19] and pro- +ton induced quasifree knockout (p, pN) reactions [20–24] +did not confirm the strong ∆S dependence. +The inconsistent dependence on ∆S calls for a deeper +understanding on the reaction mechanisms and corre- +lations in nuclei [25]. +Although the diffraction and +stripping mechanisms have been well established in the +eikonal model down to ∼100 MeV/nucleon [26, 27], mul- +tiple scattering, excitation and decay of the knockout +residue, beyond the eikonal reaction model +[28, 29] or +Pauli-blocking +[30, 31] have been proposed as possible +mechanisms that could reduce the deeply-bound nucleon- +removal cross sections. In particular, asymmetric PMDs +of the residue, characterized by a low-momentum tail +[32–39] and a high-momentum cutoff [36], have been ob- +served in several experiments, in contrast to the sym- +metric PMDs predicted by the lowest order eikonal +model [40–42]. +The low-momentum tail in PMDs has +been tentatively attributed to either the dissipative pro- +cesses [36, 38] or the momentum transfer to the target +in the diffraction mechanism [32]. The high-momentum +cutoff stems from the energy and momentum conserva- +tion, not fully satisfied in the eikonal model [36, 43]. +The above-mentioned studies in [10–13] have been per- +formed with light absorptive nuclear targets, 9Be or 12C, +which introduce the complexity that the final state of +the target is unknown. +Here, we report on the first +study of one-nucleon removal from a large separation- +energy asymmetric nucleus 14O (∆S = ±18.6 MeV) at +∼100 MeV / nucleon using a single-nucleon target, i.e., +protons. 14O is an ideal nucleus to study the one-nucleon +removal mechanisms at large proton-to-neutron asymme- +try. The proton and neutron removal from it involve only +the orbitals of π0p1/2 and ν0p3/2, respectively, since both +13N (Jπ +g.s. = 1/2−) and 13O (Jπ +g.s. = 3/2−) do not exhibit +bound excited states. Based on the measured PMDs and +the state-of-the-art reaction models, we show that in ad- +dition to the quasifree knockout, the inelastic scattering +and nucleon transfer also make significant contributions +to the loosely-bound proton removal and deeply-bound +neutron removal, respectively. +The experiment was performed at the Radioactive Iso- +tope Beam Factory operated by the RIKEN Nishina Cen- +ter and the Center for Nuclear Study of the University +of Tokyo. +A primary 18O beam at 230 MeV/nucleon +with an intensity of 500 pnA impinged on a 14 mm thick +9Be target. The 14O secondary beam was purified and +identified using the time-of-flight (TOF) and the energy +loss (∆E) information by the BigRIPS fragment separa- +tor [44]. The typical 14O beam intensity and purity were +9 × 103 particles per second and 78%, respectively. The +14O beam was then tracked onto a 2.40(34)-mm thick +solid hydrogen target (SHT) [45] by two multi-wire drift +chambers (MWDCs). +The beam energy at the target +1.6 +1.7 +1.8 +1.9 +2 +2.1 +Q +/ +A +4 +5 +6 +7 +8 +9 +" +Z +" +1 +10 +2 +10 +3 +10 +4 +10 +5 +10 +(a) +CUT 1 +CUT 2 +100 105 110 115 120 125 130 + [mm/ns] +v +0 +10 +20 +30 +40 +50 + [arb. unit] +E +∆ +1 +10 +2 +10 +(b) +O +13 +C +10 +w/ CUT 1 +100 105 110 115 120 125 130 + [mm/ns] +v +0 +10 +20 +30 +40 +50 + [arb. unit] +E +∆ +1 +10 +2 +10 +(c) +w/ CUT 2 +O +15 +N +13 +C +11 +FIG. 1. Particle identification (PID) of the projectile-like re- +action residues transmitted to the focal plane of the SAMU- +RAI spectrometer. (a) PID using the ∆E-Bρ-TOF method. +The ∆E-velocity spectra with the A/Q selections from 1.59 +to 1.66 (b) and from 1.81 to 1.93 (c).The black contours in +(b) and (c) show the selections for 13O and 13N, respectively. +center was 94 MeV/nucleon with a narrow spread of 0.2 +MeV/nucleon (σ). The target density was determined to +be 86 mg/cm3 by the monitored temperature of the tar- +get cell. The target thickness and its uncertainty were +extracted by measuring the momentum change of the +unreacted 14O beam with and without the SHT. The +empty-target setting was also used to measure the back- +ground events generated by non-target beam-line materi- +als, which were subtracted in the cross section and PMD +analyses. +The reaction residues were measured by the SAMURAI +spectrometer [46], with a magnetic field set at 1.49 Tesla +with the SHT and 1.51 Tesla without the SHT. The po- +sition and angle of the particles were measured by two +MWDCs located before and after the dipole magnet. A +10-mm thick plastic scintillator array hodoscope located +downstream of the spectrometer was used to measure the +∆E and to determine the TOF together with the time +information of the beam particle measured by a 0.2-mm +thick plastic scintillator before the SHT. The magnetic +rigidity Bρ and the flight length L from the SHT to +hodoscope were deduced from multidimensional-fit func- +tions using the positions and angles of the residues before +and after the magnet as inputs. The functions were ob- +tained with Geant4 [47] simulations and the multidimen- +sional fit package of ROOT [48]. The obtained functions +reproduce the simulated Bρ and L with relative devia- +tions below 0.02 %. The experimental PMD response to +14O beam was used for convolution with the theoretical + +3 +TABLE I. Experimental and theoretical cross sections of one- +nucleon removal from 14O at 94 MeV/nucleon. The deduced +reduction factors Rs = σexp/σth are also given. +Residue +Jπ +σexp +SF +Theory +σsp +σth +Rs +[mb] +[mb] [mb] +13Ng.s. +1/2− 10.7(16) 1.58 +DWIA +5.2 +8.8 +1.22(18) +Inelastic +- +9 +Sum +17.8 +0.60(9) +QTC +7.0 +11.9 0.90(13) +Inelastic +- +9 +Sum +20.9 +0.51(8) +13Og.s. +3/2− 16.7(24) 3.42 +DWIA +6.3 +23.2 0.72(10) +Transfer +3 +11 +Sum +34.2 +0.49(7) +QTC +w/o transfer 10.2 37.6 +0.44(6) +QTC +13.5 49.7 +0.34(5) +PMDs of 13O and 13N presented later, taking into ac- +count the different energy losses in beam-line materials. +The reaction residues were identified using the ∆E- +Bρ-TOF and ∆E-velocity method. 13O and 13N can be +unambiguously selected with the selection cuts shown in +Fig. 1. In Fig. 1(a), the calculated atomic number “Z” us- +ing the Bethe-Bloch formula for 13O (A/Q = 1.625) and +14O (A/Q = 1.75) both show tails extending to smaller +“Z” region. The “Z”-tail of 14O is caused by unreacted +14O projectiles interacting in the hodoscope, while the +“Z”-tail of 13O has a strong component steaming from +the low-energy 13O which stops into the hodoscope. As +demonstrated in the ∆E-velocity correlation in Fig. 1(b) +and (c), most 13O stopped in the hodoscope and had +∆E proportional to the velocity, while most 13N punched +through the hodoscope and had ∆E anti-proportional to +the velocity. +The resulted experimental cross sections for one-proton +and one-neutron removal from 14O are 10.7(16) mb and +16.7(24) mb, respectively, listed in Table. I. In the cross +section extraction, the momentum acceptance, 94(1)% +for 13O and 96(1)% for 12N, determined from Geant4 +simulations and 7(1)% reaction loss in the beam-line ma- +terials have been taken into account. In addition, a loss +of 5(1) % was considered based on simulations with the +INCL model [49], corresponding to 13O or 13N events out- +side of the gates in Fig. 1 (b) and (c). The cross section +errors for 13O and 13N contain statistical uncertainties +(0.6 % and 1.3 %), particle selections (0.9 % and 2.3 %) +and systematic uncertainties (14.2 % and 14.7 %) mainly +resulting from the uncertainty of the target thickness. +The experimental momentum distributions from 13O +and 13N are shown in Fig. 2. At first sight, they exhibit +qualitatively the features of the PMDs obtained for one- +nucleon removal from 14O at 53 MeV/nucleon with a 9Be +target [36]. An asymmetric PMD with a low-momentum +tail and a high-momentum sharp edge are observed in the +deeply-bound neutron removal channel, while the PMD +from the loosely-bound proton removal is close to sym- +metric. +The experimental cross sections and PMDs were com- +pared to predictions combining reaction and structure +inputs. +The SFs for the removed proton and neutron +from 14O were obtained from shell-model calculations +performed in the psd-model space with the YSOX inter- +action [50] limited to 5 ℏω excitation using the KSHELL +code [51]. +The SP energy of the π1s1/2 orbit was de- +creased by 0.375 MeV to have a good reproduction of +the low-lying energy level structure of 14O. The result- +ing SFs are 1.58 and 3.42 for 13N and 13O, respectively. +OXBASH shell-model calculations [52] with the com- +monly used WBT and WBP interactions [53] result in +slightly larger SFs of 1.82 and 3.72. +For the (p, pN) knockout process, we adopted the state- +of-the-art DWIA [43, 54–57] and the QTC (Quantum +Transfer-to-the-Continuum) [22, 58] models. +See Sup- +plemental Material (SM) [59] for details of the calcula- +tions. The DWIA and QTC reaction models have been +developed and benchmarked for (p, pN) reaction at beam +energies higher than 200 MeV/nucleon [22, 57]. Above +200 MeV/nucleon, both models have been demonstrated +to reproduce well the shape of the experimental momen- +tum distributions [22, 60–62], and the SP cross sections +(σsp) from the two models are also consistent with each +other within 20% [63]. +The obtained σsp for the 14O(p, 2p)13N reaction are +5.2 mb and 7.0 mb from the DWIA and QTC calcu- +lations, respectively. +In addition, we considered also +the inelastic excitation of 14O to its low-lying excited +states located above Sp and below ∼ S2p, which decay +to the ground state of 13N via one-proton emission (See +SM [59]). Giant-resonance excitations were not consid- +ered. A total inelastic cross section of 9 mb was obtained. +The theoretical cross sections σth are summarized in Ta- +ble. I. With the DWIA or QTC calculated knockout cross +sections, the obtained σth are 17.8 mb or 20.9 mb, leading +to Rs of 0.60(9) and 0.51(8). +In Fig. 2 (a) and (b), the PMD of 13N is shown and +compared with the theoretical PMDs from the DWIA +and QTC calculations with inelastic scattering contri- +bution. +Due to the kinematics, PMD peak position +from (p, p′) is about 50 MeV/c lower than that from +(p, 2p). +The summed distribution combining the (p, +2p) and (p, p′) PMDs is close to symmetric and re- +produces well the data. +The good agreement of the +theoretical distributions and the experimental ones con- +firms the predicted strong inelastic-scattering compo- +nent to the loosely-bound proton removal, which leads +to fractional contributions of 51% with the DWIA and +of 43% with the QTC. The inelastic-scattering compo- +nent has also been observed with the invariant-mass tech- +nique in the case of one-nucleon removal with a 9Be +target [39, 64]. +Percentage contributions of 17% and +21% from the inelastic scattering have been extracted + +4 +5000 +5200 +5400 +5600 +5800 +0 +20 +40 +60 +)] +c +b / (MeV/ +µ + [ +� � +P +/d +σ +d +DWIA +Inelastic +Sum +O (-1p) +14 +(a) +O +14 +Unreacted +5000 +5200 +5400 +5600 +5800 +0 +20 +40 +60 +)] +c +b / (MeV/ +µ + [ +� � +P +/d +σ +d +QTC +Inelastic +Sum +(b) +O (-1p) +14 +5000 +5200 +5400 +5600 +5800 +]c + [MeV/ +� � +P +0 +20 +40 +60 +)] +c +b / (MeV/ +µ + [ +� � +P +/d +σ +d +DWIA +Transfer +Sum +O (-1n) +14 +(c) +5000 +5200 +5400 +5600 +5800 +]c + [MeV/ +� � +P +0 +20 +40 +60 +)] +c +b / (MeV/ +µ + [ +� � +P +/d +σ +d +QTC +w/o Transfer +Transfer +O (-1n) +14 +(d) +FIG. 2. PMDs of 13N and 13O from the one-nucleon removal +of 14O at 94 MeV/nucleon. The black filled markers show the +experimental data. +The orange bands represent the uncer- +tainties from the background subtractions. The grey empty +bins indicate the other systematic uncertainties. +The data +are compared to the DWIA and QTC reaction model calcula- +tions (blue-dotted lines), with additional contributions from +the inelastic excitation for 13N and (p, d) transfer for 13O +(red-dashed lines). +The blue-solid line in (a) indicates the +PMD of the unreacted 14O beam (shifted by −200 MeV/c) for +demonstration of the experimental PMD response. Theoreti- +cal distributions have been convoluted with the experimental +PMD response and their integrals have been normalised to +the data. +for the one-proton removal from 9C and 13O at around +65 MeV/nucleon [39]. If the inelastic-scattering compo- +nent is not taken into account, the present one-proton +removal Rs will be around unity, coinciding with the +loosely-bound nucleon-removal Rs from eikonal model +based analysis [10–12, 26]. The low-lying excited states +considered here have multiparticle-multihole configura- +tions. It was shown recently that inelastic scattering with +large momentum transfer has the advantage of populat- +ing multiparticle-multihole states [65]. Such states are +beyond the descriptions of the (p, pN) and the eikonal +models, which assume beforehand that the projectile is a +single-particle state plus an inert core [8]. +For the deeply-bound neutron removal, σsp of 14O(p, +pn)13O were calculated to be 6.3 mb and 13.5 mb from +the DWIA and the QTC, respectively. +The QTC cal- +culation without (p, d) transfer is 10.2 mb, still larger +than the DWIA result. Other effects, such as low-energy +neutron-core absorption, contribute to this difference. To +study the (p, d) transfer effect, we performed the QTC +calculation with the outgoing channel coupled only to the +deuteron ground state, that is equivalent to the so-called +DWBA (Distorted-Wave Born Approximation) calcula- +tion (See SM [59]). +The obtained σsp for the transfer +reaction is 3 mb. The (p, d) transfer is considered in the +QTC formalism but not in the DWIA. With a neutron +SF of 3.42, the combination of the DWIA calculation +for 14O(p, pn)13O and the DWBA calculation for 14O(p, +d)13O results in a σth of 34.2 mb, while QTC leads to a +σth of 49.7 mb. The corresponding Rs are 0.49(7) and +0.34(5). +The PMD of 13O is shown in Fig. 2 (c) and (d), and +compared with those from the DWIA+DWBA and the +QTC calculations. The data are well reproduced by com- +bining the contributions from the DWIA and the DWBA, +in which the latter corresponding to (p, d) transfer con- +tributes to ∼30%. As discussed by the previous DWIA +calculation [43], our data support the interpretation that +the low-momentum tail is caused by the attractive po- +tential between the outgoing nucleons and 13O. On the +other hand, the (p, d) transfer reaction creates a sharp +high-momentum edge, as observed in the data, due to the +two-body kinematics of the transfer reaction. The sharp +edge is found in a kinematic region inaccessible to (p, pn) +knockout and is thus a proof of significant transfer contri- +bution. Since the QTC formalism treats (p, d) transfer +consistently with the (p, pn), it reproduces better the +sharp high-momentum side than the DWIA. However, +the QTC does not reproduce the low-momentum tail as +well as the DWIA. The reason might be due to the differ- +ent treatment of the final state interaction in QTC, espe- +cially that the nucleon-residue interaction at low relative +energy is not explicitly treated in the QTC formalism. +It is the first time the PMD measured near 100 +MeV/nucleon shows a distinctive contribution from the +(p, d) transfer reaction, usually neglected at such beam +energies [25]. +One-nucleon pickup cross sections have +been measured around 60 MeV/nucleon with heavy-ion +beams on 12C or 9Be target [66–69]. Here, the extracted +one-neutron transfer cross section is higher, due to the +momentum matching of the well bound neutron. +The +product of the momentum transfer q and the radius of +14O nucleus R is around (1–2) ℏ at forward angles, which +fits the momentum matching condition [17]. Further cal- +culations at 300 MeV/nucleon show that the qR product +increases to (3–5) ℏ and the (p, d) transfer cross sec- +tion decreases to about 0.2 mb, negligible compared to +the quasifree knockout cross sections [21, 42]. The (p, +d) transfer contribution should thus be assessed for the +neutron removal reactions at intermediate energies, espe- +cially at energies below 100 MeV/nucleon. We infer that +the proton removal with a 9Be target may also contain +non-negligible transfer contributions, where the removed +proton combines one neutron from 9Be forming bound +or unbound d + α + α clusters, since Sn of 9Be is only +1.7 MeV and a three cluster model n + α + α provides a +reliable description of the 9Be nucleus [70]. + +5 +20 +- +10 +- +0 +10 +20 + [MeV] +S +D +0 +0.2 +0.4 +0.6 +0.8 +1 +1.2 +1.4 +th +s + / +exp +s + = +s +R +DWIA w/ Inelastic & Transfer +QTC w/ Inelastic +w/o Inelastic & Transfer +Graph +w/o Inelastic & Transfer +FIG. 3. Rs as a function of ∆S from the present work (blue +dots and black squares) compared to trends extracted from +Be/C induced nucleon removal cross sections analysed with +the eikonal model [10–12] (grey shaded region). The square +brackets indicate the total systematic uncertainties. Red-solid +and black-dashed lines are shown to guide the eyes. +The Rs as a function of ∆S is shown in Fig. 3. Most +light-ion-induced nucleon removal Rs lie within a band +with a slope of −1.6 × 10−2 MeV−1 and a half width +of 0.1 [10–12], as shown by the shaded grey region in +Fig. 3. On the other hand, the analyses of low-energy +one-nucleon transfer [16, 18, 19, 71] and high-energy +quasifree scattering data [20–22, 24] result in slope ab- +solute values of (10−3 – 10−5) MeV−1. By considering +the two data sets of the present work, we obtain a slope +of −3.0(5)(5) × 10−3 MeV−1 when the DWIA together +with the inelastic and transfer calculations are consid- +ered, and of −4.6(4)(7) × 10−3 MeV−1 when the QTC +and the inelastic scattering are considered. Both slopes +are negative and their absolute values are almost zero, +indicating Rs have a weak ∆S dependence. +For com- +parison, we also extract the Rs if the inelastic scattering +and nucleon transfer are neglected in the cross section +calculations. As shown in Fig. 3, the resulting Rs slopes +are 3–5 times larger in the absolute values and look com- +patible with the strong ∆S dependence indicated by the +light-ion-induced nucleon removal. +In summary, we have reported on the first study of +the one-nucleon removal reaction from a large separation- +energy asymmetric nucleus 14O (∆S = ±18.6 MeV) us- +ing a proton target at ∼100 MeV/nucleon, a widely use +energy regime for rare-isotope studies. +The measured +PMDs and cross sections were compared to the state- +of-the-art reaction models, including quasifree knockout, +inelastic scattering and nucleon transfer calculations. In +the loosely-bound proton removal channel, the (p, p′) in- +elastic scattering and the (p, 2p) quasifree knockout are +found of almost equal contributions, advocating for an +explicit treatment of the inelastic scattering for quan- +titative interpretation of loosely-bound nucleon removal +cross sections. A highly asymmetric PMD was observed +in the deeply-bound neutron removal channel, which was +reproduced by combining the (p, pn) knockout compo- +nent from the DWIA calculation and the (p, d) transfer +component from the DWBA calculation. We observed a +distinctive contribution of ∼30% in the high-momentum +part of the residue PMD from the deeply-bound nucleon +stripping (p, d) transfer reaction, usually not considered +at such beam energies. The reduction factors extracted +from the present two new data sets show a weak ∆S +dependence, which become markedly larger if the inelas- +tic scattering and nucleon transfer contributions are not +taken into account. +We +are +grateful +to +the +RIKEN +Nishina +Center +accelerator staff for providing the stable and high- +intensity 18O beam and to the BigRIPS team for the +smooth operation of the secondary beam. +This work +was supported by the Deutsche Forschungsgemeinschaft +(DFG, German Research Foundation)—Projektnummer +279384907–SFB 1245. Y. L. S. and A. O. acknowledge +the support from the Alexander von Humboldt foun- +dation. +Y. L. S. acknowledges the support of Marie +Sk�lodowska-Curie Individual Fellowship (H2020-MSCA- +IF-2015-705023) from the European Union and the sup- +port from the Helmholtz International Center for FAIR. +K.O. acknowledges the support by Grant-in-Aid for Sci- +entific Research JP21H00125. M.G.R. acknowledges fi- +nancial support by MCIN/AEI /10.13039 /501100011033 +under I+D+i project No. PID2020-114687GB-I00, by +the Consejer´ıa de Econom´ıa, Conocimiento, Empre- +sas y Universidad, Junta de Andaluc´ıa (Spain) and +“ERDF-A Way of Making Europe” under PAIDI 2020 +project No. P20 01247, and by the European Social +Fund and Junta de Andaluc´ıa (PAIDI 2020) under grant +number DOC-01006. C.X.Y. acknowledges Guangdong +Major Project of Basic and Applied Basic Research +(2021B0301030006). J. L. acknowledges the support from +Research Grants Council (RGC) of Hong Kong (GRF- +17303717). T. N. acknowledges the JSPS Kakenhi Grants +No. JP16H02179, JP18H05404. Y. T. acknowledges the +JSPS Grant-in-Aid for Scientific Research Grants No. +JP21H01114. This work was supported by the Institute +for Basic Science (IBS-R031-D1). Y. Satou is thanked +for his help with the inelastic scattering calculations. We +thank T. Aumann, C. A. Bertulani and M. Duer for their +valuable comments on the manuscript. +∗ tpohl@ikp.tu-darmstadt.de +† ysun@ikp.tu-darmstadt.de +[1] A. Bohr and B. R. Mottleson, Nuclear Structure (Ben- +jamin , New York, 1969), Vol. I. +[2] M. G. Mayer, Phys. Rev. 75, 1969 (1949), URL https: +//link.aps.org/doi/10.1103/PhysRev.75.1969. +[3] O. Haxel, J. H. D. Jensen, and H. E. Suess, Phys. Rev. + +6 +75, 1766 (1949), URL https://link.aps.org/doi/10. +1103/PhysRev.75.1766.2. +[4] L. Lapikas, Nuclear Physics A553, 297c (1993). +[5] W. Dickhoff and C. Barbieri, +Progress in Particle +and +Nuclear +Physics +52, +377 +(2004), +ISSN +0146- +6410, URL https://www.sciencedirect.com/science/ +article/pii/S0146641004000535. +[6] T. Otsuka, A. Gade, O. Sorlin, T. Suzuki, and Y. Utsuno, +Rev. Mod. Phys. 92, 015002 (2020), URL https://link. +aps.org/doi/10.1103/RevModPhys.92.015002. +[7] F. Nowacki, A. Obertelli, and A. Poves, Progress in Par- +ticle and Nuclear Physics 120, 103866 (2021), ISSN 0146- +6410, URL https://www.sciencedirect.com/science/ +article/pii/S014664102100020X. +[8] P. +Hansen +and +J. +Tostevin, +Annual +Review +of +Nuclear +and +Particle +Science +53, +219 +(2003), +https://doi.org/10.1146/annurev.nucl.53.041002.110406, +URL +https://doi.org/10.1146/annurev.nucl.53. +041002.110406. +[9] B. A. Brown, +P. G. Hansen, +B. M. Sherrill, +and +J. A. Tostevin, Phys. Rev. C 65, 061601(R) (2002), +URL +https://link.aps.org/doi/10.1103/PhysRevC. +65.061601. +[10] A. Gade, P. Adrich, D. Bazin, M. D. Bowen, B. A. +Brown, C. M. Campbell, J. M. Cook, T. Glasmacher, +P. G. Hansen, K. Hosier, et al., Phys. Rev. C 77, +044306 (2008), URL https://link.aps.org/doi/10. +1103/PhysRevC.77.044306. +[11] J. +A. +Tostevin +and +A. +Gade, +Phys. +Rev. +C +90, +057602 (2014), URL https://link.aps.org/doi/10. +1103/PhysRevC.90.057602. +[12] J. A. Tostevin and A. Gade, +Phys. Rev. C 103, +054610 (2021), URL https://link.aps.org/doi/10. +1103/PhysRevC.103.054610. +[13] Y. Z. Sun, S. T. Wang, Y. P. Xu, D. Y. Pang, J. G. Li, +C. X. Yuan, L. F. Wan, Y. Qiao, Y. Q. Wang, and X. Y. +Chen, Phys. Rev. C 106, 034614 (2022), URL https: +//link.aps.org/doi/10.1103/PhysRevC.106.034614. +[14] J. Lee, J. A. Tostevin, B. A. Brown, F. Delaunay, W. G. +Lynch, M. J. Saelim, and M. B. Tsang, Phys. Rev. C +73, 044608 (2006), URL https://link.aps.org/doi/ +10.1103/PhysRevC.73.044608. +[15] J. Lee, M. B. Tsang, D. Bazin, D. Coupland, V. Henzl, +D. +Henzlova, +M. +Kilburn, +W. +G. +Lynch, +A. +M. +Rogers, A. Sanetullaev, et al., Phys. Rev. Lett. 104, +112701 (2010), URL https://link.aps.org/doi/10. +1103/PhysRevLett.104.112701. +[16] F. Flavigny, A. Gillibert, L. Nalpas, A. Obertelli, N. Kee- +ley, C. Barbieri, D. Beaumel, S. Boissinot, G. Bur- +gunder, A. Cipollone, et al., Phys. Rev. Lett. 110, +122503 (2013), URL https://link.aps.org/doi/10. +1103/PhysRevLett.110.122503. +[17] B. P. Kay, J. P. Schiffer, and S. J. Freeman, Phys. Rev. +Lett. 111, 042502 (2013), URL https://link.aps.org/ +doi/10.1103/PhysRevLett.111.042502. +[18] Y. Xu, D. Pang, X. Yun, C. Wen, C. Yuan, and +J. Lou, Physics Letters B 790, 308 (2019), ISSN 0370- +2693, URL http://www.sciencedirect.com/science/ +article/pii/S0370269319300504. +[19] J. Manfredi, J. Lee, A. M. Rogers, M. B. Tsang, +W. G. Lynch, C. Anderson, J. Barney, K. W. Brown, +B. Brophy, G. Cerizza, et al., Phys. Rev. C 104, +024608 (2021), URL https://link.aps.org/doi/10. +1103/PhysRevC.104.024608. +[20] S. Kawase, T. Uesaka, T. L. Tang, D. Beaumel, M. Do- +zono, T. Fukunaga, T. Fujii, N. Fukuda, A. Galindo- +Uribarri, S. Hwang, et al., Progress of Theoretical +and Experimental Physics 2018 (2018), ISSN 2050- +3911, 021D01, https://academic.oup.com/ptep/article- +pdf/2018/2/021D01/24195568/pty011.pdf, URL https: +//doi.org/10.1093/ptep/pty011. +[21] L. Atar, S. Paschalis, C. Barbieri, C. A. Bertulani, +P. D´ıaz Fern´andez, M. Holl, M. A. Najafi, V. Panin, +H. Alvarez-Pol, T. Aumann, et al. (R3B Collaboration), +Phys. Rev. Lett. 120, 052501 (2018), URL https:// +link.aps.org/doi/10.1103/PhysRevLett.120.052501. +[22] M. +G´omez-Ramos +and +A. +Moro, +Physics +Let- +ters +B +785, +511 +(2018), +ISSN +0370-2693, +URL +http://www.sciencedirect.com/science/article/ +pii/S0370269318306749. +[23] M. Holl, V. Panin, H. Alvarez-Pol, L. Atar, T. Aumann, +S. Beceiro-Novo, J. Benlliure, C. Bertulani, J. Boillos, +K. Boretzky, et al., Physics Letters B 795, 682 (2019), +ISSN 0370-2693, +URL https://www.sciencedirect. +com/science/article/pii/S0370269319304666. +[24] N. T. T. Phuc, K. Yoshida, and K. Ogata, Phys. Rev. C +100, 064604 (2019), URL https://link.aps.org/doi/ +10.1103/PhysRevC.100.064604. +[25] T. Aumann, +C. Barbieri, +D. Bazin, +C. Bertulani, +A. Bonaccorso, W. Dickhoff, A. Gade, M. G´omez- +Ramos, B. Kay, A. Moro, et al., Progress in Particle +and Nuclear Physics 118, 103847 (2021), ISSN 0146- +6410, URL https://www.sciencedirect.com/science/ +article/pii/S0146641021000016. +[26] D. Bazin, +R. J. Charity, +R. T. de Souza, +M. A. +Famiano, A. Gade, V. Henzl, D. Henzlova, S. Hu- +dan, J. Lee, S. Lukyanov, et al., Phys. Rev. Lett. +102, 232501 (2009), URL https://link.aps.org/doi/ +10.1103/PhysRevLett.102.232501. +[27] K. Wimmer, +D. Bazin, +A. Gade, +J. A. Tostevin, +T. Baugher, Z. Chajecki, D. Coupland, M. A. Fami- +ano, T. K. Ghosh, G. F. Grinyer, et al., Phys. Rev. +C 90, 064615 (2014), URL https://link.aps.org/doi/ +10.1103/PhysRevC.90.064615. +[28] C. Louchart, A. Obertelli, A. Boudard, and F. Flavigny, +Phys. Rev. C 83, 011601(R) (2011), URL https://link. +aps.org/doi/10.1103/PhysRevC.83.011601. +[29] Y. L. Sun, J. Lee, Y. L. Ye, A. Obertelli, Z. H. Li, N. Aoi, +H. J. Ong, Y. Ayyad, C. A. Bertulani, J. Chen, et al., +Phys. Rev. C 93, 044607 (2016), URL https://link. +aps.org/doi/10.1103/PhysRevC.93.044607. +[30] F. Flavigny, A. Obertelli, and I. Vida˜na, Phys. Rev. C +79, 064617 (2009), URL https://link.aps.org/doi/ +10.1103/PhysRevC.79.064617. +[31] C. A. Bertulani and C. De Conti, Phys. Rev. C 81, +064603 (2010), URL https://link.aps.org/doi/10. +1103/PhysRevC.81.064603. +[32] J. A. Tostevin, D. Bazin, B. A. Brown, T. Glasmacher, +P. G. Hansen, V. Maddalena, A. Navin, and B. M. +Sherrill, Phys. Rev. C 66, 024607 (2002), URL https: +//link.aps.org/doi/10.1103/PhysRevC.66.024607. +[33] A. Gade, D. Bazin, C. A. Bertulani, B. A. Brown, +C. M. Campbell, J. A. Church, D. C. Dinca, J. En- +ders, T. Glasmacher, P. G. Hansen, et al., Phys. Rev. +C 71, 051301(R) (2005), URL https://link.aps.org/ +doi/10.1103/PhysRevC.71.051301. +[34] K. L. Yurkewicz, D. Bazin, B. A. Brown, J. Enders, +A. Gade, T. Glasmacher, P. G. Hansen, V. Maddalena, + +7 +A. Navin, B. M. Sherrill, et al., Phys. Rev. C 74, +024304 (2006), URL https://link.aps.org/doi/10. +1103/PhysRevC.74.024304. +[35] G. F. Grinyer, D. Bazin, A. Gade, J. A. Tostevin, +P. Adrich, M. D. Bowen, B. A. Brown, C. M. Camp- +bell, J. M. Cook, T. Glasmacher, et al., Phys. Rev. Lett. +106, 162502 (2011), URL https://link.aps.org/doi/ +10.1103/PhysRevLett.106.162502. +[36] F. Flavigny, A. Obertelli, A. Bonaccorso, G. F. Grinyer, +C. Louchart, L. Nalpas, and A. Signoracci, Phys. Rev. +Lett. 108, 252501 (2012), URL https://link.aps.org/ +doi/10.1103/PhysRevLett.108.252501. +[37] R. Shane, R. J. Charity, L. G. Sobotka, D. Bazin, +B. A. Brown, A. Gade, G. F. Grinyer, S. McDaniel, +A. Ratkiewicz, D. Weisshaar, et al., Phys. Rev. C +85, 064612 (2012), URL https://link.aps.org/doi/ +10.1103/PhysRevC.85.064612. +[38] S. R. Stroberg, A. Gade, J. A. Tostevin, V. M. Bader, +T. Baugher, D. Bazin, J. S. Berryman, B. A. Brown, +C. M. Campbell, K. W. Kemper, et al., Phys. Rev. C +90, 034301 (2014), URL https://link.aps.org/doi/ +10.1103/PhysRevC.90.034301. +[39] R. J. Charity, L. G. Sobotka, and J. A. Tostevin, Phys. +Rev. C 102, 044614 (2020), URL https://link.aps. +org/doi/10.1103/PhysRevC.102.044614. +[40] C. A. Bertulani and K. W. McVoy, Phys. Rev. C +46, 2638 (1992), URL https://link.aps.org/doi/10. +1103/PhysRevC.46.2638. +[41] J. +Tostevin, +Nuclear +Physics +A +682, +320 +(2001), +ISSN 0375-9474, +URL https://www.sciencedirect. +com/science/article/pii/S0375947400006564. +[42] T. Aumann, C. A. Bertulani, and J. Ryckebusch, Phys. +Rev. C 88, 064610 (2013), URL https://link.aps.org/ +doi/10.1103/PhysRevC.88.064610. +[43] K. Ogata, K. Yoshida, and K. Minomo, Phys. Rev. C +92, 034616 (2015), URL https://link.aps.org/doi/ +10.1103/PhysRevC.92.034616. +[44] N. Fukuda et al., Nuclear Instruments and Methods in +Physics Research B 317, 323 (2013). +[45] Y. Matsuda et al., Nuclear Instruments and Methods in +Physics Research A 643, 6 (2011). +[46] T. Kobayashi et al., Nuclear Instruments and Methods +in Physics Research B 317, 294 (2013). +[47] S. Agostinelli et al. (GEANT4), Nucl. Instrum. Meth. +A506, 250 (2003). +[48] R. Brun and F. Rademakers, +Nuclear Instruments +and +Methods +in +Physics +Research +Section +A: +Ac- +celerators, +Spectrometers, +Detectors and Associated +Equipment +389, +81 +(1997), +ISSN +0168-9002, +new +Computing Techniques in Physics Research V, URL +https://www.sciencedirect.com/science/article/ +pii/S016890029700048X. +[49] A. Boudard, J. Cugnon, S. Leray, and C. Volant, Phys. +Rev. C 66, 044615 (2002), URL https://link.aps.org/ +doi/10.1103/PhysRevC.66.044615. +[50] C. Yuan, T. Suzuki, T. Otsuka, F. Xu, and N. Tsunoda, +Phys. Rev. C 85, 064324 (2012), URL https://link. +aps.org/doi/10.1103/PhysRevC.85.064324. +[51] N. Shimizu, T. Mizusaki, Y. Utsuno, and Y. Tsunoda, +Computer Physics Communications 244, 372 (2019), +ISSN 0010-4655, +URL https://www.sciencedirect. +com/science/article/pii/S0010465519301985. +[52] B. A. Brown, A. Etchegoyen, N. S. Godwin, W. D. M. +Rae, W. A. Richter, W. E. Ormand, E. K. Warburton, +J. S. Winfield, L. Zhao, C. H. Zimmerman, et al., MSU- +NSCL report no. 1289 (2004). +[53] E. K. Warburton and B. A. Brown, Phys. Rev. C 46, +923 (1992), URL https://link.aps.org/doi/10.1103/ +PhysRevC.46.923. +[54] N. S. Chant and P. G. Roos, +Phys. Rev. C 15, +57 (1977), URL https://link.aps.org/doi/10.1103/ +PhysRevC.15.57. +[55] N. +S. +Chant +and +P. +G. +Roos, +Phys. +Rev. +C +27, 1060 (1983), URL https://link.aps.org/doi/10. +1103/PhysRevC.27.1060. +[56] T. Wakasa, K. Ogata, and T. Noro, Progress in Par- +ticle and Nuclear Physics 96, 32 +(2017), ISSN 0146- +6410, URL http://www.sciencedirect.com/science/ +article/pii/S0146641017300558. +[57] K. Yoshida, M. G´omez-Ramos, K. Ogata, and A. M. +Moro, Phys. Rev. C 97, 024608 (2018), URL https: +//link.aps.org/doi/10.1103/PhysRevC.97.024608. +[58] A. +M. +Moro, +Phys. +Rev. +C +92, +044605 +(2015), +URL +https://link.aps.org/doi/10.1103/PhysRevC. +92.044605. +[59] See Supplemental Material at [url] for more details of +DWIA, QTC calculations and the inelastic excitation cal- +culations. +[60] Y. Sun, A. Obertelli, P. Doornenbal, C. Barbieri, Y. Cha- +zono, T. Duguet, H. Liu, P. Navr´atil, F. Nowacki, +K. Ogata, et al., Physics Letters B 802, 135215 (2020), +ISSN 0370-2693, +URL https://www.sciencedirect. +com/science/article/pii/S0370269320300198. +[61] S. Chen, J. Lee, P. Doornenbal, A. Obertelli, C. Bar- +bieri, +Y. Chazono, +P. Navr´atil, +K. Ogata, +T. Ot- +suka, +F. Raimondi, +et al., +Phys. Rev. Lett. 123, +142501 (2019), URL https://link.aps.org/doi/10. +1103/PhysRevLett.123.142501. +[62] F. Browne, +S. Chen, +P. Doornenbal, +A. Obertelli, +K. Ogata, Y. Utsuno, K. Yoshida, N. L. Achouri, +H. Baba, D. Calvet, et al., Phys. Rev. Lett. 126, +252501 (2021), URL https://link.aps.org/doi/10. +1103/PhysRevLett.126.252501. +[63] T. Aumann, C. Barbieri, D. Bazin, C. A. B. andA. +Bonaccorso, W. H. Dickhoff, A. Gade, M. G´omez-Ramos, +B. P. Kay, A. M. Moro, T. Nakamura, et al., Progress +in Particle and Nuclear Physics 118, 103847 (2021), +ISSN 0146-6410, +URL https://www.sciencedirect. +com/science/article/pii/S0146641021000016. +[64] R. +J. +Charity, +K. +W. +Brown, +J. +Oko�lowicz, +M. +P�loszajczak, +J. +M. +Elson, +W. +Reviol, +L. +G. +Sobotka, W. W. Buhro, Z. Chajecki, W. G. Lynch, +et al., Phys. Rev. C 100, 064305 (2019), URL https: +//link.aps.org/doi/10.1103/PhysRevC.100.064305. +[65] A. Gade, +B. A. Brown, +D. Weisshaar, +D. Bazin, +K. W. Brown, R. J. Charity, P. Farris, A. M. Hill, +J. Li, B. Longfellow, et al., Phys. Rev. Lett. 129, +242501 (2022), URL https://link.aps.org/doi/10. +1103/PhysRevLett.129.242501. +[66] A. Gade, P. Adrich, D. Bazin, M. D. Bowen, B. A. +Brown, C. M. Campbell, J. M. Cook, T. Glasmacher, +K. Hosier, +S. McDaniel, +et al., +Phys. Rev. C 76, +061302(R) (2007), +URL https://link.aps.org/doi/ +10.1103/PhysRevC.76.061302. +[67] S. McDaniel, A. Gade, J. A. Tostevin, T. Baugher, +D. Bazin, B. A. Brown, J. M. Cook, T. Glasmacher, +G. F. Grinyer, A. Ratkiewicz, et al., Phys. Rev. C +85, 014610 (2012), URL https://link.aps.org/doi/ + +8 +10.1103/PhysRevC.85.014610. +[68] A. Gade, +J. A. Tostevin, +V. Bader, +T. Baugher, +D. Bazin, J. S. Berryman, B. A. Brown, D. J. Hart- +ley, E. Lunderberg, F. Recchia, et al., Phys. Rev. C +93, 031601(R) (2016), URL https://link.aps.org/ +doi/10.1103/PhysRevC.93.031601. +[69] A. Gade, +J. A. Tostevin, +V. Bader, +T. Baugher, +D. Bazin, J. S. Berryman, B. A. Brown, C. A. Di- +get, T. Glasmacher, D. J. Hartley, et al., Phys. Rev. +C 93, 054315 (2016), URL https://link.aps.org/doi/ +10.1103/PhysRevC.93.054315. +[70] Y. Tang, F. Khanna, R. Herndon, and K. Wilder- +muth, Nuclear Physics 35, 421 (1962), ISSN 0029- +5582, URL https://www.sciencedirect.com/science/ +article/pii/0029558262901347. +[71] J. Lee, M. B. Tsang, and W. G. Lynch, Phys. Rev. C +75, 064320 (2007), URL https://link.aps.org/doi/ +10.1103/PhysRevC.75.064320. + +Supplemental Material for “Multiple mechanisms in proton-induced nucleon removal +at ∼100 MeV/nucleon” +T. Pohl,1, ∗ Y. L. Sun,1, 2, 3, † A. Obertelli,1, 2 J. Lee,3 M. G´omez-Ramos,4 K. Ogata,5, 6 K. Yoshida,7 +B.S. Cai,8 C.X. Yuan,8 B. A. Brown,9 H. Baba,10 D. Beaumel,11 A. Corsi,2 J. Gao,10, 12 J. Gibelin,13 +A. Gillibert,2 K. I. Hahn,14, 15 T. Isobe,10 D. Kim,14, 15 Y. Kondo,16 T. Kobayashi,17 Y. Kubota,10, 18 +P. Li,3 P. Liang,3 H. N. Liu,1, 2, 19 J. Liu,3 T. Lokotko,3 F.M. Marqu´es,13 Y. Matsuda,20, 21 +T. Motobayashi,10 T. Nakamura,16 N.A. Orr,13 H. Otsu,10 V. Panin,10, 2 S. Y. Park,14, 10 +S. Sakaguchi,5 M. Sasano,10 H. Sato,10 H. Sakurai,10, 22 Y. Shimizu,10 L. Stuhl,10, 15 D. Suzuki,10 +Y. Togano,16, 10, 23 T. Uesaka,10 H. Wang,10 X. Xu,3 Z. H. Yang,10 K. Yoneda,10 and J. Zenihiro10 +1Institut f¨ur Kernphysik, Technische Universit¨at Darmstadt, 64289 Darmstadt, Germany +2IRFU, CEA, Universit´e Paris-Saclay, F-91191 Gif-sur-Yvette, France +3Department of Physics, The University of Hong Kong, Pokfulam, Hong Kong +4Departamento de F´ısica At´omica, Molecular y Nuclear, Facultad de +F´ısica, Universidad de Sevilla, Apartado 1065, E-41080 Sevilla, Spain +5Department of Physics, Kyushu University, Fukuoka 812-8581, Japan +6Research Center for Nuclear Physics (RCNP), Osaka University, Ibaraki 567-0047, Japan +7Advanced Science Research Center, Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195, Japan +8Sino-French Institute of Nuclear Engineering and Technology, Sun Yat-Sen University, Zhuhai, 519082, Guangdong, China +9Department of Physics and Astronomy and National Superconducting Cyclotron +Laboratory, Michigan State University, East Lansing, Michigan 48824-1321, USA +10RIKEN Nishina Center, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan +11Universit´e Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France +12State Key Laboratory of Nuclear Physics and Technology, School of Physics, Peking University, Beijing 100871, China +13LPC Caen, ENSICAEN, Universit´e de Caen, CNRS/IN2P3, F-14050 Caen, France +14Department of Physics, Ewha Womans University, Seoul, South Korea +15Center for Exotic Nuclear Studies, Institute for Basic Science, Daejeon 34126, Republic of Korea +16Department of Physics, Tokyo Institute of Technology, 2-12-1 O-Okayama, Meguro, Tokyo, 152-8551, Japan +17Department of Physics, Tohoku University, Sendai 980-8578, Japan +18Center for Nuclear Study, University of Tokyo, RIKEN campus, Wako, Saitama 351-0198, Japan +19Key Laboratory of Beam Technology and Material Modification of Ministry of Education, +College of Nuclear Science and Technology, Beijing Normal University, Beijing 100875, China +20Cyclotron and Radioisotope Center, Tohoku University, Sendai 980-8578, Japan +21Department of Physics, Konan University, Kobe 658-8501, Japan +22Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan +23Department of Physics, Rikkyo University, 3-34-1 Nishi-Ikebukuro, Toshima, Tokyo 172-8501, Japan +(Dated: January 11, 2023) +arXiv:2301.03836v1 [nucl-ex] 10 Jan 2023 + +2 +DWIA AND QTC CALCULATION +In the DWIA calculations, we employed the folding potential with the Melbourne G-matrix interaction for calculat- +ing the distorted waves. As for the transition process, we adopted the nucleon-nucleon cross section calculated with +the Franey-Love interaction [1]. Perey correction [2] for the non-locality was applied both for the bound-state and +scattering wave functions. Energy dependence of the optical potentials was taken into account by using the scattering +energy of the emitted nucleons. In the QTC calculations, the p + N + 13O/13N three-body final state was expressed +in a basis of discretized continuum states of the p + N system. Microscopic JLM optical potential [3] was employed +for the distortion of the incident and outgoing channels. Both the G-matrix folding potential and JLM potential +were found to reproduce well the experimental differential cross section for p + 16O elastic scattering at 65 MeV. +The single-particle wave function of the knocked-out nucleon in both DWIA and QTC was obtained by solving the +Schr¨odinger equation using a Woods-Saxon potential with an adjusted depth to result in the correct binding energy +of the knocked-out nucleon. +In the QTC calculation for the (p, d) transfer, the d–13O potential was calculated with the Johnson-Soper prescrip- +tion [4], in which the p–13O and n–13O folding potential at half of the kinetic energy of the deuteron was adopted. +The obtained σsp for the transfer reaction was 3 mb. The uncertainty was about 1 mb, estimated by using the JLM +d–13O potential and by varying the interaction used for the deuteron wave function. +INELASTIC EXCITATION CALCULATION +The inelastic excitation cross section was calculated using the microscopic DWIA reaction model [5], that has +been validated for the inelastic scattering of proton on the 12C target. The structure input for the calculation is +the one-body transition densities (OBTDs) from the above mentioned shell model calculations. +We adopted the +Franey-Love nucleon-nucleon effective interaction for the interaction of the transitions. The Koning-Delaroche (KD) +phenomenological optical potential [6] was used to generate the distorted waves. The calculation reproduce reasonably +well the differential cross section of the 2+ +1 excitation of 12C measured at 120 MeV [7]. We have considered eight +excited states of 14O (0+ +2 , 0+ +3 , 2+ +1 , 2+ +2 , 0− +1 , 1− +1 , 2− +1 , 3− +1 ) that could decay via one proton emission to 13N [8], resulting +in a total inelastic cross section of 9 mb. The dominant contribution originated from the 2+ +1 , 1− +1 and 3− +1 excitations. +The uncertainty is about 1mb, estimated by performing the calculation using different effective interactions for the +OBTDs, as well as by using the M3Y nucleon-nucleon interaction, that takes the medium effects into account [9]. +CALCULATION OF σth +The theoretical loosely-bound proton removal cross sections σth are the sum of the (p, 2p) knockout cross sections +(σsp × SF × A/(A−1)) and the inelastic excitation cross section. Note that A/(A−1) is the center-of-mass correction +factor [10] and A is the mass number of the projectile, i.e., 14 in this case. +Since the (p, d) transfer process was considered in the QTC formalism but not in the DWIA, we calculated the +σth for the neutron removal as: 1) the σsp from the DWIA and the (p, d) transfer multiplied by the SF × A/(A − 1) +factor. 2) the σsp from the QTC calculation multiplied by the SF × A/(A − 1) factor. +∗ tpohl@ikp.tu-darmstadt.de +† ysun@ikp.tu-darmstadt.de +[1] M. A. Franey and W. G. Love, Phys. Rev. C 31, 488 (1985), URL https://link.aps.org/doi/10.1103/PhysRevC.31.488. +[2] F. Perey and B. Buck, Nuclear Physics 32, 353 (1962), ISSN 0029-5582, URL https://www.sciencedirect.com/science/ +article/pii/0029558262903450. +[3] J.-P. Jeukenne, A. Lejeune, and C. Mahaux, Phys. Rev. C 16, 80 (1977), URL https://link.aps.org/doi/10.1103/ +PhysRevC.16.80. +[4] R. C. Johnson and P. J. R. Soper, Phys. Rev. C 1, 976 (1970), URL https://link.aps.org/doi/10.1103/PhysRevC.1.976. +[5] R. Schaeffer and J. Raynal, computer program DWBA70, 1970 (unpublished); extended version DW81 by J. R. Comfort, +1981 (unpublished). + +3 +[6] A. Koning and J. Delaroche, Nuclear Physics A 713, 231 (2003), ISSN 0375-9474, URL https://www.sciencedirect. +com/science/article/pii/S0375947402013210. +[7] J. R. Comfort, G. L. Moake, C. C. Foster, P. Schwandt, C. D. Goodman, J. Rapaport, and W. G. Love, Phys. Rev. C 24, +1834 (1981), URL https://link.aps.org/doi/10.1103/PhysRevC.24.1834. +[8] R. J. Charity, K. W. Brown, J. Oko�lowicz, M. P�loszajczak, J. M. Elson, W. Reviol, L. G. Sobotka, W. W. Buhro, +Z. Chajecki, W. G. Lynch, et al., Phys. Rev. C 100, 064305 (2019), URL https://link.aps.org/doi/10.1103/PhysRevC. +100.064305. +[9] G. Bertsch, J. Borysowicz, H. McManus, and W. Love, Nuclear Physics A 284, 399 (1977), ISSN 0375-9474, URL https: +//www.sciencedirect.com/science/article/pii/037594747790392X. +[10] A. E. L. Dieperink and T. d. Forest, Phys. Rev. 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metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Republic of Korea 16Department of Physics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Tokyo Institute of Technology,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' 2-12-1 O-Okayama,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Meguro,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Tokyo,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' 152-8551,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Japan 17Department of Physics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Tohoku University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Sendai 980-8578,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Japan 18Center for Nuclear Study,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' University of Tokyo,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' RIKEN campus,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Wako,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Saitama 351-0198,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Japan 19Key Laboratory of Beam Technology and Material Modification of Ministry of Education,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' College of Nuclear Science and Technology,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Beijing Normal University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Beijing 100875,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' China 20Cyclotron and Radioisotope Center,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Tohoku University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Sendai 980-8578,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Japan 21Department of Physics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Konan University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Kobe 658-8501,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Japan 22Department of Physics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' University of Tokyo,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' 7-3-1 Hongo,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Bunkyo,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Tokyo 113-0033,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Japan 23Department of Physics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Rikkyo University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' 3-34-1 Nishi-Ikebukuro,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Toshima,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Tokyo 172-8501,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Japan (Dated: January 11,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' 2023) We report on the proton-induced one-nucleon removal reaction from the neutron-deficient 14O nucleus with large proton-to-neutron separation energy asymmetry Sn − Sp = 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='6 MeV at 94 MeV/nucleon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The measured inclusive cross sections and parallel momentum distributions (PMDs) of the 13N and 13O residues are compared to the state-of-the-art reaction models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' It is shown that, in addition to the quasifree knockout, the inelastic scattering and nucleon transfer con- tribute about 50% and 30% to the proton and neutron removal, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' These processes should be considered in analyses of one-nucleon removal cross sections measured at intermediate energies for quantitative nuclear-structure studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The nucleon single-particle (SP) motion is one of the most important properties of nuclei [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The first success- ful model for the description of the nuclear SP properties is the Independent Particle Model (IPM) [2, 3], assuming nucleons move freely in an effective mean-field potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' It was revealed later by (e,e′p) experiments on stable nu- clei that the SP strengths, quantified by the so called spectroscopic factors (SFs), are reduced by (30–40)% rel- ative to the IPM predictions [4, 5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The “quenching” of the SP strengths has been attributed to short- and long- range correlations [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' One main focus of today’s nuclear physics is to extend these studies towards the proton and neutron driplines to better understand nuclear structure and many-body nuclear forces [6, 7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' One-nucleon removal reactions at intermediate ener- gies near and above 100 MeV/nucleon have been a pow- erful tool to extract SP strengths of unstable nuclei [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The quenching of the SP strengths has been connected to the so-called reduction factor Rs [9], defined as the ratio of the experimental to the theoretical cross sec- tion that is usually computed using shell-model SFs and an eikonal reaction model relying on the adiabatic and eikonal approximations [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Systematic studies from light-ion-induced one-nucleon removal reactions at ∼100 MeV/nucleon [10–12] and higher incident beam ener- gies [13] revealed that Rs has a strong dependence on the arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='03836v1 [nucl-ex] 10 Jan 2023 2 proton-to-neutron asymmetry quantified as ∆S = Sn - Sp or Sp - Sn for neutron or proton removal, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' However, results from transfer reactions [14–19] and pro- ton induced quasifree knockout (p, pN) reactions [20–24] did not confirm the strong ∆S dependence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The inconsistent dependence on ∆S calls for a deeper understanding on the reaction mechanisms and corre- lations in nuclei [25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Although the diffraction and stripping mechanisms have been well established in the eikonal model down to ∼100 MeV/nucleon [26, 27], mul- tiple scattering, excitation and decay of the knockout residue, beyond the eikonal reaction model [28, 29] or Pauli-blocking [30, 31] have been proposed as possible mechanisms that could reduce the deeply-bound nucleon- removal cross sections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' In particular, asymmetric PMDs of the residue, characterized by a low-momentum tail [32–39] and a high-momentum cutoff [36], have been ob- served in several experiments, in contrast to the sym- metric PMDs predicted by the lowest order eikonal model [40–42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The low-momentum tail in PMDs has been tentatively attributed to either the dissipative pro- cesses [36, 38] or the momentum transfer to the target in the diffraction mechanism [32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The high-momentum cutoff stems from the energy and momentum conserva- tion, not fully satisfied in the eikonal model [36, 43].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The above-mentioned studies in [10–13] have been per- formed with light absorptive nuclear targets, 9Be or 12C, which introduce the complexity that the final state of the target is unknown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Here, we report on the first study of one-nucleon removal from a large separation- energy asymmetric nucleus 14O (∆S = ±18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='6 MeV) at ∼100 MeV / nucleon using a single-nucleon target, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=', protons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' 14O is an ideal nucleus to study the one-nucleon removal mechanisms at large proton-to-neutron asymme- try.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The proton and neutron removal from it involve only the orbitals of π0p1/2 and ν0p3/2, respectively, since both 13N (Jπ g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' = 1/2−) and 13O (Jπ g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' = 3/2−) do not exhibit bound excited states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Based on the measured PMDs and the state-of-the-art reaction models, we show that in ad- dition to the quasifree knockout, the inelastic scattering and nucleon transfer also make significant contributions to the loosely-bound proton removal and deeply-bound neutron removal, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The experiment was performed at the Radioactive Iso- tope Beam Factory operated by the RIKEN Nishina Cen- ter and the Center for Nuclear Study of the University of Tokyo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' A primary 18O beam at 230 MeV/nucleon with an intensity of 500 pnA impinged on a 14 mm thick 9Be target.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The 14O secondary beam was purified and identified using the time-of-flight (TOF) and the energy loss (∆E) information by the BigRIPS fragment separa- tor [44].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The typical 14O beam intensity and purity were 9 × 103 particles per second and 78%, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The 14O beam was then tracked onto a 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='40(34)-mm thick solid hydrogen target (SHT) [45] by two multi-wire drift chambers (MWDCs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The beam energy at the target 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='7 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='9 2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='1 Q / A 4 5 6 7 8 9 " Z " 1 10 2 10 3 10 4 10 5 10 (a) CUT 1 CUT 2 100 105 110 115 120 125 130 [mm/ns] v 0 10 20 30 40 50 [arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' unit] E ∆ 1 10 2 10 (b) O 13 C 10 w/ CUT 1 100 105 110 115 120 125 130 [mm/ns] v 0 10 20 30 40 50 [arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' unit] E ∆ 1 10 2 10 (c) w/ CUT 2 O 15 N 13 C 11 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Particle identification (PID) of the projectile-like re- action residues transmitted to the focal plane of the SAMU- RAI spectrometer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' (a) PID using the ∆E-Bρ-TOF method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The ∆E-velocity spectra with the A/Q selections from 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='59 to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='66 (b) and from 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='81 to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='93 (c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='The black contours in (b) and (c) show the selections for 13O and 13N, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' center was 94 MeV/nucleon with a narrow spread of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='2 MeV/nucleon (σ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The target density was determined to be 86 mg/cm3 by the monitored temperature of the tar- get cell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The target thickness and its uncertainty were extracted by measuring the momentum change of the unreacted 14O beam with and without the SHT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The empty-target setting was also used to measure the back- ground events generated by non-target beam-line materi- als, which were subtracted in the cross section and PMD analyses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The reaction residues were measured by the SAMURAI spectrometer [46], with a magnetic field set at 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='49 Tesla with the SHT and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='51 Tesla without the SHT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The po- sition and angle of the particles were measured by two MWDCs located before and after the dipole magnet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' A 10-mm thick plastic scintillator array hodoscope located downstream of the spectrometer was used to measure the ∆E and to determine the TOF together with the time information of the beam particle measured by a 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='2-mm thick plastic scintillator before the SHT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The magnetic rigidity Bρ and the flight length L from the SHT to hodoscope were deduced from multidimensional-fit func- tions using the positions and angles of the residues before and after the magnet as inputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The functions were ob- tained with Geant4 [47] simulations and the multidimen- sional fit package of ROOT [48].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The obtained functions reproduce the simulated Bρ and L with relative devia- tions below 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='02 %.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The experimental PMD response to 14O beam was used for convolution with the theoretical 3 TABLE I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Experimental and theoretical cross sections of one- nucleon removal from 14O at 94 MeV/nucleon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The deduced reduction factors Rs = σexp/σth are also given.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Residue Jπ σexp SF Theory σsp σth Rs [mb] [mb] [mb] 13Ng.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' 1/2− 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='7(16) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='58 DWIA 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='2 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='22(18) Inelastic 9 Sum 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='60(9) QTC 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='0 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='9 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='90(13) Inelastic 9 Sum 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='9 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='51(8) 13Og.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' 3/2− 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='7(24) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='42 DWIA 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='3 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='72(10) Transfer 3 11 Sum 34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='49(7) QTC w/o transfer 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='2 37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='44(6) QTC 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='5 49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='34(5) PMDs of 13O and 13N presented later, taking into ac- count the different energy losses in beam-line materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The reaction residues were identified using the ∆E- Bρ-TOF and ∆E-velocity method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' 13O and 13N can be unambiguously selected with the selection cuts shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' 1(a), the calculated atomic number “Z” us- ing the Bethe-Bloch formula for 13O (A/Q = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='625) and 14O (A/Q = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='75) both show tails extending to smaller “Z” region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The “Z”-tail of 14O is caused by unreacted 14O projectiles interacting in the hodoscope, while the “Z”-tail of 13O has a strong component steaming from the low-energy 13O which stops into the hodoscope.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' As demonstrated in the ∆E-velocity correlation in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' 1(b) and (c), most 13O stopped in the hodoscope and had ∆E proportional to the velocity, while most 13N punched through the hodoscope and had ∆E anti-proportional to the velocity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The resulted experimental cross sections for one-proton and one-neutron removal from 14O are 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='7(16) mb and 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='7(24) mb, respectively, listed in Table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' In the cross section extraction, the momentum acceptance, 94(1)% for 13O and 96(1)% for 12N, determined from Geant4 simulations and 7(1)% reaction loss in the beam-line ma- terials have been taken into account.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' In addition, a loss of 5(1) % was considered based on simulations with the INCL model [49], corresponding to 13O or 13N events out- side of the gates in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' 1 (b) and (c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The cross section errors for 13O and 13N contain statistical uncertainties (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='6 % and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='3 %), particle selections (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='9 % and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='3 %) and systematic uncertainties (14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='2 % and 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='7 %) mainly resulting from the uncertainty of the target thickness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The experimental momentum distributions from 13O and 13N are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' At first sight, they exhibit qualitatively the features of the PMDs obtained for one- nucleon removal from 14O at 53 MeV/nucleon with a 9Be target [36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' An asymmetric PMD with a low-momentum tail and a high-momentum sharp edge are observed in the deeply-bound neutron removal channel, while the PMD from the loosely-bound proton removal is close to sym- metric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The experimental cross sections and PMDs were com- pared to predictions combining reaction and structure inputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The SFs for the removed proton and neutron from 14O were obtained from shell-model calculations performed in the psd-model space with the YSOX inter- action [50] limited to 5 ℏω excitation using the KSHELL code [51].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The SP energy of the π1s1/2 orbit was de- creased by 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='375 MeV to have a good reproduction of the low-lying energy level structure of 14O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The result- ing SFs are 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='58 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='42 for 13N and 13O, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' OXBASH shell-model calculations [52] with the com- monly used WBT and WBP interactions [53] result in slightly larger SFs of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='82 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' For the (p, pN) knockout process, we adopted the state- of-the-art DWIA [43, 54–57] and the QTC (Quantum Transfer-to-the-Continuum) [22, 58] models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' See Sup- plemental Material (SM) [59] for details of the calcula- tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The DWIA and QTC reaction models have been developed and benchmarked for (p, pN) reaction at beam energies higher than 200 MeV/nucleon [22, 57].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Above 200 MeV/nucleon, both models have been demonstrated to reproduce well the shape of the experimental momen- tum distributions [22, 60–62], and the SP cross sections (σsp) from the two models are also consistent with each other within 20% [63].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The obtained σsp for the 14O(p, 2p)13N reaction are 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='2 mb and 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='0 mb from the DWIA and QTC calcu- lations, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' In addition, we considered also the inelastic excitation of 14O to its low-lying excited states located above Sp and below ∼ S2p, which decay to the ground state of 13N via one-proton emission (See SM [59]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Giant-resonance excitations were not consid- ered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' A total inelastic cross section of 9 mb was obtained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The theoretical cross sections σth are summarized in Ta- ble.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' With the DWIA or QTC calculated knockout cross sections, the obtained σth are 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='8 mb or 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='9 mb, leading to Rs of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='60(9) and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='51(8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' 2 (a) and (b), the PMD of 13N is shown and compared with the theoretical PMDs from the DWIA and QTC calculations with inelastic scattering contri- bution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Due to the kinematics, PMD peak position from (p, p′) is about 50 MeV/c lower than that from (p, 2p).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The summed distribution combining the (p, 2p) and (p, p′) PMDs is close to symmetric and re- produces well the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The good agreement of the theoretical distributions and the experimental ones con- firms the predicted strong inelastic-scattering compo- nent to the loosely-bound proton removal, which leads to fractional contributions of 51% with the DWIA and of 43% with the QTC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The inelastic-scattering compo- nent has also been observed with the invariant-mass tech- nique in the case of one-nucleon removal with a 9Be target [39, 64].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='Percentage contributions of 17% and ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='21% from the inelastic scattering have been extracted ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='5000 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='5200 ' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='40 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='60 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=')] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='c ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='b / (MeV/ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='µ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='[ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='� � ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='P ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='/d ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='σ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='d ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='QTC ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='w/o Transfer ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='Transfer ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='O (-1n) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='14 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='(d) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' PMDs of 13N and 13O from the one-nucleon removal of 14O at 94 MeV/nucleon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The black filled markers show the experimental data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The orange bands represent the uncer- tainties from the background subtractions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The grey empty bins indicate the other systematic uncertainties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The data are compared to the DWIA and QTC reaction model calcula- tions (blue-dotted lines), with additional contributions from the inelastic excitation for 13N and (p, d) transfer for 13O (red-dashed lines).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The blue-solid line in (a) indicates the PMD of the unreacted 14O beam (shifted by −200 MeV/c) for demonstration of the experimental PMD response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Theoreti- cal distributions have been convoluted with the experimental PMD response and their integrals have been normalised to the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' for the one-proton removal from 9C and 13O at around 65 MeV/nucleon [39].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' If the inelastic-scattering compo- nent is not taken into account, the present one-proton removal Rs will be around unity, coinciding with the loosely-bound nucleon-removal Rs from eikonal model based analysis [10–12, 26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The low-lying excited states considered here have multiparticle-multihole configura- tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' It was shown recently that inelastic scattering with large momentum transfer has the advantage of populat- ing multiparticle-multihole states [65].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Such states are beyond the descriptions of the (p, pN) and the eikonal models, which assume beforehand that the projectile is a single-particle state plus an inert core [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' For the deeply-bound neutron removal, σsp of 14O(p, pn)13O were calculated to be 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='3 mb and 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='5 mb from the DWIA and the QTC, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The QTC cal- culation without (p, d) transfer is 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='2 mb, still larger than the DWIA result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Other effects, such as low-energy neutron-core absorption, contribute to this difference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' To study the (p, d) transfer effect, we performed the QTC calculation with the outgoing channel coupled only to the deuteron ground state, that is equivalent to the so-called DWBA (Distorted-Wave Born Approximation) calcula- tion (See SM [59]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The obtained σsp for the transfer reaction is 3 mb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The (p, d) transfer is considered in the QTC formalism but not in the DWIA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' With a neutron SF of 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='42, the combination of the DWIA calculation for 14O(p, pn)13O and the DWBA calculation for 14O(p, d)13O results in a σth of 34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='2 mb, while QTC leads to a σth of 49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='7 mb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The corresponding Rs are 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='49(7) and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='34(5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The PMD of 13O is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' 2 (c) and (d), and compared with those from the DWIA+DWBA and the QTC calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The data are well reproduced by com- bining the contributions from the DWIA and the DWBA, in which the latter corresponding to (p, d) transfer con- tributes to ∼30%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' As discussed by the previous DWIA calculation [43], our data support the interpretation that the low-momentum tail is caused by the attractive po- tential between the outgoing nucleons and 13O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' On the other hand, the (p, d) transfer reaction creates a sharp high-momentum edge, as observed in the data, due to the two-body kinematics of the transfer reaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The sharp edge is found in a kinematic region inaccessible to (p, pn) knockout and is thus a proof of significant transfer contri- bution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Since the QTC formalism treats (p, d) transfer consistently with the (p, pn), it reproduces better the sharp high-momentum side than the DWIA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' However, the QTC does not reproduce the low-momentum tail as well as the DWIA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The reason might be due to the differ- ent treatment of the final state interaction in QTC, espe- cially that the nucleon-residue interaction at low relative energy is not explicitly treated in the QTC formalism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' It is the first time the PMD measured near 100 MeV/nucleon shows a distinctive contribution from the (p, d) transfer reaction, usually neglected at such beam energies [25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' One-nucleon pickup cross sections have been measured around 60 MeV/nucleon with heavy-ion beams on 12C or 9Be target [66–69].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Here, the extracted one-neutron transfer cross section is higher, due to the momentum matching of the well bound neutron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The product of the momentum transfer q and the radius of 14O nucleus R is around (1–2) ℏ at forward angles, which fits the momentum matching condition [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Further cal- culations at 300 MeV/nucleon show that the qR product increases to (3–5) ℏ and the (p, d) transfer cross sec- tion decreases to about 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='2 mb, negligible compared to the quasifree knockout cross sections [21, 42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The (p, d) transfer contribution should thus be assessed for the neutron removal reactions at intermediate energies, espe- cially at energies below 100 MeV/nucleon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' We infer that the proton removal with a 9Be target may also contain non-negligible transfer contributions, where the removed proton combines one neutron from 9Be forming bound or unbound d + α + α clusters, since Sn of 9Be is only 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='7 MeV and a three cluster model n + α + α provides a reliable description of the 9Be nucleus [70].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' 5 20 10 0 10 20 [MeV] S D 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='8 1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='4 th s / exp s = s R DWIA w/ Inelastic & Transfer QTC w/ Inelastic w/o Inelastic & Transfer Graph w/o Inelastic & Transfer FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Rs as a function of ∆S from the present work (blue dots and black squares) compared to trends extracted from Be/C induced nucleon removal cross sections analysed with the eikonal model [10–12] (grey shaded region).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The square brackets indicate the total systematic uncertainties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Red-solid and black-dashed lines are shown to guide the eyes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The Rs as a function of ∆S is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Most light-ion-induced nucleon removal Rs lie within a band with a slope of −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='6 × 10−2 MeV−1 and a half width of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='1 [10–12], as shown by the shaded grey region in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' On the other hand, the analyses of low-energy one-nucleon transfer [16, 18, 19, 71] and high-energy quasifree scattering data [20–22, 24] result in slope ab- solute values of (10−3 – 10−5) MeV−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' By considering the two data sets of the present work, we obtain a slope of −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='0(5)(5) × 10−3 MeV−1 when the DWIA together with the inelastic and transfer calculations are consid- ered, and of −4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='6(4)(7) × 10−3 MeV−1 when the QTC and the inelastic scattering are considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Both slopes are negative and their absolute values are almost zero, indicating Rs have a weak ∆S dependence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' For com- parison, we also extract the Rs if the inelastic scattering and nucleon transfer are neglected in the cross section calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' 3, the resulting Rs slopes are 3–5 times larger in the absolute values and look com- patible with the strong ∆S dependence indicated by the light-ion-induced nucleon removal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' In summary, we have reported on the first study of the one-nucleon removal reaction from a large separation- energy asymmetric nucleus 14O (∆S = ±18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='6 MeV) us- ing a proton target at ∼100 MeV/nucleon, a widely use energy regime for rare-isotope studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The measured PMDs and cross sections were compared to the state- of-the-art reaction models, including quasifree knockout, inelastic scattering and nucleon transfer calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' In the loosely-bound proton removal channel, the (p, p′) in- elastic scattering and the (p, 2p) quasifree knockout are found of almost equal contributions, advocating for an explicit treatment of the inelastic scattering for quan- titative interpretation of loosely-bound nucleon removal cross sections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' A highly asymmetric PMD was observed in the deeply-bound neutron removal channel, which was reproduced by combining the (p, pn) knockout compo- nent from the DWIA calculation and the (p, d) transfer component from the DWBA calculation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' We observed a distinctive contribution of ∼30% in the high-momentum part of the residue PMD from the deeply-bound nucleon stripping (p, d) transfer reaction, usually not considered at such beam energies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The reduction factors extracted from the present two new data sets show a weak ∆S dependence, which become markedly larger if the inelas- tic scattering and nucleon transfer contributions are not taken into account.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' We are grateful to the RIKEN Nishina Center accelerator staff for providing the stable and high- intensity 18O beam and to the BigRIPS team for the smooth operation of the secondary beam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' This work was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)—Projektnummer 279384907–SFB 1245.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' acknowledge the support from the Alexander von Humboldt foun- dation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' acknowledges the support of Marie Sk�lodowska-Curie Individual Fellowship (H2020-MSCA- IF-2015-705023) from the European Union and the sup- port from the Helmholtz International Center for FAIR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' acknowledges the support by Grant-in-Aid for Sci- entific Research JP21H00125.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' acknowledges fi- nancial support by MCIN/AEI /10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='13039 /501100011033 under I+D+i project No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' PID2020-114687GB-I00, by the Consejer´ıa de Econom´ıa, Conocimiento, Empre- sas y Universidad, Junta de Andaluc´ıa (Spain) and “ERDF-A Way of Making Europe” under PAIDI 2020 project No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' P20 01247, and by the European Social Fund and Junta de Andaluc´ıa (PAIDI 2020) under grant number DOC-01006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' acknowledges Guangdong Major Project of Basic and Applied Basic Research (2021B0301030006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' acknowledges the support from Research Grants Council (RGC) of Hong Kong (GRF- 17303717).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' acknowledges the JSPS Kakenhi Grants No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' JP16H02179, JP18H05404.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' acknowledges the JSPS Grant-in-Aid for Scientific Research Grants No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' JP21H01114.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' This work was supported by the Institute for Basic Science (IBS-R031-D1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Satou is thanked for his help with the inelastic scattering calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' We thank T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Aumann, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Bertulani and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Duer for their valuable comments on the manuscript.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' ∗ tpohl@ikp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='tu-darmstadt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='de † ysun@ikp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='tu-darmstadt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='de [1] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Bohr and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Mottleson, Nuclear Structure (Ben- jamin , New York, 1969), Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [2] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Mayer, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' 75, 1969 (1949), URL https: //link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='1103/PhysRev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='1969.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [3] O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Haxel, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Jensen, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Suess, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' 6 75, 1766 (1949), URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' 1103/PhysRev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='1766.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [4] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Lapikas, Nuclear Physics A553, 297c (1993).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [5] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Dickhoff and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Barbieri, Progress in Particle and Nuclear Physics 52, 377 (2004), ISSN 0146- 6410, URL https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='sciencedirect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='com/science/ article/pii/S0146641004000535.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [6] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Otsuka, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Gade, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Sorlin, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Suzuki, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Utsuno, Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' 92, 015002 (2020), URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='1103/RevModPhys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='015002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [7] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Nowacki, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Obertelli, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Poves, Progress in Par- ticle and Nuclear Physics 120, 103866 (2021), ISSN 0146- 6410, URL https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='sciencedirect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='com/science/ article/pii/S014664102100020X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [8] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Hansen and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Tostevin, Annual Review of Nuclear and Particle Science 53, 219 (2003), https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='1146/annurev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='nucl.' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' 041002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='110406.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [9] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Brown, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Hansen, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Sherrill, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Tostevin, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' C 65, 061601(R) (2002), URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='1103/PhysRevC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' 65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='061601.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [10] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Gade, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Adrich, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Bazin, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Bowen, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Brown, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Campbell, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Cook, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Glasmacher, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Hansen, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Hosier, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=', Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' C 77, 044306 (2008), URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' 1103/PhysRevC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='044306.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [11] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Tostevin and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Gade, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' C 90, 057602 (2014), URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' 1103/PhysRevC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='057602.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [12] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Tostevin and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Gade, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' C 103, 054610 (2021), URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' 1103/PhysRevC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='054610.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [13] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Sun, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Wang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Xu, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Pang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Li, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Yuan, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Wan, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Qiao, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Wang, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Chen, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' C 106, 034614 (2022), URL https: //link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='1103/PhysRevC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='034614.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [14] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Lee, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Tostevin, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Brown, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Delaunay, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Lynch, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Saelim, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Tsang, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' C 73, 044608 (2006), URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='org/doi/ 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='1103/PhysRevC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='044608.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [15] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Lee, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Tsang, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Bazin, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Coupland, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Henzl, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Henzlova, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Kilburn, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Lynch, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Rogers, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Sanetullaev, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=', Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' 104, 112701 (2010), URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' 1103/PhysRevLett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='112701.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [16] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Flavigny, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Gillibert, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Nalpas, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Obertelli, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Kee- ley, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Barbieri, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Beaumel, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Boissinot, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Bur- gunder, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Cipollone, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=', Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' 110, 122503 (2013), URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' 1103/PhysRevLett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='110.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='122503.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [17] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Kay, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Schiffer, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Freeman, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' 111, 042502 (2013), URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='org/ doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='1103/PhysRevLett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='111.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='042502.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [18] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Xu, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Pang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Yun, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Wen, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Yuan, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Lou, Physics Letters B 790, 308 (2019), ISSN 0370- 2693, URL http://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='sciencedirect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='com/science/ article/pii/S0370269319300504.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [19] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Manfredi, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Lee, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Rogers, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Tsang, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Lynch, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Anderson, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Barney, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Brown, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Brophy, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Cerizza, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=', Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' C 104, 024608 (2021), URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' 1103/PhysRevC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='024608.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [20] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Kawase, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Uesaka, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Tang, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Beaumel, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Do- zono, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Fukunaga, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Fujii, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Fukuda, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Galindo- Uribarri, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Hwang, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=', Progress of Theoretical and Experimental Physics 2018 (2018), ISSN 2050- 3911, 021D01, https://academic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='oup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='com/ptep/article- pdf/2018/2/021D01/24195568/pty011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='pdf, URL https: //doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='1093/ptep/pty011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [21] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Atar, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Paschalis, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Barbieri, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Bertulani, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' D´ıaz Fern´andez, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Holl, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Najafi, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Panin, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Alvarez-Pol, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Aumann, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' (R3B Collaboration), Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' 120, 052501 (2018), URL https:// link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='1103/PhysRevLett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='120.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='052501.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [22] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' G´omez-Ramos and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Moro, Physics Let- ters B 785, 511 (2018), ISSN 0370-2693, URL http://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='sciencedirect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='com/science/article/ pii/S0370269318306749.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [23] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Holl, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Panin, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Alvarez-Pol, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Atar, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Aumann, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Beceiro-Novo, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Benlliure, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Bertulani, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Boillos, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Boretzky, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=', Physics Letters B 795, 682 (2019), ISSN 0370-2693, URL https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='sciencedirect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' com/science/article/pii/S0370269319304666.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [24] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Phuc, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Yoshida, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Ogata, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' C 100, 064604 (2019), URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='org/doi/ 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='1103/PhysRevC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='064604.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [25] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Aumann, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Barbieri, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Bazin, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Bertulani, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Bonaccorso, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Dickhoff, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Gade, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' G´omez- Ramos, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Kay, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Moro, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=', Progress in Particle and Nuclear Physics 118, 103847 (2021), ISSN 0146- 6410, URL https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='sciencedirect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='com/science/ article/pii/S0146641021000016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [26] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Bazin, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Charity, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' de Souza, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Famiano, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Gade, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Henzl, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Henzlova, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Hu- dan, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Lee, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Lukyanov, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=', Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' 102, 232501 (2009), URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='org/doi/ 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='1103/PhysRevLett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='232501.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [27] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Wimmer, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Bazin, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Gade, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Tostevin, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Baugher, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Chajecki, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Coupland, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Fami- ano, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Ghosh, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Grinyer, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=', Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' C 90, 064615 (2014), URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='org/doi/ 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='1103/PhysRevC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='064615.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [28] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Louchart, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Obertelli, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Boudard, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Flavigny, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' C 83, 011601(R) (2011), URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='1103/PhysRevC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='011601.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [29] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Sun, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Lee, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Ye, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Obertelli, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Li, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Aoi, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Ong, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Ayyad, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Bertulani, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Chen, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=', Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' C 93, 044607 (2016), URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='1103/PhysRevC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='044607.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [30] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Flavigny, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Obertelli, and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Vida˜na, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' C 79, 064617 (2009), URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='org/doi/ 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='1103/PhysRevC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='064617.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [31] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Bertulani and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' De Conti, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' C 81, 064603 (2010), URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' 1103/PhysRevC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='064603.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [32] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Tostevin, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Bazin, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Brown, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Glasmacher, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Hansen, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Maddalena, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Navin, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Sherrill, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' C 66, 024607 (2002), URL https: //link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='1103/PhysRevC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='024607.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [33] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Gade, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Bazin, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Bertulani, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Brown, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Campbell, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Church, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Dinca, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' En- ders, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Glasmacher, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Hansen, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=', Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' C 71, 051301(R) (2005), URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='org/ doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='1103/PhysRevC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='051301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [34] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Yurkewicz, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Bazin, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Brown, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Enders, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Gade, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Glasmacher, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Hansen, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Maddalena, 7 A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Navin, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Sherrill, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=', Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' C 74, 024304 (2006), URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' 1103/PhysRevC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='024304.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [35] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Grinyer, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Bazin, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Gade, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Tostevin, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Adrich, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Bowen, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Brown, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Camp- bell, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Cook, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Glasmacher, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=', Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' 106, 162502 (2011), URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='org/doi/ 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='1103/PhysRevLett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='162502.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [36] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Flavigny, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Obertelli, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Bonaccorso, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Grinyer, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Louchart, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Nalpas, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Signoracci, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' 108, 252501 (2012), URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='org/ doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='1103/PhysRevLett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='108.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='252501.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [37] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Shane, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Charity, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Sobotka, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Bazin, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Brown, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Gade, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Grinyer, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' McDaniel, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Ratkiewicz, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Weisshaar, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=', Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' C 85, 064612 (2012), URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='org/doi/ 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='1103/PhysRevC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='064612.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [38] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Stroberg, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Gade, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Tostevin, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Bader, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Baugher, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Bazin, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Berryman, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Brown, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Campbell, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Kemper, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=', Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' C 90, 034301 (2014), URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='org/doi/ 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='1103/PhysRevC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='034301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [39] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Charity, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Sobotka, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Tostevin, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' C 102, 044614 (2020), URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='1103/PhysRevC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='044614.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [40] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Bertulani and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' McVoy, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' C 46, 2638 (1992), URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' 1103/PhysRevC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='2638.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [41] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Tostevin, Nuclear Physics A 682, 320 (2001), ISSN 0375-9474, URL https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='sciencedirect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' com/science/article/pii/S0375947400006564.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [42] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Aumann, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Bertulani, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Ryckebusch, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' C 88, 064610 (2013), URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='org/ doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='1103/PhysRevC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='064610.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [43] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Ogata, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Yoshida, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Minomo, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' C 92, 034616 (2015), URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='org/doi/ 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='1103/PhysRevC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='034616.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [44] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Fukuda et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=', Nuclear Instruments and Methods in Physics Research B 317, 323 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [45] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Matsuda et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=', Nuclear Instruments and Methods in Physics Research A 643, 6 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [46] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Kobayashi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=', Nuclear Instruments and Methods in Physics Research B 317, 294 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [47] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Agostinelli et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' (GEANT4), Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Instrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Meth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' A506, 250 (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [48] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Brun and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Rademakers, Nuclear Instruments and Methods in Physics Research Section A: Ac- celerators, Spectrometers, Detectors and Associated Equipment 389, 81 (1997), ISSN 0168-9002, new Computing Techniques in Physics Research V, URL https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='sciencedirect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='com/science/article/ pii/S016890029700048X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [49] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Boudard, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Cugnon, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Leray, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Volant, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' C 66, 044615 (2002), URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='org/ doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='1103/PhysRevC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='044615.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [50] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Yuan, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Suzuki, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Otsuka, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Xu, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Tsunoda, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' C 85, 064324 (2012), URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='1103/PhysRevC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='064324.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [51] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Shimizu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Mizusaki, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Utsuno, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Tsunoda, Computer Physics Communications 244, 372 (2019), ISSN 0010-4655, URL https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='sciencedirect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' com/science/article/pii/S0010465519301985.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [52] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Brown, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Etchegoyen, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Godwin, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Rae, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Richter, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Ormand, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Warburton, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Winfield, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Zhao, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Zimmerman, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=', MSU- NSCL report no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' 1289 (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [53] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Warburton and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Brown, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' C 46, 923 (1992), URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='1103/ PhysRevC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='923.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [54] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Chant and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Roos, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' C 15, 57 (1977), URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='1103/ PhysRevC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [55] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Chant and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Roos, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' C 27, 1060 (1983), URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' 1103/PhysRevC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='1060.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [56] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Wakasa, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Ogata, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Noro, Progress in Par- ticle and Nuclear Physics 96, 32 (2017), ISSN 0146- 6410, URL http://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='sciencedirect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='com/science/ article/pii/S0146641017300558.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [57] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Yoshida, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' G´omez-Ramos, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Ogata, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Moro, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' C 97, 024608 (2018), URL https: //link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='1103/PhysRevC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='024608.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [58] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Moro, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' C 92, 044605 (2015), URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='1103/PhysRevC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' 92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='044605.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [59] See Supplemental Material at [url] for more details of DWIA, QTC calculations and the inelastic excitation cal- culations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [60] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Sun, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Obertelli, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Doornenbal, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Barbieri, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Cha- zono, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Duguet, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Liu, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Navr´atil, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Nowacki, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Ogata, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=', Physics Letters B 802, 135215 (2020), ISSN 0370-2693, URL https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='sciencedirect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' com/science/article/pii/S0370269320300198.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [61] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Chen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Lee, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Doornenbal, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Obertelli, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Bar- bieri, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Chazono, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Navr´atil, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Ogata, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Ot- suka, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Raimondi, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=', Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' 123, 142501 (2019), URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' 1103/PhysRevLett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='123.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='142501.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [62] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Browne, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Chen, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Doornenbal, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Obertelli, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Ogata, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Utsuno, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Yoshida, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Achouri, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Baba, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Calvet, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=', Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' 126, 252501 (2021), URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' 1103/PhysRevLett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='126.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='252501.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [63] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Aumann, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Barbieri, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Bazin, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' andA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Bonaccorso, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Dickhoff, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Gade, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' G´omez-Ramos, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Kay, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Moro, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Nakamura, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=', Progress in Particle and Nuclear Physics 118, 103847 (2021), ISSN 0146-6410, URL https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='sciencedirect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' com/science/article/pii/S0146641021000016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [64] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Charity, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Brown, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Oko�lowicz, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' P�loszajczak, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Elson, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Reviol, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Sobotka, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Buhro, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Chajecki, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Lynch, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=', Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' C 100, 064305 (2019), URL https: //link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='1103/PhysRevC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='064305.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [65] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Gade, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Brown, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Weisshaar, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Bazin, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Brown, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Charity, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Farris, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Hill, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Li, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Longfellow, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=', Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' 129, 242501 (2022), URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' 1103/PhysRevLett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='129.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='242501.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [66] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Gade, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Adrich, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Bazin, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Bowen, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Brown, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Campbell, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Cook, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Glasmacher, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Hosier, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' McDaniel, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=', Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' C 76, 061302(R) (2007), URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='org/doi/ 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='1103/PhysRevC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='061302.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [67] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' McDaniel, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Gade, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Tostevin, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Baugher, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Bazin, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Brown, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Cook, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Glasmacher, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Grinyer, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Ratkiewicz, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=', Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' C 85, 014610 (2012), URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='org/doi/ 8 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='1103/PhysRevC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='014610.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [68] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Gade, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Tostevin, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Bader, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Baugher, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Bazin, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Berryman, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Brown, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Hart- ley, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Lunderberg, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Recchia, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=', Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' C 93, 031601(R) (2016), URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='org/ doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='1103/PhysRevC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='031601.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [69] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Gade, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Tostevin, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Bader, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Baugher, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Bazin, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Berryman, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Brown, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Di- get, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Glasmacher, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Hartley, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=', Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' C 93, 054315 (2016), URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='org/doi/ 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='1103/PhysRevC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='054315.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [70] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Tang, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Khanna, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Herndon, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Wilder- muth, Nuclear Physics 35, 421 (1962), ISSN 0029- 5582, URL https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='sciencedirect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='com/science/ article/pii/0029558262901347.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [71] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Lee, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Tsang, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Lynch, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' C 75, 064320 (2007), URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='org/doi/ 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='1103/PhysRevC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='064320.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Supplemental Material for “Multiple mechanisms in proton-induced nucleon removal at ∼100 MeV/nucleon” T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Pohl,1, ∗ Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Sun,1, 2, 3, † A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Obertelli,1, 2 J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Lee,3 M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' G´omez-Ramos,4 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Ogata,5, 6 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Yoshida,7 B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Cai,8 C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Yuan,8 B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Brown,9 H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Baba,10 D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Beaumel,11 A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Corsi,2 J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Gao,10, 12 J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Gibelin,13 A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Gillibert,2 K.' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Beijing Normal University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Beijing 100875,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' China 20Cyclotron and Radioisotope Center,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Tohoku University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Sendai 980-8578,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Japan 21Department of Physics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Konan University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Kobe 658-8501,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Japan 22Department of Physics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' University of Tokyo,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' 7-3-1 Hongo,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Bunkyo,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Tokyo 113-0033,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Japan 23Department of Physics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Rikkyo University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' 3-34-1 Nishi-Ikebukuro,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Toshima,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Tokyo 172-8501,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Japan (Dated: January 11,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' 2023) arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='03836v1 [nucl-ex] 10 Jan 2023 2 DWIA AND QTC CALCULATION In the DWIA calculations, we employed the folding potential with the Melbourne G-matrix interaction for calculat- ing the distorted waves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' As for the transition process, we adopted the nucleon-nucleon cross section calculated with the Franey-Love interaction [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Perey correction [2] for the non-locality was applied both for the bound-state and scattering wave functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Energy dependence of the optical potentials was taken into account by using the scattering energy of the emitted nucleons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' In the QTC calculations, the p + N + 13O/13N three-body final state was expressed in a basis of discretized continuum states of the p + N system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Microscopic JLM optical potential [3] was employed for the distortion of the incident and outgoing channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Both the G-matrix folding potential and JLM potential were found to reproduce well the experimental differential cross section for p + 16O elastic scattering at 65 MeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The single-particle wave function of the knocked-out nucleon in both DWIA and QTC was obtained by solving the Schr¨odinger equation using a Woods-Saxon potential with an adjusted depth to result in the correct binding energy of the knocked-out nucleon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' In the QTC calculation for the (p, d) transfer, the d–13O potential was calculated with the Johnson-Soper prescrip- tion [4], in which the p–13O and n–13O folding potential at half of the kinetic energy of the deuteron was adopted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The obtained σsp for the transfer reaction was 3 mb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The uncertainty was about 1 mb, estimated by using the JLM d–13O potential and by varying the interaction used for the deuteron wave function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' INELASTIC EXCITATION CALCULATION The inelastic excitation cross section was calculated using the microscopic DWIA reaction model [5], that has been validated for the inelastic scattering of proton on the 12C target.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The structure input for the calculation is the one-body transition densities (OBTDs) from the above mentioned shell model calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' We adopted the Franey-Love nucleon-nucleon effective interaction for the interaction of the transitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The Koning-Delaroche (KD) phenomenological optical potential [6] was used to generate the distorted waves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The calculation reproduce reasonably well the differential cross section of the 2+ 1 excitation of 12C measured at 120 MeV [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' We have considered eight excited states of 14O (0+ 2 , 0+ 3 , 2+ 1 , 2+ 2 , 0− 1 , 1− 1 , 2− 1 , 3− 1 ) that could decay via one proton emission to 13N [8], resulting in a total inelastic cross section of 9 mb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The dominant contribution originated from the 2+ 1 , 1− 1 and 3− 1 excitations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' The uncertainty is about 1mb, estimated by performing the calculation using different effective interactions for the OBTDs, as well as by using the M3Y nucleon-nucleon interaction, that takes the medium effects into account [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' CALCULATION OF σth The theoretical loosely-bound proton removal cross sections σth are the sum of the (p, 2p) knockout cross sections (σsp × SF × A/(A−1)) and the inelastic excitation cross section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Note that A/(A−1) is the center-of-mass correction factor [10] and A is the mass number of the projectile, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=', 14 in this case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Since the (p, d) transfer process was considered in the QTC formalism but not in the DWIA, we calculated the σth for the neutron removal as: 1) the σsp from the DWIA and the (p, d) transfer multiplied by the SF × A/(A − 1) factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' 2) the σsp from the QTC calculation multiplied by the SF × A/(A − 1) factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' ∗ tpohl@ikp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='tu-darmstadt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='de † ysun@ikp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='tu-darmstadt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='de [1] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Franey and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Love, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' C 31, 488 (1985), URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='1103/PhysRevC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='488.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [2] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Perey and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Buck, Nuclear Physics 32, 353 (1962), ISSN 0029-5582, URL https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='sciencedirect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='com/science/ article/pii/0029558262903450.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [3] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='-P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Jeukenne, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Lejeune, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Mahaux, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' C 16, 80 (1977), URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='1103/ PhysRevC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [4] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Johnson and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Soper, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' C 1, 976 (1970), URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='1103/PhysRevC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='976.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [5] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Schaeffer and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Raynal, computer program DWBA70, 1970 (unpublished);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' extended version DW81 by J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Comfort, 1981 (unpublished).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' 3 [6] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Koning and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Delaroche, Nuclear Physics A 713, 231 (2003), ISSN 0375-9474, URL https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='sciencedirect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' com/science/article/pii/S0375947402013210.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [7] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Comfort, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Moake, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Foster, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Schwandt, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Goodman, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Rapaport, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Love, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' C 24, 1834 (1981), URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='1103/PhysRevC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='1834.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [8] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Charity, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Brown, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Oko�lowicz, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' P�loszajczak, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Elson, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Reviol, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Sobotka, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Buhro, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Chajecki, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Lynch, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=', Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' C 100, 064305 (2019), URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='1103/PhysRevC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' 100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='064305.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [9] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Bertsch, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Borysowicz, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' McManus, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Love, Nuclear Physics A 284, 399 (1977), ISSN 0375-9474, URL https: //www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='sciencedirect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='com/science/article/pii/037594747790392X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' [10] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Dieperink and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Forest, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' C 10, 543 (1974), URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='1103/PhysRevC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} +page_content='543.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StE2T4oBgHgl3EQfWwc0/content/2301.03836v1.pdf'} diff --git a/T9E2T4oBgHgl3EQfXQcD/content/tmp_files/2301.03841v1.pdf.txt b/T9E2T4oBgHgl3EQfXQcD/content/tmp_files/2301.03841v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..ae1e43e95332ba2d85432af9e51bf80baea8b3a2 --- /dev/null +++ b/T9E2T4oBgHgl3EQfXQcD/content/tmp_files/2301.03841v1.pdf.txt @@ -0,0 +1,155 @@ +arXiv:2301.03841v1 [astro-ph.IM] 10 Jan 2023 +FAIR solutions for a science platform to analyse Cherenkov data +online +Mathieu Servillat,1 Paula Kornecki,1 Catherine Boisson1 +1LUTH, Observatoire de Paris, Université PSL, Université de Paris, CNRS, +F-92190 Meudon, France; mathieu.servillat@obspm.fr +Abstract. +We developed a system to run quick analyses of Cherenkov data in compliance +with the FAIR Guiding Principles for scientific data management (FAIR: Findable, Ac- +cessible, Interoperable and Reusable), through the use of interoperability standards and +technologies, particularly those provided by the International Virtual Observatory Al- +liance (IVOA) to build the Virtual Observatory (VO). +We therefore provide a controlled and stable environment on a computing cluster, +in order to execute and re-execute well defined jobs. User-specific input parameters can +be specified to configure the execution of an analysis job. Provenance information is +automatically captured by the system and accessible to the user. To avoid long transfers, +the data can be placed close to the computing nodes. This system is primarily used to +analyse Cherenkov astronomy data, though it may be used for other purposes. +1. +Introduction and context +In the context of Open Science, data providers include more and more in their require- +ments the distribution of FAIR data (FAIR: Findable, Accessible, Interoperable and +Reusable), as described by the FAIR Guiding Principles for scientific data manage- +ment (Wilkinson et al. 2016). However, transforming the FAIR Principles into working +implementations of a data access system is not always straightforward. +We propose an implementation where data access, job definitions, and computing +resources are separated modules, and use standards to implement the interfaces. Data +access is based on the IVOA Table Access Protocole (TAP, Dowler et al. 2019), job def- +initions are compatible with the IVOA Provenance Data Model (Servillat et al. 2020), +and the execution of jobs on computing resources follow the IVOA Universal Worker +Service pattern (UWS, Harrison & Rixon 2016). Authentication is possible through the +OpenID Connect standard, and user management follows the SCIM standard (System +for Cross-domain Identity Management). +2. +From principles to implementation +2.1. +Findable +• Data should be described with standard metadata: we provide metadata based +on the IVOA Observation Core Metadata model (Louys et al. 2017) adapted to +Cherenkov event data, and suitable for high energy astronomy. +1 + +2 +Servillat, Kornecki and Boisson +• Metadata is served with a standard protocol: we use an IVOA TAP server based +on GAVO DaCHS (Demleitner et al. 2014) that answers to ADQL queries. +• This metadata service is publicly declared in the VO Registry (Dower et al. +2018). +2.2. +Accessible +• Data can be retrieved directly (through link or service): we indicate in the meta- +data the file type and its access URL. +• Authentication may be necessary: we use federated and token based authentica- +tion (OpenID Connect1) to connect to services like KeyCloak (at Observatoire de +Paris), eduTeams or ESCAPE IAM. +• Data is adequately identified to be found by the computing resources: data is +placed in a storage mounted to computing nodes, in order to avoid long file trans- +fers. +2.3. +Interoperable +• Interfaces of the data access system are based on standards: we use IVOA TAP +and UWS as standard interfaces with OPUS (Servillat et al. 2022). +• Data is stored in a well defined and standard data format: a common data format +is proposed and discussed for Very-high-energy Observatories (GADF2 and now +VODF3). +• Related software follow the FAIR principles for Research Software (Chue Hong +et al. 2021): Cherenkov data analyses are performed with the open source soft- +ware GammaPy (Nigro et al. 2019). +2.4. +Reusable +• Data is presented as complete datasets that contain all relevant pieces of informa- +tion for further analysis (including instrument response functions). +• Data is connected to relevant calibration files and other datasets. We propose to +use IVOA DataLink (Dowler et al. 2015) to interconnect data. +• Full and detailed provenance is available for each dataset: Provenance is au- +tomatically captured and exposed following the IVOA Provenance Data Model +(Servillat et al. 2020). +3. +Test implementations +Based on technologies and choices listed in Section §2, we thus developed a data access +prototype in line with the FAIR Principles described in Figure 1, built on the following +test implementations: +1https://openid.net/connect +2https://gamma-astro-data-formats.readthedocs.io +3https://vodf.readthedocs.io + +FAIR solutions for a science platform to analyse Cherenkov data online +3 +Figure 1. +Functional diagram of a Science Platform based on the FAIR Principles. +Test implementations are further described in §3. Colors indicate a compliance with +the FAIR principles: Findable (blue), Accessible (red), Interoperable (purple) and +Reusable (orange). +[a] TAP Distiller4: a web based interface to query a TAP server. +[b] TAP Server5: direct access to the TAP server implemented with DaCHS. +[c] OPUS6 client/server: UWS interface to run jobs on computing nodes using +OPUS (Servillat et al. 2022) +[d] ESAP7: ESFRI Science Analysis Platform developped as a toolkit during the +ESCAPE European project. +Figure 1 exposes the central position of the user that can authenticate to several +web based modules to perform data searches (TAP Distiller) or data analyses online +(OPUS CLient). The user can also directly access the TAP server or the OPUS server +4https://voparis-cta-test.obspm.fr +5http://voparis-tap-he.obspm.fr/browse/hess_dr/q +6https://voparis-uws-test.obspm.fr +7https://git.astron.nl/astron-sdc/esap-api-gateway + +4 +Servillat, Kornecki and Boisson +that implement IVOA standards (TAP+ADQL and UWS). The Data is described by +standard metadata distributed by the TAP server. The same data can be accessed by +the computing nodes. The OPUS server describes a set of jobs deployed in controlled +environments and run on the computing nodes. We currently explore a parallel access +to computing nodes and to the data based on a JupyterHub cluster (or a BinderHub +cluster), possibly deployed via the ESAP interface. +4. +Working use case +The FAIR solutions for a science platform were further tested to run a quick gammapy +analysis of Cherenkov data online, as presented in Kornecki et al. (2022). +References +Chue Hong, N. P., Katz, D. S., Barker, M., Lamprecht, A.-L., Martinez, C., Psomopoulos, F. E., +Harrow, J., Castro, L. J., Gruenpeter, M., Martinez, P. A., Honeyman, T., & et al. 2021, +FAIR Principles for Research Software (FAIR4RS Principles), Research Data Alliance. +URL https://doi.org/10.15497/RDA00065 +Demleitner, M., Neves, M. C., Rothmaier, F., & Wambsganss, J. 2014, Astronomy and Com- +puting, 7, 27. 1408.5733 +Dower, T., Demleitner, M., Benson, K., Plante, R., Auden, E., Graham, M., Greene, G., Hill, +M., Linde, T., Morris, D., O‘Mullane, W., Rixon, G., Stébé, A., & Andrews, K. 2018, +Registry Interfaces Version 1.1, IVOA Recommendation 23 July 2018 +Dowler, P., Bonnarel, F., Michel, L., & Demleitner, M. 2015, IVOA DataLink Version 1.0, +IVOA Recommendation 17 June 2015 +Dowler, P., Rixon, G., Tody, D., & Demleitner, M. 2019, Table Access Protocol Version 1.1, +IVOA Recommendation 27 September 2019 +Harrison, P. A., & Rixon, G. 2016, Universal Worker Service Pattern Version 1.1, IVOA Rec- +ommendation 24 October 2016 +Kornecki, P., Servillat, M., Boisson, C., & Fuessling, M. 2022, in Proceedings of Gamma 2022 +Symposium, PoS(Gamma2022), vol. 417, TBD. https://pos.sissa.it/417/ +Louys, M., Tody, D., Dowler, P., Durand, D., Michel, L., Bonnarel, F., Micol, A., & IVOA +DataModel Working Group 2017, Observation Data Model Core Components, its Im- +plementation in the Table Access Protocol Version 1.1, IVOA Recommendation 09 May +2017 +Nigro, C., Deil, C., Zanin, R., Hassan, T., King, J., Ruiz, J. E., Saha, L., Terrier, R., Brügge, +K., Nöthe, M., Bird, R., Lin, T. T. Y., Aleksi´c, J., Boisson, C., Contreras, J. L., Donath, +A., Jouvin, L., Kelley-Hoskins, N., Khelifi, B., Kosack, K., Rico, J., & Sinha, A. 2019, +A&A, 625, A10. arXiv:1903.06621 +Servillat, M., Aicardi, S., Cecconi, B., & Mancini, M. 2022, in Astronomical Society of the +Pacific Conference Series, edited by J. E. Ruiz, F. Pierfedereci, & P. Teuben, vol. 532 of +Astronomical Society of the Pacific Conference Series, 451. arXiv:2101.08683 +Servillat, M., Riebe, K., Boisson, C., Bonnarel, F., Galkin, A., Louys, M., Nullmeier, M., +Renault-Tinacci, N., Sanguillon, M., & Streicher, O. 2020, IVOA Provenance Data +Model Version 1.0, IVOA Recommendation 11 April 2020 +Wilkinson, M. D., Dumontier, M., Aalbersberg, I. J., Appleton, G., Axton, M., Baak, A., +Blomberg, N., Boiten, J.-W., da Silva Santos, L. B., Bourne, P. E., et al. 2016, Scientific +Data, 3 + diff --git a/T9E2T4oBgHgl3EQfXQcD/content/tmp_files/load_file.txt b/T9E2T4oBgHgl3EQfXQcD/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..96001f188557cb7af6b062083480cdf082840f7d --- /dev/null +++ b/T9E2T4oBgHgl3EQfXQcD/content/tmp_files/load_file.txt @@ -0,0 +1,223 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf,len=222 +page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content='03841v1 [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content='IM] 10 Jan 2023 FAIR solutions for a science platform to analyse Cherenkov data online Mathieu Servillat,1 Paula Kornecki,1 Catherine Boisson1 1LUTH, Observatoire de Paris, Université PSL, Université de Paris, CNRS, F-92190 Meudon, France;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' mathieu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content='servillat@obspm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content='fr Abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' We developed a system to run quick analyses of Cherenkov data in compliance with the FAIR Guiding Principles for scientific data management (FAIR: Findable, Ac- cessible, Interoperable and Reusable), through the use of interoperability standards and technologies, particularly those provided by the International Virtual Observatory Al- liance (IVOA) to build the Virtual Observatory (VO).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' We therefore provide a controlled and stable environment on a computing cluster, in order to execute and re-execute well defined jobs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' User-specific input parameters can be specified to configure the execution of an analysis job.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' Provenance information is automatically captured by the system and accessible to the user.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' To avoid long transfers, the data can be placed close to the computing nodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' This system is primarily used to analyse Cherenkov astronomy data, though it may be used for other purposes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' Introduction and context In the context of Open Science, data providers include more and more in their require- ments the distribution of FAIR data (FAIR: Findable, Accessible, Interoperable and Reusable), as described by the FAIR Guiding Principles for scientific data manage- ment (Wilkinson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' However, transforming the FAIR Principles into working implementations of a data access system is not always straightforward.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' We propose an implementation where data access, job definitions, and computing resources are separated modules, and use standards to implement the interfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' Data access is based on the IVOA Table Access Protocole (TAP, Dowler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' 2019), job def- initions are compatible with the IVOA Provenance Data Model (Servillat et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' 2020), and the execution of jobs on computing resources follow the IVOA Universal Worker Service pattern (UWS, Harrison & Rixon 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' Authentication is possible through the OpenID Connect standard, and user management follows the SCIM standard (System for Cross-domain Identity Management).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' From principles to implementation 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' Findable Data should be described with standard metadata: we provide metadata based on the IVOA Observation Core Metadata model (Louys et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' 2017) adapted to Cherenkov event data, and suitable for high energy astronomy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' 1 2 Servillat, Kornecki and Boisson Metadata is served with a standard protocol: we use an IVOA TAP server based on GAVO DaCHS (Demleitner et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' 2014) that answers to ADQL queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' This metadata service is publicly declared in the VO Registry (Dower et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' Accessible Data can be retrieved directly (through link or service): we indicate in the meta- data the file type and its access URL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' Authentication may be necessary: we use federated and token based authentica- tion (OpenID Connect1) to connect to services like KeyCloak (at Observatoire de Paris), eduTeams or ESCAPE IAM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' Data is adequately identified to be found by the computing resources: data is placed in a storage mounted to computing nodes, in order to avoid long file trans- fers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' Interoperable Interfaces of the data access system are based on standards: we use IVOA TAP and UWS as standard interfaces with OPUS (Servillat et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' Data is stored in a well defined and standard data format: a common data format is proposed and discussed for Very-high-energy Observatories (GADF2 and now VODF3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' Related software follow the FAIR principles for Research Software (Chue Hong et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' 2021): Cherenkov data analyses are performed with the open source soft- ware GammaPy (Nigro et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' Reusable Data is presented as complete datasets that contain all relevant pieces of informa- tion for further analysis (including instrument response functions).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' Data is connected to relevant calibration files and other datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' We propose to use IVOA DataLink (Dowler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' 2015) to interconnect data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' Full and detailed provenance is available for each dataset: Provenance is au- tomatically captured and exposed following the IVOA Provenance Data Model (Servillat et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' Test implementations Based on technologies and choices listed in Section §2, we thus developed a data access prototype in line with the FAIR Principles described in Figure 1, built on the following test implementations: 1https://openid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content='net/connect 2https://gamma-astro-data-formats.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content='readthedocs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content='io 3https://vodf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content='readthedocs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content='io FAIR solutions for a science platform to analyse Cherenkov data online 3 Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' Functional diagram of a Science Platform based on the FAIR Principles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' Test implementations are further described in §3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' Colors indicate a compliance with the FAIR principles: Findable (blue), Accessible (red), Interoperable (purple) and Reusable (orange).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' [a] TAP Distiller4: a web based interface to query a TAP server.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' [b] TAP Server5: direct access to the TAP server implemented with DaCHS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' [c] OPUS6 client/server: UWS interface to run jobs on computing nodes using OPUS (Servillat et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' 2022) [d] ESAP7: ESFRI Science Analysis Platform developped as a toolkit during the ESCAPE European project.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' Figure 1 exposes the central position of the user that can authenticate to several web based modules to perform data searches (TAP Distiller) or data analyses online (OPUS CLient).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' The user can also directly access the TAP server or the OPUS server 4https://voparis-cta-test.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content='obspm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content='fr 5http://voparis-tap-he.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content='obspm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content='fr/browse/hess_dr/q 6https://voparis-uws-test.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content='obspm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content='fr 7https://git.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content='astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content='nl/astron-sdc/esap-api-gateway 4 Servillat, Kornecki and Boisson that implement IVOA standards (TAP+ADQL and UWS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' The Data is described by standard metadata distributed by the TAP server.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' The same data can be accessed by the computing nodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' The OPUS server describes a set of jobs deployed in controlled environments and run on the computing nodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' We currently explore a parallel access to computing nodes and to the data based on a JupyterHub cluster (or a BinderHub cluster), possibly deployed via the ESAP interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' Working use case The FAIR solutions for a science platform were further tested to run a quick gammapy analysis of Cherenkov data online, as presented in Kornecki et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' References Chue Hong, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Katz, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Barker, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Lamprecht, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Martinez, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Psomopoulos, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Harrow, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Castro, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Gruenpeter, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Martinez, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Honeyman, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', & et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' 2021, FAIR Principles for Research Software (FAIR4RS Principles), Research Data Alliance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' URL https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content='15497/RDA00065 Demleitner, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Neves, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Rothmaier, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', & Wambsganss, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' 2014, Astronomy and Com- puting, 7, 27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' 1408.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content='5733 Dower, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Demleitner, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Benson, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Plante, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Auden, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Graham, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Greene, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Hill, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Linde, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Morris, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', O‘Mullane, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Rixon, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Stébé, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', & Andrews, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' 2018, Registry Interfaces Version 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content='1, IVOA Recommendation 23 July 2018 Dowler, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Bonnarel, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Michel, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', & Demleitner, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' 2015, IVOA DataLink Version 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content='0, IVOA Recommendation 17 June 2015 Dowler, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Rixon, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Tody, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', & Demleitner, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' 2019, Table Access Protocol Version 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content='1, IVOA Recommendation 27 September 2019 Harrison, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', & Rixon, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' 2016, Universal Worker Service Pattern Version 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content='1, IVOA Rec- ommendation 24 October 2016 Kornecki, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Servillat, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Boisson, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', & Fuessling, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' 2022, in Proceedings of Gamma 2022 Symposium, PoS(Gamma2022), vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' 417, TBD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' https://pos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content='sissa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content='it/417/ Louys, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Tody, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Dowler, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Durand, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Michel, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Bonnarel, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Micol, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', & IVOA DataModel Working Group 2017, Observation Data Model Core Components, its Im- plementation in the Table Access Protocol Version 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content='1, IVOA Recommendation 09 May 2017 Nigro, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Deil, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Zanin, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Hassan, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', King, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Ruiz, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Saha, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Terrier, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Brügge, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Nöthe, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Bird, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Lin, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Aleksi´c, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Boisson, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Contreras, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Donath, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Jouvin, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Kelley-Hoskins, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Khelifi, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Kosack, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Rico, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', & Sinha, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' 2019, A&A, 625, A10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' arXiv:1903.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content='06621 Servillat, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Aicardi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Cecconi, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', & Mancini, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' 2022, in Astronomical Society of the Pacific Conference Series, edited by J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' Ruiz, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' Pierfedereci, & P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' Teuben, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' 532 of Astronomical Society of the Pacific Conference Series, 451.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' arXiv:2101.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content='08683 Servillat, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Riebe, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Boisson, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Bonnarel, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Galkin, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Louys, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Nullmeier, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Renault-Tinacci, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Sanguillon, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', & Streicher, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' 2020, IVOA Provenance Data Model Version 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content='0, IVOA Recommendation 11 April 2020 Wilkinson, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Dumontier, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Aalbersberg, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Appleton, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Axton, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Baak, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Blomberg, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Boiten, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content='-W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', da Silva Santos, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', Bourne, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} +page_content=' 2016, Scientific Data, 3' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/T9E2T4oBgHgl3EQfXQcD/content/2301.03841v1.pdf'} diff --git a/TNE2T4oBgHgl3EQftAhR/content/tmp_files/2301.04065v1.pdf.txt b/TNE2T4oBgHgl3EQftAhR/content/tmp_files/2301.04065v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..d98fa2baea2c92637954d8d59ddc527b9d70e8f0 --- /dev/null +++ b/TNE2T4oBgHgl3EQftAhR/content/tmp_files/2301.04065v1.pdf.txt @@ -0,0 +1,633 @@ +Lower-temperature fabrication of airbridges by grayscale lithography to +increase yield of nanowire transmons in circuit QED quantum processors +T. Stavenga and L. DiCarlo +QuTech and Kavli Institute of Nanoscience, Delft University of Technology, P.O. Box 5046, 2600 GA Delft, The Netherlands +(Dated: 11 January 2023) +Quantum hardware based on circuit quantum electrodynamics makes extensive use of airbridges to suppress unwanted +modes of wave propagation in coplanar-waveguide transmission lines. Airbridges also provide an interconnect enabling +transmission lines to cross. Traditional airbridge fabrication produces a curved profile by reflowing resist at elevated +temperature prior to metallization. The elevated temperature can affect the coupling energy and even yield of pre- +fabricated Josephson elements of superconducting qubits, tuneable couplers and resonators. We employ grayscale +lithography in place of reflow to reduce the peak airbridge processing temperature from 200 to 150◦C, showing a +substantial yield increase of transmon qubits with Josephson elements realized using Al-contacted InAs nanowires. +Free-standing metallic strips bridging separate planar con- +ductors, called airbridges (ABs)1, are widely used in classi- +cal2 and quantum3–6 microwave-frequency integrated circuits. +They are most commonly employed to suppress slotline-mode +wave propagation in coplanar-waveguide transmission lines +(CPWs)7,8 by connecting the ground planes flanking the cen- +tral conductor, thereby avoiding spurious resonance modes +and reducing crosstalk. A second use of ABs is as intercon- +nect allowing transmission lines to cross with low impedance +mismatch and crosstalk. +ABs are intensely used in superconducting quantum hard- +ware based on circuit QED9,10, where CPWs are commonly +used to make resonators for qubit readout and qubit-qubit cou- +pling, as well as qubit control lines. For example, in our planar +quantum hardware architecture11 designed for surface-code +error correction, 7- and 17-qubit processors contain ∼ 600 +and ∼ 1200 ABs, respectively, of which 3 and 20 are used +for crossovers12. In the 49-qubit version, the number of AB +crossovers jumps to 130 owing to the routing of qubit control +lines from the chip periphery to more qubits at the center. Sig- +nal routing at higher qubit counts requires advanced methods +based on three-dimensional integration, including through- +silicon vias13–15, bump bonding16,17, and the chip packaging +itself18. In this context, ABs remain essential for slotline- +mode suppression and crossovers. +ABs are typically added in the final fabrication step as oth- +erwise resist non-uniformity induced by the few-µm height +of ABs can reduce yield and increase variability of post- +fabricated circuit elements (for exceptions, see Refs.19,20). +The most traditional AB fabrication method uses resist reflow +at elevated temperature to produce ABs with smooth, rounded +profile. However, many types of Josephson junctions (JJs) +are not compatible with this elevated temperature. Examples +include the semiconductor-normal-superconductor (SNS) JJs +based on InAs21 and InSb nanowires22 used in SNS trans- +mons23,24 (also called gatemons and nanowire transmons). +The temperature excursions can reduce JJ yield at worst and +unpredictably affect the JJ coupling energy at best, affecting +qubit frequency targeting. +In this Letter, we apply grayscale lithography (GSL), a +method most commonly used to fabricate microlenses25–27, to +reduce the peak AB processing temperature from 200◦C (re- +quired for standard reflow) to 150◦C (limited by resist adhe- +sion). We detail our calibration of GSL to accurately produce +a curved resist-height profile by spatial control of electron- +beam (e-beam) resist dose, with pre-compensation for prox- +imity effect and resist nonlinearity. Our main result is the +demonstration that the reduction in peak processing temper- +ature increases the yield of SNS transmons with junctions re- +alized using epitaxially grown, Al-contacted InAs nanowires. +Very recent work6 has demonstrated the use of GSL to fab- +ricate ABs with a single e-beam step, showing compatibility +with transmons based on standard superconductor-insulator- +superconductor (SIS) JJs. Our focus here is on SNS JJ com- +patibility, with emphasis on the positive impact of AB fabri- +cation at lower peak temperature as enabled by GSL. +AB fabrication by GSL (Fig. 1) starts after defining the chip +base layer containing all CPW structures and transmons, in- +cluding their SNS junctions. A layer of PMGI (blue) SF15 +(6.4 or 3 µm thick, see below) is spun and baked for 5 min +on a hotplate at 150◦C. This is found to be the lowest viable +temperature avoiding resist adhesion problems. Using e-beam +lithography and GSL, the AB profile and clearances are then +written. An AZ400K/water mixture in a 1:4 volume ratio is +used for development. The chip is dunked into the developer +for 35 s followed by a thorough water rinse for 30 s and blow- +drying. At this point, we typically check for correctness by +measuring the height profile along the curve of an AB using a +profilometer [Fig. 3(c)]. Next, a 400 nm thick layer of PMMA +495K (orange) is spun and baked in a vacuum oven at 100◦C +for 10 min, immediately followed by a 1.5 µm thick layer +of PMMA 950k (orange) spun and baked in the same way. +E-beam lithography and resist development define the lateral +dimensions of the ABs. The top-layer resists must be compat- +ible with the bottom-layer resist. This means that the top layer +solvent cannot dissolve the bottom resist after it has been de- +veloped and that the developer for the top layer resists cannot +develop the bottom layer. A 30 s buffered oxide etch with 1:1 +dilution factor is performed prior to metal deposition. We next +sputter 200 nm of NbTiN (gold) without any argon milling as +the plasma can induce currents in the SNS junctions, causing +their failure. A photoresist, 700 nm of S1805 baked at 85◦C +for 3 min, is used for protection during dicing. After dicing, +this resist is lift-off using 88◦C N-methyl pyrrolidone (NMP) +for 15 min and followed by two rinses in isopropanol (IPA) at +80◦C for 10 min. Due to the conformal nature of sputtering, +arXiv:2301.04065v1 [quant-ph] 10 Jan 2023 + +2 +FIG. 1. Overview of airbridge fabrication by the GSL method, us- +ing (left) schematics and (right) optical images. (a,b) Pre-fabrication +of the base layer. Our CPW transmission lines have 12 µm center +conductor width and 4 µm gaps between the central conductor and +the flanking ground planes. (c,d) Patterning of the PMGI (blue) bot- +tom resist layer using GSL. (e,f) Patterning of the PMMA top resist +bilayer (orange) defining the lateral dimensions of airbridges. (g, h) +Sputtering of NbTiN (gold) and liftoff. +there is a vertical edge of NbTiN left that is approximately the +height of the bottom PMMA layer. +Figure 2 shows a complete circuit QED test device with 185 +ABs fabricated by GSL and with 100% yield. The device con- +sists of 12 flux-tuneable SNS transmons each with a dedicated +readout resonator coupling to a common feedline. Six of the +transmons have dedicated flux bias lines, but all can be glob- +ally tuned using an external coil. The flux-tuneable Josephson +element in each transmon consists of two Al/InAs/Al junc- +tions in parallel with loop area ∼ 20 µm2. The two junc- +tions are fabricated from a common hexagonal InAs nanowire +with 100 nm diameter and two facets covered with epitaxi- +ally grown Al (10 nm thick). Each SNS junction is defined by +etching a ∼ 200 nm section of Al [Fig. 2(e)]. +Contrary to the traditional method of producing a curved +AB profile by reflowing the PMGI at elevated temperature +(200◦C), GSL achieves the rounding by spatial control of the +e-beam dose. For a positive resist like PMGI, a lower (higher) +dose causes slower (faster) removal of the resist, resulting in +a higher (lower) remnant resist thickness. Our desired resist- +FIG. 2. Images at various length scales of a circuit QED test device +with 100% yield of 185 airbridges fabricated by the GSL method. (a) +Optical image of the full device (7 mm × 2.3 mm), with added false- +color. The device has 12 flux-tuneable SNS transmons (red) with +dedicated readout resonators (purple) coupled to a common read- +out feedline (blue). Six of the SNS transmons have dedicated flux- +control lines (yellow). (b,e) Scanning electron micrographs (SEM) +showing (b) one SNS transmon and its dedicated readout resonator; +(c) the SNS junction pair and its connection to the transmon capaci- +tor pads; (e) zoom-in on the SNS junction pair and SQUID loop; and +(d) an example airbridge. +height profile is semi-circular, mimicking the profile achieved +in the reflow process by surface tension. To achieve this, it +is necessary to correct for proximity error as long-range scat- +tering deposits up to 30% percent of the e-beam energy at a +range exceeding 20 µm [Fig. 3(a)]. If this effect is not com- +pensated, areas with dense (sparse) features are overexposed +(underexposed). It is also important to calibrate the non-linear +dose-height correspondence (contrast curve). Non-lineariy is +desirable in typical microfabrication, as almost all processes +require a binary resist profile (so-called perfect contrast) in +which the resist is either not exposed or fully exposed. On the +other hand, a linear resist is ideal for GSL. The non-linearity +of PMGI (6.4 µm thick) is evident in the measured contrast +curve shown Fig. 3(b). We precompensate proximity and re- +sist nonlinearity using the three-dimensional proximity effect +correction (3D-PEC) module in the GenISys BEAMER soft- +ware28. The inputs are the point spread function of the energy +deposited by the e-beam lithography machine on the resist +stack, the interpolated contrast curve29 and the desired height +map [Fig. 3(c)]. The output is a prescribed position-dependent +dose. Following these calibrations, we actually reduced the +thickness of the PMGI layer to 3 µm in order to reduce stress +in the film, which at the original thickness caused cracks in + +(a) +(b) +25μm +(c) +(d) +(e) +(f) +(g) +(h)OA +a) +nssss +Sssss +ssss +0000000000100000000100006 +(b) +(C) +250μm +20μm +(d) +(e) +20 μum +2.5 μm3 +FIG. 3. Calibration of grayscale e-beam lithography. (a) CDF of the +energy of the e-beam in PMGI on top of NbTiN. Note that more than +30% of the energy is deposited beyond a 20 µm radius. (b) Calibra- +tion of PMGI height as a function of local e-beam dose (red) and fit +(blue) used for interpolation by the software. (c) Two-dimensional +image of the targeted resist height for the airbridge. (d) Image of the +dose map required to achieve the height map in (d) with precompen- +sation for proximity effect and resist nonlinearity. (e) Vertical line cut +(red) of actual PMGI resist height as measured with a profilometer +and best fit to a circle function (blue). +the resist and many nanowires to detach. By reducing the de- +velopment time from 50 to 30 s, the calibrations were found +to remain valid. This GSL process has very high yield and is +stable with time. The first and last fabrication runs performed +using the process, 16 months apart, yielded very similar air- +bridges without recipe adjustments. +GSL avoids the PMGI reflow step needed in the traditional +method, reducing the peak PMGI temperature from 200◦C to +150◦C. We devise a simplified test to investigate the effect of +PMGI peak temperature on SNS JJ room-temperature resis- +tance. This test entails spinning 3 µm of PMGI on two chips +with arrays of single junctions. Next, one chip is heated on a +hotplate for 5 min to 150◦C while the other is heated to 200◦C. +The chips are not directly placed on the hotplate; rather, as is +standard practice, a Si wafer (6" diameter) is placed in be- +tween. Finally, the resist is stripped off using a bath of NMP +at 88◦C followed by two baths of IPA at 80◦C. +For a valid comparison, it is important that initial junction +resistances for both chips be similar. Two-point resistance +measurements using a manual probe station confirm the over- +lap of cumulative distribution functions (CDFs) of initial re- +sistance for both chips, as shown in Fig. 4(a). We perform a +fit using kernel density estimation30 to each of these CDFs +and compute the derivative of the best fits to estimate the +probability distribution functions (PDFs) of resistance. The +results, shown in Fig. 5(c), reveal a pre-test concentration +around 20 kΩ for both chips. The different temperature excur- +FIG. 4. +Temperature tests of two arrays of single SNS junctions +that are exposed to either 150◦C (blue) and 200◦C (red) for 5 min +in PMGI. The tests simulate the temperature excursions of the GSL +method and the traditional reflow method, respectively. (a,b) CDFs +of junction resistance (a) prior to and (b) following the temperature +test. (c,d) PDFs derived from the CDFs (c) prior to and (d) follow- +ing the temperature test. A clear shift toward higher resistances is +observed for the 200◦C test. (e) Comparison of each junction re- +sistance before and after the test. Note the relatively similar initial +distributions of resistance and the different final distributions. +sions make the resistance distributions become qualitatively +different, as shown by the CDFs in Fig. 4(b) and the PDFs in +Fig. 4(d) (similarly obtained). For junctions exposed to 150◦C +(200◦C), the distribution of resistances shifts downward (up- +ward). The trajectory of individual junctions can be followed +in Fig. 4(e). For 150◦C, the majority of resistances stay close +to their initial values. For 200◦C, however, the majority in- +crease. Some junction resistances do decrease in both cases, +particularly ones starting at the high end. While we do not un- +derstand the reason for this decrease, we speculate that it may +arise from the different cleaning procedures used after the ini- +tial JJ contacting (see Supplementary Material) and after the +simulated AB step. +Finally, we connect the of a transmon as a qubit at cryo- +genic temperature to the room-temperature resistance of its +SNS junction pair. We deem a transmon to be operable if +we can simply observe of a power-dependent shift of the fre- +quency of its readout resonator (see Fig. S2 for an example). +In total 78 qubits were measured from 8 different devices. +These devices fall into three categories: 3 devices without +ABs, in which 18 of 25 transmons were operable; 1 device +with ABs fabricated by reflow, in which 1 of 9 transmons were +operable; and 4 devices with ABs fabricated by GSL, in which +28 of 44 transmons were operable. Figure 5(a) shows numer- +ical CDFs of the junction pair resistance for transmons that +exhibit resonator power shifts (green) and for transmons that + +(a) +(b) +(e) +1.0 +Resist height (μm) +6 +Cumulative +distribution +4 +0.5 +0.0 +0 +7 +100 +0 +500 +-25 +25 +Radial distance (μm) +Position (μm) +Dose (μC/cm2) +Design height (μm) +Dose (μC/cm2) +0 +1 +2 +w +4 +0 +250 +500 +750 +1000 +(c) +(d) +134 +134 +Position (μm) +Position (μm) +0 +0 +0 +Position (μm) +150 +0 +Position (μm) +150Pre +Post +(a) +(b) +(e) +1.0 +100 +0.8 +Cumulative +distribution +0.6 +80 +0.4 +0.2 +OR, 150°C +Resistance (kQ) +R200°C +60 +0.0 +(c) +(d) +50 +R +40 +40 +Probability +30 +20 +20 +10 +0 +0 +50 +100 +0 +50 +100 +e +Resistance (kΩ) +Fabrication4 +FIG. 5. +Study of the room-temperature resistance of the junction +pairs in operable and non-operable SNS transmons. (a) Cumulative +distribution function of the resistance for operable (green) and non- +operable (red) transmons. Here, operable is conditioned on the obser- +vation of a power-dependent frequency shift in the dedicated readout +resonator (see Fig. S2 for an example). (b) PDF derived from (a). +(c) Posterior probability [calculated from (b)] of having an operable +transmon as a function of its room-temperature JJ resistance. +do not (red). These data clearly show that the resistance corre- +sponding to an operable transmon is generally lower than that +of a non-operable one. Fits to these numerical CDFs are done +using kernel density estimation30. The derivative of each best +fit gives a probability density function (PDF) [Fig. 5(b)]. Us- +ing a Bayesian update, we extract the posterior probability of +a transmon being operable given its room-temperature resis- +tance. The probability [Fig. 5(c)] starts off close to unity and +decreases to 0.5 by ∼ 18 kΩ. The probability reduces to near +zero by ∼ 25 kΩ. We conclude that for a good SNS Joseph- +son junction it is vital that the room-temperature resistance be +as low as possible, cementing the benefits of GSL-based AB +fabrication. +In summary, we have employed grayscale lithography to re- +duce the peak temperature for airbridge processing compared +to the traditional reflow method. We have shown that low- +ering peak processing temperature from 200◦C (needed for +PMGI reflow) to 150◦C (limited by PMGI adhesion) increases +the yield of operable SNS transmons based on InAs-nanowire +Josephson junctions. We have done this in two steps. First +we showed that GSL-based fabrication produces lower room- +temperature JJ resistances. Secondly, we showed that lower +JJ resistance increases the probability of having an operable +SNS transmon at cryogenic temperature. +For future work, +it remains important to correlate the AB fabrication process +with SNS transmon coherence time. It is also worthwhile to +explore other e-beam resists that bake at lower temperatures +without suffering adhesion problems as well as optical GSL +using a direct laser writer, which could possibly lower baking +even to room temperature. +ACKNOWLEDGMENTS +We thank S. A. Khan and P. Krogstrup for supplying the +InAs nanowires, C. Zachariadis for fabrication assistance, +J. Kroll and A. Bruno for discussions, and C. Andersen for +comments on the manuscript. This research is funded by the +European Research Council (ERC) Synergy grant QC-lab and +by the Allowance for Top Consortia for Knowledge and Inno- +vation (TKIs) of the Dutch Ministry of Economic Affairs. +Correspondence and requests for materials should be ad- +dressed to L.D.C. (l.dicarlo@tudelft.nl) The data shown in all +figures of the main text and Supplementary Information are +available at http://github.com/DiCarloLab-Delft/ +Grayscale_Lithography. +1N. H. L. Koster, S. Koblowski, R. Bertenburg, S. Heinen, and I. Wolff, in +1989 19th European Microwave Conference (IEEE, 1989) pp. 666–671. +2Y. Lankwarden, A. Endo, J. Baselmans, and M. Bruijn, Journal of Low Tem- +perature Physics 167, 367 (2012). +3M. Abuwasib, P. Krantz, and P. Delsing, Journal of Vacuum Science & Tech- +nology B 31, 031601 (2013). +4Z. Chen, A. Megrant, J. Kelly, R. Barends, J. Bochmann, Y. Chen, B. Chiaro, +A. Dunsworth, E. Jeffrey, J. Mutus, P. O’Malley, C. Neill, P. Roushan, +D. Sank, A. Vainsencher, J. Wenner, T. White, A. Cleland, and J. Martinis, +App. Phys. Lett. 104, 052602 (2014). +5D. Ristè, S. Poletto, M. Z. Huang, A. Bruno, V. Vesterinen, O. P. Saira, and +L. DiCarlo, Nat. Commun. 6, 6983 (2015). +6N. Janzen, M. Kononenko, S. Ren, and A. Lupascu, App. Phys. Lett. 121, +094001 (2022). +7C. Wen, IEEE Trans. Microwave Theory Tech. 17, 1087 (1969). +8R. N. Simons, Coplanar waveguide circuits, components and systems +(Wiley-Interscience, New York, 2001). +9A. Blais, R.-S. Huang, A. Wallraff, S. M. Girvin, and R. J. Schoelkopf, Phys. +Rev. A 69, 062320 (2004). +10P. Krantz, M. Kjaergaard, F. Yan, T. P. Orlando, S. Gustavsson, and W. D. +Oliver, App. Phys. Rev. 6, 021318 (2019). +11R. Versluis, S. Poletto, N. Khammassi, B. Tarasinski, N. Haider, D. J. +Michalak, A. Bruno, K. Bertels, and L. DiCarlo, Phys. Rev. Applied 8, +034021 (2017). +12J. F. Marques, B. M. Varbanov, M. S. Moreira, H. Ali, N. Muthusubrama- +nian, C. Zachariadis, et al., Nat. Phys. 18, 80 (2022). +13J. Alfaro-Barrantes, M. Mastrangeli, D. Thoen, S. Visser, J. Bueno, +J. Baselmans, and P. Sarro, IEEE Electron Device Lett. 41, 1114 (2020). +14D. Yost, M. Schwartz, J. Mallek, D. Rosenberg, C. Stull, J. Yoder, G. Calu- +sine, M. Cook, R. Das, A. L. Day, E. B. Golden, D. K. Kim, A. Melville, +B. M. Niedzielski, W. Woods, A. J. Kerman, and W. D. Oliver, npj Quantum +Inf. 6, 1 (2020). +15J. Mallek, D. Yost, D. Rosenberg, J. Yoder, G. Calusine, M. Cook, et al., +arXiv:2103.08536 (2021). +16D. Rosenberg, D. Kim, R. Das, D. Yost, S. Gustavsson, D. Hover, P. Krantz, +A. Melville, L. Racz, G. O. Samach, S. J. Weber, F. Yan, J. L. Yoder, A. J. +Kerman, and W. D. Oliver, npj Quantum Inf. 3, 1 (2017). + +(a) +1.0 +0.8 +Cumulative +distribution +Rj qubit +0.6 +Fit +R, no qubit +0.4 +Fit +0.2 +0.0 +(b) +0.10 +0.08 +density (kQ-1) +Probability +P(Rjlq) +0.06 +P(Rjl可) +0.04 +0.02 +0.00 +(c) +1.0 +0.8 +Probability +0.6 +P(qIRj) +P(|Rj) +0.4 +0.2 +0.0 +0 +20 +40 +60 +80 +100 +Resistance (kQ)5 +17B. Foxen, J. Y. Mutus, E. Lucero, R. Graff, A. Megrant, Y. Chen, +C. Quintana, B. Burkett, J. Kelly, E. Jeffrey, Y. Yang, A. Yu, K. Arya, +R. Barends, Z. Chen, B. Chiaro, A. Dunsworth, A. Fowler, C. Gidney, +M. Giustina, T. Huang, P. Klimov, M. Neeley, C. Neill, P. Roushan, D. Sank, +A. Vainsencher, J. Wenner, T. C. White, and J. M. Martinis, Quantum Sci- +ence and Technology 3, 014005 (2017). +18N. T. Bronn, V. P. Adiga, S. B. Olivadese, X. Wu, J. M. Chow, and D. P. +Pappas, Quantum Science and Technology 3, 024007 (2018). +19C. K. Andersen, A. Remm, S. Lazar, S. Krinner, N. Lacroix, G. J. Norris, +M. Gabureac, C. Eichler, and A. Wallraff, Nat. Phys. 16, 875 (2020). +20S. Krinner, N. Lacroix, A. Remm, A. Di Paolo, E. Genois, C. Leroux, +C. Hellings, S. Lazar, F. Swiadek, J. Herrmann, G. J. Norris, C. K. Andersen, +M. Müller, Blais, C. Eichler, and A. Wallraff, Nature 605, 669 (2022). +21P. Krogstrup, N. Ziino, W. Chang, S. Albrecht, M. Madsen, E. Johnson, +J. Nygård, C. M. Marcus, and T. Jespersen, Nat. Mater. 14, 400 (2015). +22S. Heedt, M. Quintero-Pérez, F. Borsoi, A. Fursina, N. van Loo, G. P. +Mazur, M. P. Nowak, M. Ammerlaan, K. Li, S. Korneychuk, J. Shen, +M. A. Y. van de Poll, G. Badawy, S. Gazibegovic, N. de Jong, P. Aseev, +K. van Hoogdalem, E. P. Bakkers, and L. P. Kouwenhoven, Nat. Commun. +12, 1 (2021). +23T. W. Larsen, K. D. Petersson, F. Kuemmeth, T. S. Jespersen, P. Krogstrup, +J. Nygård, and C. M. Marcus, Phys. Rev. Lett. 115, 127001 (2015). +24F. Luthi, T. Stavenga, O. Enzing, A. Bruno, C. Dickel, N. Langford, M. A. +Rol, T. S. Jespersen, J. Nygård, P. Krogstrup, and L. DiCarlo, Phys. Rev. +Lett. 120, 100502 (2018). +25J. Loomis, D. Ratnayake, C. McKenna, and K. M. Walsh, Journal of Mi- +cro/Nanolithography, MEMS, and MOEMS 15, 1 (2016). +26Q. Deng, Y. Yang, H. Gao, Y. Zhou, Y. He, and S. Hu, Micromachines 8, +314 (2017). +27T. Mortelmans, D. Kazazis, V. A. Guzenko, C. Padeste, T. Braun, +H. Stahlberg, X. Li, and Y. Ekinci, Microelectronic Engineering 225, 111272 +(2020). +28Genisys beamer, https://www.genisys-gmbh.com/beamer.html. +29C. A. Mack, Journal of The Electrochemical Society 134, 148 (1987). +30F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, +M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Pas- +sos, D. Cournapeau, M. Brucher, M. Perrot, and E. Duchesnay, Journal of +Machine Learning Research 12, 2825 (2011). + +6 +SUPPLEMENTARY MATERIAL FOR ‘’LOWER-TEMPERATURE FABRICATION OF AIRBRIDGES BY GRAYSCALE +LITHOGRAPHY TO INCREASE YIELD OF NANOWIRE TRANSMONS IN CIRCUIT QED QUANTUM PROCESSORS” +This supplementary material describes the SNS junction fabrication, compares the processes for airbridge fabrication using +the GSL method and the traditional reflow method (Table S1 and Fig. S2), and shows a typical example of a power-dependent +resonator frequency shift (Fig. S2). +SNS junction fabrication +The SNS transmon fabrication recipe is adopted fromS1. First, the nanowire is transferred from a growth chip to the device +using a nanomanipulator. A 180 nm thick layer of PMMA 950k is applied and baked for 5 min on a hotplate at 150◦C. Using +e-beam lithography, a 80 nm rectangular window defined at the desired location of junction, where the Al is to be removed. +The PMMA is developed using a MIBK/IPA mixture with 1:3 volume ratio for 60 s, followed by a 10 s dunk in an ethanol/IPA +mixture with 1:3 volume ratio, and finally a 10 s rinse in IPA. The Al is etched using Transene D at 48.2◦C for 12 s, followed +immediately by two dunks in water (first 5 s and then 30 s). The junction defining process is finished by removing the PMMA +in acetone for 5 min at 55◦C and cleaning with IPA for 10 s at 55◦C followed by blow-drying. +To contact the nanowire junctions to the transmon capacitor pads, a 280 nm layer of PMMA is spun and baked for 5 min at +150◦C. The e-beam writing and development is the same as for the etch windows. After development, the chip is loaded into +a sputtering machine, where a 120 nm thick layer of NbTiN is deposited. An in-situ argon mill is first done for 90 s at 50 W +and 3 mTorr to improve the contacting to the nanowire. (The duration of this critical process was pre-optimized for the lowest +junction resistance.) Immediately afterwards, a thin NbTi sticking layer is deposited followed by the DC-sputtering of NbTiN at +2.5 mTorr and 250 W. +Airbridge fabrication using the reflow method +The fabrication process for the reflow method starts following pre-patterning of the chip base layer. A 6.4 µm thick layer of +PMGI SF15 is spun in 2 layer steps. Both layers are baked for 5 min on a hotplate at 180◦C. Then, using e-beam lithography, +a rectangular profile with clearances is made at the desired position of airbridges. An AZ400k/water mixture in a 1:4 volume +ratio is then use to develop the PMGI. The chip is dunked into the developer for 50 s, followed by a thorough water rinse for +30 s, and finished by blow-drying. The chip is then placed on a hotplate at 200◦C for 5 min to reflow the resist and thus produce +round profile. Due to surface tension, the resulting height of the PMGI at the airbridge location is higher than the original resist +height. The resulting layer is shown in Fig. S1(f). Next, a 400 nm thick layer of PMMA 495K is spun and baked on a hotplate at +150◦C for 5 min, immediately followed by a 1.5 µm thick layer of PMMA 950k spun and baked in the same way. After e-beam +lithography and development, the resist looks as in Fig. 1(g). +Requirement +GSL +Reflow +Resist contrast +low +any +Resist type +positive positive or negative +Need compatibility with solvent of top top resist stack +yes +yes +Can developer top resist stack develop the bottom resist? +no +no +TABLE S1. Comparison of the requirements for the resist used for the GSL method and the traditional reflow method. +Resonator power-induced frequency shift +We judge whether or not a transmon is operable by determining whether its dedicated readout resonator exhibits a frequency +shift when measured with increasing incident power. A typical measurement of a readout resonator as a function of incident +power on the feedline is shown in Fig. S2. In this case, there is a upward 2.2 MHz shift of the resonance frequency with +increasing power. A positive (negative) frequency shift indicates that the transmon qubit transition frequency lies above (below) +that of the resonator. For SNS transmons based on InAs nanowires, the qubit transition frequency cannot be accurately targeted, +and can fall above and below the resonator. +[S1]F. Luthi, T. Stavenga, O. Enzing, A. Bruno, C. Dickel, N. Langford, M. A. Rol, T. S. Jespersen, J. Nygård, P. Krogstrup, and L. DiCarlo, Phys. Rev. Lett. +120, 100502 (2018). + +7 +FIG. S1. +Comparison of airbridge fabrication steps using the GSL method (left, blue arrows) and the reflow method (right, red arrows). (a) +Both methods start with the pre-fabrication of the base layer. (b,e) A layer of PMGI is spun and developed for both methods. The GSL method +directly produces the round profile. (f) The reflow method requires reflow at 200◦C to produce the round profile. (c,g) A PMMA bilayer is +used to define the lateral airbridge dimensions. (d, h) NbTiN is sputtered and lifted off. + +(a) +Reflow +(e) +GSL +(b) +(f) +(c) +(g) +(d) +(h)8 +FIG. S2. Example shift of the resonance frequency of a dedicated readout resonator with increasing incident power on the feedline, indicating +that the coupled SNS transmon is operable. (a) Image plot of normalized feedline transmission as a function of probe frequency and incident +power. The resonance shifts from 6.0538 GHz at −110 dBm to 6.0560 GHz at −70 dBm. This positive shift indicates that the qubit transition +frequency is above the resonator frequency. (b) Linecuts of feedline transmission versus frequency at −110 dBm (cyan) and −70 dBm (orange). + +(b) +(a) +-70 +1.0 +1.0 +-80 +0.8 +Amplitude (a.u.) +Amplitude (a.u.) +0.8 +Power (dBm) +-90 +0.6 +0.6 +-70 dBm +-110 dBm +-100 +0.4 +0.4 +-110 +0.2 +0.2 +-120 +0.0 +6.050 +6.052 +6.054 +6.056 +6.058 +6.060 +6.050 +6.052 +6.054 +6.056 +6.058 +6.060 +Frequency (GHz) +Frequency (GHz) \ No newline at end of file diff --git a/TNE2T4oBgHgl3EQftAhR/content/tmp_files/load_file.txt b/TNE2T4oBgHgl3EQftAhR/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..e55552a9e2b0a1fcd8761355bacdb4869acc15da --- /dev/null +++ b/TNE2T4oBgHgl3EQftAhR/content/tmp_files/load_file.txt @@ -0,0 +1,700 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf,len=699 +page_content='Lower-temperature fabrication of airbridges by grayscale lithography to increase yield of nanowire transmons in circuit QED quantum processors T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Stavenga and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' DiCarlo QuTech and Kavli Institute of Nanoscience, Delft University of Technology, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content='O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Box 5046, 2600 GA Delft, The Netherlands (Dated: 11 January 2023) Quantum hardware based on circuit quantum electrodynamics makes extensive use of airbridges to suppress unwanted modes of wave propagation in coplanar-waveguide transmission lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Airbridges also provide an interconnect enabling transmission lines to cross.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Traditional airbridge fabrication produces a curved profile by reflowing resist at elevated temperature prior to metallization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' The elevated temperature can affect the coupling energy and even yield of pre- fabricated Josephson elements of superconducting qubits, tuneable couplers and resonators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' We employ grayscale lithography in place of reflow to reduce the peak airbridge processing temperature from 200 to 150◦C, showing a substantial yield increase of transmon qubits with Josephson elements realized using Al-contacted InAs nanowires.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Free-standing metallic strips bridging separate planar con- ductors, called airbridges (ABs)1, are widely used in classi- cal2 and quantum3–6 microwave-frequency integrated circuits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' They are most commonly employed to suppress slotline-mode wave propagation in coplanar-waveguide transmission lines (CPWs)7,8 by connecting the ground planes flanking the cen- tral conductor, thereby avoiding spurious resonance modes and reducing crosstalk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' A second use of ABs is as intercon- nect allowing transmission lines to cross with low impedance mismatch and crosstalk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' ABs are intensely used in superconducting quantum hard- ware based on circuit QED9,10, where CPWs are commonly used to make resonators for qubit readout and qubit-qubit cou- pling, as well as qubit control lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' For example, in our planar quantum hardware architecture11 designed for surface-code error correction, 7- and 17-qubit processors contain ∼ 600 and ∼ 1200 ABs, respectively, of which 3 and 20 are used for crossovers12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' In the 49-qubit version, the number of AB crossovers jumps to 130 owing to the routing of qubit control lines from the chip periphery to more qubits at the center.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Sig- nal routing at higher qubit counts requires advanced methods based on three-dimensional integration, including through- silicon vias13–15, bump bonding16,17, and the chip packaging itself18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' In this context, ABs remain essential for slotline- mode suppression and crossovers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' ABs are typically added in the final fabrication step as oth- erwise resist non-uniformity induced by the few-µm height of ABs can reduce yield and increase variability of post- fabricated circuit elements (for exceptions, see Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content='19,20).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' The most traditional AB fabrication method uses resist reflow at elevated temperature to produce ABs with smooth, rounded profile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' However, many types of Josephson junctions (JJs) are not compatible with this elevated temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Examples include the semiconductor-normal-superconductor (SNS) JJs based on InAs21 and InSb nanowires22 used in SNS trans- mons23,24 (also called gatemons and nanowire transmons).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' The temperature excursions can reduce JJ yield at worst and unpredictably affect the JJ coupling energy at best, affecting qubit frequency targeting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' In this Letter, we apply grayscale lithography (GSL), a method most commonly used to fabricate microlenses25–27, to reduce the peak AB processing temperature from 200◦C (re- quired for standard reflow) to 150◦C (limited by resist adhe- sion).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' We detail our calibration of GSL to accurately produce a curved resist-height profile by spatial control of electron- beam (e-beam) resist dose, with pre-compensation for prox- imity effect and resist nonlinearity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Our main result is the demonstration that the reduction in peak processing temper- ature increases the yield of SNS transmons with junctions re- alized using epitaxially grown, Al-contacted InAs nanowires.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Very recent work6 has demonstrated the use of GSL to fab- ricate ABs with a single e-beam step, showing compatibility with transmons based on standard superconductor-insulator- superconductor (SIS) JJs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Our focus here is on SNS JJ com- patibility, with emphasis on the positive impact of AB fabri- cation at lower peak temperature as enabled by GSL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' AB fabrication by GSL (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 1) starts after defining the chip base layer containing all CPW structures and transmons, in- cluding their SNS junctions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' A layer of PMGI (blue) SF15 (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content='4 or 3 µm thick, see below) is spun and baked for 5 min on a hotplate at 150◦C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' This is found to be the lowest viable temperature avoiding resist adhesion problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Using e-beam lithography and GSL, the AB profile and clearances are then written.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' An AZ400K/water mixture in a 1:4 volume ratio is used for development.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' The chip is dunked into the developer for 35 s followed by a thorough water rinse for 30 s and blow- drying.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' At this point, we typically check for correctness by measuring the height profile along the curve of an AB using a profilometer [Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 3(c)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Next, a 400 nm thick layer of PMMA 495K (orange) is spun and baked in a vacuum oven at 100◦C for 10 min, immediately followed by a 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content='5 µm thick layer of PMMA 950k (orange) spun and baked in the same way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' E-beam lithography and resist development define the lateral dimensions of the ABs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' The top-layer resists must be compat- ible with the bottom-layer resist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' This means that the top layer solvent cannot dissolve the bottom resist after it has been de- veloped and that the developer for the top layer resists cannot develop the bottom layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' A 30 s buffered oxide etch with 1:1 dilution factor is performed prior to metal deposition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' We next sputter 200 nm of NbTiN (gold) without any argon milling as the plasma can induce currents in the SNS junctions, causing their failure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' A photoresist, 700 nm of S1805 baked at 85◦C for 3 min, is used for protection during dicing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' After dicing, this resist is lift-off using 88◦C N-methyl pyrrolidone (NMP) for 15 min and followed by two rinses in isopropanol (IPA) at 80◦C for 10 min.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Due to the conformal nature of sputtering, arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content='04065v1 [quant-ph] 10 Jan 2023 2 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Overview of airbridge fabrication by the GSL method, us- ing (left) schematics and (right) optical images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' (a,b) Pre-fabrication of the base layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Our CPW transmission lines have 12 µm center conductor width and 4 µm gaps between the central conductor and the flanking ground planes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' (c,d) Patterning of the PMGI (blue) bot- tom resist layer using GSL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' (e,f) Patterning of the PMMA top resist bilayer (orange) defining the lateral dimensions of airbridges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' (g, h) Sputtering of NbTiN (gold) and liftoff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' there is a vertical edge of NbTiN left that is approximately the height of the bottom PMMA layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Figure 2 shows a complete circuit QED test device with 185 ABs fabricated by GSL and with 100% yield.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' The device con- sists of 12 flux-tuneable SNS transmons each with a dedicated readout resonator coupling to a common feedline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Six of the transmons have dedicated flux bias lines, but all can be glob- ally tuned using an external coil.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' The flux-tuneable Josephson element in each transmon consists of two Al/InAs/Al junc- tions in parallel with loop area ∼ 20 µm2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' The two junc- tions are fabricated from a common hexagonal InAs nanowire with 100 nm diameter and two facets covered with epitaxi- ally grown Al (10 nm thick).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Each SNS junction is defined by etching a ∼ 200 nm section of Al [Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 2(e)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Contrary to the traditional method of producing a curved AB profile by reflowing the PMGI at elevated temperature (200◦C), GSL achieves the rounding by spatial control of the e-beam dose.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' For a positive resist like PMGI, a lower (higher) dose causes slower (faster) removal of the resist, resulting in a higher (lower) remnant resist thickness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Our desired resist- FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Images at various length scales of a circuit QED test device with 100% yield of 185 airbridges fabricated by the GSL method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' (a) Optical image of the full device (7 mm × 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content='3 mm), with added false- color.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' The device has 12 flux-tuneable SNS transmons (red) with dedicated readout resonators (purple) coupled to a common read- out feedline (blue).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Six of the SNS transmons have dedicated flux- control lines (yellow).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' (b,e) Scanning electron micrographs (SEM) showing (b) one SNS transmon and its dedicated readout resonator;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' (c) the SNS junction pair and its connection to the transmon capaci- tor pads;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' (e) zoom-in on the SNS junction pair and SQUID loop;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' and (d) an example airbridge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' height profile is semi-circular, mimicking the profile achieved in the reflow process by surface tension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' To achieve this, it is necessary to correct for proximity error as long-range scat- tering deposits up to 30% percent of the e-beam energy at a range exceeding 20 µm [Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 3(a)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' If this effect is not com- pensated, areas with dense (sparse) features are overexposed (underexposed).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' It is also important to calibrate the non-linear dose-height correspondence (contrast curve).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Non-lineariy is desirable in typical microfabrication, as almost all processes require a binary resist profile (so-called perfect contrast) in which the resist is either not exposed or fully exposed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' On the other hand, a linear resist is ideal for GSL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' The non-linearity of PMGI (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content='4 µm thick) is evident in the measured contrast curve shown Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 3(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' We precompensate proximity and re- sist nonlinearity using the three-dimensional proximity effect correction (3D-PEC) module in the GenISys BEAMER soft- ware28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' The inputs are the point spread function of the energy deposited by the e-beam lithography machine on the resist stack, the interpolated contrast curve29 and the desired height map [Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 3(c)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' The output is a prescribed position-dependent dose.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Following these calibrations, we actually reduced the thickness of the PMGI layer to 3 µm in order to reduce stress in the film, which at the original thickness caused cracks in (a) (b) 25μm (c) (d) (e) (f) (g) (h)OA a) nssss Sssss ssss 0000000000100000000100006 (b) (C) 250μm 20μm (d) (e) 20 μum 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content='5 μm3 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Calibration of grayscale e-beam lithography.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' (a) CDF of the energy of the e-beam in PMGI on top of NbTiN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Note that more than 30% of the energy is deposited beyond a 20 µm radius.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' (b) Calibra- tion of PMGI height as a function of local e-beam dose (red) and fit (blue) used for interpolation by the software.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' (c) Two-dimensional image of the targeted resist height for the airbridge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' (d) Image of the dose map required to achieve the height map in (d) with precompen- sation for proximity effect and resist nonlinearity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' (e) Vertical line cut (red) of actual PMGI resist height as measured with a profilometer and best fit to a circle function (blue).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' the resist and many nanowires to detach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' By reducing the de- velopment time from 50 to 30 s, the calibrations were found to remain valid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' This GSL process has very high yield and is stable with time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' The first and last fabrication runs performed using the process, 16 months apart, yielded very similar air- bridges without recipe adjustments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' GSL avoids the PMGI reflow step needed in the traditional method, reducing the peak PMGI temperature from 200◦C to 150◦C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' We devise a simplified test to investigate the effect of PMGI peak temperature on SNS JJ room-temperature resis- tance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' This test entails spinning 3 µm of PMGI on two chips with arrays of single junctions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Next, one chip is heated on a hotplate for 5 min to 150◦C while the other is heated to 200◦C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' The chips are not directly placed on the hotplate;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' rather, as is standard practice, a Si wafer (6" diameter) is placed in be- tween.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Finally, the resist is stripped off using a bath of NMP at 88◦C followed by two baths of IPA at 80◦C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' For a valid comparison, it is important that initial junction resistances for both chips be similar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Two-point resistance measurements using a manual probe station confirm the over- lap of cumulative distribution functions (CDFs) of initial re- sistance for both chips, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 4(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' We perform a fit using kernel density estimation30 to each of these CDFs and compute the derivative of the best fits to estimate the probability distribution functions (PDFs) of resistance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' The results, shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 5(c), reveal a pre-test concentration around 20 kΩ for both chips.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' The different temperature excur- FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Temperature tests of two arrays of single SNS junctions that are exposed to either 150◦C (blue) and 200◦C (red) for 5 min in PMGI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' The tests simulate the temperature excursions of the GSL method and the traditional reflow method, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' (a,b) CDFs of junction resistance (a) prior to and (b) following the temperature test.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' (c,d) PDFs derived from the CDFs (c) prior to and (d) follow- ing the temperature test.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' A clear shift toward higher resistances is observed for the 200◦C test.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' (e) Comparison of each junction re- sistance before and after the test.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Note the relatively similar initial distributions of resistance and the different final distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' sions make the resistance distributions become qualitatively different, as shown by the CDFs in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 4(b) and the PDFs in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 4(d) (similarly obtained).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' For junctions exposed to 150◦C (200◦C), the distribution of resistances shifts downward (up- ward).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' The trajectory of individual junctions can be followed in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 4(e).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' For 150◦C, the majority of resistances stay close to their initial values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' For 200◦C, however, the majority in- crease.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Some junction resistances do decrease in both cases, particularly ones starting at the high end.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' While we do not un- derstand the reason for this decrease, we speculate that it may arise from the different cleaning procedures used after the ini- tial JJ contacting (see Supplementary Material) and after the simulated AB step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Finally, we connect the of a transmon as a qubit at cryo- genic temperature to the room-temperature resistance of its SNS junction pair.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' We deem a transmon to be operable if we can simply observe of a power-dependent shift of the fre- quency of its readout resonator (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' S2 for an example).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' In total 78 qubits were measured from 8 different devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' These devices fall into three categories: 3 devices without ABs, in which 18 of 25 transmons were operable;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 1 device with ABs fabricated by reflow, in which 1 of 9 transmons were operable;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' and 4 devices with ABs fabricated by GSL, in which 28 of 44 transmons were operable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Figure 5(a) shows numer- ical CDFs of the junction pair resistance for transmons that exhibit resonator power shifts (green) and for transmons that (a) (b) (e) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content='0 Resist height (μm) 6 Cumulative distribution 4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content='0 0 7 100 0 500 25 25 Radial distance (μm) Position (μm) Dose (μC/cm2) Design height (μm) Dose (μC/cm2) 0 1 2 w 4 0 250 500 750 1000 (c) (d) 134 134 Position (μm) Position (μm) 0 0 0 Position (μm) 150 0 Position (μm) 150Pre Post (a) (b) (e) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content='0 100 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content='8 Cumulative distribution 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content='6 80 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content='2 OR, 150°C Resistance (kQ) R200°C 60 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content='0 (c) (d) 50 R 40 40 Probability 30 20 20 10 0 0 50 100 0 50 100 e Resistance (kΩ) Fabrication4 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Study of the room-temperature resistance of the junction pairs in operable and non-operable SNS transmons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' (a) Cumulative distribution function of the resistance for operable (green) and non- operable (red) transmons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Here, operable is conditioned on the obser- vation of a power-dependent frequency shift in the dedicated readout resonator (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' S2 for an example).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' (b) PDF derived from (a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' (c) Posterior probability [calculated from (b)] of having an operable transmon as a function of its room-temperature JJ resistance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' do not (red).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' These data clearly show that the resistance corre- sponding to an operable transmon is generally lower than that of a non-operable one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Fits to these numerical CDFs are done using kernel density estimation30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' The derivative of each best fit gives a probability density function (PDF) [Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 5(b)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Us- ing a Bayesian update, we extract the posterior probability of a transmon being operable given its room-temperature resis- tance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' The probability [Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 5(c)] starts off close to unity and decreases to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content='5 by ∼ 18 kΩ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' The probability reduces to near zero by ∼ 25 kΩ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' We conclude that for a good SNS Joseph- son junction it is vital that the room-temperature resistance be as low as possible, cementing the benefits of GSL-based AB fabrication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' In summary, we have employed grayscale lithography to re- duce the peak temperature for airbridge processing compared to the traditional reflow method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' We have shown that low- ering peak processing temperature from 200◦C (needed for PMGI reflow) to 150◦C (limited by PMGI adhesion) increases the yield of operable SNS transmons based on InAs-nanowire Josephson junctions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' We have done this in two steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' First we showed that GSL-based fabrication produces lower room- temperature JJ resistances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Secondly, we showed that lower JJ resistance increases the probability of having an operable SNS transmon at cryogenic temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' For future work, it remains important to correlate the AB fabrication process with SNS transmon coherence time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' It is also worthwhile to explore other e-beam resists that bake at lower temperatures without suffering adhesion problems as well as optical GSL using a direct laser writer, which could possibly lower baking even to room temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' ACKNOWLEDGMENTS We thank S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Khan and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Krogstrup for supplying the InAs nanowires, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Zachariadis for fabrication assistance, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Kroll and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Bruno for discussions, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Andersen for comments on the manuscript.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' This research is funded by the European Research Council (ERC) Synergy grant QC-lab and by the Allowance for Top Consortia for Knowledge and Inno- vation (TKIs) of the Dutch Ministry of Economic Affairs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Correspondence and requests for materials should be ad- dressed to L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' (l.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content='dicarlo@tudelft.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content='nl) The data shown in all figures of the main text and Supplementary Information are available at http://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content='com/DiCarloLab-Delft/ Grayscale_Lithography.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 1N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Koster, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Koblowski, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Bertenburg, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Heinen, and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Wolff, in 1989 19th European Microwave Conference (IEEE, 1989) pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 666–671.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 2Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Lankwarden, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Endo, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Baselmans, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Bruijn, Journal of Low Tem- perature Physics 167, 367 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 3M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Abuwasib, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Krantz, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Delsing, Journal of Vacuum Science & Tech- nology B 31, 031601 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 4Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Chen, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Megrant, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Kelly, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Barends, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Bochmann, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Chen, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Chiaro, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Dunsworth, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Jeffrey, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Mutus, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' O’Malley, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Neill, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Roushan, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Sank, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Vainsencher, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Wenner, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' White, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Cleland, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Martinis, App.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 104, 052602 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 5D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Ristè, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Poletto, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Huang, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Bruno, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Vesterinen, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Saira, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' DiCarlo, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 6, 6983 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 6N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Janzen, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Kononenko, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Ren, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Lupascu, App.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 121, 094001 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 7C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Wen, IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Microwave Theory Tech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 17, 1087 (1969).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 8R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Simons, Coplanar waveguide circuits, components and systems (Wiley-Interscience, New York, 2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 9A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Blais, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Huang, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Wallraff, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Girvin, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Schoelkopf, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' A 69, 062320 (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 10P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Krantz, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Kjaergaard, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Yan, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Orlando, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Gustavsson, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Oliver, App.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 6, 021318 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 11R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Versluis, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Poletto, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Khammassi, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Tarasinski, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Haider, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Michalak, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Bruno, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Bertels, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' DiCarlo, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Applied 8, 034021 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 12J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Marques, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Varbanov, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Moreira, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Ali, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Muthusubrama- nian, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Zachariadis, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=', Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 18, 80 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 13J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Alfaro-Barrantes, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Mastrangeli, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Thoen, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Visser, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Bueno, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Baselmans, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Sarro, IEEE Electron Device Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 41, 1114 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 14D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Yost, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Schwartz, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Mallek, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Rosenberg, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Stull, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Yoder, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Calu- sine, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Cook, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Das, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Day, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Golden, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Kim, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Melville, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Niedzielski, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Woods, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Kerman, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Oliver, npj Quantum Inf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 6, 1 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 15J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Mallek, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Yost, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Rosenberg, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Yoder, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Calusine, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Cook, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=', arXiv:2103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content='08536 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 16D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Rosenberg, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Kim, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Das, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Yost, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Gustavsson, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Hover, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Krantz, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Melville, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Racz, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Samach, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Weber, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Yan, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Yoder, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Kerman, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Oliver, npj Quantum Inf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 3, 1 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' (a) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content='8 Cumulative distribution Rj qubit 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content='6 Fit R, no qubit 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content='4 Fit 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content='0 (b) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content='08 density (kQ-1) Probability P(Rjlq) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content='06 P(Rjl可) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content='04 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content='02 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content='00 (c) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content='8 Probability 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content='6 P(qIRj) P(|Rj) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content='0 0 20 40 60 80 100 Resistance (kQ)5 17B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Foxen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Mutus, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Lucero, R.' 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Dunsworth, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Fowler, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Gidney, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Giustina, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Huang, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Klimov, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Neeley, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Neill, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Roushan, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Sank, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Vainsencher, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Wenner, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' White, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Martinis, Quantum Sci- ence and Technology 3, 014005 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 18N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Bronn, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Adiga, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Olivadese, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Wu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Chow, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Pappas, Quantum Science and Technology 3, 024007 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 19C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Andersen, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Remm, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Lazar, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Krinner, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Lacroix, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Norris, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Gabureac, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Eichler, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Wallraff, Nat.' metadata={'source': 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+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Norris, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Andersen, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Müller, Blais, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Eichler, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Wallraff, Nature 605, 669 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 21P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Krogstrup, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Ziino, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Chang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Albrecht, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Madsen, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Johnson, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Nygård, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Marcus, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Jespersen, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Mater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 14, 400 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 22S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Heedt, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Quintero-Pérez, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Borsoi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Fursina, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' van Loo, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Mazur, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Nowak, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Ammerlaan, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Li, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Korneychuk, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Shen, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' van de Poll, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Badawy, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Gazibegovic, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' de Jong, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Aseev, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' van Hoogdalem, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Bakkers, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Kouwenhoven, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 12, 1 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 23T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Larsen, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Petersson, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Kuemmeth, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Jespersen, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Krogstrup, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Nygård, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Marcus, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 115, 127001 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 24F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Luthi, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Stavenga, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Enzing, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Bruno, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Dickel, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Langford, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Rol, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Jespersen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Nygård, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Krogstrup, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' DiCarlo, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 120, 100502 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 25J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Loomis, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Ratnayake, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' McKenna, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Walsh, Journal of Mi- cro/Nanolithography, MEMS, and MOEMS 15, 1 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 26Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Deng, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Yang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Gao, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Zhou, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' He, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Hu, Micromachines 8, 314 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 27T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Mortelmans, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Kazazis, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Guzenko, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Padeste, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Braun, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Stahlberg, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Li, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Ekinci, Microelectronic Engineering 225, 111272 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 28Genisys beamer, https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content='genisys-gmbh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content='com/beamer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content='html.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 29C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Mack, Journal of The Electrochemical Society 134, 148 (1987).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 30F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Pedregosa, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Varoquaux, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Gramfort, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Michel, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Thirion, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Grisel, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Blondel, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Prettenhofer, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Weiss, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Dubourg, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Vanderplas, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Pas- sos, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Cournapeau, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Brucher, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Perrot, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Duchesnay, Journal of Machine Learning Research 12, 2825 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 6 SUPPLEMENTARY MATERIAL FOR ‘’LOWER-TEMPERATURE FABRICATION OF AIRBRIDGES BY GRAYSCALE LITHOGRAPHY TO INCREASE YIELD OF NANOWIRE TRANSMONS IN CIRCUIT QED QUANTUM PROCESSORS” This supplementary material describes the SNS junction fabrication, compares the processes for airbridge fabrication using the GSL method and the traditional reflow method (Table S1 and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' S2), and shows a typical example of a power-dependent resonator frequency shift (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' S2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' SNS junction fabrication The SNS transmon fabrication recipe is adopted fromS1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' First, the nanowire is transferred from a growth chip to the device using a nanomanipulator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' A 180 nm thick layer of PMMA 950k is applied and baked for 5 min on a hotplate at 150◦C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Using e-beam lithography, a 80 nm rectangular window defined at the desired location of junction, where the Al is to be removed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' The PMMA is developed using a MIBK/IPA mixture with 1:3 volume ratio for 60 s, followed by a 10 s dunk in an ethanol/IPA mixture with 1:3 volume ratio, and finally a 10 s rinse in IPA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' The Al is etched using Transene D at 48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content='2◦C for 12 s, followed immediately by two dunks in water (first 5 s and then 30 s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' The junction defining process is finished by removing the PMMA in acetone for 5 min at 55◦C and cleaning with IPA for 10 s at 55◦C followed by blow-drying.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' To contact the nanowire junctions to the transmon capacitor pads, a 280 nm layer of PMMA is spun and baked for 5 min at 150◦C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' The e-beam writing and development is the same as for the etch windows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' After development, the chip is loaded into a sputtering machine, where a 120 nm thick layer of NbTiN is deposited.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' An in-situ argon mill is first done for 90 s at 50 W and 3 mTorr to improve the contacting to the nanowire.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' (The duration of this critical process was pre-optimized for the lowest junction resistance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=') Immediately afterwards, a thin NbTi sticking layer is deposited followed by the DC-sputtering of NbTiN at 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content='5 mTorr and 250 W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Airbridge fabrication using the reflow method The fabrication process for the reflow method starts following pre-patterning of the chip base layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' A 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content='4 µm thick layer of PMGI SF15 is spun in 2 layer steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Both layers are baked for 5 min on a hotplate at 180◦C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Then, using e-beam lithography, a rectangular profile with clearances is made at the desired position of airbridges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' An AZ400k/water mixture in a 1:4 volume ratio is then use to develop the PMGI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' The chip is dunked into the developer for 50 s, followed by a thorough water rinse for 30 s, and finished by blow-drying.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' The chip is then placed on a hotplate at 200◦C for 5 min to reflow the resist and thus produce round profile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Due to surface tension, the resulting height of the PMGI at the airbridge location is higher than the original resist height.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' The resulting layer is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' S1(f).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Next, a 400 nm thick layer of PMMA 495K is spun and baked on a hotplate at 150◦C for 5 min, immediately followed by a 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content='5 µm thick layer of PMMA 950k spun and baked in the same way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' After e-beam lithography and development, the resist looks as in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 1(g).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Requirement GSL Reflow Resist contrast low any Resist type positive positive or negative Need compatibility with solvent of top top resist stack yes yes Can developer top resist stack develop the bottom resist?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' no no TABLE S1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Comparison of the requirements for the resist used for the GSL method and the traditional reflow method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Resonator power-induced frequency shift We judge whether or not a transmon is operable by determining whether its dedicated readout resonator exhibits a frequency shift when measured with increasing incident power.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' A typical measurement of a readout resonator as a function of incident power on the feedline is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' S2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' In this case, there is a upward 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content='2 MHz shift of the resonance frequency with increasing power.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' A positive (negative) frequency shift indicates that the transmon qubit transition frequency lies above (below) that of the resonator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' For SNS transmons based on InAs nanowires, the qubit transition frequency cannot be accurately targeted, and can fall above and below the resonator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' [S1]F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Luthi, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Stavenga, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Enzing, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Bruno, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Dickel, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Langford, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Rol, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Jespersen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Nygård, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Krogstrup, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' DiCarlo, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 120, 100502 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' 7 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' S1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Comparison of airbridge fabrication steps using the GSL method (left, blue arrows) and the reflow method (right, red arrows).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' (a) Both methods start with the pre-fabrication of the base layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' (b,e) A layer of PMGI is spun and developed for both methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' The GSL method directly produces the round profile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' (f) The reflow method requires reflow at 200◦C to produce the round profile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' (c,g) A PMMA bilayer is used to define the lateral airbridge dimensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' (d, h) NbTiN is sputtered and lifted off.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' (a) Reflow (e) GSL (b) (f) (c) (g) (d) (h)8 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' S2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' Example shift of the resonance frequency of a dedicated readout resonator with increasing incident power on the feedline, indicating that the coupled SNS transmon is operable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' (a) Image plot of normalized feedline transmission as a function of probe frequency and incident power.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' The resonance shifts from 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content='0538 GHz at −110 dBm to 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content='0560 GHz at −70 dBm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' This positive shift indicates that the qubit transition frequency is above the resonator frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' (b) Linecuts of feedline transmission versus frequency at −110 dBm (cyan) and −70 dBm (orange).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content=' (b) (a) 70 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content='0 80 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content='8 Amplitude (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQftAhR/content/2301.04065v1.pdf'} +page_content='u.' metadata={'source': 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index 0000000000000000000000000000000000000000..25ab344c8d99a2b890b75b2c08c34afc3b7c88d2 --- /dev/null +++ b/UNE1T4oBgHgl3EQfugXX/content/tmp_files/2301.03390v1.pdf.txt @@ -0,0 +1,1464 @@ +arXiv:2301.03390v1 [cs.DS] 9 Jan 2023 +Space-Query Tradeoffs in Range Subgraph Counting and Listing +Shiyuan Deng, Shangqi Lu, Yufei Tao +Department of Computer Science and Engineering +Chinese University of Hong Kong +Hong Kong, China +{sydeng,sqlu,taoyf}@cse.cuhk.edu.hk +January 10, 2023 +Abstract +This paper initializes the study of range subgraph counting and range subgraph listing, both +of which are motivated by the significant demands in practice to perform graph analytics on +subgraphs pertinent to only selected, as opposed to all, vertices. In the first problem, there is +an undirected graph G where each vertex carries a real-valued attribute. Given an interval q +and a pattern Q, a query counts the number of occurrences of Q in the subgraph of G induced +by the vertices whose attributes fall in q. The second problem has the same setup except that +a query needs to enumerate (rather than count) those occurrences with a small delay. In both +problems, our goal is to understand the tradeoff between space usage and query cost, or more +specifically: (i) given a target on query efficiency, how much pre-computed information about +G must we store? (ii) Or conversely, given a budget on space usage, what is the best query time +we can hope for? We establish a suite of upper- and lower-bound results on such tradeoffs for +various query patterns. +This research was supported in part by GRF Projects 14207820, 14203421, and 14222822 from +HKRGC. +1 + +1 +Introduction +Consider G = (V, E) as a data graph and Q as a pattern graph. A subgraph of G, if isomorphic to +Q, is said to be an occurrence of Q. The goal of pattern searching is to either list the occurrences of +Q or to count the number of them. Both are fundamental problems in computer science and have +attracted considerable attention in the past few decades. +This paper studies pattern searching in vertex-induced subgraphs. Here, a query selects a subset +U ⊆ V of vertices and needs to count/list the occurrences of Q in G′, where G′ is the subgraph of G +induced by U. Note that if an occurrence uses any vertex outside U, the occurrence should not be +counted/listed. Trivially, one can answer the query by first generating G′ and then counting/listing +Q in G′ “from scratch”, but this does not leverage the power of preprocessing. Instead, our goal +is to store G in a data structure that can answer all queries with non-trivial guarantees. +It is +intriguing to investigate how much we can minimize the query time subject to a space budget, and +conversely, how much space we must consume to achieve a target query time. +Vertex selection in database systems is done with a predicate q, which determines U as {v ∈ +V | v satisfies q}. Concentrating on range predicates, the problems we consider are: +Problem 1 (Range Subgraph Counting). +G = (V, E) is an undirected graph where +each vertex v ∈ V carries a real-valued attribute Av. +For an interval q = [x1, x2], define +Vq = {v ∈ V | x1 ≤ Av ≤ x2} and Gq as the subgraph of G induced by Vq. +Let Q be +a connected (only one connected component) pattern graph with O(1) vertices. +Given an +interval q, a query returns the number of occurrences of Q in Gq. The pattern Q is fixed for +all queries. +Problem 2 (Range Subgraph Listing). +Same setup except that a query reports the +occurrences of Q in Gq. +Universal Notations. +Several notations will apply throughout the paper. +Set n = |V | and +m = |E|. Symbol ω < 2.37286 [1] represents the matrix multiplication exponent. The notations +˜O(.) and ˜Ω(.) hide a factor polylogarithmic to the underlying problem’s parameters. +1.1 +Motivation +Practical Applications. Subgraph patterns are important for understanding the characteristics +of a data graph G, as has been documented in a long string of papers, e.g., [2, 3, 8, 10, 11, 17, 18, +24–28,30,33,36–38,50]. In practice, analysts are interested in not only patterns from the whole G +but also those pertinent only to selected vertices. Consider a social network G where each vertex +represents an individual. A graph’s clustering coefficient [49], a popular measurement in network +science, is the ratio between the number of triangles (3-cliques1) and the number of wedges (2- +paths2). The coefficient of G, however, is just a single value revealing little about the features of +specific demographic groups. It is more informative to, for example, compare the coefficients of (i) +the subgraph of G induced by people with ages ∈ [20, 30], and (ii) that induced by age ∈ [60, 70]. +A step further, by putting together the coefficients induced by “age ∈ [i · 10, (i + 1) · 10]” for each +i ∈ [1, 10], one obtains an interesting comparison across different age groups. Refined analysis can +then concentrate on the pattern occurrences of a target group. The power of the above analysis owes +1An ℓ-clique is a clique with ℓ vertices. +2An ℓ-path is a path with ℓ edges. +2 + +Problem +Pattern Q +Space +Query +Remark +1 (cnt) +any fixed Q +O(n2) +˜O(1) +near optimal† +1 +wedge +˜O(m2/λ2) +˜O(λ) +for any λ ∈ [1, √m], near optimal† +1 (lower +wedge +˜O(m2−δ/λ2) +˜O(λ) +for λ ∈ [1, √m] and any δ > 0, +bound) +impossible +subj. to strong set disjointness conj. +1 +ℓ-clique +O(m) +˜O(1) +2 (rep) +any fixed Q +˜O(m + mρ∗/∆) +delay ˜O(∆) +for any ∆ ≥ 1, +ρ∗ = frac. edge covering num. of Q +2 +triangle +O(m) +delay ˜O(1 + (m∗) +ω−1 +ω+1 ) +m∗ = num. of edges in +at least one triangle in Gq +2 +ℓ-star +O(m) +delay ˜O(1) +near optimal +2 +2ℓ-cycle +˜O(#Pℓ) +delay ˜O(1) +#Pℓ = num. of ℓ-paths in G +Remark: “near optimal” means no polynomial improvement (i.e., nδ for arbitrary small constant δ > 0) +possbile. The near optimality marked with † is subject to the strong set disjointness conjecture. +Table 1: A summary of our results +to queries of Problem 1 and 2 with arbitrary selection ranges. Designing effective data structures +is essential to avoid lengthy response time. +Importance of Space-Query Tradeoffs. One should not confuse the space-query tradeoff with +the tradeoff between preprocessing time and query cost, as has been extensively studied on join +algorithms [5, 12, 20–23, 35, 41–43, 45]. Both tradeoffs are important, but they matter in different +ways. Unlike preprocessing time, which is “one-time cost” (because a structure, once built, can +be used forever), the space consumption is permanent. In other words, the space-query tradeoff +has a (much) more durable effect on the underlying database system. However, in spite of their +importance, the space-query tradeoffs on joins have received surprisingly little attention: we are +aware of only a single paper [20], which, as will be discussed in Section 1.3, does not consider +query predicates (or equivalently, only one query, which always outputs the entire join, exists) and +concerns only reporting (but not counting). Our work can be thought of as a step in the same +direction as [20] because, as explained in Section 5, subgraph searching can be cast as a join problem +(in fact, some of our results are explicitly about joins), and actually the first step on predicate-driven +queries and counting. +Finally, it is worth mentioning that a useful structure, no matter how little space it occupies, +must be constructible in polynomial time. This is true for all the structures developed in our paper. +In fact, each of our structures can be built with at most the time needed to find all the occurrences +of the query pattern Q, ignoring polylog factors. +1.2 +Our Contributions +Table 1 summarizes the main results of this paper. Next, we will explain the results in detail. +1.2.1 +Problem 1 +Wedges. We will show: +Theorem 1.1. Consider Problem 1 with Q = wedge. For any real value λ ∈ [1, √m], there is a +structure of ˜O(m2/λ2) space that answers a query in ˜O(λ) time. +3 + +The space-query tradeoff may look disappointing. After all, wedge counting is easy in one-off +computation: we can count the number of wedges in G using O(n + m) time. It is natural to +wonder whether the space in Theorem 1.1 is necessary. We answer the question by showing that +any substantial improvement to Theorem 1.1 will yield a major breakthrough on set disjointness: +Set Disjointness. The data is a collection of s ≥ 2 sets S1, S2, ..., Ss. Given distinct set ids +a, b ∈ [1, s], a query returns whether Sa ∩ Sb is empty. +Let N = �s +i=1 |Si| be the input size of set disjointness. Given any λ ∈ [1, +√ +N], there is a simple +structure of O(N 2/λ2) space with O(λ) query time (see Appendix B). Improving the tradeoff by a +polynomial factor even for one arbitrary λ has been a long-standing open problem. The strong set +disjointness conjecture [31,32] states that a structure with query time λ must use ˜Ω(N 2/λ2) space +for any λ ≥ 1. We will prove: +Theorem 1.2. Consider Problem 1 with Q = wedge. Fix any λ ∈ [1, √m] and any constant δ > 0. +Suppose that we can obtain a structure of ˜O(m2−δ/λ2) space answering a query in ˜O(λ) time. Then, +for any set disjointness input of size N, we can obtain a structure of ˜O(N 2−δ/λ2) space answering +a query in ˜O(λ) time (thus breaking the strong set disjointness conjecture). +Cliques. We will show: +Theorem 1.3. For Problem 1 with Q = ℓ-clique, there is a structure of O(m) space answering a +query in ˜O(1) time. +Counting triangles (ℓ = 3) appears harder than counting wedges: in one-off computation, the +fastest known algorithm for the former takes O(m +2ω +ω+1) time. It is thus surprising to see Q = triangle +easier than Q = wedge in Problem 1. From Theorem 1.1 and 1.3, one sees that the problem of +calculating the clustering coefficient (see Section 1.1) of Gq for any q boils down to counting the +wedges in Gq. Effectively, this implies optimal settlement of that problem (subject to the strong +set disjointness conjecture), which bears practical significance due to the popularity of clustering +coefficients. +Arbitrary Subgraphs. We will show: +Theorem 1.4. For any Q, there is a structure for Problem 1 that uses O(n2) space and answers +a query in ˜O(1) time. +The above result is difficult to improve: reducing the space by an nδ factor for any constant +δ > 0 breaks the strong set disjointness conjecture. To explain, assume n = O(m).3 If there was a +structure of O(n2−δ) = O(m2−δ) space and ˜O(1) query time, applying the structure to Q = wedge +would yield a breakthrough on set disjointness by way of Theorem 1.2. The reader should note +that the hardness comes from producing a guarantee on all Q; it is possible to do better for special +patterns (Theorem 1.3). The hardness thus endows Q = wedge with unique significance in Problem +1. Theorem 1.4 further implies that Problem 1 under Q = wedge is the hardest when G is the +sparsest: m = o(n1+ǫ) for any constant ǫ > 0. To see why, set m = n1+ǫ, which gives n2 = m +2 +1+ǫ . +Since +2 +1+ǫ = 2 − +2ǫ +1+ǫ, Theorem 1.4 yields a structure of O(m2−δ) space and ˜O(1) query time with +δ = +2ǫ +1+ǫ, improving Theorem 1.1 by a polynomial factor at λ = ˜O(1). +3Discard “isolated” vertices with no incident edges. +4 + +1.2.2 +Problem 2 +A listing query ensures a delay ∆ if it reports a new occurrence of Q or declares “no more occur- +rences” within ∆ time after the previous occurrence4. +Arbitrary Subgraphs. We will show: +Theorem 1.5. For any Q and ∆ ≥ 1, there is a structure for Problem 2 that uses ˜O(m + mρ∗/∆) +space and has a query delay of ˜O(∆), where ρ∗ is the fractional edge covering number of Q. +Imagine assigning each edge of Q a non-negative weight such that (i) for each vertex of Q, all its +incident edges receive a combined weight at least 1 and (ii) the total weight of all edges is minimized. +The fractional edge covering number ρ∗ of Q is the total weight of an optimal assignment. The +maximum number of occurrences of Q in G is O(mρ∗) [4] and the bound is tight in the worst case. +Our structure actually settles a problem on natural joins: +Range Join. Let R be a set of O(1) relations each with O(1) real-valued attributes. Denote +by join(R) the natural join result on the relations in R. Given an interval q = [x1, x2], a query +reports all the tuples t ∈ join(R) such that every attribute of t falls in q. +Let N be the total number of tuples in the relations of R. For any ∆ ≥ 1, we give a structure of +˜O(N + N ρ∗/∆) space answering a query with an ˜O(∆) delay. Here, the fractional edge covering +number ρ∗ is with respect to the join’s hypergraph (details deferred to Section 5). +The challenge behind Theorem 1.5 is to design a structure that works for all Q. It is possible to +do better for specific Q. Next, we present three examples that are not only important subproblems +themselves but also illustrate different techniques. +Triangles. We will show: +Theorem 1.6. For Problem 2 with Q = triangle, there is a structure of O(m) space answering a +query with an ˜O(1 + (m∗) +ω−1 +ω+1) delay, where m∗ is the number of edges appearing in at least one +reported triangle. +The fractional edge covering number ρ∗ is 1.5 for Q = triangle. To ensure ˜O(m) space, Theo- +rem 1.5 needs to set ∆ = √m. As ω−1 +ω+1 < 0.408, Theorem 1.6 achieves a polynomial improvement +in delay. The reader should note that the value m∗ in Theorem 1.6 never exceeds m but can be +much less (this happens when there are few triangles to list). Problem 2 with Q = triangle and q +fixed to (−∞, ∞) was used as a motivating problem in the previous work of [20], which described +a structure of O(m) space with a delay ˜O(√m) and is thus strictly improved by Theorem 1.6. +ℓ-Stars. An ℓ-star is a tree with ℓ leaves and one non-leaf vertex (a wedge is a 2-star). We will +show: +Theorem 1.7. For Problem 2 where Q = ℓ-star, there is a structure of O(m) space answering a +query with an ˜O(1) delay. +As a corollary, for any interval q, O(m) space suffices to detect the presence of an ℓ-star in +Gq using ˜O(1) time. For Q = wedge, this means that the hardness manifested by Theorem 1.2 is +indeed due to counting. +2ℓ-Cycles5. We will show: +4The reader may assume that a dummy occurrence is always output at the beginning of a query algorithm. +5A cycle with 2ℓ vertices. +5 + +Theorem 1.8. For Problem 2 with Q = 2ℓ-cycle where ℓ ≥ 2, there is a structure of ˜O(#Pℓ) space +answering a query with an ˜O(1) delay, where #Pℓ is the number of ℓ-paths in G. +The fractional edge covering number ρ∗ is ℓ for a 2ℓ-cycle. Theorem 1.5 needs ˜O(mℓ) space +to achieve an ˜O(1) delay. The space in Theorem 1.8 is significantly better. For ℓ = 2 (Q = 4- +cycle), the space is ˜O(nm) which is the maximum number of wedges in G. For ℓ > 2, the space is +˜O(m⌈(ℓ+1)/2⌉) which is the maximum number of ℓ-paths in G. +1.3 +Related Work +The preceding sections have covered the most relevant existing results. We will now proceed to +discuss other related work. +Pattern searching has been extensively studied in one-off computation. We refer the reader +to [3,8,10,17,18,27,28,30,37,50] and [2,11,17,24–26,33,36,38,39], as well as the references therein, +for algorithms on counting and listing, respectively. Those algorithms can be applied in Problem +1 and 2 after Gq has been generated. Our focus in this work is to avoid a full generation of Gq +because doing so can take Ω(m) time. +In the other extreme, one can precompute the set S of occurrences of Q in G. +The size +of S is O(mρ∗) (AGM bound), assuming that Q has a constant size. By resorting to standard +computational geometry techniques [19], we can store S in structures of ˜O(mρ∗) space to answer +a query of Problem 1 in ˜O(1) time and a query of Problem 2 with an ˜O(1) delay. For Problem +1, Theorem 1.4 achieves a better space bound on every Q with ρ∗ ≥ 2. When ρ∗ < 2, Q has at +most three vertices: a 1-path (single edge), a wedge, or a triangle. We have resolved the wedge and +triangle cases (Theorem 1.1 and 1.3), while Problem 1 is trivial for Q = 1-path. For Problem 2, +Theorem 1.5 captures the above extreme idea as a special case with ∆ = ˜O(1) and offers a tunable +space-query tradeoff. +A relational event graph, introduced by Bannister et al. [6], is a graph G = (V, E) where every +edge e ∈ E carries a real-valued timestamp. For an interval q = [x1, x2], let Gedge +q +be the subgraph +of G induced by all the edges whose timestamps are covered by q. +A pattern searching query +counts/lists the occurrences of a pattern Q in Gedge +q +. +See [6, 14, 15] for several data structures +designed for such queries. Similar as it sounds, pattern searching on a relational event graph is +drastically different from Problem 1 and 2 such that there is little overlap — in neither results nor +techniques — between our solutions and those in [6,14,15]. +Delay minimization is an important topic in the literature of joins and conjunctive queries; +see [5,9,12,13,20–23,34,35,41,43–45] and their references. Regarding our problems, we are not aware +of previous work giving a result better than what has already been mentioned. Our formulation +of range join listing (Section 1.2.2) suggests that the presence of query predicates can pose new +challenges on joins (also conjunctive queries) from the indexing’s perspective. Deep and Koutris [20] +proved a result equivalent to Theorem 1.5 (up to an ˜O(1) factor) on Problem 2, but only in the +special scenario where a query concerns the whole G, i.e., fixing the query range q to (−∞, ∞). +2 +Preliminaries +In this section, we will describe several technical tools to be deployed in our solutions. +Structures for Multidimensional Points. +We will utilize some well-known geometry data +structures as introduced below. The reader does not need to be bothered with the details of these +6 + +structures because we will apply them as “black boxes”. Let P be a set of n points in d-dimensional +space Rd where d is a constant. Given a rectangle q of the form [x1, y1] × [x2, y2] × ... × [xd, yd], +a range reporting query enumerates the points in P ∩ q. We can create a range tree [7, 19] on P, +which uses ˜O(n) space and permits us to answer such a query with an ˜O(1) delay. When d = 2, we +can replace the range tree with a Chazelle’s structure [16] which retains the aforementioned query +performance but reduces the space consumption to O(n). +We will also need range sum queries on P in the scenario where each point in P is 2D (i.e., +d = 2) and carries a real-valued weight. Given a rectangle q = [x1, y1] × [x2, y2], such a query +reports the total weight of the points in P ∩ q. We can again build a Chazelle’s structure of [16] +on P which occupies O(n) space and answers a query in ˜O(1) time. +From “Delays with Duplicates” to “Delays under Distinctness”. +Let us consider a +duplicate-removal scenario often encountered in designing algorithms with small delays. Suppose +that we have an algorithm A for enumerating a set S of elements. With a delay of ∆, A can report +an element e ∈ S, but cannot guarantee that e has never been reported before. The good news, on +the other hand, is that A can output the same element at most α times for some α ≥ 1 . +By modifying a buffering technique in [47], we can convert A into an algorithm that enumerates +only the distinct elements of S with a delay of O(α · ∆ log |S|). Conceptually, divide the execution +of A into epochs, each of which runs for α · ∆ time6. As A runs, we use a buffer B to stash the +set of distinct elements that have been found by A but not yet reported. Every time A finds an +element e ∈ S, we check whether e has ever existed in B (this takes O(log |S|) time, using a binary +search tree maintained on all the elements that have ever been found so far). If so, e is ignored; +otherwise, it is added to B. At the end of each epoch, we output an arbitrary element from B and +remove it from B. Finally, after A has terminated, we simply output the remaining elements in B. +B always contains at least one element at the end of each epoch. To see why, consider the +end of the t-th epoch for some t ≥ 1. At this moment, A has been running for t · α · ∆ time and +therefore must have reported t · α elements, which may not be distinct. However, as each element +can be reported at most α times, there must be at least t (distinct) ones among those t·α elements. +Since we have reported only t − 1 elements in the preceding epochs, B must still have at least one +element at the end of epoch t. It is now straightforward to verify that the modified algorithm has +a delay of O(α · ∆ log |S|) in enumerating the distinct elements of S. +3 +Problem 1: Matching Upper and Lower Bounds +This section will establish the conditional lower bound in Theorem 1.2 and its matching upper bound +in Theorem 1.4. Our discussion on the upper bound will also establish Theorem 1.3. Throughout +the paper, we will assume that the vertices of G have distinct attribute values. The assumption +loses no generality because one can break ties by vertex id. +3.1 +Lower Bound +Suppose that Problem 1 under Q = wedge admits a structure that uses ˜O(m2−δ/λ2) space and +answers a query in ˜O(λ) time for some λ ≥ 1. +We will design a structure for set disjointness +that uses ˜O(N 2−δ/λ2) space and answers a query in ˜O(λ) time. Recall that the data input to set +disjointness consists of s ≥ 2 sets S1, ..., Ss with a total size of N. Define U = �s +i=1 Si. +6Recall that “time” in the RAM model is defined as the number of atomic operations (e.g., addition, multiplication, +comparison, accessing a memory word, etc.) executed. Each epoch is essentially a sequence of α · ∆ such operations. +7 + +Create a graph G = (V, E) as follows. V has 2s + |U| vertices, including 2s set vertices and |U| +element vertices. Each set Si (i ∈ [1, s]) defines two set vertices, whose attribute values are set to i +and s + i, respectively. Each element in U defines an element vertex with the same attribute value +s + 1/2. Set E contains 2N edges: for each element e ∈ Si, add to E two edges each between the +element vertex of e and a set vertex of Si. Now, create a Problem-1 structure under Q = wedge on +G. The structure occupies ˜O(N 2−δ/λ2) space. +Consider a set disjointness query with set ids a and b. +Assuming w.l.o.g. a < b, we issue +four Problem-1 wedge-counting queries on G with intervals q1 = [a, s + b], q2 = [a + 1, s + b], +q3 = [a, s + b − 1], and q4 = [a + 1, s + b − 1], respectively. Let c1, c2, ..., c4 be the counts returned. +We declare Sa∩Sb non-empty if and only if c1−c2−c3+c4 > 0. The query time is ˜O(λ). Appendix A +proves the algorithm’s correctness. This completes the proof of Theorem 1.2. +3.2 +Upper Bound +Next, we will attack Problem 1 by allowing Q to be an arbitrary pattern graph. Consider any +occurrence of Q in G. Let u (resp. v) be the vertex in this occurrence with the smallest (resp. +largest) attribute. We register the occurrence at the pair (u, v). Denote by cu,v the number of +occurrences registered at (u, v). +For a query with q = [x1, x2], an occurrence registered at (u, v) appears in Gq (i.e., the subgraph +of G induced by Vq) if and only if Au ≥ x1 and Av ≤ x2. We can therefore convert the problem to +range sum on 2D points. For each pair (u, v) ∈ V ×V , create a point (Au, Av) with weight cu,v. Let +P be the set of points created; clearly, |P| = O(n2). The query result is simply the total weight of +all the points in P covered by the rectangle [x1, ∞) × (−∞, x2] (a range sum operation). We can +store P in a Chazelle’s structure (see Section 2) that occupies O(|P|) = O(n2) space and performs +a range sum operation in ˜O(1) time. This establishes Theorem 1.4. +Improvement for Cliques. The space of our structure can be lowered to O(m) when Q is a +clique. The crucial observation is that registering an occurrence at (u, v) implies {u, v} ∈ E. We +add to P only the points (Au, Av) with a non-zero cu,v (points with zero weights do not affect +a range sum operation). This reduces the size of P to at most m and, hence, the space of the +Chazelle’s structure to O(m). We thus complete the proof of Theorem 1.3. +4 +Problem 1: Wedges +The section will explain how to achieve the guarantees in Theorem 1.1 for Problem 1 under Q = +wedge. We will represent a wedge occurrence in G = (V, E) as wedge(u, v, w) where u, v, and w are +vertices in V , and {u, v} and {v, w} are edges in E. Let us introduce a slightly different problem: +Colored Range Wedge Counting. Define G = (V, E) and Av for each v ∈ V as in Problem +1. Each vertex in V is colored black or white. Given an interval q, a query returns the number +of occurrences wedge(u, v, w) such that Au ∈ q, Aw ∈ q, and v is black. +Note that no requirements exist on Av and the colors of u and w. +Let C be a set of subsets of V . We call C a canonical collection if +• (P4-1) each vertex of V appears in ˜O(1) subsets in C; +8 + +• (P4-2) for any interval q, we can partition Vq (i.e., the set of vertices in V with attribute +values in q) into ˜O(1) disjoint subsets, each being a member of C. The ids of these subsets +can be obtained in ˜O(1) time. +It is rudimentary to find a canonical collection C satisfying � +U∈C |U| = ˜O(n).7 We will work with +such a C henceforth. In Appendix B, we prove: +Lemma 4.1. Consider the colored range wedge counting problem. For any real value λ ∈ [1, √m], +there is a structure of ˜O(m2/λ2) space that answers a query in ˜O(λ) time. +Equipped with the above, we now return to Problem 1 with Q = wedge. +Structure. For each U ∈ C (where U is a subset of V ), we create a graph GU by adding edges in +three steps: +1. Initialize GU as an empty graph with no vertices and edges. +2. For every vertex u ∈ U, we add all its edges in G (i.e., the original data graph) to GU. The +addition of an edge {u, v} creates vertex v in GU if v is not present in GU yet. +3. Finally, color a vertex in GU black if it comes from U, or white otherwise. +We now build a structure of Lemma 4.1 on GU, which uses ˜O(|EU|2/λ2) space where EU is the set +of edges in GU. By Property P4-1, each edge {u, v} of G can be added to the EU of ˜O(1) subsets +U ∈ C. It thus follows that � +U∈C |EU| = ˜O(m). The structures of all U ∈ C occupy ˜O(m2/λ2) +space in total. +Query. Consider now a (Problem-1) query with interval q. By Property P4-2, in ˜O(1) time we +can pick h = ˜O(1) members U1, ..., Uh from C to partition Vq. For each i ∈ [1, h], issue a colored +range wedge counting query with interval q on GUi. We return the sum of the h queries’ outputs. +The overall query time is h · ˜O(λ) = ˜O(λ). +To verify correctness, first observe that every wedge(u, v, w) counted by the colored query on GUi +satisfies: Au ∈ q, Aw ∈ q (definition of colored range wedge counting), and Av ∈ q (because v being +black means v ∈ Ui ⊆ Vq). Conversely, every occurrence wedge(u, v, w) satisfying {Au, Av, Aw} ⊆ q +is counted only once: by the colored query on GUi where Ui is the only subset (among all i ∈ [1, h]) +containing v. Indeed, for any Uj with j ̸= i, v is either absent in GUj or is white; in neither case +can the wedge be counted. Correctness now follows. +5 +Problem 2: Arbitrary Subgraphs +We now proceed to tackle Problem 2 for an arbitrary query pattern Q. We will, in fact, solve +the range join problem defined in Section 1.2.2. As shown in Appendix D, it is relatively easy to +convert our structure to prove Theorem 1.5. +For a relation R ∈ R (recall that R is the set of input relations; see Section 1.2.2) its scheme, +scheme(R), is the set of attributes in R. Let X = � +R∈R scheme(R). The input size N can now be +7It suffices to build a binary search tree T on the vertices’ attribute values. Each node in T defines a subset in +C, which consists of every v ∈ V whose attribute Av is stored in the node’s subtree. It is well known (see, e.g., [46]) +that, for any interval q, there exist O(log n) canonical nodes in T whose subtrees are disjoint and together contain +all and only the attribute values in q. Those nodes can be found in O(log n) time and satisfy Property P4-2 with +respect to Vq. +9 + +expressed as � +R∈R |R|. We will assume, w.l.o.g., that (i) the relations in R have distinct schemes, +(ii) N is a power of 2, and (iii) each attribute X ∈ X has a domain dom(X) comprising the integers +in [1, N]. Given an interval q = [x1, x2], a query lists every tuple t in join(R) — the natural join +result on R — satisfying t[X] ∈ q for all X ∈ X, where t[X] is the tuple’s value under attribute X. +We want to design a structure of small space to answer such queries with a small delay. +It will be convenient to work with a hypergraph G = (X, E) where E = {scheme(R) | R ∈ R}. +Given an edge e ∈ E, we use Re to denote the (only) relation R ∈ R whose scheme is e. For a +function W that assigns a non-negative weight W(e) to every e ∈ E, its lump-sum is � +e∈E W(e). +The function W is a fractional edge covering if � +e∈E:X∈e W(e) ≥ 1 holds on every attribute X ∈ X. +The fractional edge covering number ρ∗ of G is the smallest lump-sum of all fractional edge coverings. +Henceforth, we will use W to represent an optimal assignment function with lump-sum ρ∗. +The section’s main result is: +Theorem 5.1. For the range join problem (see Section 1.2.2), given any ∆ ≥ 1, there is a structure +of ˜O(N + N ρ∗/∆) space that answers a query with an ˜O(∆) delay. +5.1 +A Generalization of the AGM Bound +The classical AGM bound [4] states that |join(R)| ≤ � +e∈E |Re|W (e). Next, we will present a more +general version of this inequality. +Set d = |X| and impose an arbitrary ordering on the d attributes: X1, X2, ..., Xd. Given intervals +I1, I2, ..., Id where Ii ⊆ dom(Xi) for each i ∈ [1, d], define B(I1, ..., Id) as the d-dimensional box +I1 × ... × Id. For a relation R ∈ R, we use R ⋉ B(I1, ..., Id) to represent the set of tuples t ∈ R such +that t[Xi] ∈ Ii for every i satisfying Xi ∈ scheme(R). +We prove in Appendix C: +Lemma 5.2. Let Ii, i ∈ [1, d], be a set of disjoint intervals in dom(Xi). Then: +� +I1∈I1 +� +I2∈I2 +... +� +Id∈Id +� +e∈E +|Re ⋉ B(I1, ..., Id)|W (e) ≤ +� +e∈E +|Re|W (e). +(1) +To see how (1) captures the AGM bound, consider the special Ii with size |dom(Xi)|, namely, +each interval in Ii is a value in dom(Xi) and vice versa. Thus, |Re ⋉ B(I1, ..., Id)| is either 0 or 1 +such that the left hand side of (1) is precisely |join(R)|. The real power of (1), however, comes from +allowing Ii to be an arbitrary set of disjoint intervals, a feature crucial for us to prove Theorem 5.1. +A remark is in order about why Lemma 5.2 is not trivial. It would be if the term � +e∈E |Re ⋉ +B(I1, ..., Id)|W (e) in (1) was replaced by the output size of the join on the relations in {Re ⋉ +B(I1, ..., Id) | e ∈ E}. By the AGM bound, the term � +e∈E |Re ⋉ B(I1, ..., Id)|W (e) is an upper bound +on the size of the join {Re⋉B(I1, ..., Id) | e ∈ E}. The non-trivial goal is to show that the summation +of all those upper bounds (i.e., the left hand side of (1)) still cannot exceed � +e∈E |Re|W (e). +5.2 +Range Join +This subsection serves as a proof of Theorem 5.1. Given an ℓ ≥ 0, we call an interval a level-ℓ +dyadic interval if it has the form [i · 2ℓ + 1, (i + 1) · 2ℓ] for some integer i ≥ 0. Because N is a power +of 2, for each ℓ ∈ [0, log2 N], we can partition [1, N] into N/2ℓ disjoint level-ℓ dyadic intervals. +10 + +A dyadic combination is a sequence of d dyadic intervals (I1, ..., Id); recall that d = |X|. The +combination defines a (natural) join instance on the relations in {Re ⋉ B(I1, ..., Id) | e ∈ E}. We +will denote the instance as RI1,...,Id. Define +AGM(I1, ..., Id) += +� +e∈E +|Re ⋉ B(I1, ..., Id)|W (e). +(2) +The AGM bound assures us that |join(RI1,...,Id)| ≤ AGM(I1, ..., Id). +Structure. A dyadic combination (I1, ..., Id) with a non-empty join(RI1,...,Id) is said to be heavy +if AGM(I1, ..., Id) > ∆, or light otherwise. For each heavy combination, we build a structure of [20] +that can enumerate the tuples in join(RI1,...,Id) with an ˜O(∆) delay. +The structure’s space is +bounded by O(AGM(I1, ..., Id)/∆).8 +We argue that the structures on all the heavy (dyadic) combinations use ˜O(N ρ∗/∆) space in +total. Fix d arbitrary level numbers ℓ1, ..., ℓd each between 0 and log2 N. For i ∈ [1, d], let Ii +be the set of all level-ℓi dyadic intervals. The total space occupied by the structures of all heavy +combinations (I1, ..., Id) ∈ I1 × ... × Id is +1 +∆ +� +(I1,...,Id)∈I1×...×Id +AGM(I1, ..., Id). +(3) +up to an ˜O(1) factor. The above includes a term for every light combination but such terms can +only over-estimate the space. +Each Ii is a set of disjoint intervals in dom(Xi). +Applying the +definition in (2) and Lemma 5.2, we can see that (3) is bounded by N ρ∗/∆, noticing that the right +hand side of (1) is at most N ρ∗. +In the above analysis, we have fixed a set of ℓ1, ..., ℓd. As each ℓi has O(log N) choices, all +together there are O(logd N) = ˜O(1) different sets of ℓ1, ..., ℓd. We can now conclude that the +overall space is ˜O(N ρ∗/∆). +Finally, we need a hash table to check in constant time whether a dyadic combination is heavy. +The hash table occupies ˜O(N ρ∗/∆) space because our earlier analysis implies a bound ˜O(N ρ∗/∆) +on the number of heavy dyadic combinations. The overall space of our entire structure is therefore +˜O(N + N ρ∗/∆), where the term ˜O(N) counts the space for storing the relations of R. +Query. Consider a range join query with interval q = [x1, x2]. We consider, w.l.o.g., that x1 and +x2 are integers in [1, N]. In ˜O(1) time, we can partition the box B(q, ..., q +� �� � +t +) into O(logd N) = ˜O(1) +disjoint boxes, each in the form B(I1, ..., Id) where (I1, ..., Id) is a dyadic combination; we say that +(I1, ..., Id) is canonical for q. The query result is +� +canonical (I1, ..., Id) +join(RI1,...,Id). +The results join(RI1,...,Id) of all the canonical (I1, ..., Id) are disjoint. If a canonical (I1, ..., Id) is +heavy, we enumerate join(RI1,...,Id) with an ˜O(∆) delay using the structure of [20] on (I1, ..., Id). +Otherwise, we apply a worst-case optimal join algorithm [39, 40, 48] to compute join(RI1,...,Id). +8Strictly speaking, the space should also account for the relations in RI1,...,Id. In our context, it suffices to store +the relations of R once and generate the relations in RI1,...,Id when answering a query. Appendix D has additional +details about [20]. +11 + +The algorithm finishes in ˜O(AGM(I1, ..., Id)) time, which is ˜O(∆) by definition of light dyadic +combination. Our algorithm guarantees a delay of ˜O(∆). This completes the proof of Theorem 5.1. +Remark. In [36], Khamis et al. used dyadic intervals in their algorithm for one-off computation +of join(R). Their main technical issue was to select “good” dyadic boxes (i.e., boxes of the form +B(I1, ..., Id)) to cover the tuples in join(R) once. That issue is non-existent in our context, where +the primary obstacle is to argue that the total space given in (3) is affordable. +We overcame +the obstacle using Lemma 5.2, which, though perpahs no longer surprising given all the existing +variations of the AGM bound, deserves a careful treatment that, we believe, has not appeared +before. +6 +Problem 2: Triangles +This section will describe a structure for Problem 2 under Q = triangle. We will first attack, in +Section 6.1 and 6.2, two fundamental problems whose solutions are vital to establishing Theorem 1.6, +the proof of which is presented in Section 6.3. +6.1 +The Range Triangle Edges Problem +This subsection will discuss the following standalone problem. +Range Triangle Edges (RTE). Let G be an undirected graph with m edges. Given an +interval q = [x1, x2], a query returns: (i) all the edges appearing in at least one triangle of Gq; +and (ii) Θ(m∗) triangles where m∗ is the number of edges reported in (i). +We will develop a structure of O(m) space that can answer a query in ˜O(m∗) time. Furthermore, +the query can enumerate the m∗ edges and the Θ(m∗) triangles both with a delay ∆. +Let us represent a triangle occurrence in G as triangle(u, v, w) where u, v, and w are the triangle’s +vertices. Ordering is important: we will always adhere to the convention Au < Av < Aw. Given +an interval q, we denote by E∗ +q the set of edges showing up in at least one triangle of Gq. Hence, +m∗ = |E∗ +q|. If triangle(u, v, w) appears in Gq, we call {u, v} a type-1 edge, {v, w} a type-2 edge, +and {u, w} a type-3 edge. The total number of edges of all three types is between m∗ and 3m∗.9. +Next, we explain how to extract the edges of each type in Gq. +Type 1 and 2. We will discuss only type 1 because type 2 is symmetric. For each edge {u, v} in +G (assume, w.l.o.g., Au < Av), identify a sentinel vertex w∗ for {u, v} as follows: +• w∗ = null if G has no occurrence of the form triangle(u, v, w); +• otherwise, w∗ has the smallest attribute among all the vertices w making a triangle occurrence +triangle(u, v, w) in G. +Consider any interval q = [x1, x2]. Observe that {u, v} is a type-1 edge for q if and only if +x1 ≤ Au and Aw∗ ≤ x2. This motivates us to convert type-1 edge retrieval to range reporting on +2D points (introduced in Section 2). Towards the purpose, create a set P of points, which has +a point (Au, Aw∗) for every {u, v} whose sentinel w∗ is not null. Attach edge {u, v} to the point +(Au, Aw∗) so that the former can be fetched along with the latter. The size of P is at most m. +Given q = [x1, x2], we can find all the type-1 edges by enumerating the points of P inside the +9An edge can be of different types in various triangle occurrences. +12 + +rectangle [x1, ∞) × (−∞, x2]. Hence, we can store P in a Chazelle’s structure (see Section 2) that +has O(|P|) = O(m) space and ensures an ˜O(1) delay in reporting the type-1 edges of any q. +Type 3. A similar approach works for type 3. Let {u, w} be an edge appearing in at least one +occurrence triangle(u, v, w) in G. It is a type-3 edge of q = [x1, x2] if and only if x1 ≤ Au and +Aw ≤ x2. By adapting the earlier discussion in a straightforward manner, we conclude that there +is a structure of O(m) space allowing us to retrieve all the type-3 edges with an ˜O(1) delay. +Listing Θ(m∗) Triangles. The above has explained how to retrieve E∗ +q, but an RTE query still +needs to report Θ(m∗) triangles. Next, we remedy the issue by slightly modifying our solution so +far. +Recall that, in dealing with type 1, we attached the edge {u, v} to the point (Au, Aw∗) generated +from the edge. Now, we attach triangle(u, v, w∗) to (Au, Aw∗) as well. This way, when (Au, Aw∗) +is found, we obtain both {u, v} and triangle(u, v, w∗) for free. After applying the same idea to +type-2 and type-3, we can assert that, whenever the query algorithm finds a type-1, -2, or -3 edge, +it must have also found a triangle in Gq. Therefore, the algorithm can report the triangles in Gq +with an ˜O(1) delay, although the same triangle may be reported up to three times10. By applying +the duplicate-removal technique in Section 2, we now have an algorithm that can enumerate Θ(m∗) +distinct triangles with an ˜O(1) delay. The number of distinct triangles reported is at least m∗/3 +and at most 3m∗. +6.2 +The Small-Delay Triangle Listing Problem +In this subsection, we will concentrate on a standalone problem defined as follows. +Small-Delay Triangle Listing (SDTL). G is an undirected graph with m edges, each of +which appears in at least one triangle. We are given Ω(m) free triangles and O(m) forbidden +triangles. Design an algorithm to enumerate all the triangles of G — except for the forbidden +ones — with a small delay (free triangles must be enumerated). No preprocessing is allowed. +We will settle the problem with an algorithm of delay ˜O(m +ω−1 +ω+1). +Suppose that G has OUT triangles in total. Our starting point is an algorithm of Bjorklund et +al. [11] which is able to list k triangles in α · m +3(ω−1) +ω+1 k +3−ω +ω+1 time, where α = ˜O(1), for a parameter +k ∈ [Ω(m), OUT]. As far as the algorithm of [11] is concerned, we can consider OUT known because +it can be found in O(m2ω/(ω+1)) time [3] which is O(m +3(ω−1) +ω+1 k +3−ω +ω+1). The algorithm of Bjorklund et +al. does not have a small delay, but we will turn it into one that does. +We run the algorithm of Bjorklund et al. [11] with geometrically-increasing k and, in each run, +report only some, but not all, of the triangles. How many triangles are reported in each run is +decided strategically to keep the delay small. Let S0 +no be the set of forbidden triangles and S0 +yes the +set of free triangles in the beginning. Set k0 = |S0 +no| + |S0 +yes|. When running the algorithm of [11] +for the i-th time, we set its parameter k to ki = min{3ik0, OUT}. We enforce the invariant that, +when run i starts, there are always a set Si−1 +no +of forbidden triangles and a set Si−1 +yes of free triangles. +The set Si−1 +yes will be reported with a small delay during the i-th run (details to be clarified shortly). +10An occurrence triangle(u, v, w) can be reported only when {u, v}, {v, w}, or {u, w} is output as a type-1, -2, or +-3 edge, respectively. +13 + +Specifically, suppose that the i-th run finds a set Si +raw of ki triangles (some of which have been +output in previous runs). We generate the forbidden and free sets for the next run as follows: +Si +no = Si−1 +no ∪ Si−1 +yes and then Si +yes += +Si +raw \ Si +no. +Run i finishes in α · m +3(ω−1) +ω+1 k +3−ω +ω+1 +i +time. We instruct the run to output a triangle from Si−1 +yes every +α · m +3(ω−1) +ω+1 k +3−ω +ω+1 +i +|Si−1 +yes | +(4) +atomic operations. We will show |Si−1 +yes | = Ω(ki), with which the delay in (4) can be bounded as: +˜O + +m +3(ω−1) +ω+1 +k +2ω−2 +ω+1 +i + + = ˜O +� +m +ω−1 +ω+1 +� +(5) +where the equality used ki ≥ k0 = Ω(m). +For i = 1, |Si−1 +yes | = Ω(k0) follows directly from the definition of the SDTL problem (i.e., we +have Ω(m) free triangles to start with). To prove |Si−1 +yes | = Ω(ki) for i ≥ 2, we derive: +|Si−1 +no | ≤ |S0 +no| + |S0 +yes| + +i−2 +� +j=1 +|Sj +raw| = k0 + +i−2 +� +j=1 +3j · k0 = +i−2 +� +j=0 +3j · k0 < 3i−1k0 +2 +. +Therefore: +|Si−1 +yes | +≥ +|Si−1 +raw | − |Si−1 +no | > ki−1 − 3i−1k0/2 = ki−1/2 = Ω(ki). +We now conclude that the delay of our algorithm is as given in (5). +6.3 +Proof of Theorem 1.6 +We are ready to explain how to solve Problem 2 with Q = triangle. In preprocessing, we build an +RTE structure (Section 6.1) on G. Now, consider a (Problem-2) query with interval q. We start by +issuing an RTE query to retrieve E∗ +q, i.e., the set of edges appearing in at least one triangle of Gq. +This, in effect, generates G∗ +q, which is the subgraph of Gq induced by the edges in E∗ +q. In addition, +the RTE query has also enumerated a set S of Θ(m∗) triangles in Gq, where m∗ = |E∗ +q|. The size +of S falls in [m∗ +3 , 3m∗]. +Our remaining mission is to enumerate the triangles in G∗ +q that are outside S. Note that G∗ +q +is a graph with m∗ edges and at least Θ(m∗) triangles. This motivates us to convert the mission +to the SDTL problem, which has been solved in Section 6.2. However, the SDTL problem requires +Θ(m∗) free triangles and O(m∗) forbidden triangles as part of the input. Unfortunately, we do not +seem to have these triangles at the moment. +We overcome this obstacle by, interestingly, dividing S into Syes and Sno, such that Syes (resp. +Sno) serves as the set of free (resp. forbidden) triangles. Recall that the RTE query algorithm, +denoted as A, is designed to enumerate an edge in E∗ +q with a delay ∆ = ˜O(1) and a triangle in S also +with a delay ∆. Therefore, it must finish within tmax = max{∆·(|E∗ +q |+1), ∆·(|S|+1)} ≤ ∆·(3m∗+1) +time. We can now apply the buffering technique in Section 2 with α = 18 to turn A into an algorithm +14 + +that outputs a triangle at the end of each epoch, which has a length 18∆. The total number of +epochs is at most tmax +18∆ ≤ 3m∗+1 +18 +. Thus, when A finishes, we have output at most (3m∗ + 1)/18 +triangles, whereas the buffer B (defined in Section 2) still has at least |S|− 3m∗+1 +18 += Θ(m∗) triangles. +We can, thus, set Syes to the content of B when A finishes, and Sno to the set of triangles already +output. +We can now apply the SDTL algorithm on G∗ +q and, thus, complete the proof of Theorem 1.6. +7 +Problem 2: Near-Constant Delays +This section will focus on two instances of Problem 2 where it is possible to achieve ˜O(1) delays +with space substantially smaller than Theorem 1.5. We will discuss first Q = ℓ-star in Section 7.1 +and then Q = 2ℓ-cycle in Section 7.2. We will focus on explaining how to enumerate a perhaps- +not-distinct occurrence with an ˜O(1) delay, while ensuring each occurrence to be output only a +constant number of times. Owing to the duplicate-removal method in Section 2, we can modify the +algorithms to enumerate only distinct occurrences with ˜O(1) delays. +7.1 +ℓ-Stars +Recall that an ℓ-star is a tree with only one non-leaf node, which we will refer to as the star’s center. +Consider a query with interval q. We refer to a node u as a q-center if Gq has at least one ℓ-star +occurrence with u as the center. Once u is found, it becomes a trivial matter to enumerate all the +ℓ-stars having u as the center with an ˜O(1) delay. Specifically, we can first (use a binary search tree +to) retrieve all the neighbors v of u in G satisfying Av ∈ q. From those neighbors, any ℓ distinct +vertices form an ℓ-star together with u (as the center). It is rudimentary to ensure an ˜O(1) delay +in enumerating all those stars. +Next, we concentrate on designing a structure to enumerate the q-centers with an ˜O(1) delay. +Consider an arbitrary ℓ-star in G with center u. Sort the star’s ℓ + 1 vertices in ascending order +of attribute and look for the position of u. If u is the r-th smallest, we will refer to the star as a +rank-r ℓ-star and u as a rank-r q-center. +Now, fix an r ∈ [1, ℓ + 1]. We will describe a structure to support the following operation: +Given an interval q, find all the rank-r q-centers, i.e., all vertices u ∈ V s.t. Gq has a rank-r +ℓ-star with u as the center. +Consider any rank-r ℓ-star in G having u as the center. Let us write out the star’s vertices as +v1, ..., vr−1, u, vr+1, ..., vℓ in ascending order of attribute. For a q = [x1, x2], the ℓ-star appears in +Gq if and only if x1 ≤ Av1 and Avℓ ≤ x2. Refer to v1 as a left r-sentinel of u and to vℓ as a +right r-sentinel of u. From all the left r-sentinels of u (one from each rank-r ℓ-star with center u), +identify the one v∗ +1 with the largest attribute. Similarly, from all the right r-sentinels of u, identify +the one v∗ +ℓ with the smallest attribute. Observe that u is a rank-r q-center if and only if x1 ≤ Av∗ +1 +and Av∗ +ℓ ≤ x2. We can therefore convert the retrieval of rank-r q-centers into range reporting on +2D points (review Section 2), in the same way as illustrated in Section 6.1. Following Section 2, +we can create a Chazelle’s structure on n points — each point created for a vertex u ∈ V in the +way explained — that has O(n) space and, given any q, can list the rank-r q-centers with an ˜O(1) +delay. This completes the proof of Theorem 1.7. +15 + +7.2 +2ℓ-Cycles +We will start with an assumption: all queries specify a fixed q = (−∞, ∞), namely, there is +effectively only one query, which enumerates all the 2ℓ-cycles in G. The assumption allows us to +explain the core ideas with the minimum technical details and will be removed eventually. +Queries with q = (−∞, ∞). Given a 2ℓ-cycle occurrence, we refer to the vertex u in the cycle +having the smallest attribute as the occurrence’s anchor. Let v be the vertex in the cycle such +that cutting the cycle at u and v gives two ℓ-paths connecting u and v. We will refer to v as the +occurrence’s inverse anchor, the pair (u, v) as an anchor pair, and the two aforementioned paths +as cycle ℓ-paths. The number of cycle ℓ-paths is at most #Pℓ (recall that #Pℓ is the total number +of ℓ-paths). +The problem may appear deceivingly simple: can’t we answer a query by simply concatenating, +for each anchor pair (u, v), every two cycle ℓ-paths from u to v? This does not work because the +two cycle ℓ-paths may share common vertices other than u and v, in which case the concatenation +does not yield a 2ℓ-cycle! This motivates a crucial notion: two cycle ℓ-paths are interior disjoint if +they (i) have the same anchor pair (u, v), and (ii) do not share any common vertex except u and +v. Concatenating two cycle ℓ-paths from u to v spawns a 2ℓ-cycle if and only if those paths are +interior disjoint. The challenge we are facing at this moment is the following problem. +Design a structure to support the following operation: given a cycle ℓ-path π from anchor u +to inverse anchor v, list all the cycle ℓ-paths interior disjoint with π with an ˜O(1) delay. +We will overcome the challenge with a structure of ˜O(#Pℓ) space. +Our main observation is that the operation can be converted to range reporting on (ℓ − 1)- +dimensional points (review Section 2). To explain, let us consider any cycle ℓ-path π from anchor +u to inverse anchor v. +After excluding u and v, the path has ℓ − 1 vertices, which we list as +w1, w2, ..., wℓ−1 in ascending order of attribute11. +Convert π into an (ℓ − 1)-dimensional point +(Aw1, ..., Awℓ−1). Let Pu,v be the set of points thus obtained from all the cycle ℓ-paths with (u, v) +as the anchor pair. +Now, consider another cycle ℓ-path π′ from u to v. List the vertices of π′ other than u and v +as w′ +1, w′ +2, ..., w′ +ℓ−1 also in ascending order of attribute. If π′ is interior disjoint with π, each Aw′ +i +(i ∈ [1, ℓ − 1]) must fall in one of the ℓ open intervals: +(−∞, Aw1), (Aw1, Aw2), ..., (Awℓ−2, Awℓ−1), (Awℓ−1, ∞). +(6) +Therefore, (Aw′ +1, ..., Aw′ +ℓ−1) — the point converted from π′ — must fall in one of the following +ℓℓ−1 = O(1) rectangles: q1 ×q2 ×...×qℓ−1, where each qi (i ∈ [1, ℓ−1]) is taken independently from +one of the intervals in (6). As per Section 2, by creating a range tree on Pu,v of ˜O(|Pu,v|) space, we +can enumerate all the points in such a rectangle with an ˜O(1) delay. +The conclusion from the above is that, for each anchor pair (u, v), we can create a range tree +of ˜O(|Pu,v|) space which, given any cycle ℓ-path cycle π from u to v, permits the enumeration of +every cycle ℓ-path π′, which is interior disjoint with π, with an ˜O(1) delay. The structures of all +the anchor pairs use in total � +anc. pair (u, v) ˜O(|Pu,v|) = ˜O(#Pℓ) space. +With the challenge conquered, listing all the 2ℓ-cycles becomes an easy matter. We simply +look at each cycle ℓ-path π, retrieve every ℓ-path π′ interior disjoint with π, and make a cycle by +concatenating π and π′. The delay in cycle reporting is ˜O(1) (each 2ℓ-cycle can be reported twice). +11The order should not be confused with the order by which the vertices appear in π. +16 + +Arbitrary Queries. +Next, we remove the constraint q = (−∞, ∞) and tackle queries with +arbitrary q. A new issue now arises: a query can no longer afford to look at all the cycle ℓ-paths. +We say that a cycle ℓ-path from anchor u to inverse anchor v contributes to Gq if it makes a 2ℓ-cycle +in Gq with another interior disjoint cycle ℓ-path. We need a way to list only the contributing cycle +ℓ-paths. +Fix any cycle ℓ-path π with anchor pair (u, v). Let Sπ be the set of 2ℓ-cycles in G that include +π and have (u, v) as the anchor pair. Take an arbitrary cycle from Sπ. By definition of anchor, u +has the smallest attribute among the cycle’s vertices. Let w be the vertex in the cycle with the +largest attribute. For q = [x1, x2], the cycle appears in Gq if and only if x1 ≤ Au and Aw ≤ x2. +Let w∗ be the vertex with the smallest attribute among all such w’s. It becomes evident that π +contributes to the Gq of q = [x1, x2] if and only if x1 ≤ Au and Aw∗ ≤ x2. We can therefore convert +the retrieval of contributing cycle ℓ-paths to range reporting on 2D points, using the method in +Section 6.1. The resulting structure (a Chazelle’s structure) stores a point converted from every +cycle ℓ-path and uses O(#Pℓ) space. Give any q, we can list the cycle ℓ-paths contributing to Gq +with an ˜O(1) delay. +Suppose that we have found a contributing cycle ℓ-path π with anchor pair (u, v). As before, +we proceed to find the cycle ℓ-paths π′ interior disjoint with π. The new requirement here, however, +is that π′ needs to be contributing as well. Recall that, in the q = (−∞, ∞) scenario, we converted +the task to range reporting on (ℓ − 1)-dimensional points. To deal with arbitrary q = [x1, x2], we +will increase the dimension by one. +To explain, in a fashion like before, let us list out the vertices of π — after excluding u and +v — as w1, ..., wℓ−1 in ascending order of attribute. +Denote by wmax the vertex in π with the +largest attribute (wmax can be v). Convert π to an ℓ-dimensional point (Aw1, ..., Awℓ−1, Awmax). +Let (Aw′ +1, ..., Aw′ +ℓ−1, Aw′max) be the point converted from π′ in the same manner. As we already +know Au ∈ [x1, x2] (recall that π is a contributing path), π′ is a path we want if and only if it +satisfies the conditions below: +• Aw′ +i (1 ≤ i ≤ ℓ − 1) falls in one of the ℓ intervals in (6); +• Aw′max ≤ x2. +Thus, the point (Aw′ +1, ..., Aw′ +ℓ−1, Aw′max) must fall in one of the following ℓℓ−1 = O(1) rectangles: +q1 × q2 × ... × qℓ−1 × (−∞, x2], where each qi (i ∈ [1, ℓ − 1]) is an interval taken independently +from (6). By the above reasoning, for each anchor pair (u, v), we create a set Pu,v of ℓ-dimensional +points, each converted from a cycle ℓ-path with anchor pair (u, v), and then build a range tree on +Pu,v. The range trees of all anchor pairs use � +anc. pair (u, v) ˜O(|Pu,v|) = ˜O(#Pℓ) space in total. +We now elaborate on the overall algorithm for answering a (Problem-2) query with parameter +q. First, enumerate all the cycle ℓ-paths contributing to Gq with an ˜O(1) delay; call this the outer +enumeration. Every time such a path π — say with anchor pair (u, v) — is obtained, we suspend +outer enumeration and utilize the range tree on Pu,v to find all the paths π′ discussed previously +with an ˜O(1) delay. +Upon the delivery of a π′, concatenate it with π and output the 2ℓ-cycle +obtained. After exhausting all such π′, we resume outer enumeration. This concludes the proof of +Theorem 1.8. +17 + +Appendix +A +Correctness of the Reduction in Section 3.1 +In our construction, Si (i ∈ [1, s]) corresponds to two set vertices with attribute values i and +i + s, respectively. To facilitate derivation, we make a copy of each set: define Si = Si−s for each +i ∈ [s + 1, 2s]. In the rest of the proof, we hold the view that each Si (i ∈ [1, 2s]) corresponds to +only one set vertex, the one with attribute value i. +Consider a wedge occurrence with vertices u, v, and w where the edges are {u, v} and {v, w}. +We classify it as one of the two types below: +• (type e-s-e) u and w are element vertices and v is a set vertex; +• (type s-e-s) u and w are set vertices and v an element vertex. +Lemma A.1. For any interval q = [x, y] satisfying 1 ≤ x < s + 1/2 < y ≤ 2s, we have +• the number of e-s-e wedges in Gq is � +i∈[x,y] +�|Si| +2 +� +; +• the number of s-e-s wedges in Gq is � +i∈[x,y],j∈[i+1,y] |Si ∩ Sj|. +Proof. To prove the first bullet, define an e-s-e tuple as (e1, Si, e2) where i ∈ q and e1 and e2 are +distinct elements in Si. +The number of such tuples is �y +i=x +�|Si| +2 +� +. +Our construction ensures a +one-one correspondence between e-s-e tuples and e-s-e wedges in Gq. +To prove the second bullet, define an s-e-s tuple as (Si, e, Sj) where x ≤ i < j ≤ y and +e ∈ Si ∩ Sj. The number of such tuples is � +i∈[x,y],j∈[i+1,y] |Si ∩ Sj|. Our construction ensures a +one-one correspondence between s-e-s tuples and s-e-s wedges in Gq. +To find out whether Sa ∩Sb is empty, our reduction issues four Problem-1 queries with intervals +q1 = [a, s+b], q2 = [a+1, s+b], q3 = [a, s+b−1], and q4 = [a+1, s+b−1], respectively. The above +lemma is applicable to all these intervals. For i ∈ [1, 4], let c′ +i (resp. c′′ +i ) be the number of e-s-e +(resp. s-e-s) wedges in Gqi; this means that ci, the total number of wedges in Gqi, equals c′ +i + c′′ +i . +According to Lemma A.1, we have: +c′ +1 − c′ +2 − c′ +3 + c′ +4 += +� +i∈[a,s+b] +�|Si| +2 +� +− +� +i∈[a+1,s+b] +�|Si| +2 +� +− +� +i∈[a,s+b−1] +�|Si| +2 +� ++ +� +i∈[a+1,s+b−1] +�|Si| +2 +� += +0 +and +c′′ +1 − c′′ +2 − c′′ +3 + c′′ +4 += + + + + +� +i∈[a,s+b] +j∈[i+1,s+b] +|Si ∩ Sj| − +� +i∈[a+1,s+b] +j∈[i+1,s+b] +|Si ∩ Sj| + + + + − + + + + +� +i∈[a,s+b−1] +j∈[i+1,s+b−1] +|Si ∩ Sj| − +� +i∈[a+1,s+b−1] +j∈[i+1,s+b−1] +|Si ∩ Sj| + + + + +18 + += +� +j∈[a+1,s+b] +|Sa ∩ Sj| − +� +j∈[a+1,s+b−1] +|Sa ∩ Sj| += +|Sa ∩ Ss+b| += +|Sa ∩ Sb|. +We thus conclude that c1 − c2 − c3 + c4 = |Sa ∩ Sb|. +B +Proof of Lemma 4.1 +Let us first consider a variant of the set disjointness problem. +Weighted Set Intersection Size. We have s ≥ 2 sets S1, S2, ..., Ss. Each Si (i ∈ [1, s]) is +associated with a function weightSi which assigns to each element e ∈ Si a value weightSi(e). +Given distinct set ids a, b ∈ [1, s], a query returns +size(Sa, Sb) = +� +e∈Sa∩Sb +weightSa(e) · weightSb(e). +(7) +Let N = �s +i=1 |Si|. For any λ ∈ [1, +√ +N], it is straightforward to build a structure of O(N 2/λ2) +space answering a query in O(λ) time. Call Si (i ∈ [1, s]) a large set if |Si| > λ, or a small set +otherwise. The number of large sets is at most N/λ. For each pair (i, j) ∈ [1, s] × [1, s], i ̸= j, +such that Si and Sj are both large, we store size(Si, Sj); the space needed is O(N 2/λ2). Given a +query with parameters a and b, return size(Sa, Sb) directly if Sa and Sb are both large. Otherwise, +assume, w.l.o.g., that Sa is small. We compute Sa ∩ Sb in O(λ) time using a hash table (for each +e ∈ Sa, check if e ∈ Sb). The result size(Sa, Sb) can then be obtained easily. +Equipped with the above, next we describe a structure for the colored range wedge counting +problem to prove Lemma 4.1. +Structure. First obtain a canonical collection C of V (defined in Section 4) satisfying � +U∈C |U| = +˜O(n). For each U ∈ C — recall that U is a subset of V — construct a weighted set as follows: +• SU = the set of black vertices adjacent to at least one vertex in U; +• for each b ∈ SU, weightSU(b) = the number of vertices in U adjacent to b. +These weighted sets constitute an instance of the weighted set intersection size problem. Build a +structure described earlier on the instance using the given parameter λ. The lemma below implies +that the structure occupies ˜O(m2/λ2) space. +Lemma B.1. � +U∈C |SU| = ˜O(m). +Proof. Each b ∈ SU is adjacent to a vertex u ∈ U. Pay a dollar to the edge {b, u} for each such +pair (b, u). Since an edge can receive a dollar only if it has a vertex in U, it can receive up to two +dollars12. |SU| is no more than the number of dollars paid. Do the above for all U ∈ C. Each edge +in G can receive ˜O(1) dollars in total because every vertex appears in ˜O(1) subsets in C (Property +P4-1 of C; see Section 4). +12Two is possible: this happens when b and u are both black and both appear in U. +19 + +For any distinct U, U ′ ∈ C, define size(SU, SU′) as in (7). On the other hand, for each U ∈ C, +define +size(SU, SU) += +� +b∈SU +�weightSU (b) +2 +� +. +We store the value size(SU, SU) for all U. The total space is ˜O(m2/λ2). +Before proceeding, the reader should note the following subtle fact about the function size(., .): +Fact B-1: size(SU, SU′) is the number of occurrences wedge(u, v, w) in G such that u ∈ SU, +w ∈ SU′, and v is black. +The fact holds even if U = U ′. +Query. Given a query with interval q, in ˜O(1) time we can pick h = ˜O(1) members U1, ..., Uh from +C that form a partition of Vq (Property P4-2 of C). The query returns +� +i,j∈[1,h]:i≤j +size(SUi, SUj). +(8) +Each size(SUi, SUj) is either explicitly stored or can be obtained from the weighted set intersection +size structure in O(λ) time. The overall query time is therefore ˜O(λ). +Fact B-1 and U1, ..., Uh forming a partition of Vq assure us that (8) counts only occurrences +wedge(u, v, w) in G such that Au ∈ q, Aw ∈ q, and v is black. +To complete the correctness +argument, we still need to show that (8) counts every such occurrence exactly once. Indeed, there +exist unique a, b ∈ [1, h] such that a ≤ b, u ∈ Ua, and w ∈ Ub. The wedge is counted only by the +term in (8) with i = a and j = b. +C +Proof of Lemma 5.2 +Let us first review H¨older’s Inequality. Fix some positive integers α and β. Let +• xi,j, for each i ∈ [1, α] and j ∈ [1, β], be non-negative real numbers; +• yj, for each j ∈ [1, β], be non-negative real numbers satisfying �β +j=1 yj ≥ 1. +Under the convention 00 = 0, H¨older’s inequality states that: +α +� +i=1 +β +� +j=1 +xyj +i,j ≤ +β +� +j=1 +� α +� +i=1 +xi,j +�yj +. +(9) +A proof can be found in [29]. +We now return to the context of Lemma 5.2. Given any j ∈ [1, d − 1] and (I1, I2, ..., Ij) ∈ +I1 × ...Ij, we will use B(I1, I2, ..., Ij) as a short-form for the d-dimensional box +B(I1, ..., Ij, dom(Xj+1), ..., dom(Xd)). +As a special case, define B(∅) = B(dom(X1), ..., dom(Xd)). +20 + +Lemma C.1. For any j ∈ [1, d], we have +� +Ij∈Ij +� +e∈E +|Re ⋉ B(I1, ..., Ij)|W (e) ≤ +� +e∈E +|Re ⋉ B(I1, ..., Ij−1)|W (e). +Proof. Define +Ej = {e ∈ E | Xj ∈ e}. +Since � +e∈Ej W(e) ≥ 1 (W is a fractional edge covering), from H¨older’s inequality (9) we have +� +Ij∈Ij +� +e∈Ej +|Re ⋉ B(I1, ..., Ij)|W (e) +≤ +� +e∈Ej +� � +Ij∈Ij +|Re ⋉ B(I1, ..., Ij)| +�W (e) +≤ +� +e∈Ej +���Re ⋉ B +� +I1, ..., Ij−1, dom(Xj) +���� +W (e) += +� +e∈Ej +|Re ⋉ B(I1, ..., Ij−1)|W (e) +(10) +where the second inequality used the fact that Ij is a set of disjoint intervals in dom(Xj). +For each e ∈ E \ Ej, Re ⋉ B(I1, ..., Ij) does not depend on Ij and can be rewritten as Re ⋉ +B(I1, ..., Ij−1). We can thus derive: +� +Ij∈Ij +� +e∈E +|Re ⋉ B(I1, ..., Ij)|W (e) += +� +Ij∈Ij +� � +e∈E\Ej +|Re ⋉ B(I1, ..., Ij)|W (e) · +� +e∈Ej +|Re ⋉ B(I1, ..., Ij)|W (e)� += +� +e∈E\Ej +|Re ⋉ B(I1, ..., Ij)|W (e) · +� +Ij∈Ij +� +e∈Ej +|Re ⋉ B(I1, ..., Ij)|W (e) +≤ +� +e∈E\Ej +|Re ⋉ B(I1, ..., Ij−1)|W (e) · +� +e∈Ej +|Re ⋉ B(I1, ..., Ij−1)|W (e) += +� +e∈E +|Re ⋉ B(I1, ..., Ij−1)|W (e). +where the inequality used (10). +21 + +We can prove Lemma 5.2 with d applications of Lemma C.1: +� +I1∈I1 +... +� +Id∈Id +� +e∈E +|Re ⋉ B(I1, ..., Id)|W (e) +≤ +� +I1∈I1 +... +� +Id−1∈Id−1 +� +e∈E +|Re ⋉ B(I1, ..., Id−1)|W (e) +≤ +� +I1∈I1 +... +� +Id−2∈Id−2 +� +e∈E +|Re ⋉ B(I1, ..., Id−2)|W (e) +≤ +... +≤ +� +I1∈I1 +� +e∈E +|Re ⋉ B(I1)|W (e) +≤ +� +e∈E +|Re|W (e). +D +Proof of Theorem 1.5 +The reader should read this proof after having finished Section 5. The basic idea is to convert +Problem 2 to range join. Let X (resp. E) be the set of vertices (resp. edges) in the pattern graph +Q. The reader should not confuse X and E with V and E: the latter two are defined on the data +graph G. For each edge e ∈ E, construct a relation Re with two attributes by inserting, for each +edge {u, v} in G, two tuples (u, v) and (v, u). This defines a join instance R = {Re | e ∈ E} with +input size N = 2m · |E| = O(m). +Every occurrence of Q corresponds to a constant number of tuples in join(R). Motivated by +this, given a Problem-2 query with interval q, we issue a range join query on R with q, which +guarantees retrieving all the occurrences. The issue, however, is that not every tuple in join(R) +gives rise to an occurrence. To see this, consider Q = 4-cycle and, hence, R has four relations with +schemes (X1, X2), (X2, X3), (X3, X4), and (X4, X1), respectively. Let {u, v} be an arbitrary edge +in E; tuples (u, v), (v, u), (u, v), and (v, u) exist in the four relations, respectively. Thus, join(R) +contains a tuple (u, v, u, v) that does not correspond to any occurrence. +The issue can be eliminated by slightly modifying the structure of [20], which we review next. +Consider an arbitrary set R of relations (with any number of attributes) defined in Section 5. Deep +and Koutris [20] proved the existence of a set B of boxes such that: +• each box has the form B(I1, ..., Id) where Ii is an interval in dom(Xi) for i ∈ [1, d]; +• the boxes are disjoint and their union is B(dom(X1), dom(X2), ...,dom(Xd)); +• for each box B(I1, ..., Id), the join instance RI1,...,Id has a non-empty result; +• each box B(I1, ..., Id) satisfies AGM(I1, ..., Id) ≤ ∆; +• |B| = O(N ρ∗/∆). +The structure of [20] simply stores B itself and uses O(N ρ∗/∆) space13. To enumerate join(R), the +algorithm of [20] looks at each B(I1, ..., Id) ∈ B and applies a worst-case optimal join algorithm +[39,40,48] to compute join(RI1,...,Id) in ˜O(AGM(I1, ..., Id)) = ˜O(∆) time. This guarantees a delay +of ˜O(∆). +13Obviously, the relations of R also need to be stored separately. +22 + +We now adapt the structure to list all the occurrences of Q in G (fixing q = (−∞, ∞)). Construct +R from G and Q as before. Apply [20] to find a set B with all the properties explained earlier. +Then, inspect each box B(I1, ..., Id) ∈ B in turn and remove it from B if all the occurrences of Q +producible from join(RI1,...,Id) can already be produced from the boxes inspected earlier. The size +of B can only decrease and therefore is still bounded by O(N ρ∗/∆). To find the occurrences, apply +a worst-case optimal join algorithm on each box in B. As each box generates at least one new +occurrence, we guarantee a delay of ˜O(∆). +To support (Problem-2) queries with arbitrary q, use the adapted structure to replace that +of [20] in the solution presented in Section 5.2. +All the analysis still holds through. +We thus +complete the proof of Theorem 1.5. +References +[1] Josh Alman and Virginia Vassilevska Williams. +A refined laser method and faster matrix +multiplication. In Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms +(SODA), pages 522–539, 2021. +[2] Noga Alon, Raphael Yuster, and Uri Zwick. Color-coding. +Journal of the ACM (JACM), +42(4):844–856, 1995. +[3] Noga Alon, Raphael Yuster, and Uri Zwick. Finding and counting given length cycles. Algo- +rithmica, 17(3):209–223, 1997. +[4] Albert Atserias, Martin Grohe, and Daniel Marx. Size bounds and query plans for relational +joins. SIAM Journal on Computing, 42(4):1737–1767, 2013. +[5] Guillaume Bagan, Arnaud Durand, and Etienne Grandjean. On acyclic conjunctive queries +and constant delay enumeration. In Computer Science Logic, pages 208–222, 2007. +[6] Michael J Bannister, Christopher DuBois, David Eppstein, and Padhraic Smyth. Windows +into relational events: Data structures for contiguous subsequences of edges. In Proceedings of +the Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 856–864, 2013. +[7] Jon Louis Bentley. Decomposable searching problems. Information Processing Letters (IPL), +8(5):244–251, 1979. +[8] Suman K. Bera, Noujan Pashanasangi, and C. Seshadhri. Near-linear time homomorphism +counting in bounded degeneracy graphs: The barrier of long induced cycles. In Proceedings of +the Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 2315–2332, 2021. +[9] Christoph Berkholz, Jens Keppeler, and Nicole Schweikardt. Answering conjunctive queries +under updates. In Proceedings of ACM Symposium on Principles of Database Systems (PODS), +pages 303–318, 2017. +[10] Andreas Bjorklund, Petteri Kaski, and Lukasz Kowalik. Counting thin subgraphs via packings +faster than meet-in-the-middle time. ACM Transactions on Algorithms, 13(4):48:1–48:26, 2017. +[11] Andreas Bjorklund, Rasmus Pagh, Virginia Vassilevska Williams, and Uri Zwick. Listing tri- +angles. In Proceedings of International Colloquium on Automata, Languages and Programming +(ICALP), pages 223–234, 2014. +23 + +[12] Nofar Carmeli and Markus Kroll. On the enumeration complexity of unions of conjunctive +queries. ACM Transactions on Database Systems (TODS), 46(2):5:1–5:41, 2021. +[13] Nofar Carmeli, Shai Zeevi, Christoph Berkholz, Benny Kimelfeld, and Nicole Schweikardt. +Answering (unions of) conjunctive queries using random access and random-order enumeration. +In Proceedings of ACM Symposium on Principles of Database Systems (PODS), pages 393–409, +2020. +[14] Farah Chanchary and Anil Maheshwari. Time windowed data structures for graphs. J. Graph +Algorithms Appl., 23(2):191–226, 2019. +[15] Farah Chanchary, Anil Maheshwari, and Michiel Smid. Querying relational event graphs using +colored range searching data structures. Discrete Applied Mathematics, 286:51–61, 2020. +[16] Bernard Chazelle. A functional approach to data structures and its use in multidimensional +searching. SIAM Journal of Computing, 17(3):427–462, 1988. +[17] N. Chiba and T. Nishizeki. Arboricity and subgraph listing algorithms. SIAM Journal of +Computing, 14(1):210–223, 1985. +[18] Radu Curticapean, Holger Dell, and D´aniel Marx. Homomorphisms are a good basis for count- +ing small subgraphs. In Proceedings of ACM Symposium on Theory of Computing (STOC), +pages 210–223, 2017. +[19] Mark de Berg, Otfried Cheong, Marc van Kreveld, and Mark Overmars. Computational Ge- +ometry: Algorithms and Applications. Springer-Verlag, 3rd edition, 2008. +[20] Shaleen Deep and Paraschos Koutris. Compressed representations of conjunctive query results. +In Proceedings of ACM Symposium on Principles of Database Systems (PODS), pages 307–322, +2018. +[21] Arnaud Durand. Fine-grained complexity analysis of queries: From decision to counting and +enumeration. In Proceedings of ACM Symposium on Principles of Database Systems (PODS), +pages 331–346, 2020. +[22] Arnaud Durand and Etienne Grandjean. First-order queries on structures of bounded degree +are computable with constant delay. ACM Trans. Comput. Log., 8(4):21, 2007. +[23] Arnaud Durand, Nicole Schweikardt, and Luc Segoufin. Enumerating answers to first-order +queries over databases of low degree. In Proceedings of ACM Symposium on Principles of +Database Systems (PODS), pages 121–131, 2014. +[24] David Eppstein. Arboricity and bipartite subgraph listing algorithms. Information Processing +Letters (IPL), 51(4):207–211, 1994. +[25] David Eppstein. Subgraph isomorphism in planar graphs and related problems. J. Graph +Algorithms Appl., 3(3):1–27, 1999. +[26] David Eppstein, Maarten Loffler, and Darren Strash. Listing all maximal cliques in sparse +graphs in near-optimal time. In International Symposium on Algorithms and Computation +(ISAAC), volume 6506, pages 403–414, 2010. +[27] Peter Floderus, Miroslaw Kowaluk, Andrzej Lingas, and Eva-Marta Lundell. Detecting and +counting small pattern graphs. SIAM J. Discret. Math., 29(3):1322–1339, 2015. +24 + +[28] Fedor V. Fomin, Daniel Lokshtanov, Venkatesh Raman, Saket Saurabh, and B. V. Raghavendra +Rao. Faster algorithms for finding and counting subgraphs. Journal of Computer and System +Sciences (JCSS), 78(3):698–706, 2012. +[29] Ehud Friedgut. Hypergraphs, entropy, and inequalities. Am. Math. Mon., 111(9):749–760, +2004. +[30] Pierre-Louis Giscard, Nils M. Kriege, and Richard C. Wilson. A general purpose algorithm for +counting simple cycles and simple paths of any length. Algorithmica, 81(7):2716–2737, 2019. +[31] Isaac Goldstein, Tsvi Kopelowitz, Moshe Lewenstein, and Ely Porat. Conditional lower bounds +for space/time tradeoffs. In Algorithms and Data Structures Workshop (WADS), pages 421– +436. Springer, 2017. +[32] Isaac Goldstein, Moshe Lewenstein, and Ely Porat. On the hardness of set disjointness and +set intersection with bounded universe. In International Symposium on Algorithms and Com- +putation (ISAAC), pages 7:1–7:22, 2019. +[33] Chinh T. Hoang, Marcin Kaminski, Joe Sawada, and R. Sritharan. Finding and listing induced +paths and cycles. Discrete Applied Mathematics, 161(4-5):633–641, 2013. +[34] Ahmet Kara, Milos Nikolic, Dan Olteanu, and Haozhe Zhang. Trade-offs in static and dynamic +evaluation of hierarchical queries. In Proceedings of ACM Symposium on Principles of Database +Systems (PODS), pages 375–392, 2020. +[35] Wojciech Kazana and Luc Segoufin. Enumeration of first-order queries on classes of structures +with bounded expansion. In Proceedings of ACM Symposium on Principles of Database Systems +(PODS), pages 297–308, 2013. +[36] Mahmoud Abo Khamis, Hung Q. Ngo, Christopher R´e, and Atri Rudra. Joins via geometric +resolutions: Worst-case and beyond. +In Proceedings of ACM Symposium on Principles of +Database Systems (PODS), pages 213–228, 2015. +[37] Ton Kloks, Dieter Kratsch, and Haiko M¨uller. Finding and counting small induced subgraphs +efficiently. Information Processing Letters (IPL), 74(3-4):115–121, 2000. +[38] Jaroslav Nesetril and Svatopluk Poljak. On the complexity of the subgraph problem. Com- +mentationes Mathematicae Universitatis Carolinae, 26(2):415–419, 1985. +[39] Hung Q. Ngo, Ely Porat, Christopher Re, and Atri Rudra. Worst-case optimal join algorithms. +Journal of the ACM (JACM), 65(3):16:1–16:40, 2018. +[40] Hung Q. Ngo, Christopher Re, and Atri Rudra. Skew strikes back: new developments in the +theory of join algorithms. SIGMOD Rec., 42(4):5–16, 2013. +[41] Dan Olteanu and Jakub Zavodny. Size bounds for factorised representations of query results. +ACM Transactions on Database Systems (TODS), 40(1):2:1–2:44, 2015. +[42] Saladi Rahul. Improved bounds for orthogonal point enclosure query and point location in or- +thogonal subdivisions in R3. In Proceedings of the Annual ACM-SIAM Symposium on Discrete +Algorithms (SODA), pages 200–211, 2015. +25 + +[43] Nicole Schweikardt, Luc Segoufin, and Alexandre Vigny. Enumeration for FO queries over +nowhere dense graphs. In Proceedings of ACM Symposium on Principles of Database Systems +(PODS), pages 151–163, 2018. +[44] Luc Segoufin. Constant delay enumeration for conjunctive queries. SIGMOD Rec., 44(1):10–17, +2015. +[45] Luc Segoufin and Alexandre Vigny. Constant delay enumeration for FO queries over databases +with local bounded expansion. In Proceedings of International Conference on Database Theory +(ICDT), volume 68, pages 20:1–20:16, 2017. +[46] Yufei Tao. Algorithmic techniques for independent query sampling. In Proceedings of ACM +Symposium on Principles of Database Systems (PODS), 2022. +[47] Yufei Tao and Ke Yi. Intersection joins under updates. Journal of Computer and System +Sciences (JCSS), 124:41–64, 2022. +[48] Todd L. Veldhuizen. Triejoin: A simple, worst-case optimal join algorithm. In Proceedings of +International Conference on Database Theory (ICDT), pages 96–106, 2014. +[49] Duncan J. Watts and Steven H. Strogatz. +Collective dynamics of ‘small-world’ networks. +Nature, 393:440–442, 1998. +[50] Virginia Vassilevska Williams and Ryan Williams. Finding, minimizing, and counting weighted +subgraphs. SIAM Journal of Computing, 42(3):831–854, 2013. +26 + diff --git a/UNE1T4oBgHgl3EQfugXX/content/tmp_files/load_file.txt b/UNE1T4oBgHgl3EQfugXX/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..6262460eddd3d27c0c314a33596e1d5c7512107f --- /dev/null +++ b/UNE1T4oBgHgl3EQfugXX/content/tmp_files/load_file.txt @@ -0,0 +1,1274 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf,len=1273 +page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='03390v1 [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='DS] 9 Jan 2023 Space-Query Tradeoffs in Range Subgraph Counting and Listing Shiyuan Deng, Shangqi Lu, Yufei Tao Department of Computer Science and Engineering Chinese University of Hong Kong Hong Kong, China {sydeng,sqlu,taoyf}@cse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='cuhk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='hk January 10, 2023 Abstract This paper initializes the study of range subgraph counting and range subgraph listing, both of which are motivated by the significant demands in practice to perform graph analytics on subgraphs pertinent to only selected, as opposed to all, vertices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' In the first problem, there is an undirected graph G where each vertex carries a real-valued attribute.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Given an interval q and a pattern Q, a query counts the number of occurrences of Q in the subgraph of G induced by the vertices whose attributes fall in q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The second problem has the same setup except that a query needs to enumerate (rather than count) those occurrences with a small delay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' In both problems, our goal is to understand the tradeoff between space usage and query cost, or more specifically: (i) given a target on query efficiency, how much pre-computed information about G must we store?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' (ii) Or conversely, given a budget on space usage, what is the best query time we can hope for?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We establish a suite of upper- and lower-bound results on such tradeoffs for various query patterns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' This research was supported in part by GRF Projects 14207820, 14203421, and 14222822 from HKRGC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' 1 1 Introduction Consider G = (V, E) as a data graph and Q as a pattern graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' A subgraph of G, if isomorphic to Q, is said to be an occurrence of Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The goal of pattern searching is to either list the occurrences of Q or to count the number of them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Both are fundamental problems in computer science and have attracted considerable attention in the past few decades.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' This paper studies pattern searching in vertex-induced subgraphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Here, a query selects a subset U ⊆ V of vertices and needs to count/list the occurrences of Q in G′, where G′ is the subgraph of G induced by U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Note that if an occurrence uses any vertex outside U, the occurrence should not be counted/listed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Trivially, one can answer the query by first generating G′ and then counting/listing Q in G′ “from scratch”, but this does not leverage the power of preprocessing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Instead, our goal is to store G in a data structure that can answer all queries with non-trivial guarantees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' It is intriguing to investigate how much we can minimize the query time subject to a space budget, and conversely, how much space we must consume to achieve a target query time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Vertex selection in database systems is done with a predicate q, which determines U as {v ∈ V | v satisfies q}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Concentrating on range predicates, the problems we consider are: Problem 1 (Range Subgraph Counting).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' G = (V, E) is an undirected graph where each vertex v ∈ V carries a real-valued attribute Av.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' For an interval q = [x1, x2], define Vq = {v ∈ V | x1 ≤ Av ≤ x2} and Gq as the subgraph of G induced by Vq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Let Q be a connected (only one connected component) pattern graph with O(1) vertices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Given an interval q, a query returns the number of occurrences of Q in Gq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The pattern Q is fixed for all queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Problem 2 (Range Subgraph Listing).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Same setup except that a query reports the occurrences of Q in Gq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Universal Notations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Several notations will apply throughout the paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Set n = |V | and m = |E|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Symbol ω < 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='37286 [1] represents the matrix multiplication exponent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The notations ˜O(.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=') and ˜Ω(.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=') hide a factor polylogarithmic to the underlying problem’s parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='1 Motivation Practical Applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Subgraph patterns are important for understanding the characteristics of a data graph G, as has been documented in a long string of papers, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', [2, 3, 8, 10, 11, 17, 18, 24–28,30,33,36–38,50].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' In practice, analysts are interested in not only patterns from the whole G but also those pertinent only to selected vertices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Consider a social network G where each vertex represents an individual.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' A graph’s clustering coefficient [49], a popular measurement in network science, is the ratio between the number of triangles (3-cliques1) and the number of wedges (2- paths2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The coefficient of G, however, is just a single value revealing little about the features of specific demographic groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' It is more informative to, for example, compare the coefficients of (i) the subgraph of G induced by people with ages ∈ [20, 30], and (ii) that induced by age ∈ [60, 70].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' A step further, by putting together the coefficients induced by “age ∈ [i · 10, (i + 1) · 10]” for each i ∈ [1, 10], one obtains an interesting comparison across different age groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Refined analysis can then concentrate on the pattern occurrences of a target group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The power of the above analysis owes 1An ℓ-clique is a clique with ℓ vertices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' 2An ℓ-path is a path with ℓ edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' 2 Problem Pattern Q Space Query Remark 1 (cnt) any fixed Q O(n2) ˜O(1) near optimal† 1 wedge ˜O(m2/λ2) ˜O(λ) for any λ ∈ [1, √m], near optimal† 1 (lower wedge ˜O(m2−δ/λ2) ˜O(λ) for λ ∈ [1, √m] and any δ > 0, bound) impossible subj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' to strong set disjointness conj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' 1 ℓ-clique O(m) ˜O(1) 2 (rep) any fixed Q ˜O(m + mρ∗/∆) delay ˜O(∆) for any ∆ ≥ 1, ρ∗ = frac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' edge covering num.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' of Q 2 triangle O(m) delay ˜O(1 + (m∗) ω−1 ω+1 ) m∗ = num.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' of edges in at least one triangle in Gq 2 ℓ-star O(m) delay ˜O(1) near optimal 2 2ℓ-cycle ˜O(#Pℓ) delay ˜O(1) #Pℓ = num.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' of ℓ-paths in G Remark: “near optimal” means no polynomial improvement (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', nδ for arbitrary small constant δ > 0) possbile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The near optimality marked with † is subject to the strong set disjointness conjecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Table 1: A summary of our results to queries of Problem 1 and 2 with arbitrary selection ranges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Designing effective data structures is essential to avoid lengthy response time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Importance of Space-Query Tradeoffs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' One should not confuse the space-query tradeoff with the tradeoff between preprocessing time and query cost, as has been extensively studied on join algorithms [5, 12, 20–23, 35, 41–43, 45].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Both tradeoffs are important, but they matter in different ways.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Unlike preprocessing time, which is “one-time cost” (because a structure, once built, can be used forever), the space consumption is permanent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' In other words, the space-query tradeoff has a (much) more durable effect on the underlying database system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' However, in spite of their importance, the space-query tradeoffs on joins have received surprisingly little attention: we are aware of only a single paper [20], which, as will be discussed in Section 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='3, does not consider query predicates (or equivalently, only one query, which always outputs the entire join, exists) and concerns only reporting (but not counting).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Our work can be thought of as a step in the same direction as [20] because, as explained in Section 5, subgraph searching can be cast as a join problem (in fact, some of our results are explicitly about joins), and actually the first step on predicate-driven queries and counting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Finally, it is worth mentioning that a useful structure, no matter how little space it occupies, must be constructible in polynomial time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' This is true for all the structures developed in our paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' In fact, each of our structures can be built with at most the time needed to find all the occurrences of the query pattern Q, ignoring polylog factors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='2 Our Contributions Table 1 summarizes the main results of this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Next, we will explain the results in detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='1 Problem 1 Wedges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We will show: Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Consider Problem 1 with Q = wedge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' For any real value λ ∈ [1, √m], there is a structure of ˜O(m2/λ2) space that answers a query in ˜O(λ) time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' 3 The space-query tradeoff may look disappointing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' After all, wedge counting is easy in one-off computation: we can count the number of wedges in G using O(n + m) time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' It is natural to wonder whether the space in Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='1 is necessary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We answer the question by showing that any substantial improvement to Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='1 will yield a major breakthrough on set disjointness: Set Disjointness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The data is a collection of s ≥ 2 sets S1, S2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Ss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Given distinct set ids a, b ∈ [1, s], a query returns whether Sa ∩ Sb is empty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Let N = �s i=1 |Si| be the input size of set disjointness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Given any λ ∈ [1, √ N], there is a simple structure of O(N 2/λ2) space with O(λ) query time (see Appendix B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Improving the tradeoff by a polynomial factor even for one arbitrary λ has been a long-standing open problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The strong set disjointness conjecture [31,32] states that a structure with query time λ must use ˜Ω(N 2/λ2) space for any λ ≥ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We will prove: Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Consider Problem 1 with Q = wedge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Fix any λ ∈ [1, √m] and any constant δ > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Suppose that we can obtain a structure of ˜O(m2−δ/λ2) space answering a query in ˜O(λ) time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Then, for any set disjointness input of size N, we can obtain a structure of ˜O(N 2−δ/λ2) space answering a query in ˜O(λ) time (thus breaking the strong set disjointness conjecture).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Cliques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We will show: Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' For Problem 1 with Q = ℓ-clique, there is a structure of O(m) space answering a query in ˜O(1) time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Counting triangles (ℓ = 3) appears harder than counting wedges: in one-off computation, the fastest known algorithm for the former takes O(m 2ω ω+1) time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' It is thus surprising to see Q = triangle easier than Q = wedge in Problem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' From Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='1 and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='3, one sees that the problem of calculating the clustering coefficient (see Section 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='1) of Gq for any q boils down to counting the wedges in Gq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Effectively, this implies optimal settlement of that problem (subject to the strong set disjointness conjecture), which bears practical significance due to the popularity of clustering coefficients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Arbitrary Subgraphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We will show: Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' For any Q, there is a structure for Problem 1 that uses O(n2) space and answers a query in ˜O(1) time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The above result is difficult to improve: reducing the space by an nδ factor for any constant δ > 0 breaks the strong set disjointness conjecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' To explain, assume n = O(m).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='3 If there was a structure of O(n2−δ) = O(m2−δ) space and ˜O(1) query time, applying the structure to Q = wedge would yield a breakthrough on set disjointness by way of Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The reader should note that the hardness comes from producing a guarantee on all Q;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' it is possible to do better for special patterns (Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The hardness thus endows Q = wedge with unique significance in Problem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='4 further implies that Problem 1 under Q = wedge is the hardest when G is the sparsest: m = o(n1+ǫ) for any constant ǫ > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' To see why, set m = n1+ǫ, which gives n2 = m 2 1+ǫ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Since 2 1+ǫ = 2 − 2ǫ 1+ǫ, Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='4 yields a structure of O(m2−δ) space and ˜O(1) query time with δ = 2ǫ 1+ǫ, improving Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='1 by a polynomial factor at λ = ˜O(1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' 3Discard “isolated” vertices with no incident edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' 4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='2 Problem 2 A listing query ensures a delay ∆ if it reports a new occurrence of Q or declares “no more occur- rences” within ∆ time after the previous occurrence4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Arbitrary Subgraphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We will show: Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' For any Q and ∆ ≥ 1, there is a structure for Problem 2 that uses ˜O(m + mρ∗/∆) space and has a query delay of ˜O(∆), where ρ∗ is the fractional edge covering number of Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Imagine assigning each edge of Q a non-negative weight such that (i) for each vertex of Q, all its incident edges receive a combined weight at least 1 and (ii) the total weight of all edges is minimized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The fractional edge covering number ρ∗ of Q is the total weight of an optimal assignment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The maximum number of occurrences of Q in G is O(mρ∗) [4] and the bound is tight in the worst case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Our structure actually settles a problem on natural joins: Range Join.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Let R be a set of O(1) relations each with O(1) real-valued attributes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Denote by join(R) the natural join result on the relations in R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Given an interval q = [x1, x2], a query reports all the tuples t ∈ join(R) such that every attribute of t falls in q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Let N be the total number of tuples in the relations of R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' For any ∆ ≥ 1, we give a structure of ˜O(N + N ρ∗/∆) space answering a query with an ˜O(∆) delay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Here, the fractional edge covering number ρ∗ is with respect to the join’s hypergraph (details deferred to Section 5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The challenge behind Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='5 is to design a structure that works for all Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' It is possible to do better for specific Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Next, we present three examples that are not only important subproblems themselves but also illustrate different techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Triangles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We will show: Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' For Problem 2 with Q = triangle, there is a structure of O(m) space answering a query with an ˜O(1 + (m∗) ω−1 ω+1) delay, where m∗ is the number of edges appearing in at least one reported triangle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The fractional edge covering number ρ∗ is 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='5 for Q = triangle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' To ensure ˜O(m) space, Theo- rem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='5 needs to set ∆ = √m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' As ω−1 ω+1 < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='408, Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='6 achieves a polynomial improvement in delay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The reader should note that the value m∗ in Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='6 never exceeds m but can be much less (this happens when there are few triangles to list).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Problem 2 with Q = triangle and q fixed to (−∞, ∞) was used as a motivating problem in the previous work of [20], which described a structure of O(m) space with a delay ˜O(√m) and is thus strictly improved by Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' ℓ-Stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' An ℓ-star is a tree with ℓ leaves and one non-leaf vertex (a wedge is a 2-star).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We will show: Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' For Problem 2 where Q = ℓ-star, there is a structure of O(m) space answering a query with an ˜O(1) delay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' As a corollary, for any interval q, O(m) space suffices to detect the presence of an ℓ-star in Gq using ˜O(1) time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' For Q = wedge, this means that the hardness manifested by Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='2 is indeed due to counting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' 2ℓ-Cycles5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We will show: 4The reader may assume that a dummy occurrence is always output at the beginning of a query algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' 5A cycle with 2ℓ vertices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' 5 Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' For Problem 2 with Q = 2ℓ-cycle where ℓ ≥ 2, there is a structure of ˜O(#Pℓ) space answering a query with an ˜O(1) delay, where #Pℓ is the number of ℓ-paths in G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The fractional edge covering number ρ∗ is ℓ for a 2ℓ-cycle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='5 needs ˜O(mℓ) space to achieve an ˜O(1) delay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The space in Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='8 is significantly better.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' For ℓ = 2 (Q = 4- cycle), the space is ˜O(nm) which is the maximum number of wedges in G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' For ℓ > 2, the space is ˜O(m⌈(ℓ+1)/2⌉) which is the maximum number of ℓ-paths in G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='3 Related Work The preceding sections have covered the most relevant existing results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We will now proceed to discuss other related work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Pattern searching has been extensively studied in one-off computation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We refer the reader to [3,8,10,17,18,27,28,30,37,50] and [2,11,17,24–26,33,36,38,39], as well as the references therein, for algorithms on counting and listing, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Those algorithms can be applied in Problem 1 and 2 after Gq has been generated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Our focus in this work is to avoid a full generation of Gq because doing so can take Ω(m) time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' In the other extreme, one can precompute the set S of occurrences of Q in G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The size of S is O(mρ∗) (AGM bound), assuming that Q has a constant size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' By resorting to standard computational geometry techniques [19], we can store S in structures of ˜O(mρ∗) space to answer a query of Problem 1 in ˜O(1) time and a query of Problem 2 with an ˜O(1) delay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' For Problem 1, Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='4 achieves a better space bound on every Q with ρ∗ ≥ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' When ρ∗ < 2, Q has at most three vertices: a 1-path (single edge), a wedge, or a triangle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We have resolved the wedge and triangle cases (Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='1 and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='3), while Problem 1 is trivial for Q = 1-path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' For Problem 2, Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='5 captures the above extreme idea as a special case with ∆ = ˜O(1) and offers a tunable space-query tradeoff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' A relational event graph, introduced by Bannister et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' [6], is a graph G = (V, E) where every edge e ∈ E carries a real-valued timestamp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' For an interval q = [x1, x2], let Gedge q be the subgraph of G induced by all the edges whose timestamps are covered by q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' A pattern searching query counts/lists the occurrences of a pattern Q in Gedge q .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' See [6, 14, 15] for several data structures designed for such queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Similar as it sounds, pattern searching on a relational event graph is drastically different from Problem 1 and 2 such that there is little overlap — in neither results nor techniques — between our solutions and those in [6,14,15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Delay minimization is an important topic in the literature of joins and conjunctive queries;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' see [5,9,12,13,20–23,34,35,41,43–45] and their references.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Regarding our problems, we are not aware of previous work giving a result better than what has already been mentioned.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Our formulation of range join listing (Section 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='2) suggests that the presence of query predicates can pose new challenges on joins (also conjunctive queries) from the indexing’s perspective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Deep and Koutris [20] proved a result equivalent to Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='5 (up to an ˜O(1) factor) on Problem 2, but only in the special scenario where a query concerns the whole G, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', fixing the query range q to (−∞, ∞).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' 2 Preliminaries In this section, we will describe several technical tools to be deployed in our solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Structures for Multidimensional Points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We will utilize some well-known geometry data structures as introduced below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The reader does not need to be bothered with the details of these 6 structures because we will apply them as “black boxes”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Let P be a set of n points in d-dimensional space Rd where d is a constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Given a rectangle q of the form [x1, y1] × [x2, y2] × .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' × [xd, yd], a range reporting query enumerates the points in P ∩ q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We can create a range tree [7, 19] on P, which uses ˜O(n) space and permits us to answer such a query with an ˜O(1) delay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' When d = 2, we can replace the range tree with a Chazelle’s structure [16] which retains the aforementioned query performance but reduces the space consumption to O(n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We will also need range sum queries on P in the scenario where each point in P is 2D (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', d = 2) and carries a real-valued weight.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Given a rectangle q = [x1, y1] × [x2, y2], such a query reports the total weight of the points in P ∩ q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We can again build a Chazelle’s structure of [16] on P which occupies O(n) space and answers a query in ˜O(1) time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' From “Delays with Duplicates” to “Delays under Distinctness”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Let us consider a duplicate-removal scenario often encountered in designing algorithms with small delays.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Suppose that we have an algorithm A for enumerating a set S of elements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' With a delay of ∆, A can report an element e ∈ S, but cannot guarantee that e has never been reported before.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The good news, on the other hand, is that A can output the same element at most α times for some α ≥ 1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' By modifying a buffering technique in [47], we can convert A into an algorithm that enumerates only the distinct elements of S with a delay of O(α · ∆ log |S|).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Conceptually, divide the execution of A into epochs, each of which runs for α · ∆ time6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' As A runs, we use a buffer B to stash the set of distinct elements that have been found by A but not yet reported.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Every time A finds an element e ∈ S, we check whether e has ever existed in B (this takes O(log |S|) time, using a binary search tree maintained on all the elements that have ever been found so far).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' If so, e is ignored;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' otherwise, it is added to B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' At the end of each epoch, we output an arbitrary element from B and remove it from B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Finally, after A has terminated, we simply output the remaining elements in B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' B always contains at least one element at the end of each epoch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' To see why, consider the end of the t-th epoch for some t ≥ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' At this moment, A has been running for t · α · ∆ time and therefore must have reported t · α elements, which may not be distinct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' However, as each element can be reported at most α times, there must be at least t (distinct) ones among those t·α elements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Since we have reported only t − 1 elements in the preceding epochs, B must still have at least one element at the end of epoch t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' It is now straightforward to verify that the modified algorithm has a delay of O(α · ∆ log |S|) in enumerating the distinct elements of S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' 3 Problem 1: Matching Upper and Lower Bounds This section will establish the conditional lower bound in Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='2 and its matching upper bound in Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Our discussion on the upper bound will also establish Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Throughout the paper, we will assume that the vertices of G have distinct attribute values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The assumption loses no generality because one can break ties by vertex id.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='1 Lower Bound Suppose that Problem 1 under Q = wedge admits a structure that uses ˜O(m2−δ/λ2) space and answers a query in ˜O(λ) time for some λ ≥ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We will design a structure for set disjointness that uses ˜O(N 2−δ/λ2) space and answers a query in ˜O(λ) time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Recall that the data input to set disjointness consists of s ≥ 2 sets S1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Ss with a total size of N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Define U = �s i=1 Si.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' 6Recall that “time” in the RAM model is defined as the number of atomic operations (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', addition, multiplication, comparison, accessing a memory word, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=') executed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Each epoch is essentially a sequence of α · ∆ such operations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' 7 Create a graph G = (V, E) as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' V has 2s + |U| vertices, including 2s set vertices and |U| element vertices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Each set Si (i ∈ [1, s]) defines two set vertices, whose attribute values are set to i and s + i, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Each element in U defines an element vertex with the same attribute value s + 1/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Set E contains 2N edges: for each element e ∈ Si, add to E two edges each between the element vertex of e and a set vertex of Si.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Now, create a Problem-1 structure under Q = wedge on G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The structure occupies ˜O(N 2−δ/λ2) space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Consider a set disjointness query with set ids a and b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Assuming w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='l.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='o.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' a < b, we issue four Problem-1 wedge-counting queries on G with intervals q1 = [a, s + b], q2 = [a + 1, s + b], q3 = [a, s + b − 1], and q4 = [a + 1, s + b − 1], respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Let c1, c2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', c4 be the counts returned.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We declare Sa∩Sb non-empty if and only if c1−c2−c3+c4 > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The query time is ˜O(λ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Appendix A proves the algorithm’s correctness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' This completes the proof of Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='2 Upper Bound Next, we will attack Problem 1 by allowing Q to be an arbitrary pattern graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Consider any occurrence of Q in G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Let u (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' v) be the vertex in this occurrence with the smallest (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' largest) attribute.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We register the occurrence at the pair (u, v).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Denote by cu,v the number of occurrences registered at (u, v).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' For a query with q = [x1, x2], an occurrence registered at (u, v) appears in Gq (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', the subgraph of G induced by Vq) if and only if Au ≥ x1 and Av ≤ x2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We can therefore convert the problem to range sum on 2D points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' For each pair (u, v) ∈ V ×V , create a point (Au, Av) with weight cu,v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Let P be the set of points created;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' clearly, |P| = O(n2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The query result is simply the total weight of all the points in P covered by the rectangle [x1, ∞) × (−∞, x2] (a range sum operation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We can store P in a Chazelle’s structure (see Section 2) that occupies O(|P|) = O(n2) space and performs a range sum operation in ˜O(1) time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' This establishes Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Improvement for Cliques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The space of our structure can be lowered to O(m) when Q is a clique.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The crucial observation is that registering an occurrence at (u, v) implies {u, v} ∈ E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We add to P only the points (Au, Av) with a non-zero cu,v (points with zero weights do not affect a range sum operation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' This reduces the size of P to at most m and, hence, the space of the Chazelle’s structure to O(m).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We thus complete the proof of Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' 4 Problem 1: Wedges The section will explain how to achieve the guarantees in Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='1 for Problem 1 under Q = wedge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We will represent a wedge occurrence in G = (V, E) as wedge(u, v, w) where u, v, and w are vertices in V , and {u, v} and {v, w} are edges in E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Let us introduce a slightly different problem: Colored Range Wedge Counting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Define G = (V, E) and Av for each v ∈ V as in Problem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Each vertex in V is colored black or white.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Given an interval q, a query returns the number of occurrences wedge(u, v, w) such that Au ∈ q, Aw ∈ q, and v is black.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Note that no requirements exist on Av and the colors of u and w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Let C be a set of subsets of V .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We call C a canonical collection if (P4-1) each vertex of V appears in ˜O(1) subsets in C;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' 8 (P4-2) for any interval q, we can partition Vq (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', the set of vertices in V with attribute values in q) into ˜O(1) disjoint subsets, each being a member of C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The ids of these subsets can be obtained in ˜O(1) time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' It is rudimentary to find a canonical collection C satisfying � U∈C |U| = ˜O(n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='7 We will work with such a C henceforth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' In Appendix B, we prove: Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Consider the colored range wedge counting problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' For any real value λ ∈ [1, √m], there is a structure of ˜O(m2/λ2) space that answers a query in ˜O(λ) time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Equipped with the above, we now return to Problem 1 with Q = wedge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' For each U ∈ C (where U is a subset of V ), we create a graph GU by adding edges in three steps: 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Initialize GU as an empty graph with no vertices and edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' For every vertex u ∈ U, we add all its edges in G (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', the original data graph) to GU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The addition of an edge {u, v} creates vertex v in GU if v is not present in GU yet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Finally, color a vertex in GU black if it comes from U, or white otherwise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We now build a structure of Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='1 on GU, which uses ˜O(|EU|2/λ2) space where EU is the set of edges in GU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' By Property P4-1, each edge {u, v} of G can be added to the EU of ˜O(1) subsets U ∈ C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' It thus follows that � U∈C |EU| = ˜O(m).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The structures of all U ∈ C occupy ˜O(m2/λ2) space in total.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Query.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Consider now a (Problem-1) query with interval q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' By Property P4-2, in ˜O(1) time we can pick h = ˜O(1) members U1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Uh from C to partition Vq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' For each i ∈ [1, h], issue a colored range wedge counting query with interval q on GUi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We return the sum of the h queries’ outputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The overall query time is h · ˜O(λ) = ˜O(λ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' To verify correctness, first observe that every wedge(u, v, w) counted by the colored query on GUi satisfies: Au ∈ q, Aw ∈ q (definition of colored range wedge counting), and Av ∈ q (because v being black means v ∈ Ui ⊆ Vq).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Conversely, every occurrence wedge(u, v, w) satisfying {Au, Av, Aw} ⊆ q is counted only once: by the colored query on GUi where Ui is the only subset (among all i ∈ [1, h]) containing v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Indeed, for any Uj with j ̸= i, v is either absent in GUj or is white;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' in neither case can the wedge be counted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Correctness now follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' 5 Problem 2: Arbitrary Subgraphs We now proceed to tackle Problem 2 for an arbitrary query pattern Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We will, in fact, solve the range join problem defined in Section 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' As shown in Appendix D, it is relatively easy to convert our structure to prove Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' For a relation R ∈ R (recall that R is the set of input relations;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' see Section 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='2) its scheme, scheme(R), is the set of attributes in R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Let X = � R∈R scheme(R).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The input size N can now be 7It suffices to build a binary search tree T on the vertices’ attribute values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Each node in T defines a subset in C, which consists of every v ∈ V whose attribute Av is stored in the node’s subtree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' It is well known (see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', [46]) that, for any interval q, there exist O(log n) canonical nodes in T whose subtrees are disjoint and together contain all and only the attribute values in q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Those nodes can be found in O(log n) time and satisfy Property P4-2 with respect to Vq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' 9 expressed as � R∈R |R|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We will assume, w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='l.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='o.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', that (i) the relations in R have distinct schemes, (ii) N is a power of 2, and (iii) each attribute X ∈ X has a domain dom(X) comprising the integers in [1, N].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Given an interval q = [x1, x2], a query lists every tuple t in join(R) — the natural join result on R — satisfying t[X] ∈ q for all X ∈ X, where t[X] is the tuple’s value under attribute X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We want to design a structure of small space to answer such queries with a small delay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' It will be convenient to work with a hypergraph G = (X, E) where E = {scheme(R) | R ∈ R}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Given an edge e ∈ E, we use Re to denote the (only) relation R ∈ R whose scheme is e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' For a function W that assigns a non-negative weight W(e) to every e ∈ E, its lump-sum is � e∈E W(e).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The function W is a fractional edge covering if � e∈E:X∈e W(e) ≥ 1 holds on every attribute X ∈ X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The fractional edge covering number ρ∗ of G is the smallest lump-sum of all fractional edge coverings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Henceforth, we will use W to represent an optimal assignment function with lump-sum ρ∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The section’s main result is: Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' For the range join problem (see Section 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='2), given any ∆ ≥ 1, there is a structure of ˜O(N + N ρ∗/∆) space that answers a query with an ˜O(∆) delay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='1 A Generalization of the AGM Bound The classical AGM bound [4] states that |join(R)| ≤ � e∈E |Re|W (e).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Next, we will present a more general version of this inequality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Set d = |X| and impose an arbitrary ordering on the d attributes: X1, X2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Xd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Given intervals I1, I2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Id where Ii ⊆ dom(Xi) for each i ∈ [1, d], define B(I1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Id) as the d-dimensional box I1 × .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' × Id.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' For a relation R ∈ R, we use R ⋉ B(I1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Id) to represent the set of tuples t ∈ R such that t[Xi] ∈ Ii for every i satisfying Xi ∈ scheme(R).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We prove in Appendix C: Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Let Ii, i ∈ [1, d], be a set of disjoint intervals in dom(Xi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Then: � I1∈I1 � I2∈I2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' � Id∈Id � e∈E |Re ⋉ B(I1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Id)|W (e) ≤ � e∈E |Re|W (e).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' (1) To see how (1) captures the AGM bound, consider the special Ii with size |dom(Xi)|, namely, each interval in Ii is a value in dom(Xi) and vice versa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Thus, |Re ⋉ B(I1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Id)| is either 0 or 1 such that the left hand side of (1) is precisely |join(R)|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The real power of (1), however, comes from allowing Ii to be an arbitrary set of disjoint intervals, a feature crucial for us to prove Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' A remark is in order about why Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='2 is not trivial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' It would be if the term � e∈E |Re ⋉ B(I1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Id)|W (e) in (1) was replaced by the output size of the join on the relations in {Re ⋉ B(I1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Id) | e ∈ E}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' By the AGM bound, the term � e∈E |Re ⋉ B(I1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Id)|W (e) is an upper bound on the size of the join {Re⋉B(I1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Id) | e ∈ E}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The non-trivial goal is to show that the summation of all those upper bounds (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', the left hand side of (1)) still cannot exceed � e∈E |Re|W (e).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='2 Range Join This subsection serves as a proof of Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Given an ℓ ≥ 0, we call an interval a level-ℓ dyadic interval if it has the form [i · 2ℓ + 1, (i + 1) · 2ℓ] for some integer i ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Because N is a power of 2, for each ℓ ∈ [0, log2 N], we can partition [1, N] into N/2ℓ disjoint level-ℓ dyadic intervals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' 10 A dyadic combination is a sequence of d dyadic intervals (I1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Id);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' recall that d = |X|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The combination defines a (natural) join instance on the relations in {Re ⋉ B(I1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Id) | e ∈ E}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We will denote the instance as RI1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=',Id.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Define AGM(I1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Id) = � e∈E |Re ⋉ B(I1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Id)|W (e).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' (2) The AGM bound assures us that |join(RI1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=',Id)| ≤ AGM(I1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Id).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' A dyadic combination (I1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Id) with a non-empty join(RI1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=',Id) is said to be heavy if AGM(I1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Id) > ∆, or light otherwise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' For each heavy combination, we build a structure of [20] that can enumerate the tuples in join(RI1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=',Id) with an ˜O(∆) delay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The structure’s space is bounded by O(AGM(I1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Id)/∆).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='8 We argue that the structures on all the heavy (dyadic) combinations use ˜O(N ρ∗/∆) space in total.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Fix d arbitrary level numbers ℓ1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', ℓd each between 0 and log2 N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' For i ∈ [1, d], let Ii be the set of all level-ℓi dyadic intervals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The total space occupied by the structures of all heavy combinations (I1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Id) ∈ I1 × .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' × Id is 1 ∆ � (I1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=',Id)∈I1×.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='×Id AGM(I1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Id).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' (3) up to an ˜O(1) factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The above includes a term for every light combination but such terms can only over-estimate the space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Each Ii is a set of disjoint intervals in dom(Xi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Applying the definition in (2) and Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='2, we can see that (3) is bounded by N ρ∗/∆, noticing that the right hand side of (1) is at most N ρ∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' In the above analysis, we have fixed a set of ℓ1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', ℓd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' As each ℓi has O(log N) choices, all together there are O(logd N) = ˜O(1) different sets of ℓ1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', ℓd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We can now conclude that the overall space is ˜O(N ρ∗/∆).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Finally, we need a hash table to check in constant time whether a dyadic combination is heavy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The hash table occupies ˜O(N ρ∗/∆) space because our earlier analysis implies a bound ˜O(N ρ∗/∆) on the number of heavy dyadic combinations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The overall space of our entire structure is therefore ˜O(N + N ρ∗/∆), where the term ˜O(N) counts the space for storing the relations of R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Query.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Consider a range join query with interval q = [x1, x2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We consider, w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='l.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='o.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', that x1 and x2 are integers in [1, N].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' In ˜O(1) time, we can partition the box B(q, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', q � �� � t ) into O(logd N) = ˜O(1) disjoint boxes, each in the form B(I1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Id) where (I1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Id) is a dyadic combination;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' we say that (I1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Id) is canonical for q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The query result is � canonical (I1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Id) join(RI1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=',Id).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The results join(RI1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=',Id) of all the canonical (I1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Id) are disjoint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' If a canonical (I1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Id) is heavy, we enumerate join(RI1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=',Id) with an ˜O(∆) delay using the structure of [20] on (I1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Id).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Otherwise, we apply a worst-case optimal join algorithm [39, 40, 48] to compute join(RI1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=',Id).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' 8Strictly speaking, the space should also account for the relations in RI1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=',Id.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' In our context, it suffices to store the relations of R once and generate the relations in RI1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=',Id when answering a query.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Appendix D has additional details about [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' 11 The algorithm finishes in ˜O(AGM(I1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Id)) time, which is ˜O(∆) by definition of light dyadic combination.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Our algorithm guarantees a delay of ˜O(∆).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' This completes the proof of Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Remark.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' In [36], Khamis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' used dyadic intervals in their algorithm for one-off computation of join(R).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Their main technical issue was to select “good” dyadic boxes (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', boxes of the form B(I1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Id)) to cover the tuples in join(R) once.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' That issue is non-existent in our context, where the primary obstacle is to argue that the total space given in (3) is affordable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We overcame the obstacle using Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='2, which, though perpahs no longer surprising given all the existing variations of the AGM bound, deserves a careful treatment that, we believe, has not appeared before.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' 6 Problem 2: Triangles This section will describe a structure for Problem 2 under Q = triangle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We will first attack, in Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='1 and 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='2, two fundamental problems whose solutions are vital to establishing Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='6, the proof of which is presented in Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='1 The Range Triangle Edges Problem This subsection will discuss the following standalone problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Range Triangle Edges (RTE).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Let G be an undirected graph with m edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Given an interval q = [x1, x2], a query returns: (i) all the edges appearing in at least one triangle of Gq;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' and (ii) Θ(m∗) triangles where m∗ is the number of edges reported in (i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We will develop a structure of O(m) space that can answer a query in ˜O(m∗) time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Furthermore, the query can enumerate the m∗ edges and the Θ(m∗) triangles both with a delay ∆.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Let us represent a triangle occurrence in G as triangle(u, v, w) where u, v, and w are the triangle’s vertices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Ordering is important: we will always adhere to the convention Au < Av < Aw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Given an interval q, we denote by E∗ q the set of edges showing up in at least one triangle of Gq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Hence, m∗ = |E∗ q|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' If triangle(u, v, w) appears in Gq, we call {u, v} a type-1 edge, {v, w} a type-2 edge, and {u, w} a type-3 edge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The total number of edges of all three types is between m∗ and 3m∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Next, we explain how to extract the edges of each type in Gq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Type 1 and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We will discuss only type 1 because type 2 is symmetric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' For each edge {u, v} in G (assume, w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='l.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='o.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Au < Av), identify a sentinel vertex w∗ for {u, v} as follows: w∗ = null if G has no occurrence of the form triangle(u, v, w);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' otherwise, w∗ has the smallest attribute among all the vertices w making a triangle occurrence triangle(u, v, w) in G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Consider any interval q = [x1, x2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Observe that {u, v} is a type-1 edge for q if and only if x1 ≤ Au and Aw∗ ≤ x2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' This motivates us to convert type-1 edge retrieval to range reporting on 2D points (introduced in Section 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Towards the purpose, create a set P of points, which has a point (Au, Aw∗) for every {u, v} whose sentinel w∗ is not null.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Attach edge {u, v} to the point (Au, Aw∗) so that the former can be fetched along with the latter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The size of P is at most m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Given q = [x1, x2], we can find all the type-1 edges by enumerating the points of P inside the 9An edge can be of different types in various triangle occurrences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' 12 rectangle [x1, ∞) × (−∞, x2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Hence, we can store P in a Chazelle’s structure (see Section 2) that has O(|P|) = O(m) space and ensures an ˜O(1) delay in reporting the type-1 edges of any q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Type 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' A similar approach works for type 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Let {u, w} be an edge appearing in at least one occurrence triangle(u, v, w) in G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' It is a type-3 edge of q = [x1, x2] if and only if x1 ≤ Au and Aw ≤ x2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' By adapting the earlier discussion in a straightforward manner, we conclude that there is a structure of O(m) space allowing us to retrieve all the type-3 edges with an ˜O(1) delay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Listing Θ(m∗) Triangles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The above has explained how to retrieve E∗ q, but an RTE query still needs to report Θ(m∗) triangles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Next, we remedy the issue by slightly modifying our solution so far.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Recall that, in dealing with type 1, we attached the edge {u, v} to the point (Au, Aw∗) generated from the edge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Now, we attach triangle(u, v, w∗) to (Au, Aw∗) as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' This way, when (Au, Aw∗) is found, we obtain both {u, v} and triangle(u, v, w∗) for free.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' After applying the same idea to type-2 and type-3, we can assert that, whenever the query algorithm finds a type-1, -2, or -3 edge, it must have also found a triangle in Gq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Therefore, the algorithm can report the triangles in Gq with an ˜O(1) delay, although the same triangle may be reported up to three times10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' By applying the duplicate-removal technique in Section 2, we now have an algorithm that can enumerate Θ(m∗) distinct triangles with an ˜O(1) delay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The number of distinct triangles reported is at least m∗/3 and at most 3m∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='2 The Small-Delay Triangle Listing Problem In this subsection, we will concentrate on a standalone problem defined as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Small-Delay Triangle Listing (SDTL).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' G is an undirected graph with m edges, each of which appears in at least one triangle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We are given Ω(m) free triangles and O(m) forbidden triangles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Design an algorithm to enumerate all the triangles of G — except for the forbidden ones — with a small delay (free triangles must be enumerated).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' No preprocessing is allowed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We will settle the problem with an algorithm of delay ˜O(m ω−1 ω+1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Suppose that G has OUT triangles in total.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Our starting point is an algorithm of Bjorklund et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' [11] which is able to list k triangles in α · m 3(ω−1) ω+1 k 3−ω ω+1 time, where α = ˜O(1), for a parameter k ∈ [Ω(m), OUT].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' As far as the algorithm of [11] is concerned, we can consider OUT known because it can be found in O(m2ω/(ω+1)) time [3] which is O(m 3(ω−1) ω+1 k 3−ω ω+1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The algorithm of Bjorklund et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' does not have a small delay, but we will turn it into one that does.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We run the algorithm of Bjorklund et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' [11] with geometrically-increasing k and, in each run, report only some, but not all, of the triangles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' How many triangles are reported in each run is decided strategically to keep the delay small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Let S0 no be the set of forbidden triangles and S0 yes the set of free triangles in the beginning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Set k0 = |S0 no| + |S0 yes|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' When running the algorithm of [11] for the i-th time, we set its parameter k to ki = min{3ik0, OUT}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We enforce the invariant that, when run i starts, there are always a set Si−1 no of forbidden triangles and a set Si−1 yes of free triangles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The set Si−1 yes will be reported with a small delay during the i-th run (details to be clarified shortly).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' 10An occurrence triangle(u, v, w) can be reported only when {u, v}, {v, w}, or {u, w} is output as a type-1, -2, or 3 edge, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' 13 Specifically, suppose that the i-th run finds a set Si raw of ki triangles (some of which have been output in previous runs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We generate the forbidden and free sets for the next run as follows: Si no = Si−1 no ∪ Si−1 yes and then Si yes = Si raw \\ Si no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Run i finishes in α · m 3(ω−1) ω+1 k 3−ω ω+1 i time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We instruct the run to output a triangle from Si−1 yes every α · m 3(ω−1) ω+1 k 3−ω ω+1 i |Si−1 yes | (4) atomic operations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We will show |Si−1 yes | = Ω(ki), with which the delay in (4) can be bounded as: ˜O \uf8eb \uf8edm 3(ω−1) ω+1 k 2ω−2 ω+1 i \uf8f6 \uf8f8 = ˜O � m ω−1 ω+1 � (5) where the equality used ki ≥ k0 = Ω(m).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' For i = 1, |Si−1 yes | = Ω(k0) follows directly from the definition of the SDTL problem (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', we have Ω(m) free triangles to start with).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' To prove |Si−1 yes | = Ω(ki) for i ≥ 2, we derive: |Si−1 no | ≤ |S0 no| + |S0 yes| + i−2 � j=1 |Sj raw| = k0 + i−2 � j=1 3j · k0 = i−2 � j=0 3j · k0 < 3i−1k0 2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Therefore: |Si−1 yes | ≥ |Si−1 raw | − |Si−1 no | > ki−1 − 3i−1k0/2 = ki−1/2 = Ω(ki).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We now conclude that the delay of our algorithm is as given in (5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='3 Proof of Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='6 We are ready to explain how to solve Problem 2 with Q = triangle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' In preprocessing, we build an RTE structure (Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='1) on G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Now, consider a (Problem-2) query with interval q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We start by issuing an RTE query to retrieve E∗ q, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', the set of edges appearing in at least one triangle of Gq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' This, in effect, generates G∗ q, which is the subgraph of Gq induced by the edges in E∗ q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' In addition, the RTE query has also enumerated a set S of Θ(m∗) triangles in Gq, where m∗ = |E∗ q|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The size of S falls in [m∗ 3 , 3m∗].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Our remaining mission is to enumerate the triangles in G∗ q that are outside S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Note that G∗ q is a graph with m∗ edges and at least Θ(m∗) triangles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' This motivates us to convert the mission to the SDTL problem, which has been solved in Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' However, the SDTL problem requires Θ(m∗) free triangles and O(m∗) forbidden triangles as part of the input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Unfortunately, we do not seem to have these triangles at the moment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We overcome this obstacle by, interestingly, dividing S into Syes and Sno, such that Syes (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Sno) serves as the set of free (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' forbidden) triangles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Recall that the RTE query algorithm, denoted as A, is designed to enumerate an edge in E∗ q with a delay ∆ = ˜O(1) and a triangle in S also with a delay ∆.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Therefore, it must finish within tmax = max{∆·(|E∗ q |+1), ∆·(|S|+1)} ≤ ∆·(3m∗+1) time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We can now apply the buffering technique in Section 2 with α = 18 to turn A into an algorithm 14 that outputs a triangle at the end of each epoch, which has a length 18∆.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The total number of epochs is at most tmax 18∆ ≤ 3m∗+1 18 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Thus, when A finishes, we have output at most (3m∗ + 1)/18 triangles, whereas the buffer B (defined in Section 2) still has at least |S|− 3m∗+1 18 = Θ(m∗) triangles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We can, thus, set Syes to the content of B when A finishes, and Sno to the set of triangles already output.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We can now apply the SDTL algorithm on G∗ q and, thus, complete the proof of Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' 7 Problem 2: Near-Constant Delays This section will focus on two instances of Problem 2 where it is possible to achieve ˜O(1) delays with space substantially smaller than Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We will discuss first Q = ℓ-star in Section 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='1 and then Q = 2ℓ-cycle in Section 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We will focus on explaining how to enumerate a perhaps- not-distinct occurrence with an ˜O(1) delay, while ensuring each occurrence to be output only a constant number of times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Owing to the duplicate-removal method in Section 2, we can modify the algorithms to enumerate only distinct occurrences with ˜O(1) delays.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='1 ℓ-Stars Recall that an ℓ-star is a tree with only one non-leaf node, which we will refer to as the star’s center.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Consider a query with interval q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We refer to a node u as a q-center if Gq has at least one ℓ-star occurrence with u as the center.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Once u is found, it becomes a trivial matter to enumerate all the ℓ-stars having u as the center with an ˜O(1) delay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Specifically, we can first (use a binary search tree to) retrieve all the neighbors v of u in G satisfying Av ∈ q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' From those neighbors, any ℓ distinct vertices form an ℓ-star together with u (as the center).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' It is rudimentary to ensure an ˜O(1) delay in enumerating all those stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Next, we concentrate on designing a structure to enumerate the q-centers with an ˜O(1) delay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Consider an arbitrary ℓ-star in G with center u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Sort the star’s ℓ + 1 vertices in ascending order of attribute and look for the position of u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' If u is the r-th smallest, we will refer to the star as a rank-r ℓ-star and u as a rank-r q-center.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Now, fix an r ∈ [1, ℓ + 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We will describe a structure to support the following operation: Given an interval q, find all the rank-r q-centers, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', all vertices u ∈ V s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Gq has a rank-r ℓ-star with u as the center.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Consider any rank-r ℓ-star in G having u as the center.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Let us write out the star’s vertices as v1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', vr−1, u, vr+1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', vℓ in ascending order of attribute.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' For a q = [x1, x2], the ℓ-star appears in Gq if and only if x1 ≤ Av1 and Avℓ ≤ x2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Refer to v1 as a left r-sentinel of u and to vℓ as a right r-sentinel of u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' From all the left r-sentinels of u (one from each rank-r ℓ-star with center u), identify the one v∗ 1 with the largest attribute.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Similarly, from all the right r-sentinels of u, identify the one v∗ ℓ with the smallest attribute.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Observe that u is a rank-r q-center if and only if x1 ≤ Av∗ 1 and Av∗ ℓ ≤ x2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We can therefore convert the retrieval of rank-r q-centers into range reporting on 2D points (review Section 2), in the same way as illustrated in Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Following Section 2, we can create a Chazelle’s structure on n points — each point created for a vertex u ∈ V in the way explained — that has O(n) space and, given any q, can list the rank-r q-centers with an ˜O(1) delay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' This completes the proof of Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' 15 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='2 2ℓ-Cycles We will start with an assumption: all queries specify a fixed q = (−∞, ∞), namely, there is effectively only one query, which enumerates all the 2ℓ-cycles in G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The assumption allows us to explain the core ideas with the minimum technical details and will be removed eventually.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Queries with q = (−∞, ∞).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Given a 2ℓ-cycle occurrence, we refer to the vertex u in the cycle having the smallest attribute as the occurrence’s anchor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Let v be the vertex in the cycle such that cutting the cycle at u and v gives two ℓ-paths connecting u and v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We will refer to v as the occurrence’s inverse anchor, the pair (u, v) as an anchor pair, and the two aforementioned paths as cycle ℓ-paths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The number of cycle ℓ-paths is at most #Pℓ (recall that #Pℓ is the total number of ℓ-paths).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The problem may appear deceivingly simple: can’t we answer a query by simply concatenating, for each anchor pair (u, v), every two cycle ℓ-paths from u to v?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' This does not work because the two cycle ℓ-paths may share common vertices other than u and v, in which case the concatenation does not yield a 2ℓ-cycle!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' This motivates a crucial notion: two cycle ℓ-paths are interior disjoint if they (i) have the same anchor pair (u, v), and (ii) do not share any common vertex except u and v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Concatenating two cycle ℓ-paths from u to v spawns a 2ℓ-cycle if and only if those paths are interior disjoint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The challenge we are facing at this moment is the following problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Design a structure to support the following operation: given a cycle ℓ-path π from anchor u to inverse anchor v, list all the cycle ℓ-paths interior disjoint with π with an ˜O(1) delay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We will overcome the challenge with a structure of ˜O(#Pℓ) space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Our main observation is that the operation can be converted to range reporting on (ℓ − 1)- dimensional points (review Section 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' To explain, let us consider any cycle ℓ-path π from anchor u to inverse anchor v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' After excluding u and v, the path has ℓ − 1 vertices, which we list as w1, w2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', wℓ−1 in ascending order of attribute11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Convert π into an (ℓ − 1)-dimensional point (Aw1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Awℓ−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Let Pu,v be the set of points thus obtained from all the cycle ℓ-paths with (u, v) as the anchor pair.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Now, consider another cycle ℓ-path π′ from u to v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' List the vertices of π′ other than u and v as w′ 1, w′ 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', w′ ℓ−1 also in ascending order of attribute.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' If π′ is interior disjoint with π, each Aw′ i (i ∈ [1, ℓ − 1]) must fall in one of the ℓ open intervals: (−∞, Aw1), (Aw1, Aw2), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', (Awℓ−2, Awℓ−1), (Awℓ−1, ∞).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' (6) Therefore, (Aw′ 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Aw′ ℓ−1) — the point converted from π′ — must fall in one of the following ℓℓ−1 = O(1) rectangles: q1 ×q2 ×.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='×qℓ−1, where each qi (i ∈ [1, ℓ−1]) is taken independently from one of the intervals in (6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' As per Section 2, by creating a range tree on Pu,v of ˜O(|Pu,v|) space, we can enumerate all the points in such a rectangle with an ˜O(1) delay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The conclusion from the above is that, for each anchor pair (u, v), we can create a range tree of ˜O(|Pu,v|) space which, given any cycle ℓ-path cycle π from u to v, permits the enumeration of every cycle ℓ-path π′, which is interior disjoint with π, with an ˜O(1) delay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The structures of all the anchor pairs use in total � anc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' pair (u, v) ˜O(|Pu,v|) = ˜O(#Pℓ) space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' With the challenge conquered, listing all the 2ℓ-cycles becomes an easy matter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We simply look at each cycle ℓ-path π, retrieve every ℓ-path π′ interior disjoint with π, and make a cycle by concatenating π and π′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The delay in cycle reporting is ˜O(1) (each 2ℓ-cycle can be reported twice).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' 11The order should not be confused with the order by which the vertices appear in π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' 16 Arbitrary Queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Next, we remove the constraint q = (−∞, ∞) and tackle queries with arbitrary q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' A new issue now arises: a query can no longer afford to look at all the cycle ℓ-paths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We say that a cycle ℓ-path from anchor u to inverse anchor v contributes to Gq if it makes a 2ℓ-cycle in Gq with another interior disjoint cycle ℓ-path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We need a way to list only the contributing cycle ℓ-paths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Fix any cycle ℓ-path π with anchor pair (u, v).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Let Sπ be the set of 2ℓ-cycles in G that include π and have (u, v) as the anchor pair.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Take an arbitrary cycle from Sπ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' By definition of anchor, u has the smallest attribute among the cycle’s vertices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Let w be the vertex in the cycle with the largest attribute.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' For q = [x1, x2], the cycle appears in Gq if and only if x1 ≤ Au and Aw ≤ x2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Let w∗ be the vertex with the smallest attribute among all such w’s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' It becomes evident that π contributes to the Gq of q = [x1, x2] if and only if x1 ≤ Au and Aw∗ ≤ x2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We can therefore convert the retrieval of contributing cycle ℓ-paths to range reporting on 2D points, using the method in Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The resulting structure (a Chazelle’s structure) stores a point converted from every cycle ℓ-path and uses O(#Pℓ) space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Give any q, we can list the cycle ℓ-paths contributing to Gq with an ˜O(1) delay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Suppose that we have found a contributing cycle ℓ-path π with anchor pair (u, v).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' As before, we proceed to find the cycle ℓ-paths π′ interior disjoint with π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The new requirement here, however, is that π′ needs to be contributing as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Recall that, in the q = (−∞, ∞) scenario, we converted the task to range reporting on (ℓ − 1)-dimensional points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' To deal with arbitrary q = [x1, x2], we will increase the dimension by one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' To explain, in a fashion like before, let us list out the vertices of π — after excluding u and v — as w1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', wℓ−1 in ascending order of attribute.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Denote by wmax the vertex in π with the largest attribute (wmax can be v).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Convert π to an ℓ-dimensional point (Aw1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Awℓ−1, Awmax).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Let (Aw′ 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Aw′ ℓ−1, Aw′max) be the point converted from π′ in the same manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' As we already know Au ∈ [x1, x2] (recall that π is a contributing path), π′ is a path we want if and only if it satisfies the conditions below: Aw′ i (1 ≤ i ≤ ℓ − 1) falls in one of the ℓ intervals in (6);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Aw′max ≤ x2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Thus, the point (Aw′ 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Aw′ ℓ−1, Aw′max) must fall in one of the following ℓℓ−1 = O(1) rectangles: q1 × q2 × .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' × qℓ−1 × (−∞, x2], where each qi (i ∈ [1, ℓ − 1]) is an interval taken independently from (6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' By the above reasoning, for each anchor pair (u, v), we create a set Pu,v of ℓ-dimensional points, each converted from a cycle ℓ-path with anchor pair (u, v), and then build a range tree on Pu,v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The range trees of all anchor pairs use � anc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' pair (u, v) ˜O(|Pu,v|) = ˜O(#Pℓ) space in total.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We now elaborate on the overall algorithm for answering a (Problem-2) query with parameter q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' First, enumerate all the cycle ℓ-paths contributing to Gq with an ˜O(1) delay;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' call this the outer enumeration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Every time such a path π — say with anchor pair (u, v) — is obtained, we suspend outer enumeration and utilize the range tree on Pu,v to find all the paths π′ discussed previously with an ˜O(1) delay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Upon the delivery of a π′, concatenate it with π and output the 2ℓ-cycle obtained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' After exhausting all such π′, we resume outer enumeration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' This concludes the proof of Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' 17 Appendix A Correctness of the Reduction in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='1 In our construction, Si (i ∈ [1, s]) corresponds to two set vertices with attribute values i and i + s, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' To facilitate derivation, we make a copy of each set: define Si = Si−s for each i ∈ [s + 1, 2s].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' In the rest of the proof, we hold the view that each Si (i ∈ [1, 2s]) corresponds to only one set vertex, the one with attribute value i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Consider a wedge occurrence with vertices u, v, and w where the edges are {u, v} and {v, w}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We classify it as one of the two types below: (type e-s-e) u and w are element vertices and v is a set vertex;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' (type s-e-s) u and w are set vertices and v an element vertex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' For any interval q = [x, y] satisfying 1 ≤ x < s + 1/2 < y ≤ 2s, we have the number of e-s-e wedges in Gq is � i∈[x,y] �|Si| 2 � ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' the number of s-e-s wedges in Gq is � i∈[x,y],j∈[i+1,y] |Si ∩ Sj|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' To prove the first bullet, define an e-s-e tuple as (e1, Si, e2) where i ∈ q and e1 and e2 are distinct elements in Si.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The number of such tuples is �y i=x �|Si| 2 � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Our construction ensures a one-one correspondence between e-s-e tuples and e-s-e wedges in Gq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' To prove the second bullet, define an s-e-s tuple as (Si, e, Sj) where x ≤ i < j ≤ y and e ∈ Si ∩ Sj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The number of such tuples is � i∈[x,y],j∈[i+1,y] |Si ∩ Sj|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Our construction ensures a one-one correspondence between s-e-s tuples and s-e-s wedges in Gq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' To find out whether Sa ∩Sb is empty, our reduction issues four Problem-1 queries with intervals q1 = [a, s+b], q2 = [a+1, s+b], q3 = [a, s+b−1], and q4 = [a+1, s+b−1], respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The above lemma is applicable to all these intervals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' For i ∈ [1, 4], let c′ i (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' c′′ i ) be the number of e-s-e (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' s-e-s) wedges in Gqi;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' this means that ci, the total number of wedges in Gqi, equals c′ i + c′′ i .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' According to Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' we have: c′ 1 − c′ 2 − c′ 3 + c′ 4 = � i∈[a,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='s+b] �|Si| 2 � − � i∈[a+1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='s+b] �|Si| 2 � − � i∈[a,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='s+b−1] �|Si| 2 � + � i∈[a+1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='s+b−1] �|Si| 2 � = 0 and c′′ 1 − c′′ 2 − c′′ 3 + c′′ 4 = \uf8eb \uf8ec \uf8ec \uf8ed � i∈[a,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='s+b] j∈[i+1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='s+b] |Si ∩ Sj| − � i∈[a+1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='s+b] j∈[i+1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='s+b] |Si ∩ Sj| \uf8f6 \uf8f7 \uf8f7 \uf8f8 − \uf8eb \uf8ec \uf8ec \uf8ed � i∈[a,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='s+b−1] j∈[i+1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='s+b−1] |Si ∩ Sj| − � i∈[a+1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='s+b−1] j∈[i+1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='s+b−1] |Si ∩ Sj| \uf8f6 \uf8f7 \uf8f7 \uf8f8 18 = � j∈[a+1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='s+b] |Sa ∩ Sj| − � j∈[a+1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='s+b−1] |Sa ∩ Sj| = |Sa ∩ Ss+b| = |Sa ∩ Sb|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We thus conclude that c1 − c2 − c3 + c4 = |Sa ∩ Sb|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' B Proof of Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='1 Let us first consider a variant of the set disjointness problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Weighted Set Intersection Size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We have s ≥ 2 sets S1, S2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Ss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Each Si (i ∈ [1, s]) is associated with a function weightSi which assigns to each element e ∈ Si a value weightSi(e).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Given distinct set ids a, b ∈ [1, s], a query returns size(Sa, Sb) = � e∈Sa∩Sb weightSa(e) · weightSb(e).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' (7) Let N = �s i=1 |Si|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' For any λ ∈ [1, √ N], it is straightforward to build a structure of O(N 2/λ2) space answering a query in O(λ) time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Call Si (i ∈ [1, s]) a large set if |Si| > λ, or a small set otherwise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The number of large sets is at most N/λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' For each pair (i, j) ∈ [1, s] × [1, s], i ̸= j, such that Si and Sj are both large, we store size(Si, Sj);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' the space needed is O(N 2/λ2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Given a query with parameters a and b, return size(Sa, Sb) directly if Sa and Sb are both large.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Otherwise, assume, w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='l.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='o.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', that Sa is small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We compute Sa ∩ Sb in O(λ) time using a hash table (for each e ∈ Sa, check if e ∈ Sb).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The result size(Sa, Sb) can then be obtained easily.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Equipped with the above, next we describe a structure for the colored range wedge counting problem to prove Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' First obtain a canonical collection C of V (defined in Section 4) satisfying � U∈C |U| = ˜O(n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' For each U ∈ C — recall that U is a subset of V — construct a weighted set as follows: SU = the set of black vertices adjacent to at least one vertex in U;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' for each b ∈ SU, weightSU(b) = the number of vertices in U adjacent to b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' These weighted sets constitute an instance of the weighted set intersection size problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Build a structure described earlier on the instance using the given parameter λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The lemma below implies that the structure occupies ˜O(m2/λ2) space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Lemma B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' � U∈C |SU| = ˜O(m).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Each b ∈ SU is adjacent to a vertex u ∈ U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Pay a dollar to the edge {b, u} for each such pair (b, u).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Since an edge can receive a dollar only if it has a vertex in U, it can receive up to two dollars12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' |SU| is no more than the number of dollars paid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Do the above for all U ∈ C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Each edge in G can receive ˜O(1) dollars in total because every vertex appears in ˜O(1) subsets in C (Property P4-1 of C;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' see Section 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' 12Two is possible: this happens when b and u are both black and both appear in U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' 19 For any distinct U, U ′ ∈ C, define size(SU, SU′) as in (7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' On the other hand, for each U ∈ C, define size(SU, SU) = � b∈SU �weightSU (b) 2 � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We store the value size(SU, SU) for all U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The total space is ˜O(m2/λ2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Before proceeding, the reader should note the following subtle fact about the function size(.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' ): Fact B-1: size(SU, SU′) is the number of occurrences wedge(u, v, w) in G such that u ∈ SU, w ∈ SU′, and v is black.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The fact holds even if U = U ′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Query.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Given a query with interval q, in ˜O(1) time we can pick h = ˜O(1) members U1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Uh from C that form a partition of Vq (Property P4-2 of C).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The query returns � i,j∈[1,h]:i≤j size(SUi, SUj).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' (8) Each size(SUi, SUj) is either explicitly stored or can be obtained from the weighted set intersection size structure in O(λ) time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The overall query time is therefore ˜O(λ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Fact B-1 and U1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Uh forming a partition of Vq assure us that (8) counts only occurrences wedge(u, v, w) in G such that Au ∈ q, Aw ∈ q, and v is black.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' To complete the correctness argument, we still need to show that (8) counts every such occurrence exactly once.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Indeed, there exist unique a, b ∈ [1, h] such that a ≤ b, u ∈ Ua, and w ∈ Ub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The wedge is counted only by the term in (8) with i = a and j = b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' C Proof of Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='2 Let us first review H¨older’s Inequality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Fix some positive integers α and β.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Let xi,j, for each i ∈ [1, α] and j ∈ [1, β], be non-negative real numbers;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' yj, for each j ∈ [1, β], be non-negative real numbers satisfying �β j=1 yj ≥ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Under the convention 00 = 0, H¨older’s inequality states that: α � i=1 β � j=1 xyj i,j ≤ β � j=1 � α � i=1 xi,j �yj .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' (9) A proof can be found in [29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We now return to the context of Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Given any j ∈ [1, d − 1] and (I1, I2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Ij) ∈ I1 × .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='Ij, we will use B(I1, I2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Ij) as a short-form for the d-dimensional box B(I1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Ij, dom(Xj+1), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', dom(Xd)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' As a special case, define B(∅) = B(dom(X1), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', dom(Xd)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' 20 Lemma C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' For any j ∈ [1, d], we have � Ij∈Ij � e∈E |Re ⋉ B(I1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Ij)|W (e) ≤ � e∈E |Re ⋉ B(I1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Ij−1)|W (e).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Define Ej = {e ∈ E | Xj ∈ e}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Since � e∈Ej W(e) ≥ 1 (W is a fractional edge covering), from H¨older’s inequality (9) we have � Ij∈Ij � e∈Ej |Re ⋉ B(I1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Ij)|W (e) ≤ � e∈Ej � � Ij∈Ij |Re ⋉ B(I1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Ij)| �W (e) ≤ � e∈Ej ���Re ⋉ B � I1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Ij−1, dom(Xj) ���� W (e) = � e∈Ej |Re ⋉ B(I1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Ij−1)|W (e) (10) where the second inequality used the fact that Ij is a set of disjoint intervals in dom(Xj).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' For each e ∈ E \\ Ej, Re ⋉ B(I1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Ij) does not depend on Ij and can be rewritten as Re ⋉ B(I1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Ij−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We can thus derive: � Ij∈Ij � e∈E |Re ⋉ B(I1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Ij)|W (e) = � Ij∈Ij � � e∈E\\Ej |Re ⋉ B(I1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Ij)|W (e) · � e∈Ej |Re ⋉ B(I1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Ij)|W (e)� = � e∈E\\Ej |Re ⋉ B(I1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Ij)|W (e) · � Ij∈Ij � e∈Ej |Re ⋉ B(I1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Ij)|W (e) ≤ � e∈E\\Ej |Re ⋉ B(I1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Ij−1)|W (e) · � e∈Ej |Re ⋉ B(I1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Ij−1)|W (e) = � e∈E |Re ⋉ B(I1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Ij−1)|W (e).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' where the inequality used (10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' 21 We can prove Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='2 with d applications of Lemma C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='1: � I1∈I1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' � Id∈Id � e∈E |Re ⋉ B(I1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Id)|W (e) ≤ � I1∈I1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' � Id−1∈Id−1 � e∈E |Re ⋉ B(I1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Id−1)|W (e) ≤ � I1∈I1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' � Id−2∈Id−2 � e∈E |Re ⋉ B(I1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Id−2)|W (e) ≤ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' ≤ � I1∈I1 � e∈E |Re ⋉ B(I1)|W (e) ≤ � e∈E |Re|W (e).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' D Proof of Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='5 The reader should read this proof after having finished Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The basic idea is to convert Problem 2 to range join.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Let X (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' E) be the set of vertices (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' edges) in the pattern graph Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The reader should not confuse X and E with V and E: the latter two are defined on the data graph G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' For each edge e ∈ E, construct a relation Re with two attributes by inserting, for each edge {u, v} in G, two tuples (u, v) and (v, u).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' This defines a join instance R = {Re | e ∈ E} with input size N = 2m · |E| = O(m).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Every occurrence of Q corresponds to a constant number of tuples in join(R).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Motivated by this, given a Problem-2 query with interval q, we issue a range join query on R with q, which guarantees retrieving all the occurrences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The issue, however, is that not every tuple in join(R) gives rise to an occurrence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' To see this, consider Q = 4-cycle and, hence, R has four relations with schemes (X1, X2), (X2, X3), (X3, X4), and (X4, X1), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Let {u, v} be an arbitrary edge in E;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' tuples (u, v), (v, u), (u, v), and (v, u) exist in the four relations, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Thus, join(R) contains a tuple (u, v, u, v) that does not correspond to any occurrence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The issue can be eliminated by slightly modifying the structure of [20], which we review next.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Consider an arbitrary set R of relations (with any number of attributes) defined in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Deep and Koutris [20] proved the existence of a set B of boxes such that: each box has the form B(I1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Id) where Ii is an interval in dom(Xi) for i ∈ [1, d];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' the boxes are disjoint and their union is B(dom(X1), dom(X2), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=',dom(Xd));' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' for each box B(I1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Id), the join instance RI1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=',Id has a non-empty result;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' each box B(I1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Id) satisfies AGM(I1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Id) ≤ ∆;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' |B| = O(N ρ∗/∆).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The structure of [20] simply stores B itself and uses O(N ρ∗/∆) space13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' To enumerate join(R), the algorithm of [20] looks at each B(I1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Id) ∈ B and applies a worst-case optimal join algorithm [39,40,48] to compute join(RI1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=',Id) in ˜O(AGM(I1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Id)) = ˜O(∆) time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' This guarantees a delay of ˜O(∆).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' 13Obviously, the relations of R also need to be stored separately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' 22 We now adapt the structure to list all the occurrences of Q in G (fixing q = (−∞, ∞)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Construct R from G and Q as before.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Apply [20] to find a set B with all the properties explained earlier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Then, inspect each box B(I1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', Id) ∈ B in turn and remove it from B if all the occurrences of Q producible from join(RI1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=',Id) can already be produced from the boxes inspected earlier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' The size of B can only decrease and therefore is still bounded by O(N ρ∗/∆).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' To find the occurrences, apply a worst-case optimal join algorithm on each box in B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' As each box generates at least one new occurrence, we guarantee a delay of ˜O(∆).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' To support (Problem-2) queries with arbitrary q, use the adapted structure to replace that of [20] in the solution presented in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' All the analysis still holds through.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' We thus complete the proof of Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' References [1] Josh Alman and Virginia Vassilevska Williams.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' A refined laser method and faster matrix multiplication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' In Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 522–539, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' [2] Noga Alon, Raphael Yuster, and Uri Zwick.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Color-coding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Journal of the ACM (JACM), 42(4):844–856, 1995.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' [3] Noga Alon, Raphael Yuster, and Uri Zwick.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Finding and counting given length cycles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Algo- rithmica, 17(3):209–223, 1997.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' [4] Albert Atserias, Martin Grohe, and Daniel Marx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Size bounds and query plans for relational joins.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' SIAM Journal on Computing, 42(4):1737–1767, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' [5] Guillaume Bagan, Arnaud Durand, and Etienne Grandjean.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' On acyclic conjunctive queries and constant delay enumeration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' In Computer Science Logic, pages 208–222, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' [6] Michael J Bannister, Christopher DuBois, David Eppstein, and Padhraic Smyth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Windows into relational events: Data structures for contiguous subsequences of edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' In Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 856–864, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' [7] Jon Louis Bentley.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Decomposable searching problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Information Processing Letters (IPL), 8(5):244–251, 1979.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' [8] Suman K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Bera, Noujan Pashanasangi, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Seshadhri.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Near-linear time homomorphism counting in bounded degeneracy graphs: The barrier of long induced cycles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' In Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 2315–2332, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' [9] Christoph Berkholz, Jens Keppeler, and Nicole Schweikardt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Answering conjunctive queries under updates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' In Proceedings of ACM Symposium on Principles of Database Systems (PODS), pages 303–318, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' [10] Andreas Bjorklund, Petteri Kaski, and Lukasz Kowalik.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Counting thin subgraphs via packings faster than meet-in-the-middle time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' ACM Transactions on Algorithms, 13(4):48:1–48:26, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' [11] Andreas Bjorklund, Rasmus Pagh, Virginia Vassilevska Williams, and Uri Zwick.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Listing tri- angles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' In Proceedings of International Colloquium on Automata, Languages and Programming (ICALP), pages 223–234, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' 23 [12] Nofar Carmeli and Markus Kroll.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' On the enumeration complexity of unions of conjunctive queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' ACM Transactions on Database Systems (TODS), 46(2):5:1–5:41, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' [13] Nofar Carmeli, Shai Zeevi, Christoph Berkholz, Benny Kimelfeld, and Nicole Schweikardt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Answering (unions of) conjunctive queries using random access and random-order enumeration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' In Proceedings of ACM Symposium on Principles of Database Systems (PODS), pages 393–409, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' [14] Farah Chanchary and Anil Maheshwari.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Time windowed data structures for graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Graph Algorithms Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', 23(2):191–226, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' [15] Farah Chanchary, Anil Maheshwari, and Michiel Smid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Querying relational event graphs using colored range searching data structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Discrete Applied Mathematics, 286:51–61, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' [16] Bernard Chazelle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' A functional approach to data structures and its use in multidimensional searching.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' SIAM Journal of Computing, 17(3):427–462, 1988.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' [17] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Chiba and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Nishizeki.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Arboricity and subgraph listing algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' SIAM Journal of Computing, 14(1):210–223, 1985.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' [18] Radu Curticapean, Holger Dell, and D´aniel Marx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Homomorphisms are a good basis for count- ing small subgraphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' In Proceedings of ACM Symposium on Theory of Computing (STOC), pages 210–223, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' [19] Mark de Berg, Otfried Cheong, Marc van Kreveld, and Mark Overmars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Computational Ge- ometry: Algorithms and Applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Springer-Verlag, 3rd edition, 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' [20] Shaleen Deep and Paraschos Koutris.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Compressed representations of conjunctive query results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' In Proceedings of ACM Symposium on Principles of Database Systems (PODS), pages 307–322, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' [21] Arnaud Durand.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Fine-grained complexity analysis of queries: From decision to counting and enumeration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' In Proceedings of ACM Symposium on Principles of Database Systems (PODS), pages 331–346, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' [22] Arnaud Durand and Etienne Grandjean.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' First-order queries on structures of bounded degree are computable with constant delay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' ACM Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Log.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', 8(4):21, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' [23] Arnaud Durand, Nicole Schweikardt, and Luc Segoufin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Enumerating answers to first-order queries over databases of low degree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' In Proceedings of ACM Symposium on Principles of Database Systems (PODS), pages 121–131, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' [24] David Eppstein.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Arboricity and bipartite subgraph listing algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Information Processing Letters (IPL), 51(4):207–211, 1994.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' [25] David Eppstein.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Subgraph isomorphism in planar graphs and related problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Graph Algorithms Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', 3(3):1–27, 1999.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' [26] David Eppstein, Maarten Loffler, and Darren Strash.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Listing all maximal cliques in sparse graphs in near-optimal time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' In International Symposium on Algorithms and Computation (ISAAC), volume 6506, pages 403–414, 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' [27] Peter Floderus, Miroslaw Kowaluk, Andrzej Lingas, and Eva-Marta Lundell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Detecting and counting small pattern graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' SIAM J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Discret.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', 29(3):1322–1339, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' 24 [28] Fedor V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Fomin, Daniel Lokshtanov, Venkatesh Raman, Saket Saurabh, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Raghavendra Rao.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Faster algorithms for finding and counting subgraphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Journal of Computer and System Sciences (JCSS), 78(3):698–706, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' [29] Ehud Friedgut.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Hypergraphs, entropy, and inequalities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Am.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Mon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', 111(9):749–760, 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' [30] Pierre-Louis Giscard, Nils M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Kriege, and Richard C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Wilson.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' A general purpose algorithm for counting simple cycles and simple paths of any length.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Algorithmica, 81(7):2716–2737, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' [31] Isaac Goldstein, Tsvi Kopelowitz, Moshe Lewenstein, and Ely Porat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Conditional lower bounds for space/time tradeoffs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' In Algorithms and Data Structures Workshop (WADS), pages 421– 436.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Springer, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' [32] Isaac Goldstein, Moshe Lewenstein, and Ely Porat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' On the hardness of set disjointness and set intersection with bounded universe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' In International Symposium on Algorithms and Com- putation (ISAAC), pages 7:1–7:22, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' [33] Chinh T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Hoang, Marcin Kaminski, Joe Sawada, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Sritharan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Finding and listing induced paths and cycles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Discrete Applied Mathematics, 161(4-5):633–641, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' [34] Ahmet Kara, Milos Nikolic, Dan Olteanu, and Haozhe Zhang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Trade-offs in static and dynamic evaluation of hierarchical queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' In Proceedings of ACM Symposium on Principles of Database Systems (PODS), pages 375–392, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' [35] Wojciech Kazana and Luc Segoufin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Enumeration of first-order queries on classes of structures with bounded expansion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' In Proceedings of ACM Symposium on Principles of Database Systems (PODS), pages 297–308, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' [36] Mahmoud Abo Khamis, Hung Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Ngo, Christopher R´e, and Atri Rudra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Joins via geometric resolutions: Worst-case and beyond.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' In Proceedings of ACM Symposium on Principles of Database Systems (PODS), pages 213–228, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' [37] Ton Kloks, Dieter Kratsch, and Haiko M¨uller.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Finding and counting small induced subgraphs efficiently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Information Processing Letters (IPL), 74(3-4):115–121, 2000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' [38] Jaroslav Nesetril and Svatopluk Poljak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' On the complexity of the subgraph problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Com- mentationes Mathematicae Universitatis Carolinae, 26(2):415–419, 1985.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' [39] Hung Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Ngo, Ely Porat, Christopher Re, and Atri Rudra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Worst-case optimal join algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Journal of the ACM (JACM), 65(3):16:1–16:40, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' [40] Hung Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Ngo, Christopher Re, and Atri Rudra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Skew strikes back: new developments in the theory of join algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' SIGMOD Rec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', 42(4):5–16, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' [41] Dan Olteanu and Jakub Zavodny.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Size bounds for factorised representations of query results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' ACM Transactions on Database Systems (TODS), 40(1):2:1–2:44, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' [42] Saladi Rahul.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Improved bounds for orthogonal point enclosure query and point location in or- thogonal subdivisions in R3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' In Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 200–211, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' 25 [43] Nicole Schweikardt, Luc Segoufin, and Alexandre Vigny.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Enumeration for FO queries over nowhere dense graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' In Proceedings of ACM Symposium on Principles of Database Systems (PODS), pages 151–163, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' [44] Luc Segoufin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Constant delay enumeration for conjunctive queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' SIGMOD Rec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=', 44(1):10–17, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' [45] Luc Segoufin and Alexandre Vigny.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Constant delay enumeration for FO queries over databases with local bounded expansion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' In Proceedings of International Conference on Database Theory (ICDT), volume 68, pages 20:1–20:16, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' [46] Yufei Tao.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Algorithmic techniques for independent query sampling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' In Proceedings of ACM Symposium on Principles of Database Systems (PODS), 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' [47] Yufei Tao and Ke Yi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Intersection joins under updates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Journal of Computer and System Sciences (JCSS), 124:41–64, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' [48] Todd L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Veldhuizen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Triejoin: A simple, worst-case optimal join algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' In Proceedings of International Conference on Database Theory (ICDT), pages 96–106, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' [49] Duncan J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Watts and Steven H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Strogatz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Collective dynamics of ‘small-world’ networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Nature, 393:440–442, 1998.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' [50] Virginia Vassilevska Williams and Ryan Williams.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' Finding, minimizing, and counting weighted subgraphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' SIAM Journal of Computing, 42(3):831–854, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} +page_content=' 26' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE1T4oBgHgl3EQfugXX/content/2301.03390v1.pdf'} diff --git 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Michalopoulos*, Muhammad Ikram Ashraf*, +and Wolfgang Gerstacker† +*Nokia Strategy and Technology, Munich, Germany, +†Institute for Digital Communications, Friedrich-Alexander-Universit¨at Erlangen-N¨urnberg, Erlangen, Germany +Abstract—Wireless high-accuracy positioning has recently at- +tracted growing research interest due to diversified nature of +applications such as industrial asset tracking, autonomous driv- +ing, process automation, and many more. However, obtaining a +highly accurate location information is hampered by challenges +due to the radio environment. A major source of error for time- +based positioning methods is inaccurate time-of-arrival (ToA) or +range estimation. Existing machine learning-based solutions to +mitigate such errors rely on propagation environment classifi- +cation hindered by a low number of classes, employ a set of +features representing channel measurements only to a limited +extent, or account for only device-specific proprietary methods +of ToA estimation. In this paper, we propose convolutional +neural networks (CNNs) to estimate and mitigate the errors of +a variety of ToA estimation methods utilizing channel impulse +responses (CIRs). Based on real-world measurements from two +independent campaigns, the proposed method yields significant +improvements in ranging accuracy (up to 37%) of the state-of- +the-art ToA estimators, often eliminating the need of optimizing +the underlying conventional methods. +Index Terms—Time-of-arrival estimation, high accuracy posi- +tioning, convolutional neural networks. +I. INTRODUCTION +Location information is vital for many applications across +various domains including industrial internet-of-things (IIoT), +emergency services, transportation, and many more. Some of +the applications, such as industrial asset tracking, autonomous +driving and process automation, require highly accurate po- +sition estimation as emphasized in 3GPP [1]. Location infor- +mation can be obtained by various approaches including time- +based, angle-based and fingerprinting-based techniques using +radio signals. One of the major approaches in widely utilized +time-based positioning is to estimate the time-of-arrival (ToA) +of the received positioning signals. Combined with time-of- +transmission (ToT), i.e., the time when the radio signal is sent +from the transmitter, ToA is used to calculate time-of-flight +(ToF), i.e., the time it takes for the radio signal to travel from +transmitter to receiver. Then, the range between transmitter +and receiver can be estimated using ToF since the radio signals +travel at a known speed, i.e., the speed of light, and can be +utilized for positioning. +The accuracy of ToA estimation is limited by various factors +such as challenging propagation conditions, synchronization +errors, measurement inaccuracies and limitations in radio re- +sources. Some of the factors, such as hardware properties and +limited radio bandwidth, are determined strictly by the cost +or regulation limitations and are more difficult to eliminate. +However, some others that are related to the propagation +environment may be detected and mitigated to some degree by +convenient post-processing especially when a large radio band- +width, e.g., that of an ultra-wideband (UWB) transmission, +is available. Among propagation environment related factors, +non-line-of-sight (NLOS) propagation is one of the primary +error sources in time-based positioning methods since it de- +correlates the time-of-flight (ToF) and the distance between +transmitter and receiver. +Various approaches have been proposed to improve the +accuracy of the time-based positioning techniques through +identifying or mitigating the effect of propagation conditions +on positioning. Binary classification of the propagation en- +vironment has been studied commonly in the form of line- +of-sight (LOS) versus non-line-of-sight (NLOS) classification +using hypothesis testing based on probabilistic models [2], +supervised machine learning (ML) [3], [4] and unsupervised +ML [5], [6]. Furthermore, multi-class classification has been +proposed by dividing NLOS propagation into two sub-classes +depending on the partial or full blockage of the LOS path [7], +[8], by adding a multipath class to the binary classification +problem [9], or by classifying the material of the LOS blocking +objects [10]. +Even though the classification approach can improve the +ranging or positioning accuracy through utilizing only the +favorable, i.e., LOS, measurements [3], [4], [5], discarding +NLOS measurements might lead to a poor positioning perfor- +mance when the number of the available measurements is low. +Moreover, such classification methods may not utilize the full +information present in the measurements since the number of +classes might be insufficient to describe the severity of the +NLOS propagation in the measurements fully. +Ranging error mitigation by processing various features +extracted from a received UWB waveform was studied by +utilizing support vector machines and Gaussian process esti- +mators [8], [11], or by fuzzy comprehensive evaluation along +with propagation channel identification [12]. Although the +methods were reported to yield an improvement in ranging, the +predetermined features extracted from the received waveform +might not represent all information in the received waveform +with respect to the ranging error. Such information loss was +overcome in [3], [13] where the ranging error was estimated +directly from a given channel impulse response (CIR) by using +arXiv:2301.04510v1 [eess.SP] 11 Jan 2023 + +artificial neural network (ANN) estimators. However, only a +specific UWB measurement and ranging device (DWM1000 +[14]) which utilizes a proprietary ranging algorithm was +considered. Although a leading-edge detection method was +mentioned to be used for ToA estimation in [14], details on +the adopted detection algorithm were not provided. In [15], +ToA estimation via convolutional neural networks (CNNs) was +studied, and the corresponding performance was compared +with that of some conventional, i.e., non-ML, ToA estimators. +However, the CNNs were trained mainly with simulation data, +and ToA error estimation was not studied which can provide +a measure of reliability of ToA estimation. +In this paper, we investigate the problem of estimating the +errors of various ToA estimators from a given CIR. Then, the +estimated errors can be mitigated to improve ranging accuracy +and, thereby, performance of a positioning system. The main +contributions of this paper are as follows: +• We propose a novel CNN-based scheme to estimate and +mitigate errors of various conventional ToA estimation +algorithms with different computational complexity such +as inflection point estimation (IFP) [16] and peak detec- +tion [17], and compare their performance to that of the +leading-edge detection (LDE) [18] and the DWM1000 +module [14] for a given CIR. +• We analyze the error mitigation performance of the +proposed CNN estimator for the cases of optimized and +suboptimal versions of the underlying ToA estimation +algorithms. +• We evaluate the performance for two independent real- +world datasets to ensure that the results are not specific +or biased to a single measurement campaign. +The analysis in this paper demonstrates that the proposed +CNN-based error mitigation scheme improves the accuracy of +the underlying conventional ToA estimators significantly even +if they are improved with a basic error mitigation method. +Furthermore, the proposed method is shown to provide a +robust ranging performance in case the parameters of the +underlying conventional ToA estimators are suboptimal. +II. SYSTEM DESCRIPTION +The considered scheme is composed of a two-step process. +In the first step, an initial ToA estimation is realized based +on a given CIR by one of the conventional methods listed in +Section II-B1. In the second step, the initial ToA estimate and +the CIR are input to an ANN to estimate the error of the initial +ToA estimation. Then, this information is utilized to mitigate +the error of initial ToA estimation, according to +� +ToA +′ = � +ToAconventional − �ϵToA, +(1) +where � +ToAconventional, �ϵToA and � +ToA +′ represent the initial ToA +estimated by a conventional method, the estimated error of +the conventional ToA estimate and the mitigated ToA, respec- +tively. +A. CIR and ToA Estimation +A CIR characterizes the communication channel and con- +tains information on the travel time of radio signals from +transmitter to receiver. Transmitted signals might arrive at +the receiver from different paths, e.g., direct, reflected, or +diffracted paths. ToA represents the arrival time of the first +arriving signal at the receiver and can be determined from a +given CIR. +B. Baseline Methods +1) Conventional ToA Estimators +In this work, we consider widely used conventional ToA +estimators, namely Peak, IFP and LDE, as well as DWM: +• Peak: The delay time of the first peak of the CIR above +a noise threshold is considered as ToA [17]. +• IFP: The delay time of the first point above a noise +threshold where the CIR concavity changes [16] is es- +timated as ToA. +• LDE: The CIR is filtered by a moving average window +whose output is further passed through two different +moving maximum window filters in parallel. The first +delay time above a noise threshold where the output of +the smaller maximum window filter exceeds the output +of the larger maximum window filter by a factor, i.e., the +leading-edge detection factor, is determined as ToA [18]. +• DWM: ToA is estimated by the DWM1000 device. The +DWM estimates used in this paper are taken from the +publicly available datasets [3], [19]. Although a leading- +edge detection method was mentioned to be used for +the ToA estimation in the device’s user manual [14], the +details of the DWM1000’s internal estimation algorithm +are not provided. +For Peak, IFP, and LDE, we define the noise threshold in +terms of the relative path strength similar to [20], formulated +as +γthi = α max{CIRi} +(2) +with the noise threshold factor α. LDE has three additional +parameters, namely the leading-edge detection factor and the +size of the small and large windows. The parameters of Peak, +IFP and LDE are optimized by an exhaustive search to yield +the lowest mean absolute ToA error. +2) Benchmark ToA Error Mitigation Method +In addition to the described conventional ToA estimators, we +consider a benchmark scheme to estimate the error of the ToA +estimation conducted by these conventional methods. Denoted +by CnstAvg, this benchmark models the ToA error as constant +and given by the mean of the error for each conventional ToA +estimator. Following the estimation of ToA error, the error can +be mitigated according to (1). +C. Ranging Based on ToA Estimation +The range, i.e., the distance between the tag and anchor, can +be estimated by multiplying the mitigated ToA by the speed +of the radio signals, i.e., speed of light, according to +�R = c( � +ToA +′ − ToT), +(3) + +CIR +Conventional +ToA estimator +� +ToAconventional* +CNN-based ToA error +mitigation scheme +CnstAvg ToA error +mitigation scheme +- +- +ToA′conventional+CNN† +ToA′conventional+CnstAvg‡ +�ϵToA +�ϵToA +*Conventional ToA estimators: Peak, IFP, LDE, DWM. +†Proposed CNN-based error mitigation scheme: Conventional+CNN (e.g., Peak+CNN). +‡Benchmark error mitigation scheme: Conventional+CnstAvg (e.g. LDE+CnstAvg). +Fig. 1: Flow diagram and the naming of the considered ToA estimators. +where c and �R represent the speed of light and the estimated +range, respectively. ToT in (3) can be eliminated by using a +two-way-ranging or a time-difference-of-arrival scheme. Sub- +sequently, positioning of a target device can be performed by +utilizing the range estimates with respect to multiple anchors +with known locations. As a result, improving the accuracy +of ToA estimates, i.e., through the error mitigation, yields an +improved ranging, thereby, a more accurate positioning. +III. PROPOSED METHOD +A. ToA Error Mitigation Using ANNs +The complex nature of NLOS or multipath propagation +poses a challenge to accurate modelling of ToA estimation +error based on an input CIR. Therefore, an ANN seems a +sensible choice to model the error of the ToA estimation. +We employ a one-dimensional CNN similar to [3], [13] to +estimate the error of the conventional ToA estimators based +on the input CIR, since CNNs are shown to be useful in +identifying spatial correlations among the input samples [21]. +Besides the CIR, � +ToAconventional is also input to the CNN. Then, +the output of the CNN, � +ϵToA, is used to mitigate the error of +the conventional ToA estimator according to (1). +The utilized CNN comprises 3 convolutional layers followed +by a fully connected layer. 16 output channels are used in each +convolutional layer with a kernel size of 5 and a stride of 2 +where no pooling layer is used in order to avoid a potential +information loss. The rectified linear unit (ReLU) is used as the +activation function in each neuron except for the output layer, +and dropout regularization with a factor of 0.5 is utilized to +prevent over-fitting. The CNNs are trained by using the Adam +optimizer [22] with a learning rate of 10−3 and a batch size +of 32 to minimize the mean-squared error (MSE) between the +estimated and the real ToA error. +The parameters of the CNN estimator are optimized using +training and validation data. It was observed that increasing +the number of hidden layers or number of output channels +further does not result in a significant additional performance +gain. +0 +25 +50 +75 +100 +125 +150 +175 +Time index +0.2 +0.0 +0.2 +0.4 +0.6 +0.8 +1.0 +Normalized CIR Magnitude +Random shift +Padding +157-sample CIR +Pre-processed CIR +Original ToA label +Pre-processed ToA label +Fig. 2: Randomly shifted and padded CIRs using the described pre-processing. +B. Dataset Description and Pre-processing +1) Datasets +We have used two publicly available datasets comprising +real-world UWB measurements, which we refer to as Office +and Room. Office dataset, given in [3], pertains to two dif- +ferent office environments, Office1 and Office2. Room dataset, +described in [13] and given in [19], comprises measurements +taken in different sized office-like rooms with different dimen- +sions. The measurements in both datasets are taken with 499.2 +MHz of bandwidth at 3993.6 MHz of center frequency. +It is assumed that the propagation channel between trans- +mitter and receiver is reciprocal, i.e., identical, for forward +and backward transmit directions, and the channel coherence +time is larger than the reply time of the applied two-way +ranging system. Such assumptions are realistic and required +since a single CIR is provided per each two-way ranging in +the datasets. +2) ToA Labeling +The ToA delay time estimated by DWM, � +ToADWM, the +corresponding ranging error, ϵR, and time resolution of the +CIR (i.e., the absolute time lapse between consecutive CIR +indices), δt, are given (or can be obtained) from the datasets +[3], [19]. Utilizing this information, we determine the ground- +truth ToA indices, i.e., ToA labels, according to +ToAtrue = � +ToADWM − ϵR +c δt +. +(4) +As such, the ranging error is converted into a ToA error which +is subtracted from the estimated ToA to determine the true +ToA. +It should be noted that labeling real ToA in real-world CIR +measurements is challenging and the introduced labeling may +contain errors due to the clock drift, finite bandwidth and finite +sampling rate. +3) Data Pre-processing +Only 152 (out of 1016) samples after the first detected path +were considered for each CIR in [3], whereas additional 5 CIR +samples prior to the detected first path were also considered +in [13] yielding CIRs with 157 samples. We further add a +random number of noise-like samples (maximum 30 samples) +prior to each CIR shifting CIRs randomly with respect to the +time axis to eliminate a potential bias, and apply padding to +the end of CIRs accordingly, yielding CIRs with 187 samples + +0.0 +0.1 +0.2 +0.3 +0.4 +0.5 +0.6 +0.7 +0.8 +Ranging Error (m) +0.0 +0.2 +0.4 +0.6 +0.8 +1.0 +CDF +0.10 +0.15 +0.20 +0.25 +0.30 +0.35 +0.40 +0.75 +0.80 +0.85 +0.90 +0.95 +DWM+CNN +Peak+CNN +IFP+CNN +LDE+CNN +LDE +Peak +IFP +DWM +(a) +0.0 +0.1 +0.2 +0.3 +0.4 +0.5 +0.6 +0.7 +0.8 +Ranging Error (m) +0.0 +0.2 +0.4 +0.6 +0.8 +1.0 +CDF +0.10 +0.15 +0.20 +0.25 +0.30 +0.35 +0.40 +0.75 +0.80 +0.85 +0.90 +0.95 +DWM+CNN +Peak+CNN +IFP+CNN +LDE+CNN +DWM+CnstAvg +Peak+CnstAvg +IFP+CnstAvg +LDE+CnstAvg +(b) +0 +20 +40 +60 +80 +90th% |R| (cm) +90th% +|R| + (cm): +LDE+CNN +22.0 +LDE +27.0 +LDE+CnstAvg +29.0 +Peak+CnstAvg +35.0 +Peak+CNN +22.0 +Peak +85.0 +IFP+CnstAvg +35.0 +IFP+CNN +25.0 +IFP +35.0 +DWM+CnstAvg +19.0 +DWM +25.0 +DWM+CNN +16.0 +(c) +0 +20 +40 +60 +Mean |R| (cm) +mean +|R| + (cm): +LDE+CNN +10.0 +LDE +13.0 +LDE+CnstAvg +12.0 +Peak+CnstAvg +20.0 +Peak+CNN +11.0 +Peak +57.0 +IFP+CnstAvg +20.0 +IFP+CNN +12.0 +IFP +20.0 +DWM+CnstAvg +10.0 +DWM +12.0 +DWM+CNN +8.0 +(d) +Fig. 3: The CDF of ranging error of the proposed CNN-based estimator in comparison to (a) conventional ToA estimators and (b) benchmark CnstAvg +estimators, and comparison of (c) 90th percentile and (d) mean absolute ranging error of the considered schemes +for Room dataset. +as shown in Fig. 2. The ToA labels are shifted together, i.e., +by the same amount, with the CIRs. +Each CIR is normalized by its maximum value before being +input to the proposed CNN estimator to prevent a potential +bias that might be caused by varying absolute amplitudes of +the CIR samples. +The datasets are divided into training, validation and test +data for the CNN. Further, to enable a fair comparison, the +training and validation data are used together to optimize +the parameters of the conventional ToA estimators and the +benchmark error mitigation method. The test data is selected +from measurements taken in another environment (i.e., another +office or another sized-room) than the training and validation +data to assess the generalizability of the results. This approach +is in line with the recent 3GPP agreements on evaluating the +generalization performance of ML models used for positioning +[23]. Training and validation data comprise 70% and 30% +of the measurements belonging to the same environment, re- +spectively, resulting in approximately 5000 training samples in +each scenario for the Office dataset. To make a fair comparison +between the two datasets, we also use approximately 5000 +training samples for each scenario in the Room dataset. It is +noted that the Office dataset includes repeated measurements +taken from each anchor-tag location pair, i.e., not all training +samples is associated with a different anchor-tag location pair, +unlike the Room dataset. +IV. PERFORMANCE EVALUATION +In this section, we present performance results based on +real-world measurements for the proposed (CNN) and the +benchmark (CnstAvg) ToA error mitigation methods as well +as conventional, i.e., unmitigated, ToA estimators (LDE, IFP, +Peak, DWM). The naming of the estimators considered in this +paper is shown in Fig. 1. We utilize the PyTorch framework to +train the CNN. The results are generated based on 10 random +selections of training and test measurement samples for each +scenario to average out potential variations across data chunks. +A. Ranging Accuracy Evaluation +As evaluation metric, we consider the absolute ranging error, +ϵ|R|, given by +ϵ|R| = | ˆR − Rtrue|, +(5) +where Rtrue denotes the real range obtained from the datasets +[3], [19]. +We provide the CDF of the ranging error for different +ToA estimation schemes in Figs. 3 and 4, for Office and +Room datasets, respectively. It can be observed from Figs. +3-4 that the proposed CNN-based error mitigation scheme +improves the accuracy of the conventional ToA estimators. The +improvement in 90th percentile ranging error varies between +19-74% and 4-38% for Room and Office datasets, respectively, +depending on the utilized conventional ToA estimator. The +smaller improvement for the Office dataset can be explained by +the fact that the Office dataset contains repeated measurements +taken for the same anchor-tag location pairs, unlike the Room +dataset. As a result, there is a lower number of measure- +ments taken for unique anchor-tag location pairs leading to +an insufficient amount of unique data for the CNN to be +trained. Furthermore, all methods perform worse in Office +dataset than in Room dataset despite the same measurement +and ranging module, DWM1000, used. This can be explained +by the different propagation environments, i.e., the propagation +environment for Office dataset might be more challenging, or a +discrepancy in the calibration of the DWM1000 module, e.g., +antenna delay calibration. +Comparing the two error mitigation methods, i.e., CNN and +CnstAvg, the proposed CNN-based method further yields a +considerably better performance than CnstAvg in most cases, +and a similar performance in the worst case, depending on +the underlying conventional ToA estimator. The gain of the +CNN estimator over CnstAvg estimator lies between 16-37% +and 3-16% in Room and Office datasets, respectively, in 90th +percentile ranging accuracy. Our performance evaluation also +enables a comparison of conventional ToA estimators from the +literature. Figures 3a and 4a show that LDE outperforms IFP +and Peak. Peak is observed to show the worst performance +in both datasets possibly due to the susceptibility of the peak +detection to multipath propagation [18], [24]. +B. Comparison with DWM +Figure 3a shows that DWM outperforms LDE slightly +whereas LDE has a marginally better performance than DWM +according to Fig. 4a. The similar performance of DWM and +LDE can be explained by the fact that a leading-edge detection + +0.00 +0.25 +0.50 +0.75 +1.00 +1.25 +1.50 +1.75 +2.00 +Ranging Error (m) +0.0 +0.2 +0.4 +0.6 +0.8 +1.0 +CDF +0.5 +0.6 +0.7 +0.8 +0.9 +1.0 +0.75 +0.80 +0.85 +0.90 +0.95 +LDE+CNN +Peak+CNN +IFP+CNN +DWM+CNN +LDE +Peak +IFP +DWM +(a) +0.00 +0.25 +0.50 +0.75 +1.00 +1.25 +1.50 +1.75 +2.00 +Ranging Error (m) +0.0 +0.2 +0.4 +0.6 +0.8 +1.0 +CDF +0.5 +0.6 +0.7 +0.8 +0.9 +1.0 +0.75 +0.80 +0.85 +0.90 +0.95 +LDE+CNN +Peak+CNN +IFP+CNN +DWM+CNN +LDE+CnstAvg +Peak+CnstAvg +IFP+CnstAvg +DWM+CnstAvg +(b) +0 +20 +40 +60 +80 +90th% |R| (cm) +90th% +|R| + (cm): +LDE+CNN +62.0 +LDE +71.0 +LDE+CnstAvg +65.0 +Peak+CnstAvg +75.0 +Peak+CNN +73.0 +Peak +117.0 +IFP+CnstAvg +81.0 +IFP+CNN +78.0 +IFP +81.0 +DWM+CnstAvg +74.0 +DWM +87.0 +DWM+CNN +62.0 +(c) +0 +20 +40 +60 +Mean |R| (cm) +mean +|R| + (cm): +LDE+CNN +32.0 +LDE +33.0 +LDE+CnstAvg +33.0 +Peak+CnstAvg +39.0 +Peak+CNN +36.0 +Peak +59.0 +IFP+CnstAvg +51.0 +IFP+CNN +47.0 +IFP +52.0 +DWM+CnstAvg +39.0 +DWM +36.0 +DWM+CNN +34.0 +(d) +Fig. 4: The CDF of ranging error of the proposed CNN-based estimator in comparison to (a) conventional ToA estimators and (b) benchmark CnstAvg +estimators, and (c) 90th percentile and (d) mean absolute ranging errors of the considered schemes +for Office dataset. +method was utilized by the DWM1000 device. Another obser- +vation is that CnstAvg degrades the performance of DWM, i.e., +CnstAvg+DWM performs worse than DWM, in mean absolute +ranging error for Office dataset. This can be explained by +the fact that the average ToA estimation error of DWM is +substantially different for Office1 and Office2, i.e., for training +and test data. +Accuracy performance comparison of DWM+CNN and +LDE+CNN shows contradicting results, similar to the com- +parison between DWM and LDE. LDE+CNN outperforms +DWM+CNN for the Office dataset while DWM+CNN has the +superior performance for the Room dataset. The underlying +reason might be a discrepancy in the calibration of the +DWM1000 device in the two measurement campaigns. The +details of the DWM1000’s internal estimation algorithm were +not provided neither in the device’s user manual [14] nor +in the descriptions of the measurements campaigns [3], [13]. +Therefore, it is difficult to draw further conclusions regarding +the performance of DWM-related estimators. +C. Effect of Utilizing Sub-optimal Conventional Methods +Various approaches can be used to optimize the parameters +of the conventional methods. For instance, as an alternative +to selecting the noise threshold in terms of the relative path +strength [20], it can also be determined in terms of the +thermal noise [11]. Additionally, the number and density of the +candidate values of an exhaustive or grid search might yield +different optimized parameters. As a result, the parameters of +the utilized conventional ToA estimators can be sup-obtimal. +In Table I, we provide the results related to the impact +of optimizing the conventional ToA estimators. Such impact +could not be evaluated for DWM since it is based on a propri- +etary detection algorithm. It can be observed from Table I that +the performance of the conventional ToA estimators heavily +depends on the parameter optimization for the measurements +in both datasets. The proposed CNN estimator provides a ro- +bust ranging estimation, in case the utilized conventional ToA +estimators are not optimized carefully. Specifically, using the +proposed CNN estimator, the loss in ranging performance due +to suboptimal parameters of the conventional ToA estimators +is at most 8 cm at 90th percentile for both datasets, compared +TABLE I: 90th percentile absolute ranging errors of the considered +ToA estimators and the increase in ranging error due to suboptimal +(underlying) conventional ToA estimators. +ToA (error) +estimation method +90th%(ϵ|R|) (cm) +Office dataset +Room dataset +Ranging error when +conventional estimators +are optimized +LDE +LDE +71 +27 +LDE+CnstAvg +65 +29 +LDE+CNN +62 +22 +Peak +Peak +117 +85 +Peak+CnstAvg +75 +35 +Peak+CNN +73 +22 +IFP +IFP +81 +35 +IFP+CnstAvg +81 +35 +IFP+CNN +78 +25 +Increase in ranging +error due to suboptimal +conventional estimator +LDE +LDE ++28 ++12 +LDE+CnstAvg ++12 ++3 +LDE+CNN ++8 ++0 +Peak +Peak ++31 ++22 +Peak+CnstAvg ++18 ++13 +Peak+CNN ++4 ++7 +IFP +IFP ++37 ++34 +IFP+CnstAvg ++11 ++21 +IFP+CNN ++6 ++6 +to 21 cm of CnstAvg and 37 cm of the conventional ToA +estimators. +D. Complexity Analysis +Finding peaks of the input CIR dominates the computational +complexity of Peak requiring O(N) operations, where N +denotes the length of the CIRs. The complexity of IFP is +mainly determined by the calculation of the gradient where +a subtraction and a division is performed for each element +yielding a complexity of O(N). LDE is composed of a +moving average filter followed by two moving maximum +filters where the outputs of the two moving maximum windows +are compared element-wise. The window size is constant in +all three filters, and the window is shifted through the CIR +yielding an overall complexity of O(N). +Each one-dimensional convolutional layer of the proposed +CNN is associated to a constant filter size, and a constant +number of filters is shifted along the input CIR. The subse- +quent single fully connected layer maps the output of the last +convolutional layer to a scalar resulting in an overall complex- +ity of O(N). Although the dependence of the complexity on +the input CIR size is linear for the considered estimators, the +complexities of the estimators are different. Table II shows the + +TABLE II: Computation time of the conventional estimators and the additional +latency caused by the CNN mitigation scheme for one sample. +Estimator +Peak +IFP +LDE ++CNN +Time (ms) +0.07 +0.12 +0.39 ++0.35 +time complexity of inference of the estimators that are imple- +mented using Pytorch, numpy and scipy libraries of Python +programming language running on a computer equipped with +Intel(R) Xeon(R) CPU E5-2680 v4 @ 2.40GHz and 24 GB of +RAM. The additional latency caused by the proposed CNN- +based error mitigation scheme is comparable to the latency of +the widely used LDE estimator. +V. CONCLUSIONS +In this paper, we have proposed a supervised ML approach +based on CNNs for estimation of the error of conventional ToA +estimators. These estimates are in turn used for mitigating such +errors to improve the ranging accuracy. We have evaluated +the performance of the proposed methods using real-world +measurements collected from various environments. We first +observed that the performance of the conventional ToA esti- +mators differ significantly from each other, and further require +optimization of their parameters for an improved performance. +While the errors of the conventional ToA estimators could be +mitigated partly by a simple benchmark mitigation scheme, +such approach might even result in a worse performance in +some cases. +As an alternative, the proposed CNN-based error mitigation +method can improve the ranging accuracy of the conven- +tional ToA estimators with an acceptable amount of added +latency. The proposed estimator was shown to outperform the +benchmark error mitigation scheme by up to 16-37% in 90th +percentile ranging accuracy depending on the environment. +In addition, it was shown that the proposed CNN estimator +provides a robust ranging performance, with only less than 8 +cm of additional ranging error in 90th percentile, in case the +parameters of the underlying ToA estimators are suboptimal. +Thus, the CNN estimator can eliminate the necessity of care- +fully optimizing the underlying conventional ToA estimators, +depending on the accuracy requirements. In this way, the +proposed method offers an attractive solution for improving +the ranging accuracy, providing a robust performance under +different conventional ToA estimation algorithms and across +various propagation environments. +In addition to the proposed use of ML to mitigate the error +of conventional ToA estimators, ML methods can be also +applied to estimate the ToA directly, i.e., without requiring +a conventional ToA estimator. Further research is needed to +compare the performance of these two approaches. +REFERENCES +[1] +3GPP, “Study on NR positioning enhancements,” TR38.857, V2.0.0, +2021. +[2] +I. Guvenc, C.C. Chong, and F. Watanabe, “NLOS identification and +mitigation for UWB localization systems,” in Proc. IEEE Int. Conf. +Wireless Commun. Networking (WCNC), pp. 1571-1576, 2007. +[3] +K. Bregar and M. Mohorˇciˇc, “Improving Indoor Localization Us- +ing Convolutional Neural Networks on Computationally Restricted +Devices,” IEEE Access, vol. 6, pp. 17429-17441, 2018. +[4] +M. Stahlke, S. Kram, C. Mutschler, and T. Mahr, “NLOS Detection +using UWB Channel Impulse Responses and Convolutional Neural +Networks,” in Proc. of International Conference on Localization and +GNSS (ICL-GNSS), pp. 1-6, 2020. +[5] +A. Kirmaz, D. S. Michalopoulos, I. Balan, and W. Gerstacker, +“LOS/NLOS Classification Using Scenario-Dependent Unsuper- +vised Machine Learning,” in Proc. of IEEE 32nd Annual Interna- +tional Symposium on Personal, Indoor and Mobile Radio Commu- +nications (PIMRC), pp. 1134-1140, 2021. +[6] +J. Fan and A. S. Awan, “Non-Line-of-Sight Identification Based on +Unsupervised Machine Learning in Ultra-Wideband Systems,” IEEE +Access, vol. 7, pp. 32464-32471, 2019. +[7] +M. Kolakowski and J. Modelski, “Detection of direct path compo- +nent absence in NLOS UWB channel,” in Proc. of 22nd Interna- +tional Microwave and Radar Conference (MIKON), pp. 247-250, +2018. +[8] +V. Barral, C. J. Escudero, J. A. Garc´ıa-Naya, and R. Maneiro- +Catoira, “NLOS Identification and Mitigation Using Low-Cost +UWB Devices,” Sensors, vol. 19, no. 16, pp. 3464, 2019. +[9] +C. Lian Sang, B. Steinhagen, J.D. Homburg, M. Adams, M. Hesse, +and U. R¨uckert, “Identification of NLOS and Multi-Path Conditions +in UWB Localization Using Machine Learning Methods,” Appl. Sci., +vol. 10, no. 11, pp. 3980, 2020. +[10] +Y. Kong, C. Li, Z. Chen, and X. Zhao, “Recognition of Blocking +Categories for UWB Positioning in Complex Indoor Environment,” +Sensors, vol. 20, no. 15, pp. 4178, 2020. +[11] +H. Wymeersch, S. Marano, W. M. Gifford, and M. Z. Win, “A +Machine Learning Approach to Ranging Error Mitigation for UWB +Localization,” IEEE Trans. Commun., vol. 60, no. 6, pp. 1719-1728, +2012. +[12] +K. Yu, K. Wen, Y. Li, S. Zhang, and K. Zhang, “A Novel NLOS +Mitigation Algorithm for UWB Localization in Harsh Indoor En- +vironments,” IEEE Transactions on Vehicular Technology, vol. 68, +no. 1, pp. 686-699, 2019. +[13] +S. Angarano, V. Mazzia, F. Salvetti, G. Fantin, and M. Chiaberge, +“Robust Ultra-wideband Range Error Mitigation with Deep Learn- +ing at the Edge,” Engineering Applications of Artificial Intelligence, +vol. 102, pp. 104278, 2021. +[14] +Decawave Ltd. DW1000 User Manual. Accessed: May 3, 2022. [On- +line]. Available: https://www.decawave.com/dw1000/usermanual/ +[15] +T. Feigl, E. Eberlein, S. Kram and C. Mutschler, “Robust ToA- +Estimation using Convolutional Neural Networks on Randomized +Channel Models,” in Proc. of International Conference on Indoor +Positioning and Indoor Navigation (IPIN), pp. 1-8, 2019. +[16] +G. Hofmann and M. Breiling, “Device and method for determining +a time of arrival of a receive sequence”, 2009. US Patent 7,627,063. +[17] +C. Falsi, D. Dardari, L. Mucchi, and M. Z. Win, “Time of arrival +estimation for UWB localizers in realistic environments”, EURASIP +J. Appl. Signal Process., vol. 2006, pp. 1–13, 2006. +[18] +B. Merkl, “The future of the operating room: Surgical preplanning +and navigation using high accuracy ultra-wideband positioning and +advanced bone measurement,” Ph.D. dissertation, Dept. Biomed. +Eng., Univ. Tennessee, Knoxville, TN, 2008. +[19] +S. Angarano, V. Mazzia, F. Salvetti, G. Fantin, and M. Chiaberge, +“Deep UWB,” Zenodo, 2020, doi: 10.5281/zenodo.4399187. +[20] +J.-Y. Lee and R. A. Scholtz, “Ranging in a dense multipath envi- +ronment using an UWB radio link,” IEEE J. Sel. Areas Commun., +vol. 20, no. 9, pp. 1677-1683, Dec. 2002. +[21] +Y. LeCun, L. Bottou, Y. Bengio, and P. Haffner, “Gradient based +learning applied to document recognition”, in Proc. of the IEEE, +vol. 86, no. 11, pp. 2278–2324, 1998. +[22] +D. P. Kingma and J. L. Ba, “Adam: A method for stochastic +optimization”, in Proc. of Int. Conf. Learn. Represent. (ICLR), 2015. +[23] +3GPP, “R1-2212817, (Final) Summary #5 of Evaluation on AI/ML +for positioning accuracy enhancement”, Nov. 2022. +[24] +M. J. Kuhn, M. R. Mahfouz, C. Zhang, B. C. Merkl and A. E. Fathy, +“A System-Level Simulation Framework for UWB Localization”, +Ph.D. dissertation, University of Tennessee, Knoxville, 2008. + diff --git a/VNE3T4oBgHgl3EQfawrQ/content/tmp_files/load_file.txt b/VNE3T4oBgHgl3EQfawrQ/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..62215ba7f3f9d9e50f9c2e976f783ff68c3d97ad --- /dev/null +++ b/VNE3T4oBgHgl3EQfawrQ/content/tmp_files/load_file.txt @@ -0,0 +1,672 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf,len=671 +page_content='Time of Arrival Error Estimation for Positioning Using Convolutional Neural Networks Anil Kirmaz*†, Taylan S¸ahin*, Diomidis S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Michalopoulos*, Muhammad Ikram Ashraf*, and Wolfgang Gerstacker† Nokia Strategy and Technology, Munich, Germany, †Institute for Digital Communications, Friedrich-Alexander-Universit¨at Erlangen-N¨urnberg, Erlangen, Germany Abstract—Wireless high-accuracy positioning has recently at- tracted growing research interest due to diversified nature of applications such as industrial asset tracking, autonomous driv- ing, process automation, and many more.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' However, obtaining a highly accurate location information is hampered by challenges due to the radio environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' A major source of error for time- based positioning methods is inaccurate time-of-arrival (ToA) or range estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Existing machine learning-based solutions to mitigate such errors rely on propagation environment classifi- cation hindered by a low number of classes, employ a set of features representing channel measurements only to a limited extent, or account for only device-specific proprietary methods of ToA estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' In this paper, we propose convolutional neural networks (CNNs) to estimate and mitigate the errors of a variety of ToA estimation methods utilizing channel impulse responses (CIRs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Based on real-world measurements from two independent campaigns, the proposed method yields significant improvements in ranging accuracy (up to 37%) of the state-of- the-art ToA estimators, often eliminating the need of optimizing the underlying conventional methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Index Terms—Time-of-arrival estimation, high accuracy posi- tioning, convolutional neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' INTRODUCTION Location information is vital for many applications across various domains including industrial internet-of-things (IIoT), emergency services, transportation, and many more.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Some of the applications, such as industrial asset tracking, autonomous driving and process automation, require highly accurate po- sition estimation as emphasized in 3GPP [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Location infor- mation can be obtained by various approaches including time- based, angle-based and fingerprinting-based techniques using radio signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' One of the major approaches in widely utilized time-based positioning is to estimate the time-of-arrival (ToA) of the received positioning signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Combined with time-of- transmission (ToT), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=', the time when the radio signal is sent from the transmitter, ToA is used to calculate time-of-flight (ToF), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=', the time it takes for the radio signal to travel from transmitter to receiver.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Then, the range between transmitter and receiver can be estimated using ToF since the radio signals travel at a known speed, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=', the speed of light, and can be utilized for positioning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' The accuracy of ToA estimation is limited by various factors such as challenging propagation conditions, synchronization errors, measurement inaccuracies and limitations in radio re- sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Some of the factors, such as hardware properties and limited radio bandwidth, are determined strictly by the cost or regulation limitations and are more difficult to eliminate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' However, some others that are related to the propagation environment may be detected and mitigated to some degree by convenient post-processing especially when a large radio band- width, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=', that of an ultra-wideband (UWB) transmission, is available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Among propagation environment related factors, non-line-of-sight (NLOS) propagation is one of the primary error sources in time-based positioning methods since it de- correlates the time-of-flight (ToF) and the distance between transmitter and receiver.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Various approaches have been proposed to improve the accuracy of the time-based positioning techniques through identifying or mitigating the effect of propagation conditions on positioning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Binary classification of the propagation en- vironment has been studied commonly in the form of line- of-sight (LOS) versus non-line-of-sight (NLOS) classification using hypothesis testing based on probabilistic models [2], supervised machine learning (ML) [3], [4] and unsupervised ML [5], [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Furthermore, multi-class classification has been proposed by dividing NLOS propagation into two sub-classes depending on the partial or full blockage of the LOS path [7], [8], by adding a multipath class to the binary classification problem [9], or by classifying the material of the LOS blocking objects [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Even though the classification approach can improve the ranging or positioning accuracy through utilizing only the favorable, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=', LOS, measurements [3], [4], [5], discarding NLOS measurements might lead to a poor positioning perfor- mance when the number of the available measurements is low.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Moreover, such classification methods may not utilize the full information present in the measurements since the number of classes might be insufficient to describe the severity of the NLOS propagation in the measurements fully.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Ranging error mitigation by processing various features extracted from a received UWB waveform was studied by utilizing support vector machines and Gaussian process esti- mators [8], [11], or by fuzzy comprehensive evaluation along with propagation channel identification [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Although the methods were reported to yield an improvement in ranging, the predetermined features extracted from the received waveform might not represent all information in the received waveform with respect to the ranging error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Such information loss was overcome in [3], [13] where the ranging error was estimated directly from a given channel impulse response (CIR) by using arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='04510v1 [eess.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='SP] 11 Jan 2023 artificial neural network (ANN) estimators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' However, only a specific UWB measurement and ranging device (DWM1000 [14]) which utilizes a proprietary ranging algorithm was considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Although a leading-edge detection method was mentioned to be used for ToA estimation in [14], details on the adopted detection algorithm were not provided.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' In [15], ToA estimation via convolutional neural networks (CNNs) was studied, and the corresponding performance was compared with that of some conventional, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=', non-ML, ToA estimators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' However, the CNNs were trained mainly with simulation data, and ToA error estimation was not studied which can provide a measure of reliability of ToA estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' In this paper, we investigate the problem of estimating the errors of various ToA estimators from a given CIR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Then, the estimated errors can be mitigated to improve ranging accuracy and, thereby, performance of a positioning system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' The main contributions of this paper are as follows: We propose a novel CNN-based scheme to estimate and mitigate errors of various conventional ToA estimation algorithms with different computational complexity such as inflection point estimation (IFP) [16] and peak detec- tion [17], and compare their performance to that of the leading-edge detection (LDE) [18] and the DWM1000 module [14] for a given CIR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' We analyze the error mitigation performance of the proposed CNN estimator for the cases of optimized and suboptimal versions of the underlying ToA estimation algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' We evaluate the performance for two independent real- world datasets to ensure that the results are not specific or biased to a single measurement campaign.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' The analysis in this paper demonstrates that the proposed CNN-based error mitigation scheme improves the accuracy of the underlying conventional ToA estimators significantly even if they are improved with a basic error mitigation method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Furthermore, the proposed method is shown to provide a robust ranging performance in case the parameters of the underlying conventional ToA estimators are suboptimal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' SYSTEM DESCRIPTION The considered scheme is composed of a two-step process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' In the first step, an initial ToA estimation is realized based on a given CIR by one of the conventional methods listed in Section II-B1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' In the second step, the initial ToA estimate and the CIR are input to an ANN to estimate the error of the initial ToA estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Then, this information is utilized to mitigate the error of initial ToA estimation, according to � ToA ′ = � ToAconventional − �ϵToA, (1) where � ToAconventional, �ϵToA and � ToA ′ represent the initial ToA estimated by a conventional method, the estimated error of the conventional ToA estimate and the mitigated ToA, respec- tively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' CIR and ToA Estimation A CIR characterizes the communication channel and con- tains information on the travel time of radio signals from transmitter to receiver.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Transmitted signals might arrive at the receiver from different paths, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=', direct, reflected, or diffracted paths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' ToA represents the arrival time of the first arriving signal at the receiver and can be determined from a given CIR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Baseline Methods 1) Conventional ToA Estimators In this work, we consider widely used conventional ToA estimators, namely Peak, IFP and LDE, as well as DWM: Peak: The delay time of the first peak of the CIR above a noise threshold is considered as ToA [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' IFP: The delay time of the first point above a noise threshold where the CIR concavity changes [16] is es- timated as ToA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' LDE: The CIR is filtered by a moving average window whose output is further passed through two different moving maximum window filters in parallel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' The first delay time above a noise threshold where the output of the smaller maximum window filter exceeds the output of the larger maximum window filter by a factor, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=', the leading-edge detection factor, is determined as ToA [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' DWM: ToA is estimated by the DWM1000 device.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' The DWM estimates used in this paper are taken from the publicly available datasets [3], [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Although a leading- edge detection method was mentioned to be used for the ToA estimation in the device’s user manual [14], the details of the DWM1000’s internal estimation algorithm are not provided.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' For Peak, IFP, and LDE, we define the noise threshold in terms of the relative path strength similar to [20], formulated as γthi = α max{CIRi} (2) with the noise threshold factor α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' LDE has three additional parameters, namely the leading-edge detection factor and the size of the small and large windows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' The parameters of Peak, IFP and LDE are optimized by an exhaustive search to yield the lowest mean absolute ToA error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' 2) Benchmark ToA Error Mitigation Method In addition to the described conventional ToA estimators, we consider a benchmark scheme to estimate the error of the ToA estimation conducted by these conventional methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Denoted by CnstAvg, this benchmark models the ToA error as constant and given by the mean of the error for each conventional ToA estimator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Following the estimation of ToA error, the error can be mitigated according to (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Ranging Based on ToA Estimation The range, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=', the distance between the tag and anchor, can be estimated by multiplying the mitigated ToA by the speed of the radio signals, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=', speed of light, according to �R = c( � ToA ′ − ToT), (3) CIR Conventional ToA estimator � ToAconventional* CNN-based ToA error mitigation scheme CnstAvg ToA error mitigation scheme ToA′conventional+CNN† ToA′conventional+CnstAvg‡ �ϵToA �ϵToA Conventional ToA estimators: Peak, IFP, LDE, DWM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' †Proposed CNN-based error mitigation scheme: Conventional+CNN (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=', Peak+CNN).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' ‡Benchmark error mitigation scheme: Conventional+CnstAvg (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' LDE+CnstAvg).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' 1: Flow diagram and the naming of the considered ToA estimators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' where c and �R represent the speed of light and the estimated range, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' ToT in (3) can be eliminated by using a two-way-ranging or a time-difference-of-arrival scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Sub- sequently, positioning of a target device can be performed by utilizing the range estimates with respect to multiple anchors with known locations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' As a result, improving the accuracy of ToA estimates, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=', through the error mitigation, yields an improved ranging, thereby, a more accurate positioning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' PROPOSED METHOD A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' ToA Error Mitigation Using ANNs The complex nature of NLOS or multipath propagation poses a challenge to accurate modelling of ToA estimation error based on an input CIR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Therefore, an ANN seems a sensible choice to model the error of the ToA estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' We employ a one-dimensional CNN similar to [3], [13] to estimate the error of the conventional ToA estimators based on the input CIR, since CNNs are shown to be useful in identifying spatial correlations among the input samples [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Besides the CIR, � ToAconventional is also input to the CNN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Then, the output of the CNN, � ϵToA, is used to mitigate the error of the conventional ToA estimator according to (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' The utilized CNN comprises 3 convolutional layers followed by a fully connected layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' 16 output channels are used in each convolutional layer with a kernel size of 5 and a stride of 2 where no pooling layer is used in order to avoid a potential information loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' The rectified linear unit (ReLU) is used as the activation function in each neuron except for the output layer, and dropout regularization with a factor of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='5 is utilized to prevent over-fitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' The CNNs are trained by using the Adam optimizer [22] with a learning rate of 10−3 and a batch size of 32 to minimize the mean-squared error (MSE) between the estimated and the real ToA error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' The parameters of the CNN estimator are optimized using training and validation data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' It was observed that increasing the number of hidden layers or number of output channels further does not result in a significant additional performance gain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' 0 25 50 75 100 125 150 175 Time index 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='0 Normalized CIR Magnitude Random shift Padding 157-sample CIR Pre-processed CIR Original ToA label Pre-processed ToA label Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' 2: Randomly shifted and padded CIRs using the described pre-processing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Dataset Description and Pre-processing 1) Datasets We have used two publicly available datasets comprising real-world UWB measurements, which we refer to as Office and Room.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Office dataset, given in [3], pertains to two dif- ferent office environments, Office1 and Office2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Room dataset, described in [13] and given in [19], comprises measurements taken in different sized office-like rooms with different dimen- sions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' The measurements in both datasets are taken with 499.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='2 MHz of bandwidth at 3993.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='6 MHz of center frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' It is assumed that the propagation channel between trans- mitter and receiver is reciprocal, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=', identical, for forward and backward transmit directions, and the channel coherence time is larger than the reply time of the applied two-way ranging system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Such assumptions are realistic and required since a single CIR is provided per each two-way ranging in the datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' 2) ToA Labeling The ToA delay time estimated by DWM, � ToADWM, the corresponding ranging error, ϵR, and time resolution of the CIR (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=', the absolute time lapse between consecutive CIR indices), δt, are given (or can be obtained) from the datasets [3], [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Utilizing this information, we determine the ground- truth ToA indices, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=', ToA labels, according to ToAtrue = � ToADWM − ϵR c δt .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' (4) As such, the ranging error is converted into a ToA error which is subtracted from the estimated ToA to determine the true ToA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' It should be noted that labeling real ToA in real-world CIR measurements is challenging and the introduced labeling may contain errors due to the clock drift, finite bandwidth and finite sampling rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' 3) Data Pre-processing Only 152 (out of 1016) samples after the first detected path were considered for each CIR in [3], whereas additional 5 CIR samples prior to the detected first path were also considered in [13] yielding CIRs with 157 samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' We further add a random number of noise-like samples (maximum 30 samples) prior to each CIR shifting CIRs randomly with respect to the time axis to eliminate a potential bias, and apply padding to the end of CIRs accordingly, yielding CIRs with 187 samples 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='8 Ranging Error (m) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='0 CDF 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='30 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='35 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='40 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='75 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='80 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='85 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='90 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='95 DWM+CNN Peak+CNN IFP+CNN LDE+CNN LDE Peak IFP DWM (a) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='8 Ranging Error (m) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='0 CDF 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='25 0.' metadata={'source': 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metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='0 IFP+CnstAvg 35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='0 IFP+CNN 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='0 IFP 35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='0 DWM+CnstAvg 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='0 DWM 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='0 DWM+CNN 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='0 (c) 0 20 40 60 Mean |R| (cm) mean |R| (cm): LDE+CNN 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='0 LDE 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='0 LDE+CnstAvg 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='0 Peak+CnstAvg 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='0 Peak+CNN 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='0 Peak 57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='0 IFP+CnstAvg 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='0 IFP+CNN 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='0 IFP 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='0 DWM+CnstAvg 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='0 DWM 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='0 DWM+CNN 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='0 (d) Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' 3: The CDF of ranging error of the proposed CNN-based estimator in comparison to (a) conventional ToA estimators and (b) benchmark CnstAvg estimators, and comparison of (c) 90th percentile and (d) mean absolute ranging error of the considered schemes for Room dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' The ToA labels are shifted together, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=', by the same amount, with the CIRs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Each CIR is normalized by its maximum value before being input to the proposed CNN estimator to prevent a potential bias that might be caused by varying absolute amplitudes of the CIR samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' The datasets are divided into training, validation and test data for the CNN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Further, to enable a fair comparison, the training and validation data are used together to optimize the parameters of the conventional ToA estimators and the benchmark error mitigation method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' The test data is selected from measurements taken in another environment (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=', another office or another sized-room) than the training and validation data to assess the generalizability of the results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' This approach is in line with the recent 3GPP agreements on evaluating the generalization performance of ML models used for positioning [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Training and validation data comprise 70% and 30% of the measurements belonging to the same environment, re- spectively, resulting in approximately 5000 training samples in each scenario for the Office dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' To make a fair comparison between the two datasets, we also use approximately 5000 training samples for each scenario in the Room dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' It is noted that the Office dataset includes repeated measurements taken from each anchor-tag location pair, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=', not all training samples is associated with a different anchor-tag location pair, unlike the Room dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' PERFORMANCE EVALUATION In this section, we present performance results based on real-world measurements for the proposed (CNN) and the benchmark (CnstAvg) ToA error mitigation methods as well as conventional, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=', unmitigated, ToA estimators (LDE, IFP, Peak, DWM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' The naming of the estimators considered in this paper is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' We utilize the PyTorch framework to train the CNN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' The results are generated based on 10 random selections of training and test measurement samples for each scenario to average out potential variations across data chunks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Ranging Accuracy Evaluation As evaluation metric, we consider the absolute ranging error, ϵ|R|, given by ϵ|R| = | ˆR − Rtrue|, (5) where Rtrue denotes the real range obtained from the datasets [3], [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' We provide the CDF of the ranging error for different ToA estimation schemes in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' 3 and 4, for Office and Room datasets, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' It can be observed from Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' 3-4 that the proposed CNN-based error mitigation scheme improves the accuracy of the conventional ToA estimators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' The improvement in 90th percentile ranging error varies between 19-74% and 4-38% for Room and Office datasets, respectively, depending on the utilized conventional ToA estimator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' The smaller improvement for the Office dataset can be explained by the fact that the Office dataset contains repeated measurements taken for the same anchor-tag location pairs, unlike the Room dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' As a result, there is a lower number of measure- ments taken for unique anchor-tag location pairs leading to an insufficient amount of unique data for the CNN to be trained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Furthermore, all methods perform worse in Office dataset than in Room dataset despite the same measurement and ranging module, DWM1000, used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' This can be explained by the different propagation environments, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=', the propagation environment for Office dataset might be more challenging, or a discrepancy in the calibration of the DWM1000 module, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=', antenna delay calibration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Comparing the two error mitigation methods, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=', CNN and CnstAvg, the proposed CNN-based method further yields a considerably better performance than CnstAvg in most cases, and a similar performance in the worst case, depending on the underlying conventional ToA estimator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' The gain of the CNN estimator over CnstAvg estimator lies between 16-37% and 3-16% in Room and Office datasets, respectively, in 90th percentile ranging accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Our performance evaluation also enables a comparison of conventional ToA estimators from the literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Figures 3a and 4a show that LDE outperforms IFP and Peak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Peak is observed to show the worst performance in both datasets possibly due to the susceptibility of the peak detection to multipath propagation [18], [24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Comparison with DWM Figure 3a shows that DWM outperforms LDE slightly whereas LDE has a marginally better performance than DWM according to Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' 4a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' The similar performance of DWM and LDE can be explained by the fact that a leading-edge detection 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} 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metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='00 Ranging Error (m) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='0 CDF 0.' 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='80 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='85 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='90 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='95 LDE+CNN Peak+CNN IFP+CNN DWM+CNN LDE Peak IFP DWM (a) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} 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+page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='0 CDF 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='9 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='75 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='80 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='85 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='90 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='95 LDE+CNN Peak+CNN IFP+CNN DWM+CNN LDE+CnstAvg Peak+CnstAvg IFP+CnstAvg DWM+CnstAvg (b) 0 20 40 60 80 90th% |R| (cm) 90th% |R| (cm): LDE+CNN 62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='0 LDE 71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='0 LDE+CnstAvg 65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='0 Peak+CnstAvg 75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='0 Peak+CNN 73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='0 Peak 117.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='0 IFP+CnstAvg 81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='0 IFP+CNN 78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='0 IFP 81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='0 DWM+CnstAvg 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='0 DWM 87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='0 DWM+CNN 62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='0 (c) 0 20 40 60 Mean |R| (cm) mean |R| (cm): LDE+CNN 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='0 LDE 33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='0 LDE+CnstAvg 33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='0 Peak+CnstAvg 39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='0 Peak+CNN 36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='0 Peak 59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='0 IFP+CnstAvg 51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='0 IFP+CNN 47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='0 IFP 52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='0 DWM+CnstAvg 39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='0 DWM 36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='0 DWM+CNN 34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='0 (d) Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' 4: The CDF of ranging error of the proposed CNN-based estimator in comparison to (a) conventional ToA estimators and (b) benchmark CnstAvg estimators, and (c) 90th percentile and (d) mean absolute ranging errors of the considered schemes for Office dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' method was utilized by the DWM1000 device.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Another obser- vation is that CnstAvg degrades the performance of DWM, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=', CnstAvg+DWM performs worse than DWM, in mean absolute ranging error for Office dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' This can be explained by the fact that the average ToA estimation error of DWM is substantially different for Office1 and Office2, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=', for training and test data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Accuracy performance comparison of DWM+CNN and LDE+CNN shows contradicting results, similar to the com- parison between DWM and LDE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' LDE+CNN outperforms DWM+CNN for the Office dataset while DWM+CNN has the superior performance for the Room dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' The underlying reason might be a discrepancy in the calibration of the DWM1000 device in the two measurement campaigns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' The details of the DWM1000’s internal estimation algorithm were not provided neither in the device’s user manual [14] nor in the descriptions of the measurements campaigns [3], [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Therefore, it is difficult to draw further conclusions regarding the performance of DWM-related estimators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Effect of Utilizing Sub-optimal Conventional Methods Various approaches can be used to optimize the parameters of the conventional methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' For instance, as an alternative to selecting the noise threshold in terms of the relative path strength [20], it can also be determined in terms of the thermal noise [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Additionally, the number and density of the candidate values of an exhaustive or grid search might yield different optimized parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' As a result, the parameters of the utilized conventional ToA estimators can be sup-obtimal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' In Table I, we provide the results related to the impact of optimizing the conventional ToA estimators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Such impact could not be evaluated for DWM since it is based on a propri- etary detection algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' It can be observed from Table I that the performance of the conventional ToA estimators heavily depends on the parameter optimization for the measurements in both datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' The proposed CNN estimator provides a ro- bust ranging estimation, in case the utilized conventional ToA estimators are not optimized carefully.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Specifically, using the proposed CNN estimator, the loss in ranging performance due to suboptimal parameters of the conventional ToA estimators is at most 8 cm at 90th percentile for both datasets, compared TABLE I: 90th percentile absolute ranging errors of the considered ToA estimators and the increase in ranging error due to suboptimal (underlying) conventional ToA estimators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='ToA (error) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='estimation method ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='90th%(ϵ|R|) (cm) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='Office dataset ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='Room dataset ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='Ranging error when ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='conventional estimators ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='are optimized ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='LDE ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='LDE ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='71 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='27 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='LDE+CnstAvg ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='65 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='29 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='LDE+CNN ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='62 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='22 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='Peak ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='Peak ' 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='22 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='IFP ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='IFP ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='81 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='35 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='IFP+CnstAvg ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='81 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='35 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='IFP+CNN ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='78 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='25 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='Increase in ranging ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='error due to suboptimal ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='conventional estimator ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='LDE ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='LDE ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='+28 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='+12 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='LDE+CnstAvg ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='+12 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='+3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='LDE+CNN ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='+8 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='+0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='Peak ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='Peak ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='+31 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='+22 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='Peak+CnstAvg ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='+18 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='+13 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='Peak+CNN ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='+4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='+7 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='IFP ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='IFP ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='+37 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='+34 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='IFP+CnstAvg ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='+11 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='+21 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='IFP+CNN ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='+6 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='+6 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='to 21 cm of CnstAvg and 37 cm of the conventional ToA ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='estimators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Complexity Analysis Finding peaks of the input CIR dominates the computational complexity of Peak requiring O(N) operations, where N denotes the length of the CIRs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' The complexity of IFP is mainly determined by the calculation of the gradient where a subtraction and a division is performed for each element yielding a complexity of O(N).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' LDE is composed of a moving average filter followed by two moving maximum filters where the outputs of the two moving maximum windows are compared element-wise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' The window size is constant in all three filters, and the window is shifted through the CIR yielding an overall complexity of O(N).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Each one-dimensional convolutional layer of the proposed CNN is associated to a constant filter size, and a constant number of filters is shifted along the input CIR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' The subse- quent single fully connected layer maps the output of the last convolutional layer to a scalar resulting in an overall complex- ity of O(N).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Although the dependence of the complexity on the input CIR size is linear for the considered estimators, the complexities of the estimators are different.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Table II shows the TABLE II: Computation time of the conventional estimators and the additional latency caused by the CNN mitigation scheme for one sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Estimator Peak IFP LDE +CNN Time (ms) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='07 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='12 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='39 +0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='35 time complexity of inference of the estimators that are imple- mented using Pytorch, numpy and scipy libraries of Python programming language running on a computer equipped with Intel(R) Xeon(R) CPU E5-2680 v4 @ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='40GHz and 24 GB of RAM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' The additional latency caused by the proposed CNN- based error mitigation scheme is comparable to the latency of the widely used LDE estimator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' CONCLUSIONS In this paper, we have proposed a supervised ML approach based on CNNs for estimation of the error of conventional ToA estimators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' These estimates are in turn used for mitigating such errors to improve the ranging accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' We have evaluated the performance of the proposed methods using real-world measurements collected from various environments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' We first observed that the performance of the conventional ToA esti- mators differ significantly from each other, and further require optimization of their parameters for an improved performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' While the errors of the conventional ToA estimators could be mitigated partly by a simple benchmark mitigation scheme, such approach might even result in a worse performance in some cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' As an alternative, the proposed CNN-based error mitigation method can improve the ranging accuracy of the conven- tional ToA estimators with an acceptable amount of added latency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' The proposed estimator was shown to outperform the benchmark error mitigation scheme by up to 16-37% in 90th percentile ranging accuracy depending on the environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' In addition, it was shown that the proposed CNN estimator provides a robust ranging performance, with only less than 8 cm of additional ranging error in 90th percentile, in case the parameters of the underlying ToA estimators are suboptimal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Thus, the CNN estimator can eliminate the necessity of care- fully optimizing the underlying conventional ToA estimators, depending on the accuracy requirements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' In this way, the proposed method offers an attractive solution for improving the ranging accuracy, providing a robust performance under different conventional ToA estimation algorithms and across various propagation environments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' In addition to the proposed use of ML to mitigate the error of conventional ToA estimators, ML methods can be also applied to estimate the ToA directly, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=', without requiring a conventional ToA estimator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Further research is needed to compare the performance of these two approaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' REFERENCES [1] 3GPP, “Study on NR positioning enhancements,” TR38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='857, V2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='0, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' [2] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Guvenc, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Chong, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Watanabe, “NLOS identification and mitigation for UWB localization systems,” in Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' IEEE Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Wireless Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Networking (WCNC), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' 1571-1576, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' [3] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Bregar and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Mohorˇciˇc, “Improving Indoor Localization Us- ing Convolutional Neural Networks on Computationally Restricted Devices,” IEEE Access, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' 6, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' 17429-17441, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' [4] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Stahlke, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Kram, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Mutschler, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Mahr, “NLOS Detection using UWB Channel Impulse Responses and Convolutional Neural Networks,” in Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' of International Conference on Localization and GNSS (ICL-GNSS), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' 1-6, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' [5] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Kirmaz, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Michalopoulos, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Balan, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Gerstacker, “LOS/NLOS Classification Using Scenario-Dependent Unsuper- vised Machine Learning,” in Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' of IEEE 32nd Annual Interna- tional Symposium on Personal, Indoor and Mobile Radio Commu- nications (PIMRC), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' 1134-1140, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' [6] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Fan and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Awan, “Non-Line-of-Sight Identification Based on Unsupervised Machine Learning in Ultra-Wideband Systems,” IEEE Access, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' 7, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' 32464-32471, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' [7] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Kolakowski and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Modelski, “Detection of direct path compo- nent absence in NLOS UWB channel,” in Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' of 22nd Interna- tional Microwave and Radar Conference (MIKON), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' 247-250, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' [8] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Barral, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Escudero, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Garc´ıa-Naya, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Maneiro- Catoira, “NLOS Identification and Mitigation Using Low-Cost UWB Devices,” Sensors, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' 19, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' 16, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' 3464, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' [9] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Lian Sang, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Steinhagen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Homburg, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Adams, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Hesse, and U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' R¨uckert, “Identification of NLOS and Multi-Path Conditions in UWB Localization Using Machine Learning Methods,” Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' 10, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' 11, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' 3980, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' [10] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Kong, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Li, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Chen, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Zhao, “Recognition of Blocking Categories for UWB Positioning in Complex Indoor Environment,” Sensors, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' 20, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' 15, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' 4178, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' [11] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Wymeersch, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Marano, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Gifford, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Win, “A Machine Learning Approach to Ranging Error Mitigation for UWB Localization,” IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' 60, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' 6, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' 1719-1728, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' [12] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Yu, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Wen, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Li, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Zhang, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Zhang, “A Novel NLOS Mitigation Algorithm for UWB Localization in Harsh Indoor En- vironments,” IEEE Transactions on Vehicular Technology, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' 68, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' 686-699, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' [13] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Angarano, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Mazzia, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Salvetti, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Fantin, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Chiaberge, “Robust Ultra-wideband Range Error Mitigation with Deep Learn- ing at the Edge,” Engineering Applications of Artificial Intelligence, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' 102, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' 104278, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' [14] Decawave Ltd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' DW1000 User Manual.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Accessed: May 3, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' [On- line].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Available: https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='decawave.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='com/dw1000/usermanual/ [15] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Feigl, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Eberlein, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Kram and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Mutschler, “Robust ToA- Estimation using Convolutional Neural Networks on Randomized Channel Models,” in Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' of International Conference on Indoor Positioning and Indoor Navigation (IPIN), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' 1-8, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' [16] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Hofmann and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Breiling, “Device and method for determining a time of arrival of a receive sequence”, 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' US Patent 7,627,063.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' [17] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Falsi, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Dardari, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Mucchi, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Win, “Time of arrival estimation for UWB localizers in realistic environments”, EURASIP J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Signal Process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' 2006, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' 1–13, 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' [18] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Merkl, “The future of the operating room: Surgical preplanning and navigation using high accuracy ultra-wideband positioning and advanced bone measurement,” Ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' dissertation, Dept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Biomed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Eng.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=', Univ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Tennessee, Knoxville, TN, 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' [19] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Angarano, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Mazzia, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Salvetti, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Fantin, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Chiaberge, “Deep UWB,” Zenodo, 2020, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='5281/zenodo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='4399187.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' [20] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Lee and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Scholtz, “Ranging in a dense multipath envi- ronment using an UWB radio link,” IEEE J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Sel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Areas Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' 20, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' 9, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' 1677-1683, Dec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' 2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' [21] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' LeCun, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Bottou, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Bengio, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Haffner, “Gradient based learning applied to document recognition”, in Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' of the IEEE, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' 86, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' 11, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' 2278–2324, 1998.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' [22] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Kingma and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Ba, “Adam: A method for stochastic optimization”, in Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' of Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Learn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Represent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' (ICLR), 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' [23] 3GPP, “R1-2212817, (Final) Summary #5 of Evaluation on AI/ML for positioning accuracy enhancement”, Nov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' [24] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Kuhn, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Mahfouz, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Zhang, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Merkl and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' Fathy, “A System-Level Simulation Framework for UWB Localization”, Ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} +page_content=' dissertation, University of Tennessee, Knoxville, 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/VNE3T4oBgHgl3EQfawrQ/content/2301.04510v1.pdf'} diff --git a/W9AzT4oBgHgl3EQf1v5O/content/tmp_files/2301.01803v1.pdf.txt b/W9AzT4oBgHgl3EQf1v5O/content/tmp_files/2301.01803v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..69cc19f076af831f8b05fa42c507cfaa8e16d4ab --- /dev/null +++ b/W9AzT4oBgHgl3EQf1v5O/content/tmp_files/2301.01803v1.pdf.txt @@ -0,0 +1,1353 @@ +On doubly symmetric periodic orbits +Urs Frauenfelder, Agustin Moreno +Abstract +In this article, for Hamiltonian systems with two degrees of freedom, +we study doubly symmetric periodic orbits, i.e. those which are symmet- +ric with respect to two (distinct) commuting antisymplectic involutions. +These are ubiquitous in several problems of interest in mechanics. We +show that, in dimension four, doubly symmetric periodic orbits cannot +be negative hyperbolic. This has a number of consequences: (1) all cov- +ers of doubly symmetric orbits are good, in the sense of Symplectic Field +Theory [6]; (2) a non-degenerate doubly symmetric orbit is stable if and +only if its CZ-index is odd; (3) a doubly symmetric orbit does not un- +dergo period doubling bifurcation; and (4) there is always a stable orbit +in any collection of doubly symmetric periodic orbits with negative SFT- +Euler characteristic (as coined in [11]). The above results follow from: +(5) a symmetric orbit is negative hyperbolic if and only its two B-signs +(introduced in [10]) differ. +Contents +1 +Introduction +1 +2 +Examples of doubly symmetric periodic orbits +7 +2.1 +The direct and retrograde periodic orbit in Hill’s lunar problem . +7 +2.2 +The Levi-Civita regularization . . . . . . . . . . . . . . . . . . . . +7 +2.3 +Langmuir’s periodic orbit +. . . . . . . . . . . . . . . . . . . . . . +8 +2.4 +Symmetric frozen planets +. . . . . . . . . . . . . . . . . . . . . . +10 +3 +Real couples +10 +4 +Doubly symmetric periodic orbits +13 +5 +The reduced monodromy +17 +1 +Introduction +This article deals with the study of doubly symmetric periodic orbits in dimen- +sion four, i.e. for Hamiltonian systems with two degrees of freedom. These are +1 +arXiv:2301.01803v1 [math.SG] 4 Jan 2023 + +t=0 +t= /2 +symmetric points +τ +L=Fix(ρ) +L =Fix(ρ ) +L =Fix(ρ ) +1 +1 +2 +2 +Figure 1: Left: A symmetric orbit. Right: A doubly symmetric orbit. +ubiquitous in problems of interest in mechanics; we give several examples in +Section 2. Let us introduce the basic concepts. +Symmetric orbits. Consider a symplectic manifold (M, ω) endowed with +an antisymplectic involution ρ : M → M (i.e. ρ2 = id, ρ∗ = ω = −ω), also +referred to as a real structure. Its fixed point set L = Fix(ρ) is a Lagrangian +submanifold of M. +Given a Hamiltonian H : M → R, we say that ρ is a +symmetry of the Hamiltonian system induced by H, if H ◦ ρ = H. +In this +situation, a symmetric periodic orbit is a periodic orbit v : S1 = R/τR → M +satisfying ρ(v(−t)) = v(t) for all t. A symmetric periodic orbit can also be +thought of as a chord starting and ending in L, where the endpoints coincide +with v(0), v(τ/2) (the symmetric points), see Figure 1. +Now suppose we have two distinct antisymplectic involutions ρ1 and ρ2 which +commute with each other. In this case we have two Lagrangian submanifolds +L1 = Fix(ρ1) and L2 = Fix(ρ2). Given a chord from L1 to L2 we can apply ρ2 +to it to get a chord from L1 to itself. Now apply ρ1 to this chord. The resulting +periodic orbit is then doubly symmetric, as it is symmetric with respect to both +ρ1, ρ2, see again Figure 1. We provide a more formal definition of the notion of +a doubly symmetric periodic orbits in Section 4. +Reduced monodromy. Suppose that (M, ω) is a four-dimensional sym- +plectic manifold, H : M → R is a smooth Hamiltonian, and v is a nonconstant +periodic orbit of the Hamiltonian vector field XH of H of period τ. By preser- +vation of energy H is constant along v, i.e., v lies for all times on a level set +Σ = H−1(c) for some c ∈ R. The differential of the flow φt +H induces a map on +the two-dimensional quotient vector space +Mv := dφτ +H(v(0)): Tv(0)Σ/⟨XH(v(0))⟩ → Tv(0)Σ/⟨XH(v(0))⟩, +referred to as the reduced monodromy. +The reduced monodromy is a two- +dimensional symplectic transformation, i.e., det Mv = 1. Depending on the +2 + +trace of its reduced monodromy, periodic orbits on a four-dimensional sym- +plectic manifold are now partitioned into three classes. +Positive hyperbolic: tr(Mv) > 2, in which case the reduced monodromy has +two positive, real eigenvalues inverse to each other. +Negative hyperbolic: tr(Mv) < 2, in which case the reduced monodromy has +two negative, real eigenvalues inverse to each other. +Elliptic: −2 ≤ tr(Mv) ≤ 2. If the trace is precisely two, the reduced mon- +odromy has one as an eigenvalue with algebraic multiplicity two. If the +trace is precisely minus two, it has minus one as an eigenvalue with al- +gebraic multiplicity two. Otherwise it has two nonreal eigenvalues on the +unit circle conjugated to each other. +In the language of Symplectic Field Theory, an even cover of a negative hyper- +bolic orbit is called bad; otherwise a periodic orbit is called good. Here we prove +the following: +Theorem A: For a Hamiltonian system with two degrees of freedom, a doubly +symmetric periodic orbit cannot be negative hyperbolic. +In particular, it follows from Theorem A that all covers of a doubly symmetric +periodic orbit are good periodic orbits. +Stability. While elliptic periodic orbits are stable, hyperbolic ones are un- +stable. +On the other hand, elliptic and negative hyperbolic orbits have odd +Conley-Zehnder index, while positive hyperbolic ones have even Conley-Zehnder +index. For the second statement it is better to exclude the degenerate case where +the trace of the reduced monodromy is two, since in this case there are different +conventions on how to define the Conley-Zehnder index. We see from this that if +we can exclude negative hyperbolic orbits, the question of stability of a periodic +orbit can be answered in terms of the parity of its Conley-Zehnder index. In +particular, we have the following Corollary of Theorem A: +Corollary B: +Suppose that v is a nondegenerate doubly symmetric periodic +orbit of a Hamiltonian system with two degrees of freedom. Then it it stable if +and only if its Conley-Zehnder index is odd. +Overview of proof of Theorem A. The proof of Theorem A uses a real ver- +sion of Krein theory for the reduced monodromy of a symmetric periodic orbit. +Given a symmetric orbit v, the differential of the antisymplectic involution at +v(0) ∈ L = Fix(ρ) induces an antisymplectic involution +R: Tv(0)Σ/⟨XH(v(0))⟩ → Tv(0)Σ/⟨XH(v(0))⟩, +i.e. an orientation reversing involution on the two-dimensional vector space +Tv(0)Σ/⟨XH(v(0)). The involution R conjugates the reduced monodromy with +3 + +its inverse, i.e. +RMvR = M −1 +v . +(1) +We choose a symplectic basis on Tv(0)Σ/⟨XH(v(0)) such that the involution R +gets identified with the matrix +R = +� +1 +0 +0 +−1 +� +and the reduced monodromy is given by a matrix +Mv = +� a +b +c +d +� +satisfying the determinant condition ad − bc = 1. It follows from (1) that a = d +so that +Mv = +� a +b +c +a +� +, +a2 − bc = 1. +In particular, the question to which class the periodic orbit belongs is completely +answered by the entry a of the reduced monodromy matrix. For fixed a, if an off- +diagonal entry is not zero, then it completely determines the other one in view of +the determinant condition. On the other hand, the off-diagonal entries depends +on the choice of the symplectic basis used to identify the reduced monodromy +with a matrix. Since the symplectic basis vectors are required to be eigenvectors +of the antisymplectic involution R, such a symplectic basis is determined up to +a scaling factor, so that the identification of the reduced monodromy with a +matrix is unique up to conjugation by a matrix of the form +� µ +0 +0 +1 +µ +� +, +µ ∈ R \ {0}. +In particular, while the value of b is not an invariant, its sign is an invariant. +Following [10] we refer to sign(b) as the B-sign of the reduced monodromy, see +also [25]. In the case elliptic case, by [10, Appendix B], the B-sign gives the same +information as the Krein type of the eigenvalues of the reduced monodromy (as +introduced in [15, 16, 17, 18, 19]). In the hyperbolic case the eigenvalues have +no Krein type. Therefore the B-sign in the hyperbolic case is an additional +invariant of the real structure ρ. +A symmetric periodic orbit intersects the Lagrangian L = Fix(ρ) in its two +symmetric points. From the reduced monodromies of each symmetric point we +obtain a B-sign, so that a symmetric periodic orbit is actually endowed with +two B-signs. The main observation to prove Theorem A is the following: +Theorem C: +A symmetric periodic orbit of a Hamiltonian system with two +degrees of freedom is negative hyperbolic if and only if its two B-signs are dif- +ferent. +4 + +If the symmetric periodic orbit is elliptic it is actually clear that the two B-signs +have to agree. Indeed, as already mentioned, in the elliptic case the B-sign is +just determined by the Krein sign of the eigenvalues. Since reduced monodromy +matrices of a periodic orbit for different starting points are all conjugated to +each other, Theorem C follows in the elliptic case. What remains to be exam- +ined is the hyperbolic case, namely that in the positive hyperbolic case the two +B-signs agree, while in the negative hyperbolic case they disagree. To address +this, in Section 3 we introduce the notion of real couples, so that Theorem C +becomes a consequence of Proposition 3.2 below. +The strategy to prove Theorem A is now rather obvious. One shows that the +additional real structure for a doubly symmetric periodic orbit forces the two +B-signs to agree, so that, in view of Theorem C, a doubly periodic orbit cannot +be negative hyperbolic. This is carried out in Section 5 where Theorem A is +referred to as Corollary 5.1. +Period doubling bifurcation. When considered in families, periodic orbits +may undergo bifurcation, by which a non-degenerate orbit becomes degenerate +(i.e. 1 becomes an eigenvalue of its monodromy), and new orbits may appear. +Generic bifurcations in dimension four are well understood, see e.g. [1, p. 599]. +However, the presence of symmetry, and in particular the presence of doubly +symmetric orbits, is non-generic, and hence one expects new phenomena. And +indeed, what follows aligns well with this expectation. +As a particular case of bifurcations, the transition from an elliptic periodic +orbit to a negative hyperbolic orbit leads to a period doubling bifurcation, by +which a new orbit appears, whose period is close to double the period of the +original orbit. In the case where the negative hyperbolic orbit is symmetric, its +two different B-signs can actually be useful to figure out where the new periodic +orbit of double period bifurcates, see [9]. Namely, bifurcation happens near the +symmetric point where the B-sign does not jump. Moreover, a consequence of +Theorem A is the following, which emphasizes the non-generic nature of sym- +metry: +Corollary D: +In dimension four, doubly symmetric periodic orbits do not +undergo period doubling bifurcation. +Indeed, as in period doubling bifurcation the orbit itself does not bifurcate +(its double cover does), the orbit after such a bifurcation would have to be dou- +bly symmetric if the orbit before bifurcation is, thus contradicting Theorem A. +We remark that Corollary D fails in dimension six, i.e. for systems with three +degrees of freedom. Indeed, see e.g. [11, Section 6] for a numerical example of a +planar-to-spatial period doubling bifurcation of doubly symmetric orbits. +SFT-Euler characteristic. In order to address the situation of more general +bifurcations than period doubling bifurcation (in the presence of symmetry), +we consider a Floer numerical invariant. Namely, following [10], the SFT-Euler +5 + +characteristic of a periodic orbit v is by definition the Euler characteristic of its +local Floer homology, given by +χSF T (v) = #{good positive hyperbolic} − #{elliptic, negative hyperbolic}. +Here, one counts each type of orbit that appears after a generic perturbation +of the orbit v, so that it bifurcates into a collection of non-degenerate orbits. +We remark that bad orbits do not contribute to this number. Note also that +this number is ±1 in the case where v is itself non-degenerate, depending on +its type. The remarkable fact, which follows from Floer theory, is that χSF T (v) +is independent of the perturbation, and so in particular it remains invariant +under bifurcations of v. It is therefore very useful in order to study non-generic +bifurcations. +Moreover, given a collection of periodic orbits (which may not necessarily +arise from a bifurcation, but e.g. as critical points of an action functional, with +a priori fixed homotopy class) one can also consider the same number computed +via the above formula. Its invariance under arbitrary homotopies will of course +not be guaranteed, and will depend on the particular situation. An example +of interest, for which a suitable homotopy invariance holds, are frozen planets. +These are periodic orbits for the Helium problem which we discuss in more detail +in Section 2. Due to the interaction between the two electrons in Helium, frozen +planets cannot be approached by perturbative methods but instead one can +replace the instantaneous interaction of the two electrons by a mean interaction. +If one interpolates between mean and instantaneous interaction one obtains a +homotopy of a frozen planet problem for which one has compactness in the +symmetric case [8]. This allows one to define a version of the Euler characteristic +for frozen planets which is invariant under this homotopy [5], and which agrees +with the SFT-Euler charactersitic χSF T for the instantaneous interaction. The +Euler characteristic for this problem is −1, see the remark after Corollary B in +[5]. For each negative energy, this implies the existence of a symmetric frozen +planet orbit for the instantaneous interaction, see Corollary C in [4]. +This +follows by homotopy invariance of the Euler characteristic, and the existence +(proved analytically in [7]) of a unique nondegenerate symmetric orbit for the +mean interaction. +With these motivations in mind, the following is again a consequence of +Theorem A: +Corollary E: In dimension four, suppose that a collection of doubly sym- +metric periodic orbits has negative SFT-Euler characteristic. +Then a stable +periodic orbit exists. +Indeed, Theorem A and the formula defining χSF T imply the existence of an +elliptic orbit, and one needs to recall that elliptic orbits are precisely the stable +orbits for a Hamiltonian system in dimension four. +Acknowledgements. +A. Moreno is supported by the National Science +Foundation under Grant No. DMS-1926686, and by the Sonderforschungsbereich +TRR 191 Symplectic Structures in Geometry, Algebra and Dynamics, funded +by the DFG (Projektnummer 281071066 – TRR 191). +6 + +2 +Examples of doubly symmetric periodic orbits +2.1 +The direct and retrograde periodic orbit in Hill’s lunar +problem +Hill’s lunar Hamiltonian goes back to Hill’s groundbreaking work on the orbit +of our Moon [14], describing its motion around the Earth and the Sun. The +Earth lies in the center of the frame of reference, while the Sun, assumed to be +infinitely much heavier than the Earth, lies at infinity. The Hamiltonian reads +H : T ∗(R2 \ {0}) → R, +(q, p) �→ 1 +2 +� +(p1 + q2)2 + (p2 − q1)2� +− 1 +|q| − 3 +2q2 +1. +It is invariant under the two commuting antisymplectic involutions +ρ1, ρ2 : T ∗R2 → T ∗R2 +given, for (q, p) ∈ T ∗R2, by +ρ1(q1, q2, p1, p2) = (q1, −q2, −p1, p2), +ρ2(q1, q2, p1, p2) = (−q1, q2, p1, −p2). +The fixed point sets of the two antisymplectic involutions are the conormal bun- +dles of the x-axis and the y-axis, respectively. If one studies a doubly symmetric +periodic orbit in configuration space R2 \ {0}, this means that it starts perpen- +dicularly at the x-axis, after a quarter period hits the y-axis perpendicularly, +then gets reflected at the y-axis for the next quarter period, and finally gets +reflected at the x-axis for the second half of the period. Such periodic orbits +can be found by a shooting argument where one shoots perpendicularly from +the x-axis for a varying starting point at the x-axis, until one hits the y-axis +perpendicularly. Birkhoff used in [2] this shooting argument to prove the ex- +istence of the retrograde periodic orbit for all energies below the first critical +value, see also [12, Chapter 8.3.2]. Although the retrograde periodic orbit looks +simpler than the direct one [13], astronomers are actually often more interested +in the direct one, since our Moon and actually most moons in our solar system +are direct. However, there are prominent counterexamples. Triton, the largest +moon of the planet Neptun, is for example retrograde. +2.2 +The Levi-Civita regularization +Hill’s lunar problem arises as a limit case of the restricted three-body problem, +see for instance [12, Chapter 5.8.2]. In the restricted three-body problem the +masses of the Sun and the Earth are comparable and their distance is finite. +Different from the Hill’s lunar problem, the restricted three-body problem is +only invariant under the antisymplectic involution +ρ: T ∗R2 → T ∗R2, +(q1, q2, p1, p2) �→ (q1, −q2, −p1, p2) +obtained from reflection at the x-axis, but not anymore under the antisymplec- +tic involution corresponding to reflection at the y-axis. +7 + +We identify R2 with the complex plane C and denote by C∗ := C \ {0} the +complex plane pointed at the origin. We consider the squaring map +ℓ: C∗ → C∗, +z �→ z2. +Note that the squaring map is a two-to-one covering. The contragradient (or +symplectic lift) of the squaring map is the symplectic map +L: T ∗C∗ → T ∗C∗, +(z, w) �→ +� +z2, w +2¯z +� +, +where ¯z is the complex conjugate of z. This map was used by Levi-Civita to +regularise two-body collisions [21] and therefore it is known under the name of +Levi-Civita regularization. On T ∗C we have the two commuting antisymplectic +involutions +σ1, σ2 : T ∗C → T ∗C +which are given, for (z, w) ∈ C × C = T ∗C, by +σ1(z, w) = (¯z, − ¯w), +σ2(z, w) = (−¯z, ¯w). +The Levi-Civita regularization lifts the restriction of the antisymplectic involu- +tion ρ to T ∗C∗ to the restriction of σ1 and σ2 to T ∗C∗, so that we have +L ◦ σ1 +�� +T ∗C∗ = ρ +�� +T ∗C∗ ◦ L, +L ◦ σ2 +�� +T ∗C∗ = ρ +�� +T ∗C∗ ◦ L. +Now suppose that v = (q, p) is a periodic orbit in T ∗C∗ which is symmetric with +respect to ρ, and such that it has odd winding number around the origin. Then +v lifts under the Levi-Civita regularisation to a periodic orbit on T ∗C∗ which is +doubly symmetric with respect to σ1 and σ2. +On the other hand, retrograde and direct orbits exist as well in the re- +stricted three-body problem. Different from Hill’s lunar problem, they are just +symmetric, but not doubly symmetric. However, the lifts under the Levi-Civita +regularisation are doubly symmetric, as the retrograde and direct periodic orbit +have winding number one around the origin. +2.3 +Langmuir’s periodic orbit +Langmuir’s periodic orbit is a periodic orbit for the Helium problem. It was first +discovered by Langmuir [20] numerically as a candidate for the ground state of +the Helium atom. For an analytic existence proof we refer to [3], and for its role +in the semiclassical treatment of Helium, to [22]. +In the Helium atom, there is a nucleus of positive charge plus two at the ori- +gin, i.e. there are two protons. It attracts two electrons of charge minus one +according to Coulomb’s law, which looks formally the same as Newton’s law. +8 + +Moreover, the two electrons repel each other, again according to Coulomb’s law. +We abbreviate by +∆ := +� +(q, q) : q ∈ C∗� +⊂ C∗ × C∗ +the diagonal. The Hamiltonian for the planar Helium problem is then a smooth +function +H : T ∗� +C∗ × C∗ \ ∆ +� +→ R +given by +H(q1, q2, p1, p2) = 1 +2|p1|2 + 1 +2|p2|2 − +2 +|q1| − +2 +|q2| + +1 +|q1 − q2|. +The Hamiltonian is invariant under the symplectic involution +σ: T ∗� +C∗ × C∗ \ ∆ +� +→ T ∗� +C∗ × C∗ \ ∆ +� +given by +σ(q1, q2, p1, p2) = (¯q2, ¯q1, ¯p2, ¯p1), +consisting of the combination of particle interchange and reflection at the x-axis. +The Langmuir Hamiltonian is the restriction of H to the fixed point set of σ +Hσ := H +�� +Fix(σ) : Fix(σ) → R. +The fixed points set consists of points (q1, q2, p1, p2) ∈ T ∗(C∗ × C∗ \ ∆) which +satisfy +q1 = ¯q2 =: q, +p1 = ¯p2 =: p. +It therefore suffices to consider the Langmuir Hamiltonian on the cotangent +bundle of the upper halfplane +H = +� +q = q1 + iq2 ∈ C : q2 > 0 +� +where it is given by +Hσ(q, p) = |p|2 − 4 +|q| + 1 +2q2 +. +On the cotangent bundle of the uper halfplane we have the two antisymplectic +involutions +ρ1, ρ2 : T ∗H → T ∗H +given by +ρ1(q, p) = (−¯q, ¯p), +ρ2(q, p) = (q, −p), +under both of which Hσ is invariant. The fixed point set of ρ1 is the conormal +bundle of the positive imaginary axis, while the fixed point set of ρ2 consists of +brake points, i.e. at which the velocity is zero. The Langmuir orbit for the first +electron e− +1 starts perpendicularly at the imaginary axis and brakes at a quarter +of the period, and is therefore a doubly symmetric periodic orbit with respect to +ρ1 and ρ2. The second electron e− +2 similarly has an associated Langmuir orbit, +obtained by conjugation of that of e− +1 , see Figure 2. +9 + +brake points ++2 +e- +e- +1 +2 +Figure 2: Langmuir’s doubly symmetric orbit, and its symmetric version. ++2 +e- +1 +e- +2 +brake points +Figure 3: A frozen planet configuration. +2.4 +Symmetric frozen planets +Other examples of periodic orbits for the Helium problem are frozen planet +orbits. In this examples both electrons lie on a line on the same side of the +nucleus. The inner electron makes consecutive collisions with the nucleus. The +outer electron, the actual “frozen planet”, which is attracted by the nucleus +but repelled by the inner electron, stays almost stationary but librates slightly. +Frozen planet orbits were discovered by physicists [22, 23] in the context of +semiclassics. They recently attracted the interest of mathematicians [4, 24]. A +frozen planet orbit is called symmetric if the two electrons brake at the same +time, and at the time the inner electron collides with the nucleus the outer +electron brakes again, see Figure 3. If one applies the Levi–Civita regularization +to a symmetric frozen planet one obtains a doubly symmetric periodic orbit. +3 +Real couples +A real symplectic vector space is a triple (V, ω, R) consisting of a symplectic +vector space (V, ω) and a linear antisymplectic involution R: V → V , i.e. R2 = +Id, R∗ω = −ω. +Definition 3.1 Assume that (V1, ω1, R1) and (V2, ω2, R2) are real symplectic +10 + +vector spaces. A real couple (Ψ, Φ) is a tuple of linear symplectic maps +Ψ: (V1, ω1) → (V2, ω2), +Φ: (V2, ω2) → (V1, ω1) +which are related by +R2ΨR1 = Φ−1. +(2) +Note that if (Ψ, Φ) is a real couple, then (Φ, Ψ) is one as well, since it follows +from (2) that +R1ΦR2 = R1R−1 +1 Ψ−1R−1 +2 R2 = Ψ−1. +If (Ψ, Φ) is a real couple then its composition +ΦΨ: (V1, ω1) → (V1, ω1) +is a linear symplectic map from the fixed symplectic vector space (V1, ω1) into +itself which has the special property that it is conjugated to its inverse via the +antisymplectic involution R1. Indeed, +R1ΦΨR1 += +R1ΦR2R2ΨR1 = Ψ−1Φ−1 = (ΦΨ)−1. +(3) +We now consider more closely the two-dimensional case. Note that every two- +dimensional real symplectic vector space is conjugated to R2, endowed with its +standard symplectic structure and antisymplectic involution +R = +� 1 +0 +0 +−1 +� +. +After such conjugation, a real couple then consists of a pair of matrices +(A, B) ∈ SL(2; R) × SL(2; R) +such that +RAR = B−1. +(4) +Writing +A = +� a +b +c +d +� +, +ad − bc = 1 +we have +RAR += +� 1 +0 +0 +−1 +� � a +b +c +d +� � 1 +0 +0 +−1 +� += +� 1 +0 +0 +−1 +� � a +−b +c +−d +� += +� +a +−b +−c +d +� +and therefore +B = (RAR)−1 = +� +d +b +c +a +� +. +11 + +Hence their products are given by the following matrices +AB = +� a +b +c +d +� � d +b +c +a +� += +� ad + bc +2ab +2cd +ad + bc +� +(5) +and +BA = +� +d +b +c +a +� � a +b +c +d +� += +� ad + bc +2bd +2ac +ad + bc +� +. +(6) +Since +BA = B(AB)B−1 +the two product are conjugated to each other in SL(2; R). Moreover, they both +belong to the subspace +SLR(2; R) := +� +M = +� α +β +γ +α +� +: α2 − βγ = 1 +� +of SL(2; R). If M ∈ SLR(2; R) satisfies tr(M) ̸= ±2 we define its real Krein +sign as +κ(M) := sign(β). +Note that the trace condition implies that α ̸= ±1 so that, in view of the +determinant condition α2 − βγ, we have that β ̸= 0, and so its sign is well +defined. The following proposition is now straightforward to prove. +Proposition 3.2 The real Krein signs of AB and BA differ, if and only if +tr(AB) = tr(BA) < −2, +(7) +i.e., if and only if AB and therefore as well BA are negative hyperbolic. +Proof: +By (5) and (6) the trace condition (7) is equivalent to the inequality +ad + bc < −1. +In view of the determinant condition ad − bc = 1 this in turn is equivalent to +the inequality +ad < 0, +i.e., the requirement that the signs of a and d are different. Having once more a +look at (5) and (6), we see that this happens if and only if the real Krein signs +of AB and BA disagree. This proves the proposition. +□ +In the following we assume that (Ψ, Φ) is a real couple between real symplectic +vector spaces (V1, ω1, R1) and (V2, ω2, R2). +Definition 3.3 The real couple (Ψ, Φ) is called symmetric if there exists a +linear map +S : V1 → V2 +12 + +which is antisymplectic, i.e., +S∗ω2 = −ω1 +and satisfies +Ψ = SΨ−1S, +Φ−1 = SΦS, +R2SR1 = S. +(8) +For a symmetric real couple +T := SR1 = R2S : (V1, ω1) → (V2, ω2) +is a linear symplectic map which in view of +TR1 = S = R2T +interchanges the two real structures, so that T leads to an identification of +the two real symplectic vector spaces (V1, ω1, R1) and (V2, ω2, R2). In the two- +dimensional case if we identify this further with R2 endowed with its standard +symplectic form and standard real structure R, then not only R1 and R2 are +identified with R, but so is S. The real tuple becomes identified with a pair +(A, B) of SL(2, R)-matrices which not only satisfy (4) but due to (8) also satisfy +RAR = A−1, +RBR = B−1, +i.e., both matrices are conjugated to their inverse via R and therefore lie in the +subspace SLR(2; R) of SL(2; R). This implies that +A = B = +� a +b +c +a +� +, +a2 − bc = 1 +and therefore +AB = BA. +In particular, AB and BA have the same real Krein sign. Therefore we obtain +the following corollary from Proposition 3.2. +Corollary 3.4 Suppose that (Ψ, Φ) is a two-dimensional symmetric real couple. +Then neither ΦΨ nor ΨΦ are negative hyperbolic. +4 +Doubly symmetric periodic orbits +Suppose that (M, ω) is a symplectic manifold and H : M → R is a smooth +Hamiltonian. The Hamiltonian vector field XH of H is implicitly defined by the +condition +dH = ω(·, XH). +We abbreviate by S1 = R/Z the circle. A simple periodic orbit is a bijective +map v: S1 → R for which there exists τ > 0 such that v solves the ODE +∂tv(t) = τXH(v(t)), +t ∈ S1. +13 + +Since for a simple periodic orbit the map is bijective the Hamiltonian vector +field XH is nonvanishing along v and therefore τ is uniquely determined by v. +We refer to τ as the period of the simple periodic orbit v. We abbreviate by +PH ⊂ C∞(S1, M) +the set of simple periodic orbits of the Hamiltonian vector field XH. +A real symplectic manifold is a triple (M, ω, ρ) where (M, ω) is a symplectic +manifold and ρ ∈ Diff(M) is an antisymplectic involution on M, i.e., +ρ2 = id, +ρ∗ω = −ω. +If H : M → R is a smooth function on a real symplectic manifold which is +invariant under the antisymplectic involution, i.e., +H ◦ ρ = H, +then its Hamiltonian vector field is anti-invariant, i.e., +ρ∗XH = −XH. +We then obtain an involution +I : PH → PH, +v �→ ρ ◦ v− +where v− is the orbit traversed backwards, i.e., +v−(t) = v(−t), +t ∈ S1. +A simple symmetric periodic orbit is a fixed point of I, i.e, v ∈ PH satisfying +I(v) = v. +We abbreviate by +PI +H := Fix(I) ⊂ PH +the set of simple symmetric periodic orbits. We remark that the fixed point set +of an antisymplectic involution +L := Fix(ρ) +is a Lagrangian submanifold of M. Note that if v ∈ PI +H then +v +� +0 +� +, v +� 1 +2 +� +∈ L +so that v[0, 1 +2 ] can be interpreted as a chord from L to L. +A doubly real symplectic manifold is a quadruple (M, ω, ρ1, ρ2) where (M, ω) +is a symplectic manifold and ρ1, ρ2 ∈ Diff(M) are two distinct antisymplectic +14 + +involutions which commute with each other. Note since ρ1 and ρ2 commute +their composition +σ := ρ1 ◦ ρ2 = ρ2 ◦ ρ1 +is a symplectic involution on (M, ω). Suppose that (M, ω, ρ1, ρ2) is a doubly +real symplectic manifold and H : M → R is a smooth map which is invariant +under both involutions ρ1 and ρ2. We then have on the set of simple periodic +orbits PH two involutions +I1 : PH → PH, +v �→ ρ1 ◦ v−, +I2 : PH → PH, +v �→ ρ2 ◦ v−. +Moreover, we have two Lagrangian submanifolds of M +L1 = Fix(ρ1), +L2 = Fix(ρ2). +Definition 4.1 Suppose that (M, ω, ρ1, ρ2) is a doubly real symplectic manifold +and H : M → R is a smooth function invariant under both involutions ρ1 and ρ2. +A simple symmetric periodic orbit v ∈ PI1 +H of ρ1 is called doubly symmetric +if +ρ2 ◦ v +� +0 +� += v +� 1 +2 +� +. +(9) +Observe that since for a symmetric periodic orbit v(1/2) lies in the fixed point +set of ρ1 condition (9) is equivalent to +σ ◦ v +� +0 +� += v +� 1 +2 +� +. +Doubly symmetric periodic orbits with respect to ρ1 are in natural one-to-one +correspondence with double symmetric periodic orbits with respect to ρ2. For +r ∈ S1 and v ∈ PH we denote by +r∗v ∈ PH +the reparametrized simple periodic orbit +r∗v(t) = v(r + t), +t ∈ S1. +We have the following lemma. +Lemma 4.2 An orbit v ∈ PI1 +H is doubly symmetric with respect to ρ2 if and +only if +� 1 +4 +� +∗v ∈ PI2 +H is doubly symmetric with respect to ρ1. +Proof: Suppose that v ∈ PI1 +H is doubly symmetric with respect to ρ2. After +reparametrization a simple periodic orbit is still a simple periodic orbit so that +we have +� 1 +4 +� +∗v ∈ PH. +Since H is invariant under ρ2 we have that +I2 +�� 1 +4 +� +∗v +� +∈ PH. +15 + +Using (9) we compute +I2 +�� 1 +4 +� +∗v +�� 1 +4 +� += +ρ2 ◦ +�� 1 +4 +� +∗v +�−� 1 +4 +� += +ρ2 +�� 1 +4 +� +∗v +�� +− 1 +4 +� += +ρ2 ◦ v +� 1 +4 − 1 +4 +� += +ρ2 ◦ v(0) += +v +� 1 +2 +� += +�� 1 +4 +� +∗v +�� 1 +4 +� +. +That means that +� 1 +4 +� +∗v and I2 +�� 1 +4 +� +∗v +� +are solutions of the same first order ODE +which at time 1 +4 go through the same point. Therefore from the uniqueness of +the initial value problem of first order ODE’s we deduce that +I2 +�� 1 +4 +� +∗v +� += +� 1 +4 +� +∗v +and hence +� 1 +4 +� +∗v ∈ PI2 +H . +It remains to check its double symmetry with respect to ρ1. For that we compute +ρ1 ◦ +�� 1 +4 +� +∗v +� +(0) += +ρ1 ◦ v +� 1 +4 +� += +v +� +− 1 +4 +� += +v +� 3 +4 +� += +�� 1 +4 +� +∗v +�� 1 +2 +� +. +Here we have used in the second equation that v is symmetric with respect to +ρ1 and in the third equation that it is one-periodic. This shows that +� 1 +4 +� +∗v is +doubly symmetric with respect to ρ1. +It remains to check that if +� 1 +4 +� +∗v ∈ PI2 +H is doubly symmetric with respect to ρ1 +it follows that v ∈ PI1 +H is doubly symmetriy with respect to ρ2. Interchanging +in the previous discussion the roles of ρ1 and ρ2 we obtain that +� 1 +4 +� +∗ +� 1 +4 +� +∗v = +� 1 +2 +� +∗v ∈ PI1 +H +16 + +is doubly symmetric with respect to ρ2. The fact that +� 1 +2 +� +∗v is invariant under +I1 implies that +I1v(t) += +ρ1 ◦ v−(t) += +ρ1 ◦ v(−t) += +ρ1 ◦ +�� 1 +2 +� +∗v +�� +− t − 1 +2 +� += +ρ1 ◦ +�� 1 +2 +� +∗v +�−� +t + 1 +2 +� += +I1 +�� 1 +2 +� +∗v +�� +t + 1 +2 +� += +�� 1 +2 +� +∗v +�� +t + 1 +2 +� += +v +� +t + 1) += +v(t), +so that v ∈ PI1 +H is as well invariant under I1. Since +� 1 +2 +� +∗v is doubly symmetric +with respect to ρ2 we obtain further that +ρ2 ◦ v(0) += +ρ2 ◦ +�� 1 +2 +� +∗v +�� +− 1 +2 +� += +ρ2 ◦ +�� 1 +2 +� +∗v +�� 1 +2 +� += +ρ2 +2 ◦ +�� 1 +2 +� +∗v +�� +0 +� += +�� 1 +2 +� +∗v +�� +0 +� += +v +� 1 +2 +� +, +so that v is doubly symmetric with respect to ρ2 as well. This finishes the proof +of the lemma. +□ +5 +The reduced monodromy +Suppose that (M, ω) is a symplectic manifold and H : M → R is a smooth +function. +We denote by φt +H the flow of the Hamiltonian vector field of H, +characterized by +φ0 +H(x) = x, +d +dtφt +H(x) = XH(φt +H(x)), +x ∈ M. +If v is a simple periodic orbit of XH of period τ we have +φτ +H(v(0)) = v(0), +i.e., v(0) is a fixed point of φτ +H. The differential of the flow +dφτ +H(v(0)): Tv(0)M → Tv(0)M +17 + +is a linear symplectic map of the symplectic vector space (Tv(0)M, ωv(0)) into +itself. This map is referred to as the unreduced monodromy. Since H is au- +tonomous, i.e., does not depend on time, we have +dφτ +H(v(0))XH(v(0)) = XH(v(0)). +Moreover, by preservation of energy the Hamiltonian H is preserved along the +flow of its Hamiltonian vector field. In particular, if c is the energy of v, i.e., +the value H attains along v, the differential of the flow maps the tangent space +Tv(0)Σ of the energy hypersurface +Σ = H−1(c) +back to itself. Therefore the unreduced monodromy induces a linear map +Mv := dφτ +H(v(0)): Tv(0)Σ/⟨XH(v(0))⟩ → Tv(0)Σ/⟨XH(v(0))⟩ +which is still symplectic for the symplectic structure on Tv(0)Σ/⟨XH(v(0))⟩ in- +duced from ωv(0). This map is referred to as the reduced monodromy. Instead +of restricting our attention to 0 we could consider the reduced monodromy +M t +v := dφτ +H(v(t)): Tv(t)Σ/⟨XH(v(t))⟩ → Tv(t)Σ/⟨XH(v(t))⟩ +for any t ∈ S1. Note that for different times t the reduced monodromies are +symplectically conjugated to each other by the flow. +Suppose now in addition that ρ is a real structure on (M, ω) under which H +is invariant and v ∈ PI +H is a symmetric periodic orbit. Since both points v(0) +and v +� 1 +2 +� +lie in the fixed point set of ρ the differential of ρ gives rise to linear +antisymplectic involutions +dρ +� +v +� +0 +�� +: Tv(0)M → Tv(0)M, +dρ +� +v +� 1 +2 +�� +: Tv(1/2)M → Tv(1/2)M +which induce real structures on the quotient spaces Tv(0)Σ/⟨XH(v(0))⟩ respec- +tively Tv(1/2)Σ/⟨XH(v(1/2))⟩. Since the Hamiltonian vector field is anti-invariant, +the antisymplectic involution ρ conjugates the forward flow to the backward flow +ρφt +Hρ = φ−t +H . +In particular, differentiating this identity we have +dρ +� +v +� 1 +2 +�� +◦ dφτ/2 +H +� +v +� +0 +�� +◦ dρ +� +v +� +0 +�� += +� +dφτ/2 +H +� +v +� 1 +2 +���−1 +. +Therefore the induced maps +Ψ := dφτ/2 +H +� +v +� +0 +�� +: Tv(0)Σ/⟨XH(v(0))⟩ → Tv(1/2)Σ/⟨XH(v(1/2))⟩ +and +Φ := dφτ/2 +H +� +v +� 1 +2 +�� +: Tv(1/2)Σ/⟨XH(v(1/2))⟩ → Tv(0)Σ/⟨XH(v(0))⟩ +18 + +give rise to a real couple (Ψ, Φ). Note that the compositions coincide with the +reduced monodromies at times 0 and 1 +2 +ΦΨ = dφτ +H +� +v +� +0 +�� +, +ΨΦ = dφτ +H +� +v +� 1 +2 +�� +. +Now we even assume that the symplectic manifold (M, ω) is doubly real with +real structures ρ1 and ρ2 under both of which H is invariant and v ∈ PI1 +H is +doubly symmetric with respect to ρ2. The differential of ρ2 gives rise to a linear +antisymplectic map +dρ2(v(0)): Tv(0)M → Tv(1/2)M +which induces an antisymplectic map on the quotient spaces +S : Tv(0)Σ/⟨XH(v(0))⟩ → Tv(1/2)Σ/⟨XH(v(1/2))⟩. +Since ρ1 commutes with ρ2 this map interchanges the real structures. +By +Lemma 4.2 we have that +� 1 +4 +� +∗v ∈ PI2 +H and therefore S makes the real cou- +ple (Ψ, Φ) symmetric. Therefore we obtain, as a consequence of Corollary 3.4, +the following corollary, which is Theorem A from the Introduction: +Corollary 5.1 A doubly symmetric periodic orbit on a four-dimensional sym- +plectic manifold cannot be negative hyperbolic. +References +[1] R. Abraham, J. Marsden, Foundations of Mechanics, 2nd ed. Addison- +Wesley, New York (1978). +[2] G. Birkhoff, +The +restricted +problem +of +three +bodies, +Rend. Circ. Matem. Palermo 39 (1915), 265–334. +[3] K. Cieliebak, U. Frauenfelder, M. Schwingenheuer, On Langmuir’s periodic +orbit, Arch. Math. (Basel) 118 (2022), no. 4, 413–425. +[4] K. Cieliebak, U. Frauenfelder, E. Volkov, A variational approach to frozen +planet orbits in helium, to appear in Ann. Inst. H. Poincar´e. +[5] K. Cieliebak, U. Frauenfelder, E. Volkov, Nondegeneracy and integral count +of frozen planets in Helium, arXiv: 2209.12634 +[6] Y. Eliashberg, A. Givental, H. Hofer Introduction to Symplectic Field The- +ory, Geom. Funct. Anal. 2000, Special Volume, Part II, 560–673. +[7] U. Frauenfelder, Helium and Hamiltonian delay equations, Israel Journal of +Mathematics 246, 239–260 (2021). +[8] U. Frauenfelder, +A +compactness +theorem +for +frozen +planets, +arXiv: +2010:15532, to appear in J. Topology and Analysis. +19 + +[9] U. Frauenfelder, D. Koh, U. Frauenfelder, On Floer-type numerical invari- +ants, GIT quotients, and orbit bifurcations of real-life planetary systems, +arXiv:2206.00627 +[10] U. Frauenfelder, A. Moreno, On GIT quotients of the symplectic group, sta- +bility and bifurcations of symmetric orbits, arXiv:2109.09147 +[11] U. Frauenfelder, D. Koh, A. Moreno, Symplectic methods in the numerical +search of orbits in real-life planetary systems , Preprint arXiv:2206.00627. +[12] U. Frauenfelder, O. van Koert,The restricted three-body problem and holo- +morphic curves, Pathways in Mathematics, Birkh¨auser/Springer, Cham +(2018). +[13] M. H´enon, Numerical exploration of the restricted problem. V. Hill’s case: +Periodic orbits and their stability, Astron. Astrophys. 1, 223–238. +[14] G. Hill, Researches in the lunar theory, Amer. J. Math.1 (1878), 5–26, 129– +147, 245–260. +[15] Krein, M.: Generalization of certain investigations of A.M. Liapunov on +linear differential equations with periodic coefficients. Doklady Akad. Nauk +USSR 73 (1950) 445-448. +[16] M. Krein, On the application of an algebraic proposition in the theory of +monodromy matrices, Uspekhi Math. Nauk 6 (1951) 171-177. +[17] M. Krein, On the theory of entire matrix-functions of exponential type, +Ukrainian Math. Journal 3 (1951) 164-173. +[18] M. Krein, On some maximum and minimum problems for characteristic +numbers and Liapunov stability zones., Prikl. Math. Mekh. 15 (1951) 323- +348. +[19] J. Moser, New aspects in the theory of stability of Hamiltonian systems, +Comm. Pure Appl. Math. 11 (1958) 81-114. +[20] I. Langmuir, The structure of the Helium Atom, Phys. Rev. 17 (1921), 339– +353. +[21] T. Levi-Civita, Sur la r´egularisation du probl`eme des trois corps, Acta +Math. 42 (1920), 99–144. +[22] G. Tanner, K. Richter, J. Rost, The theory of two-electron atoms: Between +ground state and complete fragmentation, Review of Modern Physics 72(2) +(2000), 497–544. +[23] D. Wintgen, K. Richter, G. Tanner,The Semi-Classical Helium Atom, in +Proceedings of the International School of Physics “Enrico Fermi”, Course +CXIX (1993), 113–143. +20 + +[24] L. Zhao, Shooting for Collinear Periodic Orbits in the Helium Model, +Preprint. +[25] B. Zhou, +Iteration +formulae +for +brake +orbit +and +index +inequalities +for +real +pseudoholomorphic +curves, +J. Fixed +Point +Theory +Appl., +https://doi.org/10.1007/s11784-021-00928-3 (2022). +U. Frauenfelder, Augsburg Universit¨at, Augsburg, Germany +E-mail address: urs.frauenfelder@math.uni-augsburg.de +A. Moreno, Institute for Advanced Study, Princeton NJ, USA/ Heidelberg Uni- +versit¨at, Heidelberg, Germany +E-mail address: agustin.moreno2191@gmail.com +21 + diff --git a/WdE0T4oBgHgl3EQfVwBf/vector_store/index.faiss b/WdE0T4oBgHgl3EQfVwBf/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..a8f91765cbd8bebe70fd01b0f7ac2f8fb237444d --- /dev/null +++ b/WdE0T4oBgHgl3EQfVwBf/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:03a1ecd60a827fe09d62764d77cb6acc11c8a3385dd18d290d51aafcb6df5b34 +size 7798829 diff --git a/XNAzT4oBgHgl3EQfKfsY/vector_store/index.pkl b/XNAzT4oBgHgl3EQfKfsY/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..2786a4056c01488890428566b6897e67343bbdc5 --- /dev/null +++ b/XNAzT4oBgHgl3EQfKfsY/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:203159f83f8b8423cff28083a9dd98392941706229004c789b1f399b12ab98e7 +size 233486 diff --git a/XdE1T4oBgHgl3EQfvwV4/vector_store/index.pkl b/XdE1T4oBgHgl3EQfvwV4/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..35b80fd30d025c2c08e936a27aa0bbd25a501fdd --- /dev/null +++ b/XdE1T4oBgHgl3EQfvwV4/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:f0163b2607814d370ea480c3bbe1c1e84e1c1f7ffb21e724cbf1839d496e58b6 +size 767640 diff --git a/YNFRT4oBgHgl3EQf_jgG/content/tmp_files/2301.13694v1.pdf.txt b/YNFRT4oBgHgl3EQf_jgG/content/tmp_files/2301.13694v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..d7d08002f139da2cc4eca887be8f59f6b3e57322 --- /dev/null +++ b/YNFRT4oBgHgl3EQf_jgG/content/tmp_files/2301.13694v1.pdf.txt @@ -0,0 +1,3300 @@ +Are Defenses for Graph Neural Networks Robust? +Felix Mujkanovic1∗, Simon Geisler1∗, Stephan Günnemann1, Aleksandar Bojchevski2 +1Dept. of Computer Science & Munich Data Science Institute, Technical University of Munich +2CISPA Helmholtz Center for Information Security +{f.mujkanovic, s.geisler, s.guennemann}@tum.de | bojchevski@cispa.de +Abstract +A cursory reading of the literature suggests that we have made a lot of progress in de- +signing effective adversarial defenses for Graph Neural Networks (GNNs). Yet, the +standard methodology has a serious flaw – virtually all of the defenses are evaluated +against non-adaptive attacks leading to overly optimistic robustness estimates. We +perform a thorough robustness analysis of 7 of the most popular defenses spanning +the entire spectrum of strategies, i.e., aimed at improving the graph, the architecture, +or the training. The results are sobering – most defenses show no or only marginal +improvement compared to an undefended baseline. We advocate using custom +adaptive attacks as a gold standard and we outline the lessons we learned from +successfully designing such attacks. Moreover, our diverse collection of perturbed +graphs forms a (black-box) unit test offering a first glance at a model’s robustness.1 +1 +Introduction +The vision community learned a bitter lesson – we need specific carefully crafted attacks to properly +evaluate the adversarial robustness of a defense. Consequently, adaptive attacks are considered the +gold standard [44]. This was not always the case; until recently, most defenses were tested only +against relatively weak static attacks. The turning point was Carlini & Wagner [3]’s work showing +that 10 methods for detecting adversarial attacks can be easily circumvented. Shortly after, Athalye +et al. [1] showed that 7 out of the 9 defenses they studied can be broken since they (implicitly) rely +on obfuscated gradients. So far, this bitter lesson is completely ignored in the graph domain. +72 +74 +76 +78 +Adversarial accuracy (%) +Soft-Median-GDC +GRAND +ProGNN +GCN +RGCN +GNNGuard +Jaccard-GCN +SVD-GCN +(a) Global, Poisoning +75 +80 +Adversarial accuracy (%) +(b) Global, Evasion +0 +20 +40 +Correct predicitons (%) +(c) Local, Poisoning +0 +20 +40 +60 +Correct predicitons (%) +Adaptive +attack +Non- +adaptive +attack +(d) Local, Evasion +Figure 1: Adaptive attacks draw a different picture of robustness. All defenses are less robust than +reported, with an undefended GCN [33] outperforming some. We show results on Cora ML for both +poisoning (attack before training) and evasion (attack after training), and both global (attack the test +set jointly) and local (attack individual nodes) setting. The perturbation budget is relative w.r.t. the +#edges for global attacks (5% evasion, 2.5% poisoning) and w.r.t. the degree for local attacks (100%). +In (a)/(b) SVD-GCN is catastrophically broken – our adaptive attacks reach 24%/9% (not visible). +Note that our non-adaptive attacks are already stronger than what is typically used (see § 5). +∗equal contribution +1 Project page: https://www.cs.cit.tum.de/daml/are-gnn-defenses-robust/ +36th Conference on Neural Information Processing Systems (NeurIPS 2022). +arXiv:2301.13694v1 [cs.LG] 31 Jan 2023 + +Virtually no existing work that proposes an allegedly robust Graph Neural Network (GNN) evaluates +against adaptive attacks, leading to overly optimistic robustness estimates. To show the seriousness of +this methodological flaw we categorize 49 works that propose a robust GNN and are published at +major conferences/journals. We then choose one defense per category (usually the most highly cited). +Not surprisingly, we show that none of the assessed models are as robust as originally advertised +in their respective papers. In Fig. 1 we summarize the results for 7 of the most popular defenses, +spanning the entire spectrum of strategies (i.e., aimed at improving the graph, the architecture, or the +training, see Table 1). +We see that in both local and global settings, as well as for both evasion and poisoning, the adversarial +accuracy under our adaptive attacks is significantly smaller compared to the routinely used non- +adaptive attacks. Even more troubling is that many of the defenses perform worse than an undefended +baseline (a vanilla GCN [33]). Importantly, the 7 defenses are not cherry-picked. We report the results +for each defense we assessed and selected each defence before running any experiments. +Adversarial robustness measures the local generalization capabilities of a model, i.e., sensitivity +to (bounded) worst-case perturbations. Certificates typically provide a lower bound on the actual +robustness while attacks provide an upper bound. Since stronger attacks directly translate into tighter +bounds our goal is to design the strongest attack possible. Our adaptive attacks have perfect knowledge +of the model, the parameters, and the data, including all defensive measures. In contrast, non-adaptive +attacks (e.g., transferred from an undefended proxy or an attack lacking knowledge about defense +measures) only show how good the defense is at suppressing a narrow subset of input perturbations.2 +Tramer et al. [44] showed that even adaptive attacks can be tricky to design with many subtle +challenges. The graph domain comes with additional challenges since graphs are typically sparse +and discrete and the representation of any node depends on its neighborhood. For this reason, we +describe the recurring themes, the lessons learned, and our systematic methodology for designing +strong adaptive attacks for all examined models. Additionally, we find that defenses are sometimes +sensitive to a common attack vector and transferring attacks can also be successful. Thus, the diverse +collection of perturbed adjacency matrices resulting from our attacks forms a (black-box) unit test +that any truly robust model should pass before moving on to adaptive evaluation. In summary: +• We survey and categorize 49 defenses published across prestigious machine learning venues. +• We design custom attacks for 7 defenses (14%), covering the spectrum of defense techniques. All +examined models forfeit a large fraction of previously reported robustness gains. +• We provide a transparent methodology and guidelines for designing strong adaptive attacks. +• Our collection of perturbed graphs can serve as a robustness unit test for GNNs. +2 +Background and preliminaries +We follow the most common setup and assume GNN [20, 33] classifiers fθ(A, X) that operate on a +symmetric binary adjacency matrix A ∈ {0, 1}n×n with binary node features X ∈ {0, 1}n×d and +node labels y ∈ {1, 2, . . . , C}n where C is the number of classes, n is the number of nodes, and m +the number of edges. A poisoning attack perturbs the graph (flips edges) prior to training, optimizing +max +˜A∈Φ(A) +ℓattack(fθ∗( ˜A, X), y) +s.t. +θ∗ = arg min +θ +ℓtrain(fθ( ˜A, X), y) +(1) +where ℓattack is the attacker’s loss, which is possibly different from ℓtrain (see § 4). In an evasion attack, +θ∗ is kept fixed and obtained by training on the clean graph minθ ℓtrain(fθ(A, X), y). In both cases, +the locality constraint Φ(A) enforces a budget ∆ by limiting the perturbation to an L0-ball around +the clean adjacency matrix: ∥ ˜A − A∥0 ≤ 2∆. Attacks on X also exist, however, this scenario is not +considered by the vast majority of defenses. For example, only one out of the seven examined ones +also discusses feature perturbations. We refer to § D for more details on adaptive feature attacks. +Threat model. Our attacks aim to either cause misclassification of the entire test set (global) or a +single node (local). To obtain the strongest attack possible (i.e., tightest robustness upper bound), +we use white-box attacks. We do not constrain the attacker beyond a simple budget constraint that +enforces a maximum number of perturbed edges. For our considerations on unnoticeability, see § A. +2 From a security perspective non-adaptive attacks (typically transfer attacks) are also relevant since a real-world +adversary is unlikely to know everything about the model and the data. +2 + +Greedy attacks. Attacking a GNN typically corresponds to solving a constrained discrete non- +convex optimization problem that – evident by this work – is hard to solve. Commonly, approximate +algorithms are used to to tackle these optimization problems. For example, the single-step Fast +Gradient Attack (FGA) flips the edges whose gradient (i.e., ∇Aℓtrain(fθ∗(A, X), y)) most strongly +indicates so. On the other hand, Nettack [67] and Metattack [66] are greedy multi-step attacks. The +greedy approaches have the nice side-effect that an attack for a high budget ∆ directly gives all +attacks for budgets lower than ∆. On the other hand, they tend to be relatively weaker. +Projected Gradient Descent (PGD). Alternatively, PGD [53] has been applied to GNNs where the +discrete adjacency matrix is relaxed to [0, 1]n×n during the gradient-based optimization and the +resulting weighted change reflects the probability of flipping an edge. After each gradient update, the +changes are projected back such that the budget holds in expectation ∥E[ ˜A] − A∥0 ≤ 2∆. Finally, +multiple samples are obtained and the strongest perturbation ˜A is chosen that obeys the budget ∆. +The biggest caveats while applying L0-PGD are the relaxation gap and limited scalability (see Geisler +et al. [17] for a detailed discussion and a scalable alternative). +Evasion vs. poisoning. Evasion can be considered the easier setting from an attack perspective since +the model is fixed fθ∗. For poisoning, on the other hand, the adjacency matrix is perturbed before +training (Eq. 1). Two general strategies exist for poisoning attacks: (1) transfer a perturbed adjacency +matrix from an evasion attack [67]; or (2) attack directly by, e.g., unrolling the training procedure +to obtain gradients through training [66]. Xu et al. [53] propose to solve Eq. 1 with alternating +optimization which was shown to be even weaker than the evasion transfer (1). Note that evasion is +particularly of interest for inductive learning and poisoning for transductive learning. +3 +Adversarial defenses +We select the defenses s.t. we capture the entire spectrum of methods improving robustness against +structure perturbations. For the selection, we extend the taxonomy proposed in [21]. We selected the +subset without cherry-picking based on the criteria elaborated below before experimentation. +Taxonomy. The top-level categories are improving the graph (e.g., preprocessing), improving the +training (e.g., adversarial training or augmentations), and improving the architecture. Many defenses +for structure perturbations either fall into the category of improving the graph or adaptively weighting +down edges through an improved architecture. Thus, we introduce further subcategories. Similar +to [21]’s discussion, unsupervised improvement of the graph finds clues in the node features and +graph structure, while supervised improvement incorporates gradient information from the learning +objective. Conversely, for adaptive edge weighting, we identify three prevalent approaches: rule- +based (e.g., using a simple metric), probabilistic (e.g., modeling a latent distribution), and robust +aggregations (e.g., with guarantees). We assign each defense to the most fitting taxon (details in § B). +Selected defenses. To evaluate a diverse set of defenses, we select one per leaf taxon.3 We prioritize +highly cited defenses published at renowned venues with publicly available code. We implement +all defenses in one unified pipeline. We present the categorization of defenses and our selection in +Table 1. Similarly to Tramer et al. [44], we exclude defenses in the “robust training” category (see § C +for a discussion). Two of the three models in the “miscellaneous” category report some improvement +in robustness, but they are not explicitly designed for defense purposes so we exclude them from our +study. Some works evaluate only against evasion [48], others only poisoning [12, 15, 58], and the rest +tackle both [17, 30, 63]. In some cases the evaluation setting is not explicitly stated and inferred by us. +For completeness, we consider each defense in all four settings (local/global and evasion/poisoning). +Next, we provide a short summary of the key ideas behind each defense (details in § E). +Improving the graph. The feature-based Jaccard-GCN [48] uses a preprocessing step to remove all +edges between nodes whose features exhibit a Jaccard similarity below a certain threshold. This was +motivated by the homophily assumption which is violated by prior attacks that tend to insert edges +between dissimilar nodes. The structure-based SVD-GCN [12] replaces the adjacency matrix with a +low-rank approximation prior to plugging it into a regular GNN. This defense was motivated by the +observation that the perturbations from Nettack tend to disproportionately affect the high-frequency +spectrum of the adjacency matrix. The key idea in ProGNN [30] is to learn the graph structure by +3 The only exception is unsupervised graph improvement, as it contains two of the most popular approaches, +which rely on orthogonal principles. One filters edges based on the node features [48], the other uses a low-rank +approximation of the adjacency matrix [12]. +3 + +Table 1: Categorization of selected defenses. Our taxonomy extends the one by Günnemann [21]. +Taxonomy +Selected Defenses +Other Defenses +Improving +graph +Unsupervised +Jaccard-GCN [48] +SVD-GCN [12] +[10, 26, 50, 59, 60] +Supervised +ProGNN [30] +[51, 43, 56] +Improving +training +Robust training +n/a (see § C) +[6, 9, 14, 22, 27, 28, 41, 52, 53, 54] +Further training principles +GRAND [15] +[5, 11, 29, 39, 42, 55, 61, 64, 65] +Improving +architecture +Adaptively +weighting +edges +Rule-based +GNNGuard [58] +[31, 36, 37, 57] +Probabilistic +RGCN [63] +[8, 13, 24, 25, 38] +Robust agg. +Soft-Median-GDC [17] +[7, 16, 47] +Miscellaneous +n/a (see above) +[40, 46, 49] +alternatingly optimizing the parameters of the GNN and the adjacency matrix (the edge weights). +The loss for the latter includes the standard cross-entropy loss, the distance to the original graph, and +three other objectives designed to promote sparsity, low rank, and feature smoothness. +Improving the training. GRAND [15] relies on random feature augmentations (zeroing features) +coupled with neighbourhood augmentations ¯X = (AX + AAX + · · · ). All randomly augmented +copies of ¯X are passed through the same MLP that is trained with a consistency regularization loss. +Improving the architecture. GNNGuard [58] filters edges in each message passing aggregation +via cosine-similarity (smoothed over layers). In the first layer of RGCN [63] we learn a Gaussian +distribution over the feature matrix and the subsequent layers then manipulate this distribution (instead +of using point estimates). For the loss we then sample from the resulting distribution. In addition, in +each layer, RGCN assigns higher/lower weights to features with low/high variance. Soft-Median-GDC +[17] replaces the message passing aggregation function in GNNs (typically a weighted mean) with a +more robust alternative by relaxing the median using differentiable sorting. +Common themes. One theme shared by some defenses is to first discover some property that can +discriminate clean from adversarial edges (e.g., high vs. low feature similarity), and then propose +a strategy based on that property (e.g., filter low similarity edges). Often they analyze the edges +from only a single attack such as Nettack [67]. The obvious pitfall of this strategy is that the attacker +can easily adapt by restricting the adversarial search space to edges that will bypass the defense’s +(implicit) filter. Another theme is to add additional loss terms to promote some robustness objectives. +Similarly, the attacker can incorporate the same terms in the attack loss to negate their influence. +4 +Methodology: How to design strong adaptive attacks +In this section, we describe our general methodology and the lessons we learned while designing +adaptive attacks. We hope these guidelines can serve as a reference for testing new defenses. +Step 1 – Understand how the defense works and categorize it. For example, some defenses rely +on preprocessing which filters out edges that meet certain criteria (e.g., Jaccard-GCN [48]). Others +introduce additional losses during training (e.g., GRAND [15]) or change the architecture (e.g., +RGCN [63]). Different defenses might need different attacks or impose extra requirements on them. +Step 2 – Probe for obvious weaknesses. Some examples include: (a) transfer adversarial edges from +another (closely related) model (see also § 6); (b) use a gradient-free (black-box) attack. For example, +in our local experiments, we use a Greedy Brute Force attack: in each step, it considers all possible +single edge flips and chooses the one that contributes most to the attack objective (details in § A). +Step 3 – Launch a gradient-based adaptive attack. For rapid prototyping, use a comparably cheap +attack such as FGA, and later advance to stronger attacks like PGD. For poisoning, strongly consider +meta-gradient-based attacks like Metattack [66] that unroll the training procedure, as they almost +always outperform just transferring perturbations from evasion. Unsurprisingly, we find that applying +PGD [53] on the meta gradients often yields even stronger attacks than the greedy Metattack, and we +refer to this new attack as Meta-PGD (details in § A). +4 + +Step 4 – Address gradient issues. Some defenses contain components that are non-differentiable, +lead to exploding or vanishing gradients, or obfuscate the gradients [1]. To circumvent these issues, +potentially: (a) adjust the defense’s hyperparameters to retain numerical stability; (b) replace the +offending component with a differentiable or stable counterpart, e.g., substitute the low-rank ap- +proximation of SVD-GCN [12] with a suitable differentiable alternative; or (c) remove components, +e.g., drop the “hard” filtering of edges done in the preprocessing of Soft-Median-GDC [17]. These +considerations also include poisoning attacks, where one also needs to pay attention to all components +of the training procedure. For example, we ignore the nuclear norm loss term in the training of +ProGNN [30] to obtain the meta-gradient. Of course, keep the entire defense intact for its final +evaluation on the found perturbations. +Step 5 – Adjust the attack loss. In previous works, the attack loss is often chosen to be the same as +the training loss, i.e., the cross-entropy (CE). This is suboptimal since CE is not consistent according +to the definition by Tramer et al. [44] – higher loss values do not indicate a stronger attack. Thus, we +use a variant of the consistent Carlini-Wagner loss [4] for local attacks, namely the logit margin (LM), +i.e., the logit difference between the ground truth class and most-likely non-true class. However, +as discussed by Geisler et al. [17], for global attacks the mean LM across all target nodes is still +suboptimal since it can “waste” budget on already misclassified nodes. Their tanh logit margin (TLM) +loss resolves this issue. If not indicated otherwise, we either use TLM or the probability margin (PM) +loss – a slight variant of LM that computes the margin after the softmax rather than before. +Step 6 – Tune the attack hyperparameters such as the number of PGD steps, the attack learning +rate, the optimizer, etc. For example, for Metattack we observed that using the Adam optimizer [32] +can weaken the attack and replacing it with SGD can increase the effectiveness. +Lessons learned. We provide a detailed description of each adaptive attack and the necessary actions +to make it as strong as possible in § E. Here, we highlight some important recurring challenges +that should be kept in mind when designing adaptive attacks. (1) Numerical issues, e.g., due to +division by tiny numbers can lead to weak attacks, and we typically resolve them via clamping. (2) +In some cases we observed that for PGD attacks it is beneficial to clip the gradients to stabilize +the adversarial optimization. (3) For a strong attack it is essential to tune its hyperparameters. (4) +Relaxing non-differentiable components and deactivating operations that filter edges/embeddings +based on a threshold in order to obtain gradients for every edge is an effective strategy. (5) If the +success of evasion-poisoning transfer depends on a fixed random initialization (see § J), it helps to +use multiple clean auxiliary models trained with different random seeds for the PGD attack – in each +PGD step we choose one model randomly. (6) Components that make the optimization more difficult +but barely help the defense can be safely deactivated. (7) It is sometimes beneficial to control the +randomness in the training loop of Meta-PGD. (8) For Meta-PGD it can help to initialize the attack +with non-zero perturbations and e.g., use the perturbed graph of a different attack. +Example 1 – SVD-GCN. To illustrate the attack process (especially steps 3 and 4) we present a +case study of how we construct an adaptive attack against SVD-GCN. Gradient-free attacks like +Nettack do not work well here as they waste budget on adversarial edges which are filtered out by +the low-rank approximation (LRA). Moreover, to the demise of gradient-based attacks, the gradients +of the adjacency matrix are very unstable due to the SVD and thus less useful. Still, we start with a +gradient-based attack as it is easier to adapt, specifically FGA, whose quick runtime enables rapid +prototyping as it requires only a single gradient calculation. To replace the LRA with a function whose +gradients are better behaved, we first decompose the perturbed adjacency matrix ˜A = A + δA and, +thus, only need gradients for δA. Next, we notice that the eigenvectors of A usually have few large +components. Perturbations along those principal dimensions are representable by the eigenvectors, +hence most likely are neither filtered out nor impact the eigenvectors. Knowing this, we approximate +the LRA in a tractable manner by element-wise multiplication of δA with weights that quantify how +well an edge aligns with the principal dimensions (details in § E). In short we replace LRA(A + δA) +with LRA(A)+δA◦Weight(A), which admits useful gradients. This approach carries over to other +attacks such as Nettack – we can incorporate the weights into its score function to avoid selecting +edges that will be filtered out. +Example 2 – ProGNN. While we approached SVD-GCN with a theoretical insight, breaking a +composite defense like ProGNN requires engineering and tinkering. When attacking ProGNN with +PGD and transferring the perturbations to poisoning we observe that the perturbations are only +effective if the model is trained with the same random seed. This over-sensitivity can be avoided by +5 + +employing lesson (5) in § 4. As ProGNN is very expensive to train due to its nuclear norm regularizer, +we drop that term when training the set of auxiliary models without hurting attack strength. For +unrolling the training we again drop the nuclear norm regularizer since it is non-differentiable. +Sometimes PGD does not find a state with high attack loss, which can be alleviated by random +restarts. As Meta-PGD optimization quickly stalls, we initialize it with a strong perturbation found by +Meta-PGD on GCN. All of these tricks combined are necessary to successfully attack ProGNN. +Effort. Breaking Jaccard-GCN (and SVD-GCN) required around half an hour (resp. three days) of +work for the initial proof of concept. Some other defenses require various adjustments that need to be +developed over time, but reusing those can quickly break even challenging defenses. It is difficult to +quantify this effort, but it can be greatly accelerated by adopting our lessons learned in § 4. In any +case, we argue that authors proposing a new defense must put in reasonable effort to break it. +5 +Evaluation of adaptive attacks +First, we provide details on the experimental setup and used metrics. We then report the main results +and findings. We refer to § A for details on the base attacks, including our Greedy Brute Force and +Meta-PGD approaches. We provide the code, configurations, and a collection of perturbed graphs on +the project website linked on the first page. +Setup. We use the two most widely used datasets in the literature, namely Cora ML [2] and Cite- +seer [19] (details in § F). Unfortunately, larger datasets are barely possible since most defenses are +not very scalable. Still, in § N, we discuss scalability and apply an adaptive attack to arXiv (170k +nodes) [23]. We repeat the experiments for five different data splits (10% training, 10% validation, +80% testing) and report the means and variances. We use an internal cluster with Nvidia GTX 1080Ti +GPUs. Most experiments can be reproduced within a few hours. However, the experiments with +ProGNN and GRAND will likely require several GPU days. +Defense hyperparameters. When first attacking the defenses, we observed that many exhibit poor +robustness using the hyperparameters provided by their authors. To not accidentally dismiss a defense +as non-robust, we tune the hyperparameters such that the clean accuracy remains constant but the +robustness w.r.t. adaptive attacks is improved. Still, we run all experiments on the untuned defenses +as well to confirm we achieve this goal. In the same way, we also tune the GCN model, which we +use as a reference to asses whether a defense has merit. We report the configurations and verify the +success of our tuning in § H. +Attacks and budget. In the global setting, we run the experiments for budgets ∆ of up to 15% of the +total number of edges in the dataset. Due to our (R)AUC metric (see below), we effectively focus on +only the lower range of evaluated budgets. We apply FGA and PGD [53] for evasion. For poisoning, +we transfer the found perturbations and also run Metattack [66] and our Meta-PGD. Recall that where +necessary, we adapt the attacks to the defenses as outlined in § 4 and detailed in § E. +In the local setting, we first draw sets of 20 target nodes per split with degrees 1, 2, 3, 5, 8-10, and +15-25 respectively (total of 120 nodes). This enables us to study how the attacks affect different types +of nodes – lower degree nodes are often conjectured to be less robust (see also § K). We then run +the experiments for relative budgets ∆ of up to 200% of the target node’s degree. For example, if +a node has 10 neighbors, and the budget ∆ = 70% then the attacker can change up to 10 · 0.7 = 7 +edges. This commonly used setup ensures that we treat both low and high-degree nodes fairly. We +use Nettack [67], FGA, PGD, and our greedy brute force attack for evasion. For poisoning, we only +transfer the found perturbations. Again, we adapt the attacks to the defenses if necessary. +In alignment with our threat model, we evaluate each found perturbation by the test set accuracy it +achieves (global) or the ratio of target nodes that remain correctly classified (local). For each budget, +we choose the strongest attack among all attempts (e.g., PGD, Metattack, Meta-PGD). This gives rise +to an envelope curve as seen in Fig. 3. We also include lower budgets as attempts, i.e., we enforce the +envelope curve to be monotonically decreasing. +We introduce a rich set of attack characteristics by also transferring the perturbations supporting the +envelope curve to every other defense. These transfer attacks then also contribute to the final envelope +curve of each defense, but in most cases their contribution is marginal. +6 + +0.0 +0.1 +0.2 +RAUC +Soft-Median-GDC +GRAND +ProGNN +GCN +RGCN +GNNGuard +Jaccard-GCN +SVD-GCN +(a) Global, Poisoning +0.2 +0.3 +0.4 +RAUC +(b) Global, Evasion +0.2 +0.4 +AUC +(c) Local, Poisoning +0.2 +0.4 +AUC +Adaptive +attack +Non- +adaptive +attack +(d) Local, Evasion +Figure 2: Adaptive vs. non-adaptive attacks with budget-agnostic (R)AUC on Cora ML (c.f. Fig. 1). +SVD-GCN (b) is disastrously broken – our adaptive attacks reach <0.02 (not visible). § F for Citeseer. +Non-adaptive attacks. We call any attack “non-adaptive” that is not aware of any changes made to +the model (including defense mechanisms). Where we report results for a non-adaptive attack (e.g., +Fig. 1 or Fig. 2), we specifically refer to an attack performed on a (potentially linearlized) GCN with +commonly used hyperparameters (i.e., untuned). We then apply the perturbed adjacency matrix to +the actual defense. In other words, we transfer the adversarial perturbation from a GCN. For our +local non-adaptive attack, we always use Nettack. In contrast, for our global non-adaptive attack, we +apply all attacks listed above, and then transfer for each budget the attack which is strongest against +the GCN. Due to this ensemble of attacks, our global non-adaptive attack is expected to be slightly +stronger than the non-adaptive attacks in most other works. +0 +2 +4 +6 +8 +Relative budget ∆ +m (%) +60 +65 +70 +75 +80 +85 +Accuracy (%) +PGD +Mettack +Meta-PGD +Envelope +MLP +RAUC +Figure 3: The dotted lines show the test +set accuracy per budget after three global +poisoning attacks against a tuned GCN +on Cora ML. Taking the envelope gives +the solid black robustness curve. The +dashed gray line denotes the accuracy of +an MLP. The shaded area is the RAUC. +Area Under the Curve (AUC). An envelope curve gives +us a detailed breakdown of the empirical robustness of a +defense for different adversarial budgets. However, it is +difficult to compare different attacks and defenses by only +visually comparing their curves in a figure (e.g., see Fig. 4). +Therefore, in addition to this breakdown per budget, we +summarize robustness using the Area Under the Curve +(AUC), which is independent of a specific choice of bud- +get ∆ and also punishes defenses that achieve robustness +by trading in too much clean accuracy. Intuitively higher +AUCs indicate more robust models, and conversely, lower +AUCs indicate stronger attacks. +As our local attacks break virtually all target nodes within +our conservative maximum budget (see § F), taking the +AUC over all budgets conveniently measures how quick +this occurs. However, for global attacks, the test set accu- +racy continues to decrease for unreasonably large budget, +and it is unclear when to stop. To avoid having to choose a maximum budget, we wish to stop when +discarding the entire tainted graph becomes the better defense. This is fulfilled by the area between +the envelope curve and the line signifying the accuracy of an MLP – a model that is oblivious to the +graph structure, at the expense of a substantially lower clean accuracy than a GNN. We call this metric +Relative AUC (RAUC) and illustrate it in Fig. 3. More formally, RAUC(c) = +� b0 +0 (c(b) − aMLP)db +s.t. b ≶ b0 =⇒ c(b) ≷ aMLP where c(·) is a piecewise linear robustness per budget curve, and aMLP +is the accuracy of the MLP baseline. We normalize the RAUC s.t. 0% is the performance of an MLP +and 100% is the optimal score (i.e., 100% accuracy). +Finding 1 – Our adaptive attacks lower robustness by 40% on average. In Fig. 2 we compare +non-adaptive attacks, the current standard to evaluate defenses, with our adaptive attacks which we +propose as a new standard. The achieved (R)AUC in each case drops on average by 40% (similarly +for Citeseer, see § F). In other words, the reported robustness in the original works proposing a +defense is roughly 40% too optimistic. We confirm a statistically significant drop (p < 0.05) with a +one-sided t-test in 85% of all cases. Considering adversarial accuracy for (small) fixed adversarial +budget (Fig. 1) instead of the summary (R)AUC over all budgets tells the same story: non-adaptive +attacks are too weak to be reliable indicators of robustness and adaptive attacks massively shrink the +alleged robustness gains. +7 + +0 +2 +4 +6 +Relative budget ∆ +m (%) +−4 +−2 +0 +2 +4 +Accuracy (%) rel. to GCN +(a) Cora ML, Pois. +0 +5 +10 +15 +Relative budget ∆ +m (%) +(b) Cora ML, Evas. +0 +1 +2 +3 +Relative budget ∆ +m (%) +(c) Citeseer, Pois. +0 +2 +4 +6 +Relative budget ∆ +m (%) +MLP +GCN +Jaccard-GCN +RGCN +ProGNN +GNNGuard +GRAND +Soft-Median-GDC +(d) Citeseer, Evas. +Figure 4: Difference (defense – undefended GCN) of adversarial accuracy for the strongest global +attack per budget. Almost half of the defenses perform worse than the GCN. We exclude SVD-GCN +since it is catastrophically broken and plotting it would make the other defenses illegible (accuracy +<24% already for a budget of 2% on Cora ML). Absolute numbers in § F. +Finding 2 – Structural robustness of GCN is not easily improved. In Fig. 4 (global) and Fig. 5 +(local) we provide a more detailed view for different adversarial budgets and different graphs. For +easier comparison we show the accuracy relative to the undefended GCN baseline. Overall, the decline +is substantial. Almost half of the examined defenses perform worse than GCN and most remaining +defenses neither meaningfully improve nor lower the robustness (see also Fig. 1 and Fig. 3). GRAND +and Soft-Medoid-GCN retain robustness in some settings, but the gains are smaller than reported. +Finding 3 – Defense effectiveness depends on dataset. As we can see in Fig. 4 and Fig. 5, our +ability to circumvent specific defenses tends to depend on the dataset. It appears that some defenses +are more suited for different datasets. For example, GRAND seems to be a good choice for Citeseer +while it is not as strong on Cora ML. The results for local attacks (Fig. 5) paint a similar picture, here +we see that Cora ML is more difficult to defend. This points to another potentially problematic pitfall: +most defenses are developed only using these two datasets as benchmarks. Is robustness even worse +on other graphs? We leave this question for future work. +80.0 +82.5 +85.0 +Clean Accuracy (%) +0.0 +0.1 +0.2 +0.3 +RAUC +GCN +Jaccard-GCN +SVD-GCN +RGCN +ProGNN +GNNGuard +GRAND +Soft-Median-GDC +Poisoning +Evasion +Figure 6: Model accuracy vs. RAUC of +the strongest global attacks on Cora ML. +We do not observe a robustness accu- +racy trade-off, but even find models with +higher accuracy to be more robust. +Finding 4 – No trade-off between accuracy and robust- +ness for structure perturbations. Instead, Fig. 6 shows +that defenses with high clean accuracy also exhibit high +RAUC, i.e., are more robust against our attacks. This ap- +pears to be in contrast to the image domain [45]. However, +we cannot exclude that future more powerful defenses +might manifest this trade-off in the graph domain. +Finding 5 – Necessity of adaptive attacks. In Fig. 7, we +show two exemplary characteristics of how an adaptive +attack bypasses defensive measures. First, to attack SVD- +GCN, it seems particularly effective to insert connections +to high-degree nodes. Second, for GNNGuard, GRAND +and Soft-Median-GDC it is disproportionally helpful to +0 +50 +100 +Relative budget +∆ +degree (%) +−20 +0 +20 +40 +Corr. pred. (%) rel. to GCN +(a) Cora ML, Pois. +0 +50 +100 +Relative budget +∆ +degree (%) +(b) Cora ML, Evas. +0 +50 +100 +Relative budget +∆ +degree (%) +(c) Citeseer, Pois. +0 +50 +100 +Relative budget +∆ +degree (%) +GCN +Jaccard-GCN +SVD-GCN +RGCN +ProGNN +GNNGuard +GRAND +Soft-Median-GDC +(d) Citeseer, Evas. +Figure 5: Difference (defense – undefended GCN) of fraction of correct predictions for the strongest +local attack per budget. Most defenses show no or only marginal gain in robustness. The dashed +vertical line shows where 95% of nodes for a GCN are misclassified on average. Abs. numbers in § F. +8 + +GCN +Jaccard-GCN +SVD-GCN +RGCN +ProGNN +GNNGuard +GRAND +Soft-Median-GDC +Global +Local +1.98 +2.10 +19.9 +1.87 +2.03 +3.18 +2.03 +2.26 +4.26 +4.33 +19.9 +4.26 +4.19 +5.56 +4.35 +4.78 +(a) Node degree +GCN +Jaccard-GCN +SVD-GCN +RGCN +ProGNN +GNNGuard +GRAND +Soft-Median-GDC +.001 +.001 +.001 +.001 +.006 +.012 +.003 +.016 +.023 +.026 +.020 +.029 +.010 +.139 +.056 +.173 +(b) Ratio of removed edges +Figure 7: Exemplary metrics characterizing the attack vector our strongest attacks, which are those +visible in Fig. I.1 and Fig. I.2. We give a more elaborate study of attack characteristics in § L. +delete edges. These examples illustrate why the existence of a one-fits-all perturbation which circum- +vents all possible defenses is unlikely. Instead, an adaptive attack is necessary to properly assess a +defense’s efficacy since different models are particularly susceptible to different perturbations. +Additional analysis. During this project, we generated a treasure trove of data. We perform a more +in-depth analysis of our attacks in the appendix. First, we study how node degree affects attacks (see +§ K). For local attacks, the required budget to misclassify a node is usually proportional to the node’s +degree. Global attacks tend to be oblivious to degree and uniformly break nodes. Next, we perform a +breakdown of each defense in terms of the sensitivity to different attacks (see § I). In short, global +attacks are dominated by PGD for evasion and Metattack/Meta-PGD for poisoning with the PM or +TLM loss. For local, our greedy brute-force is most effective, rarely beaten by PGD and Nettack. +Finally, we analyze the properties of the adversarial edges in terms of various graph statistics such as +edge centrality and frequency spectra (see § L § M). +6 +Robustness unit test +Next we systematically study how well the attacks transfer between defenses, as introduced in the +attacks and budget paragraph in § 5. In Fig. 8, we see that in 15 out of 16 cases the adaptive attack is +the most effective strategy (see main diagonal). However for many defenses, there is often a source +model or ensemble of source models (for the latter see § G) which forms a strong transfer attack. +GCN +Jaccard-GCN +RGCN +ProGNN +GNNGuard +GRAND +Soft-Median-GDC +SVD-GCN +Transfer from +GCN +Jaccard-GCN +RGCN +ProGNN +GNNGuard +GRAND +Soft-Median-GDC +SVD-GCN +Transfer to +.12 +.14 +.11 +.10 +.22 +.12 +.11 +.51 +.20 +.10 +.18 +.14 +.18 +.17 +.17 +.49 +.15 +.17 +.11 +.12 +.23 +.13 +.13 +.53 +.14 +.17 +.12 +.10 +.25 +.12 +.11 +.53 +.26 +.22 +.20 +.15 +.10 +.18 +.18 +.48 +.16 +.18 +.13 +.13 +.28 +.13 +.14 +.53 +.18 +.23 +.15 +.12 +.32 +.14 +.12 +.55 +.15 +.17 +.17 +.14 +.29 +.16 +.15 +.02 +(a) Poisoning +GCN +Jaccard-GCN +RGCN +ProGNN +GNNGuard +GRAND +Soft-Median-GDC +SVD-GCN +Transfer from +.21 +.26 +.26 +.28 +.38 +.37 +.29 +.51 +.31 +.18 +.34 +.36 +.34 +.43 +.35 +.50 +.28 +.30 +.22 +.32 +.41 +.34 +.33 +.53 +.27 +.29 +.29 +.21 +.38 +.37 +.32 +.52 +.39 +.36 +.40 +.38 +.15 +.44 +.39 +.49 +.36 +.39 +.33 +.40 +.45 +.23 +.37 +.53 +.40 +.42 +.42 +.42 +.47 +.44 +.29 +.55 +.28 +.30 +.29 +.29 +.25 +.25 +.28 +.02 +(b) Evasion +Figure 8: RAUC for the transfer of the strongest global adaptive attacks on Cora ML between models. +The columns contain the models for which the adaptive attacks were created. The rows contain the +RAUC after the transfer. With only one exception, adaptive attacks (diagonal) are most effective. +9 + +Motivated by the effectiveness of transfer attacks (especially if transferring from ProGNN [30]), we +suggest this set of perturbed graphs to be used as a bare minimum robustness unit test: one can probe +a new defense by testing against these perturbed graphs, and if there exists at least one that diminishes +the robustness gains, we can immediately conclude that the defense is not robust in the worst-case – +without the potentially elaborate process of designing a new adaptive attack. We provide instructions +on how to use this collection in the accompanying code. +Nevertheless, we cannot stress enough that this collection does not replace a properly developed +adaptive attack. For example, if one would come up with SVD-GCN and would use our collection +(excluding the perturbed graphs for SVD-GCN) the unit test would partially pass. However, as we +can see in e.g., Fig. 2, SVD-GCN can be broken with an – admittedly very distinct – adaptive attack. +7 +Related work +Excluding attacks on undefended GNNs, previous works studying adaptive attacks in the graph +domain are scarce. The recently proposed graph robustness benchmark [62] also only studies transfer +attacks. Such transfer attacks are so common in the graph domain that their usage is often not even +explicitly stated, and we find that the perturbations are most commonly transferred from Nettack or +Metattack (both use a linearized GCN). Other times, the authors of a defense only state that they +use PGD [53] (aka “topology attack”) without further explanations. In this case, the authors most +certainly refer to a PGD transfer attack on a GCN proxy. They almost never apply PGD to their actual +defense, which would yield an adaptive attack (but possibly weak, see § 4 for guidance). +An exception where the defense authors study an adaptive attack is SVD-GCN [12]. Their attack +collects the edges flipped by Nettack in a difference matrix δA, replaces its most significant singular +values and vectors with those from the clean adajcency matrix A, and finally adds it to A. Notably, +this yields a dense continuous perturbed adjacency matrix. While their SVD-GCN is susceptible to +these perturbations, the results however do not appear as catastrophic as with our adaptive attacks, +despite their severe violation of our threat model (see § 2). Geisler et al. [17] are another exception +where gradient-based greedy and PGD attacks are directly applied to their Soft-Median-GDC defense, +making them adaptive. Still, our attacks manage to further reduce their robustness estimate. +8 +Discussion +We hope that the adversarial learning community for GNNs will reflect on the bitter lesson that +evaluating adversarial robustness is not trivial. We show that on average adversarial robustness +estimates are overstated by 40%. To ease the transition into a more reliable regime of robustness +evaluation for GNNs we share our recipe for successfully designing strong adaptive attacks. +Using adaptive (white-box) attacks is also interesting from a security perspective. If a model success- +fully defends such strong attacks, it is less likely to have remaining attack vectors for a real-world +adversary. Practitioners can use our methodology to evaluate their models in hope to avoid an arms +race with attackers. Moreover, the white-box assumption lowers the chance that real-world adversaries +can leverage our findings, as it is unlikely that they have perfect knowledge. +We also urge for caution since the attacks only provide an upper bound (which with our attacks is now +40% tighter). Nevertheless, we argue that the burden of proof that a defense is truly effective should +lie with the authors proposing it. Following our methodology, the effort to design a strong adaptive +attack is reduced, so we advocate for adaptive attacks as the gold-standard for future defenses. +Acknowledgments and Disclosure of Funding +This research was supported by the Helmholtz Association under the joint research school “Munich +School for Data Science – MUDS“. +10 + +References +[1] Anish Athalye, Nicholas Carlini, and David Wagner. Obfuscated gradients give a false sense +of security: Circumventing defenses to adversarial examples. In International Conference on +Machine Learning, ICML, 2018. +[2] Aleksandar Bojchevski and Stephan Günnemann. Deep gaussian embedding of graphs: Unsuper- +vised inductive learning via ranking. In International Conference on Learning Representations, +ICLR, 2018. +[3] Nicholas Carlini and David Wagner. Adversarial examples are not easily detected: Bypassing +ten detection methods. In ACM Workshop on Artificial Intelligence and Security, AISec, 2017. +[4] Nicholas Carlini and David Wagner. Towards evaluating the robustness of neural networks. In +IEEE Symposium on Security and Privacy, 2017. +[5] Heng Chang, Yu Rong, Tingyang Xu, Yatao Bian, Shiji Zhou, Xin Wang, Junzhou Huang, and +Wenwu Zhu. Not all low-pass filters are robust in graph convolutional networks. In Advances in +Neural Information Processing Systems, NeurIPS, 2021. +[6] J. Chen, X. Lin, H. Xiong, Y. Wu, H. Zheng, and Q. Xuan. Smoothing adversarial training for +GNN. IEEE Transactions on Computational Social Systems, 8(3), 2020. +[7] Liang Chen, Jintang Li, Qibiao Peng, Yang Liu, Zibin Zheng, and Carl Yang. Understanding +structural vulnerability in graph convolutional networks. In International Joint Conference on +Artificial Intelligence, IJCAI, 2021. +[8] Lingwei Chen, Xiaoting Li, and Dinghao Wu. Enhancing robustness of graph convolutional +networks via dropping graph connections. In European Conference on Machine Learning and +Principles and Practice of Knowledge Discovery in Databases, ECML PKDD, 2021. +[9] Zhijie Deng, Yinpeng Dong, and Jun Zhu. Batch virtual adversarial training for graph convolu- +tional networks. In Workshop on Learning and Reasoning with Graph-Structured Representa- +tions at the International Conference on Machine Learning, ICML, 2019. +[10] Dongsheng Duan, Lingling Tong, Yangxi Li, Jie Lu, Lei Shi, and Cheng Zhang. AANE: +Anomaly aware network embedding for anomalous link detection. In IEEE International +Conference on Data Mining, ICDM, 2020. +[11] Pantelis Elinas, Edwin V. Bonilla, and Louis Tiao. Variational inference for graph convolu- +tional networks in the absence of graph data and adversarial settings. In Advances in Neural +Information Processing Systems, NeurIPS, 2020. +[12] Negin Entezari, Saba A. Al-Sayouri, Amirali Darvishzadeh, and Evangelos E. Papalexakis. All +you need is low (rank): Defending against adversarial attacks on graphs. In ACM International +Conference on Web Search and Data Mining, WSDM, 2020. +[13] Boyuan Feng, Yuke Wang, Z. Wang, and Yufei Ding. Uncertainty-aware attention graph neural +network for defending adversarial attacks. In AAAI Conference on Artificial Intelligence, 2021. +[14] Fuli Feng, Xiangnan He, Jie Tang, and Tat-Seng Chua. Graph adversarial training: Dynamically +regularizing based on graph structure. IEEE Transactions on Knowledge and Data Engineering, +33(6), 2021. +[15] Wenzheng Feng, Jie Zhang, Yuxiao Dong, Yu Han, Huanbo Luan, Qian Xu, Qiang Yang, Evgeny +Kharlamov, and Jie Tang. Graph random neural network for semi-supervised learning on graphs. +In International Conference on Machine Learning, ICML, 2021. +[16] Simon Geisler, Daniel Zügner, and Stephan Günnemann. Reliable graph neural networks via +robust aggregation. In Advances in Neural Information Processing Systems, NeurIPS, 2020. +[17] Simon Geisler, Tobias Schmidt, Hakan Sirin, Daniel Zügner, Aleksandar Bojchevski, and +Stephan Günnemann. Robustness of graph neural networks at scale. In Advances in Neural +Information Processing Systems, NeurIPS, 2021. +11 + +[18] Simon Geisler, Johanna Sommer, Jan Schuchardt, Aleksandar Bojchevski, and Stephan Günne- +mann. Generalization of neural combinatorial solvers through the lens of adversarial robustness. +In International Conference on Learning Representations, ICLR, 2022. +[19] C. Lee Giles, Kurt D. Bollacker, and Steve Lawrence. CiteSeer: An automatic citation indexing +system. In ACM Conference on Digital Libraries, 1998. +[20] Justin Gilmer, Samuel S. Schoenholz, Patrick F. Riley, Oriol Vinyals, and George E. Dahl. +Neural message passing for quantum chemistry. In International Conference on Machine +Learning, ICML, 2017. +[21] Stephan Günnemann. Graph neural networks: Adversarial robustness. In Lingfei Wu, Peng +Cui, Jian Pei, and Liang Zhao, editors, Graph Neural Networks: Foundations, Frontiers, and +Applications, chapter 8, . Springer, 2021. +[22] Weibo Hu, Chuan Chen, Yaomin Chang, Zibin Zheng, and Yunfei Du. Robust graph convo- +lutional networks with directional graph adversarial training. Applied Intelligence, 51(11), +2021. +[23] Weihua Hu, Matthias Fey, Marinka Zitnik, Yuxiao Dong, Hongyu Ren, Bowen Liu, Michele +Catasta, and Jure Leskovec. Open graph benchmark: Datasets for machine learning on graphs. +In Advances in Neural Information Processing Systems, NeurIPS, 2020. +[24] Vassilis N. Ioannidis and Georgios B. Giannakis. Edge dithering for robust adaptive graph +convolutional networks. In AAAI Conference on Artificial Intelligence, 2020. +[25] Vassilis N. Ioannidis, Antonio G. Marques, and Georgios B. Giannakis. Tensor graph con- +volutional networks for multi-relational and robust learning. IEEE Transactions on Signal +Processing, 68, 2020. +[26] Vassilis N. Ioannidis, Dimitris Berberidis, and Georgios B. Giannakis. Unveiling anomalous +nodes via random sampling and consensus on graphs. In IEEE International Conference on +Acoustics, Speech and Signal Processing, ICASSP, 2021. +[27] Hongwei Jin and Xinhua Zhang. Latent adversarial training of graph convolution networks. In +Workshop on Learning and Reasoning with Graph-Structured Representations at the Interna- +tional Conference on Machine Learning, ICML, 2019. +[28] Hongwei Jin and Xinhua Zhang. Robust training of graph convolutional networks via latent +perturbation. In European Conference on Machine Learning and Principles and Practice of +Knowledge Discovery in Databases, ECML PKDD, 2021. +[29] Ming Jin, Heng Chang, Wenwu Zhu, and Somayeh Sojoudi. Power up! Robust graph convo- +lutional network against evasion attacks based on graph powering. In AAAI Conference on +Artificial Intelligence, 2021. +[30] Wei Jin, Yao Ma, Xiaorui Liu, Xianfeng Tang, Suhang Wang, and Jiliang Tang. Graph structure +learning for robust graph neural networks. In ACM International Conference on Knowledge +Discovery and Data Mining, SIGKDD, 2020. +[31] Wei Jin, Tyler Derr, Yiqi Wang, Yao Ma, Zitao Liu, and Jiliang Tang. Node similarity preserving +graph convolutional networks. In ACM International Conference on Web Search and Data +Mining, WSDM, 2021. +[32] Diederik P. Kingma and Jimmy Ba. Adam: A method for stochastic optimization. In Interna- +tional Conference on Learning Representations, ICLR, 2015. +[33] Thomas N. Kipf and Max Welling. Semi-supervised classification with graph convolutional +networks. In International Conference on Learning Representations, ICLR, 2017. +[34] Jintang Li, Tao Xie, Chen Liang, Fenfang Xie, Xiangnan He, and Zibin Zheng. Adversarial +attack on large scale graph. IEEE Transactions on Knowledge and Data Engineering, 2021. +[35] Yaxin Li, Wei Jin, Han Xu, and Jiliang Tang. Deeprobust: A pytorch library for adversarial +attacks and defenses. arXiv preprint arXiv:2005.06149, 2020. +12 + +[36] Xiaorui Liu, Jiayuan Ding, Wei Jin, Han Xu, Yao Ma, Zitao Liu, and Jiliang Tang. Graph +neural networks with adaptive residual. In Advances in Neural Information Processing Systems, +NeurIPS, 2021. +[37] Xiaorui Liu, Wei Jin, Yao Ma, Yaxin Li, Hua Liu, Yiqi Wang, Ming Yan, and Jiliang Tang. +Elastic graph neural networks. In International Conference on Machine Learning, ICML, 2021. +[38] Dongsheng Luo, Wei Cheng, Wenchao Yu, Bo Zong, Jingchao Ni, Haifeng Chen, and Xiang +Zhang. Learning to drop: Robust graph neural network via topological denoising. In ACM +International Conference on Web Search and Data Mining, WSDM, 2021. +[39] Florence Regol, Soumyasundar Pal, Jianing Sun, Yingxue Zhang, Yanhui Geng, and Mark +Coates. Node copying: A random graph model for effective graph sampling. Signal Processing, +192, 2022. +[40] Uday Shankar Shanthamallu, Jayaraman J. Thiagarajan, and Andreas Spanias. Uncertainty- +matching graph neural networks to defend against poisoning attacks. In AAAI Conference on +Artificial Intelligence, 2021. +[41] Ke Sun, Zhouchen Lin, Hantao Guo, and Zhanxing Zhu. Virtual adversarial training on graph +convolutional networks in node classification. In Chinese Conference on Pattern Recognition +and Computer Vision, PRCV, 2019. +[42] Xianfeng Tang, Yandong Li, Yiwei Sun, Huaxiu Yao, Prasenjit Mitra, and Suhang Wang. Trans- +ferring robustness for graph neural network against poisoning attacks. In ACM International +Conference on Web Search and Data Mining, WSDM, 2020. +[43] Shuchang Tao, H. Shen, Q. Cao, L. Hou, and Xueqi Cheng. Adversarial immunization for +certifiable robustness on graphs. In ACM International Conference on Web Search and Data +Mining, WSDM, 2021. +[44] Florian Tramer, Nicholas Carlini, Wieland Brendel, and Aleksander Madry. On adaptive attacks +to adversarial example defenses. In Advances in Neural Information Processing Systems, +NeurIPS, 2020. +[45] Dimitris Tsipras, Shibani Santurkar, Logan Engstrom, Alexander Turner, and Aleksander +Madry. Robustness may be at odds with accuracy. In International Conference on Learning +Representations, ICLR, 2019. +[46] Haibo Wang, Chuan Zhou, Xin Chen, Jia Wu, Shirui Pan, and Jilong Wang. Graph stochastic +neural networks for semi-supervised learning. In Advances in Neural Information Processing +Systems, NeurIPS, 2020. +[47] Yiwei Wang, Shenghua Liu, Minji Yoon, Hemank Lamba, Wei Wang, Christos Faloutsos, and +Bryan Hooi. Provably robust node classification via low-pass message passing. In IEEE +International Conference on Data Mining, ICDM, 2020. +[48] Huijun Wu, Chen Wang, Yuriy Tyshetskiy, Andrew Docherty, Kai Lu, and Liming Zhu. Adver- +sarial examples for graph data: Deep insights into attack and defense. In International Joint +Conference on Artificial Intelligence, IJCAI, 2019. +[49] Tailin Wu, Hongyu Ren, Pan Li, and Jure Leskovec. Graph information bottleneck. In Advances +in Neural Information Processing Systems, NeurIPS, 2020. +[50] Yang Xiao, Jie Li, and Wengui Su. A lightweight metric defence strategy for graph neural +networks against poisoning attacks. In International Conference on Information and Communi- +cations Security, ICICS, 2021. +[51] Hui Xu, Liyao Xiang, Jiahao Yu, Anqi Cao, and Xinbing Wang. Speedup robust graph structure +learning with low-rank information. In ACM International Conference on Information & +Knowledge Management, CIKM, 2021. +[52] Jiarong Xu, Yang Yang, Junru Chen, Chunping Wang, Xin Jiang, Jiangang Lu, and Yizhou Sun. +Unsupervised adversarially-robust representation learning on graphs. In AAAI Conference on +Artificial Intelligence, 2022. +13 + +[53] Kaidi Xu, Hongge Chen, Sijia Liu, Pin Yu Chen, Tsui Wei Weng, Mingyi Hong, and Xue +Lin. Topology attack and defense for graph neural networks: An optimization perspective. In +International Joint Conference on Artificial Intelligence, IJCAI, 2019. +[54] Kaidi Xu, Sijia Liu, Pin-Yu Chen, Mengshu Sun, Caiwen Ding, Bhavya Kailkhura, and Xue +Lin. Towards an efficient and general framework of robust training for graph neural networks. +In IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP, 2020. +[55] Yuning You, Tianlong Chen, Yongduo Sui, Ting Chen, Zhangyang Wang, and Yang Shen. +Graph contrastive learning with augmentations. In Advances in Neural Information Processing +Systems, NeruIPS, 2020. +[56] Baoliang Zhang, Xiaoxin Guo, Zhenchuan Tu, and Jia Zhang. Graph alternate learning for +robust graph neural networks in node classification. Neural Computing and Applications, 34 +(11), 2022. +[57] Li Zhang and Haiping Lu. A feature-importance-aware and robust aggregator for gcn. In ACM +International Conference on Information & Knowledge Management, CIKM, 2020. +[58] Xiang Zhang and Marinka Zitnik. GNNGuard: Defending graph neural networks against +adversarial attacks. In Advances in Neural Information Processing Systems, NeurIPS, 2020. +[59] Yingxue Zhang, Sakif Hossain Khan, and Mark Coates. Comparing and detecting adversarial +attacks for graph deep learning. In Workshop on Representation Learning on Graphs and +Manifolds at the International Conference on Learning Representations, ICLR, 2019. +[60] Yingxue Zhang, Florence Regol, Soumyasundar Pal, Sakif Khan, Liheng Ma, and Mark Coates. +Detection and defense of topological adversarial attacks on graphs. In International Conference +on Artificial Intelligence and Statistics, AISTATS, 2021. +[61] Cheng Zheng, Bo Zong, Wei Cheng, Dongjin Song, Jingchao Ni, Wenchao Yu, Haifeng Chen, +and Wei Wang. Robust graph representation learning via neural sparsification. In International +Conference on Machine Learning, ICML, 2020. +[62] Qinkai Zheng, Xu Zou, Yuxiao Dong, Yukuo Cen, Da Yin, Jiarong Xu, Yang Yang, and Jie +Tang. Graph robustness benchmark: Benchmarking the adversarial robustness of graph machine +learning. In Advances in Neural Information Processing Systems, NeurIPS, 2021. +[63] Dingyuan Zhu, Peng Cui, Ziwei Zhang, and Wenwu Zhu. Robust graph convolutional networks +against adversarial attacks. In ACM International Conference on Knowledge Discovery and +Data Mining, SIGKDD, 2019. +[64] Jun Zhuang and Mohammad Al Hasan. Defending graph convolutional networks against +dynamic graph perturbations via bayesian self-supervision. In AAAI Conference on Artificial +Intelligence, 2022. +[65] Jun Zhuang and Mohammad Al Hasan. How does bayesian noisy self-supervision defend graph +convolutional networks? Neural Processing Letters, 54(4), 2022. +[66] Daniel Zügner and Stephan Günnemann. Adversarial attacks on graph neural networks via meta +learning. In International Conference on Learning Representations, ICLR, 2019. +[67] Daniel Zügner, Amir Akbarnejad, and Stephan Günnemann. Adversarial attacks on neural +networks for graph data. In ACM International Conference on Knowledge Discovery and Data +Mining, SIGKDD, 2018. +Checklist +1. For all authors... +(a) Do the main claims made in the abstract and introduction accurately reflect the paper’s +contributions and scope? [Yes] +(b) Did you describe the limitations of your work? [Yes] See § 8. +14 + +(c) Did you discuss any potential negative societal impacts of your work? [Yes] See § 8. +(d) Have you read the ethics review guidelines and ensured that your paper conforms to +them? [Yes] +2. If you are including theoretical results... +(a) Did you state the full set of assumptions of all theoretical results? [N/A] +(b) Did you include complete proofs of all theoretical results? [N/A] +3. If you ran experiments... +(a) Did you include the code, data, and instructions needed to reproduce the main experi- +mental results (either in the supplemental material or as a URL)? [Yes] See § 5. +(b) Did you specify all the training details (e.g., data splits, hyperparameters, how they +were chosen)? [Yes] See § 5, § H and provided code. +(c) Did you report error bars (e.g., with respect to the random seed after running ex- +periments multiple times)? [Yes] All experiments are repeated for five random data +splits. +(d) Did you include the total amount of compute and the type of resources used (e.g., type +of GPUs, internal cluster, or cloud provider)? [Yes] See beginning of § 5. +4. If you are using existing assets (e.g., code, data, models) or curating/releasing new assets... +(a) If your work uses existing assets, did you cite the creators? [Yes] +(b) Did you mention the license of the assets? [No] +(c) Did you include any new assets either in the supplemental material or as a URL? [Yes] +See beginning of § 5. +(d) Did you discuss whether and how consent was obtained from people whose data you’re +using/curating? [N/A] +(e) Did you discuss whether the data you are using/curating contains personally identifiable +information or offensive content? [N/A] +5. If you used crowdsourcing or conducted research with human subjects... +(a) Did you include the full text of instructions given to participants and screenshots, if +applicable? [N/A] +(b) Did you describe any potential participant risks, with links to Institutional Review +Board (IRB) approvals, if applicable? [N/A] +(c) Did you include the estimated hourly wage paid to participants and the total amount +spent on participant compensation? [N/A] +15 + +A +Attacks overview +In this section, we make the ensemble of attacks explicit and explain essential details. We then adapt +these attack primitives to circumvent the defense mechanisms (see § E). +Global evasion attacks. The goal of a global attack is to provoke the misclassification of a large +fraction of nodes (i.e., the test set) jointly, crafting a single perturbed adjacency matrix. For evasion, +we use (1) the Fast Gradient Attack (FGA) and (2) Projected Gradient Descent (PGD). In FGA, we +calculate the gradient towards the entries of the clean adjacency matrix ∇Aℓattack(fθ∗(A, X), y) and +then flip the highest-ranked edges at once s.t. we exhaust the budget ∆. In contrast, PGD requires +multiple gradient updates since it uses gradient ascent (see § 2 or explanation below for Meta-PGD). +We deviate from the PGD implementation of Xu et al. [53] is two ways: (I) we adapt the initialization +of the perturbation before the first attack gradient descent step and (II) we adjust the final sampling of +˜A. See below for more details. +Global poisoning attacks. We either (a) transfer the perturbation ˜A found by evasion attack (1) +or (2) and use it to poison training, or (b) differentiate through the training procedure by unrolling +it, thereby obtaining a meta gradient. The latter approach is taken by both (3) Metattack [66] and +(4) our Meta-PGD. Metattack greedily flips a single edge in each iteration and then obtains a new +meta gradient at the changed adjacency matrix. In Meta-PGD, we follow the same relaxation as Xu +et al. [53] (see below as well as § 2) and obtain meta gradients at the relaxed adjacency matrices. In +contrast to the greedy approach of Metattack, Meta-PGD is able to revise early decisions later on. +Meta-PGD. Next, we explain the details of Meta-PGD and we present the pseudo code for reference +in Algorithm A.1. Recall that the discrete edges are relaxed {0, 1} → [0, 1] and that the “weight” of +the perturbation reflects the probability of flipping the respective edge. +Algorithm A.1 Meta-PGD +1: Input: Adjacency matrix A, node features X, labels y, GNN fθ(·), loss ℓattack +2: Parameters: Budget ∆, iterations E, learning rates αt +3: Initialize P0 ∈ Rn×n +4: for t ∈ {1, 2, . . . , E} do +5: +Step P(t) ← P(t−1) + αt∇P(t−1) +� +ℓattack +� +f +� +A + P(t−1), X; θ = train(A + P(t−1), X, y) +� +, y +�� +6: +Projection P(t) ← Π∥E[A+P(t)]−A∥0≤2∆(P(t)) +7: Sample ˜A s.t. ∥ ˜A − A∥0 ≤ 2∆ +8: Return ˜A +In the first step of Meta-PGD, we initialize the perturbation (line 3). In contrast to Xu et al. [53]’s +suggestion, we find that initializing the perturbation with the zero matrix can cause convergence +issues. Hence, we alternatively initialize the perturbation with ˜A from an attack on a different model +(see also lesson learned #8 in § 4). +In each attack iteration, a gradient ascent step is performed on the relaxed perturbed adjacency matrix +˜A(t−1) = A + P(t−1) (line 5). For obtaining the meta gradient through the training process, the +training is unrolled. For example, with vanilla gradient descent for training fθ(A, X) = f(A, X; θ), +the meta gradient resolves to +∇P(t−1) +� +ℓattack +� +f +� +A + P(t−1), X; θ = θ0 − η +Etrain +� +k=1 +∇θk−1ℓtrain[f(A + P(t−1), X; θ = θk−1), y] +� +, y +�� +(A.1) +with number of training epochs Etrain, fixed training learning rate η, and parameters after (random) +initialization θ0. Notice that to obtain our variant of non-meta PGD, it suffices to replace the gradient +computation in line 5 with ∇P(t−1) +� +ℓattack(fθ∗(A + P(t−1), X), y) +� +. +Thereafter in line 6, the perturbation is projected such that in expectation the budget is obeyed, i.e., +Π∥E[A+P(t)]−A∥0≤2∆. First, the projection clips A + P(t−1) to be in [0, 1]. If the budget is violated +after clipping, it solves +arg min +ˆP(t) ∥ˆP(t) − P(t)∥2 +s.t. +A + ˆP(t) ∈ [0, 1]n×n and +� +|ˆP(t)| ≤ 2∆ +(A.2) +After the last iteration (line 7), each element of P(t) is interpreted as a probability and multiple +perturbations are sampled accordingly. The strongest drawn perturbed adjacency matrix (in terms of +16 + +attack loss) is chosen as ˜A. Specifically, in contrast to [53], we sample K = 100 potential solutions +that all obey the budget ∆ and then choose the one that maximizes the attack loss ℓattack. +Local attacks. For local attacks we only run evasion attacks, and then transfer them to poisoning. +This is common practice (e.g., see Zügner et al. [67] or Li et al. [34]). The attacks we use are (1) FGA, +(2) PGD, (3) Nettack [67], and a (4) Greedy Brute Force attack. Nettack greedily flips the best edges +considering a linearized GCN, whose weights are either specially trained or taken from the attacked +defense. In contrast, in each iteration, our Greedy Brute Force attack flips the current worst-case edge +for the attacked model. It determines the worst-case perturbation by evaluating the model for every +single edge flip. Notice that all examined models use two propagation steps, so we only consider +all potential edges adjoining the target node or its neighbors4. Importantly, Greedy Brute Force is +adaptive for any kind of model. Runtime-wise, the algorithm evaluates the attacked model O(∆nd) +times with the number of nodes n and the degree of the target node d. We provide pseudo code in +Algorithm A.2. +Algorithm A.2 Greedy Brute Force +1: Input: Target node i, adjacency matrix A, node features X, labels y, GNN fθ(·), loss ℓattack +2: Parameter: Budget ∆ +3: Initialize ˜A(0) = A +4: for t ∈ {1, 2, . . . , ∆} do +5: +for potential edge e adjoining i or any of i’s direct neighbors do +6: +Flip edge ˜A(t) ← ˜A(t−1) ± e +7: +Remember best ˜A(t) in terms of ℓattack(fθ∗( ˜A(t), X), y) +8: +if node i is missclassifed then +9: +Return ˜A(t) +10: +Recover best ˜A(t) +11: Return ˜A∆ +Unnoticeability typically serves as a proxy to ensure that the label of an instance (here node) has +not changed. In the image domain, it is widely accepted that a sufficiently small perturbation of the +input image w.r.t. an Lp-norm is unnoticeable (and similarly for other threat models such as rotation). +For graphs the whole subject of unnoticeability is more nuanced. The only constraint we use is the +number of edge insertions/deletion, i.e., an L0-ball around the clean adjacency matrix. +The only additional unnoticeability constraint proposed in the literature compares the clean and +perturbed graph under a power law assumption on the node degrees [67]. However, we do not include +such a constraint since (1) the degree distribution is only one (arbitrary) property to distinguish +two graphs. (2) The degree distribution is a global property with an opaque relationship to the local +class labels in node classification. (3) As demonstrated in Zügner & Günnemann [66], enforcing +an indistinguishable degree distribution only has a negligible influence on attack efficacy, i.e., their +gradient-based/adaptive attack conveniently circumvents this measure. Thus, we argue that enforcing +such a constraint is similar to an additional (weak) defense measure and is not the focus of this +work. Finally, since many defense (and attack) works in the literature considering node-classification +(including the ones we study) also only use an L0-ball constraint as a proxy for unnoticeability, +we do the same for improved consistency. Out of scope are also other domains, like combinatorial +optimization, where unnoticeability is not required since the true label of the perturbed instance is +known [18]. +4 Due to GCN-like normalization (see § E), the three-hop neighbors need to be considered to be exhaustive. +However, it is questionable if perturbing a neighbor three hops away is ever the strongest perturbation there is. +17 + +B +Defense taxonomy +Next, we give further details behind our reasoning on how to categorize defenses for GNNs. Our +taxonomy extends and largely follows Günnemann [21]’s. The three main categories are improving +the graph (§ B.1), improving the training (§ B.2), and improving the architecture (§ B.3). We assign +each defense to the category that fits best, even though some defenses additionally include ideas +fitting into other categories as well. For the assignment of defenses see Table 1. +B.1 +Improving the graph +With this category, we refer to all kinds of preprocessing of the graph. Alternatively, some approaches +make the graph learnable with the goal of improved robustness. In summary, this category addresses +changes that take place prior to the GNN (i.e., any message passing). We further distinguish (1) +unsupervised and (2) supervised approaches. +Unsupervised. Any improvements that are not entangled with a learning objective, i.e., pure pre- +processing, usually arising from clues found in the node features and graph structure. For example, +Jaccard-GCN [48] filters out edges based on the Jaccard similarity of node features, while SVD- +GCN [12] performs a low-rank approximation to filter out high-frequency perturbations. Most other +approaches from this category exploit clues from features and structure simultaneously. +Supervised. These graph improvements are entangled with the learning objective by making the +adjacency matrix learnable, often accompanied by additional regularization terms that introduce +expert assumptions about robustness. For example, ProGNN [30] treats the adjacency matrix like a +learnable parameter, and adds loss terms s.t. it remains close to the original adjacency matrix and +exhibits properties which are assumed about clean graphs like low-rankness. +B.2 +Improving the training +These approaches improve training – without changing the architecture – s.t. the learned parameters +θ∗ of the GNN exhibit improved robustness. In effect, the new training “nudges” a regular GNN +towards being more robust. We distinguish (1) robust training and (2) further training principles. +Robust training. Alternative training schemes and losses which reward the correct classification of +synthetic adversarial perturbations of the training data. With this category, Günnemann [21] targets +both straightforward adversarial training and losses stemming from certificates (i.e., improving +certifiable robustness). Neither approach is interesting to us: the former is discussed in § C, and the +latter targets provable robustness which does not lend itself to empirical evaluation. +Further training principles. This category is distinct from robust training due to the lack of a clear +mathematical definition of the training objective. It mostly captures augmentations [15, 29, 39, 42, 61] +or alternative training schemes [5, 11, 55, 64] that encourage robustness. A simple example for such +an approach is to pre-train the GNN weights on perturbed graphs [42]. Another recurring theme is to +use multiple models during training and then, e.g., enforce consistency among them [5]. +B.3 +Improving the architecture +Even though there are some exceptions (see sub-category (2) miscellaneous), the recurring theme +in this category is to somehow weight down the influence of some edges adaptively for each layer +or message passing aggregation. We refer to this type of improved architecture with (1) adaptively +weighting edges. We further distinguish between approaches that are (a) rule-based, (b) probabilistic, +or use (c) robust aggregation. +Rule-based approaches typically use some metric [31, 58], alternative message passing [36, 37], or an +auxiliary MLP [57] to filter out alleged adversarial edges. Probabilistic approaches either work with +distributions in the latent space [63], are built upon probabilistic principles like Bayesian uncertainty +quantification [13], or integrate sampling into the architecture and hence apply it also at inference +time [8, 24, 25, 38]. Robust aggregation defenses replace the message passing aggregation (typically +mean) with a more robust equivalent such as a trimmed mean, median, or soft median [7, 17]. In +relation to the trimmed mean, in this category we include also other related approaches that come +with some guarantees based on their aggregation scheme Wang et al. [47]. +18 + +C +On adversarial training defenses +The most basic form of adversarial training for structure perturbations aims to solve: +min +θ +max +A′∈Φ(A) ℓ(fθ(A′, X), y) +(C.1) +Similarly to [44, 1, 4], we exclude defenses that build on adversarial training in our study for three +reasons. +First, we observe that adversarial training requires knowing the clean A. However, for poisoning, +we would need to substitute A with an adversarially perturbed adjacency matrix ˜A. In this case, +adversarial training aims to enforce adversarial generalization A′ ∈ Φ( ˜A) for the adversarially +perturbed adjacency matrix ˜A – potentially even reinforcing the poisoning attack. +Second, an adaptive poisoning attack on adversarial training is very expensive as we need to unfold +many adversarial attacks for a single training. Thus, designing truly adaptive poisoning attacks +requires a considerable amount of resources. Scaling these attacks to such complicated training +schemes is not the main objective of this work. +Third, adversarial training for structure perturbations on GNNs seems to be an unsolved question. So +far, the robustness gains come from additional and orthogonal tricks such as self-training [53]. Hence, +adversarial training for structure perturbations requires an entire paper on its own. +D +On defenses against feature perturbations +As introduced in § 2, attacks may perturb the adjacency matrix A, the feature matrix X, or both. +However, during our survey we found that few defenses tackle feature perturbations. Similarly, 6 out +of the 7 defenses chosen by us mainly based on general popularity turn out to not consciously defend +against feature perturbations. +The only exception is SVD-GCN [12], which also applies its low-rank approximation to the binary +feature matrix. However, the authors do not report robustness under feature-only attacks; instead, they +only consider mixed structure and feature attacks found by Nettack. Given the strong bias of Nettack +towards structure perturbations, we argue that their experimental results do not confirm feature +robustness. Correspondingly, in preliminary experiments we were not able to achieve considerable +robustness gains of SVD-GCN compared to an undefended GCN – even with non-adaptive feature +perturbations. If a non-adaptive attack is strong enough, there is not much merit in applying an +adaptive attack. +To reiterate, due to the apparent scarcity of defenses apt against feature attacks, we decided to focus +our efforts on structure attacks and defenses. However, new defenses considering feature perturbations +should study robustness in the face of adaptive attacks – similarly to our work. In the following, +we give some important hints for adaptive attacks using feature perturbations. We leave attacks +that jointly consider feature and structure perturbations for future work due to the manifold open +challenges, e.g., balancing structure and feature perturbations in the budget quantity. +Baseline. To gauge the robustness of defenses w.r.t. global attacks, we introduce the RAUC metric, +which employs the accuracy of an MLP – which is perfectly robust w.r.t. structure perturbations – to +determine the maximally sensible budget to include in the summary. As MLPs are however vulnerable +to feature attacks, a different baseline model is required for this new setting. We propose to resolve +this issue by using a label propagation approach, which is oblivious to the node features and hence +perfectly robust w.r.t. feature perturbations. +Perturbations. The formulation of the set of admissible perturbations depends on what modality +the data represents, which may differ between node features and graph edges. Convenient choices +for continuous features are l-p-norms; in other cases, more complicated formulations are more +appropriate. Accordingly, one has to choose an appropriate constrained optimization scheme. +19 + +E +Examined adversarial defenses +In this section, we portray each defense and how we adapted the base attacks to each one. We refer to +Table H.1 for the used hyperparameter values for each defense. We give the used attack parameters +for a GCN below and refer to the provided code for the other defenses. +GCN. We employ an undefended GCN [33] as our baseline. A GCN first adds self loops to the +adjacency matrix A and subsequently applies GCN-normalization, thereby obtaining A′ = (D + +I)− 1 +2 (A + I)(D + I)− 1 +2 with the diagonal degree matrix D ∈ Nn×n. Then, in each GCN layer it +updates the hidden states H(l) = dropout(σ(A′H(l−1)W(l−1) + b(l−1))) where H(0) = X. We +use the non-linear ReLU activation for intermediate layers. Dropout is deactivated in the last layer +and we refer to the output before softmax activation as logits. We use Adam [32] to learn the model’s +parameters. +Attack. We do not require special tricks since the GCN is fully differentiable and does not come +with defensive measures to consider. In fact, the off-the-shelf attacks we employ are tailored to a +GCN. For PGD, we use E = 200 iterations, K = 100 samples, and a base learning rate of 0.1. For +Meta-PGD, we only lower the base learning rate to 0.01 and add gradient clipping to 1 (w.r.t. global +L2-norm). For Metattack with SGD instead of Adam for training the GCN, we use an SGD learning +rate of 1 and restrict the training to Etrain = 100 epochs. +E.1 +Jaccard-GCN +Defense. Additionally to a GCN, Jaccard-GCN [48] preprocesses the adjacency matrix. It computes +the Jaccard coefficient of the binarized features for the pair of nodes of every edge, i.e., Jij = +XiXj +min{Xi+Xj,1}. Then edges are dropped where Jij ≤ ϵ. +Adaptive attack. We do not need to adapt gradient-based attacks as the gradient is equal to zero for +dropped edges. Straightforwardly, we adapt Nettack to only consider non-dropped edges. Analogously, +we ignore these edges in the Greedy Brute Force attack for increased efficiency. +E.2 +SVD-GCN +Defense. SVD-GCN [12] preprocesses the adjacency matrix with a low-rank approximation (LRA) for +a fixed rank r, utilizing the Singular Value Decomposition (SVD) A = UΣV⊤ ≈ UrΣrV⊤ +r = Ar. +Note that the LRA is performed on A before adding self-loops and GCN-normalization (see above). +Thereafter, the dense Ar is passed to the GCN as usual. Since A is symmetric and positive semi- +definite, we interchangeably refer to the singular values/vectors also as eigenvalues/eigenvectors. +Adaptive attack. Unfortunately, the process of determining the singular vectors Ur and Vr is +highly susceptible to small perturbations, and so is its gradient. Thus, we circumvent the need of +differentiating the LRA. +We now explain the approach from a geometrical perspective. Each row of A (or interchangeably +column as A is symmetric) is interpreted as coordinates of a high-dimensional point. The r most +significant eigenvectors of A span an r-dimensional subspace, onto which the points are projected by +the LRA. Adding or removing an adversarial edge (i, j) corresponds to moving the point Ai along +dimension j, i.e., Ai ± ej (vice-versa for Aj). As hinted at in § 4, the r most significant eigenvectors +of A turn out to usually have few large components. Thus, the relevant subspace is mostly aligned +with only few dimensions. +Changes along the highest-valued eigenvectors are consequently preserved by LRA. To quantify how +much exactly such a movement along a dimension j, i.e., ej, is preserved, we project the movement +itself onto the subspace and extract the projected vector’s j-th component. More formally, we denote +the projection matrix onto the subspace as P = �r +k=0 vkvT +k where vk are the eigenvectors of A. +We now score each dimension j with (Pej)j = Pjj. Since the adjacency matrix is symmetric and +rows and columns are hence exchangeable, we then symmetrize the scores Wij = (Pii + Pjj)/2. +Finally, we decompose the perturbed adjacency matrix ˜A = A + δA and, thus, only need gradients +for δA. Using the approach sketched above, we now replace LRA(A + δA) ≈ LRA(A) + δA ◦ W. +20 + +The weights W can also be incorporated into the Greedy Brute Force attack by dropping edges +with weight < 0.2 and, for efficient early stopping, sort edges to try in order of descending weight. +Similarly, Nettack’s score function sstruct(i, j) – which attains positive and negative values, while W +is positive – can be wrapped to s′ +struct(i, j) = log(exp(sstruct(i, j)) ◦ W) = sstruct(i, j) + log W. +Note that we assume that the direction of the eigenvectors remains roughly equal after perturbing +the adjacency matrix. In practice, we find this assumption to be true. Intuitively, a change along the +dominant eigenvectors should even reinforce their significance. +E.3 +RGCN +Defense. The implementations of R(obust)GCN provided by the authors5 and in the widespread +DeepRobust [35] library6 are both consistent, but diverge slightly from the paper [63]. We use and now +present RGCN according to those reference implementations. Principally, RGCN models the hidden +states as Gaussian vectors with diagonal variance instead of sharp vectors. In addition to GCN’s A′, +a second A′′ = (D + I)−1(A + I)(D + I)−1 is prepared to propagate the variances. The mean +and variance of this hidden Gaussian distribution are initialized as M(0) = V(0) = X. Each layer +first computes an intermediate distributions given by ˆM(l) = elu(dropout(M(l−1))W(l−1) +M +) and +ˆV(l) = relu(dropout(V(l−1))W(l−1) +V +). Then, attention coefficients α(l) = e−γ ˆV(l) are calculated +with the aim to subdue high-variance dimensions (where exponentiation is element-wise and γ +is a hyperparameter). The final distributions are obtained with M(l) = A′ ˆM′(l) ◦ α(l). Note the +absence of bias terms. After the last layer, point estimates are sampled from the distributions via +the reparameterization trick, i.e., scalars are sampled from a standard Gaussian and arranged in a +matrix R. These samples are then used to obtain the logits via M(L) + R ◦ (V(L) + ϵ) +1 +2 (where +the square root applies element-wise and ϵ is a hyperparameter). Adam is the default optimizer. +The loss is extended with the regularizer β � +i KL(N( ˆM(1) +i , diag( ˆV(1) +i +))∥N(0, I)) (where β is a +hyperparameter). +Adaptive attack. A direct gradient attack suffices for a strong adaptive attack. Only when unrolling +the training procedure for Metattack and Meta-PGD, we increase hyperparameter ϵ from 10−8 to +10−2 to retain numerical stability. +E.4 +ProGNN +Defense. We use and present Pro(perty)GNN [30] exactly following the implementation provided by +the authors in their DeepRobust [35] library6. ProGNN learns an alternative adjacency matrix S that is +initialized with A. A regular GCN – which, as usual, adds self-loops and applies GCN-normalization +– is trained using S, which is simultaneously updated in every τ-th epoch. For that, first a gradient +descent step is performed on S with learning rate η and momentum µ towards minimizing the principal +training loss alongside two regularizers that measure deviation β1∥S − A∥2 +F and feature smoothness +β2 +2 +� +i,j Sij∥ Xi +√di − +Xj +√ +dj ∥2 (where di = � +j Sij + 10−3). Next, the singular value decomposition +UΣVT of the updated S is computed, and S is again updated to be U max(0, Σ − ηβ3)VT to +promote low-rankness. Thereafter, S is again updated to be sgn(S) ◦ max(0, |S| − ηβ4) to promote +sparsity. Finally, the epoch’s resulting S is obtained by clamping its elements between 0 and 1. +Adaptive attack. Designing an adaptive attack for ProGNN proved to be a challenging endeavor. We +describe the collection of tricks in § 4’s Example 2. +E.5 +GNNGuard +Defense. We closely follow the authors’ implementation7 as it deviates from the formal definitions in +the paper [58]. GNNGuard adopts a regular GCN and, before each layer, it adaptively weights down +alleged adversarial edges. Thus, each layer has a unique propagation matrix A(l) that is used instead +of A′. +5 https://github.com/ZW-ZHANG/RobustGCN +6 https://github.com/DSE-MSU/DeepRobust +7 https://github.com/mims-harvard/GNNGuard +21 + +GNNGuard’s rule-based edge reweighting can be clustered into four consecutive steps: (1) the +edges are reweighted based on the pair-wise cosine similarity C(l) +ij = +H(l−1) +i +·H(l−1) +j +∥H(l−1) +i +∥∥H(l−1) +j +∥ according to +S(l) = A ◦ C(l) ◦ I[C(l) ≥ 0.1], where edges with too dissimilar node embeddings are removed (see +Iverson bracket I[C(l) ≥ 0.1]). Then, (2) the matrix is rescaled Γ(l) +ij = S(l) +ij /s(l) +i +with s(l) +i += � +j S(l) +ij +For stability, if s(l) +i +< ϵ, s(l) +i +is set to 1 (here ϵ is a small constant). Next, (3) self-loops are added and +Γ(l) is non-linarily transformed according to ˆΓ(l) = exp̸=0(Γ(l) +diag 1/1 + d(l)), where exp̸=0 only +operates on nonzero elements and d(l) +i += ∥Γ(l) +i ∥0 is the row-wise number of nonzero entries. Last, +(4) the result is smoothed over the layers with Ω(l) = σ(ρ)Ω(l−1) + (1 − σ(ρ))ˆΓ(l) with learnable +parameter ρ and sigmoid function σ(·). +The resulting reweighted adjacency matrix Ω(l) is then GCN-normalized (without adding self-loops) +and passed on to a GCN layer. Note that steps (1) to (3) are excluded from back-propagation during +training. When comparing with the GNNGuard paper, one notices that among other deviations, we +have omitted learnable edge pruning because it is disabled in the reference implementation. +Adaptive attack. The hyperparameter ϵ must be increased from 10−6 to 10−2 during the attack +to retain numerical stability. In contrast to the reference implementation but as stated above, it is +important to place the hard filtering step I[C(l) ≥ 0.1] for S(l) s.t. the gradient calculation w.r.t. A is +not suppressed for these entries. +E.6 +GRAND +Defense. The Graph Random Neural Network (GRAND) [15] model is the only defense from our +selection that is not based on a GCN. First, A is endowed with self-loops and GCN-normalized to +obtain A′. Also, each row of X is l1-normalized, yielding X′. Next, rows from X′ are randomly +dropped with probability δ during training to generate a random augmentation, and X′ is scaled by +1 − δ during inference to compensate, thereby obtaining ˆX. Those preprocessed node features are +then propagated multiple times along the graph to get X = +1 +K+1 +�K +k=0 A′k ˆX. Finally, dropout is +applied once to X, and the result is plugged into a 2-layer MLP with dropout and ReLU activation to +obtain class probabilities Z. The authors also propose an alternative architecture using a GCN instead +of an MLP, however, we do not explore this option since the MLP version is superior according to +their own results. +GRAND is trained with Adam. The training loss comprises the mean of the cross-entropy losses of S +model evaluations, thereby incorporating multiple random augmentations. Additionally, a consistency +regularizer is added to enforce similar class probabilities across all evaluations. More formally, first +the probabilities are averaged across all evaluations: Z = 1 +S +�S +s=1 Z(s). Next, each node’s categorical +distribution is sharpened according to a temperature hyperparameter T, i.e., Z +′ +ij = Z +1 +T +ij /� +c Z +1 +T +ic . The +final regularizer penalizes the distance between the class probabilities and the sharpened averaged +distributions, namely β +S +�S +s=1 ∥Z(s) − Z +′∥2 +F . +Adaptive attack. When unrolling the training procedure for Metattack and Meta-PGD, to reduce the +memory footprint, we reduce the number of random augmentations per epoch to 1, and we use a +manual gradient calculation for the propagation operation. We also initialize Meta-PGD with a strong +perturbation found by Meta-PGD on ProGNN. Otherwise, the attack has issues finding a perturbation +with high loss; it presumably stalls in a local optimum. It is surprising that “only” initializing from +GCN instead of ProGNN does not give a satisfyingly strong attack. Finally, we use the same random +seed for every iteration of Metattack and Meta-PGD, as otherwise the constantly changing random +graph augmentations make the optimization very noisy. +E.7 +Soft-Median-GDC +Defense. The Soft-Median-GDC [17] deviates in two ways from a GCN: (1) it uses Personalized +Page Rank (PPR) with restart probability α = 0.15 to further preprocess the adjacency matrix after +adding self-loops and applying GCN-normalization. The result is then sparsified using a row-wise +top-k operation (k = 64). (2) the message passing aggregation is replaced with a robust estimator +22 + +called Soft-Median. From the perspective of node i, a GCN uses the message passing aggregation +H(l) +i += AiH(l−1) which can be interpreted as a weighted mean/sum. In Soft-Median-GDC, the +“weights” Ai are replaced with a scaled version of Ai ◦ softmax (−c/T +√ +d). Here the vector c denotes +the distance between hidden embedding of a neighboring node to the neighborhood-specific weighted +dimension-wise median: ci = ∥ Median(Ai, H(l−1)) − H(l−1) +i +∥. To keep the scale, these weights +are scaled s.t. they sum up to � Ai. +Adaptive attack. During gradient-based attacks, we adjust the c of every node s.t. it now captures +the distance to all other nodes, not only neighbors. This of course modifies the values of c, but is +necessary to obtain a nonzero gradient w.r.t. to all candidate edges. We initialize PGD with a strong +perturbation found by a similar attack on GCN, and initialize Meta-PGD with a perturbation from +a similar attack on ProGNN (as with GRAND, using an attack against GCN as a base would be +insufficient here). +F +Evaluation of adaptive attacks +In Table F.1, we summarize the variants of the datasets we use, both of which we have precisely +extracted from Nettack’s code8. In Fig. F.1, we complement Fig. 2 and compare the (R)AUC of all +defenses on Citeseer. The robustness estimates for the defenses on Citeseer are also much lower +as originally reported. For completeness, we give absolute envelope curve plots for all settings and +datasets as well as for higher budgets in Fig. F.2 and Fig. F.3 (compare with Fig. 4 and Fig. 5). +Table F.1: Statistics of the datasets we used. We measure homophily as the fraction of edges which +connect nodes of the same class. +Dataset +Nodes +Undirected Edges +Features +Classes +Avg. Degree +Homophily +Cora ML [2] +2485 +5069 +1433 +7 +4.08 +0.804 +Citeseer [19] +2110 +3668 +3703 +6 +3.477 +0.736 +0.00 +0.02 +0.04 +RAUC +Soft-Median-GDC +GRAND +RGCN +ProGNN +GCN +GNNGuard +Jaccard-GCN +SVD-GCN +(a) Global, Poisoning +0.00 +0.05 +0.10 +0.15 +RAUC +(b) Global, Evasion +0.2 +0.4 +AUC +(c) Local, Poisoning +0.2 +0.4 +0.6 +AUC +Adaptive +attack +Non- +adaptive +attack +(d) Local, Evasion +Figure F.1: Variant of Fig. 2 for Citeseer. +8 https://github.com/danielzuegner/nettack +23 + +MLP +GCN +Jaccard-GCN +SVD-GCN +RGCN +ProGNN +GNNGuard +GRAND +Soft-Median-GDC +0 +2 +4 +6 +8 +10 +12 +14 +Relative budget ∆ +m (%) +40 +50 +60 +70 +80 +Accuracy (%) +(a) Cora ML, Poisoning +0 +2 +4 +6 +8 +10 +12 +14 +Relative budget ∆ +m (%) +60 +65 +70 +75 +80 +85 +Accuracy (%) +(b) Cora ML, Evasion +0 +2 +4 +6 +8 +10 +12 +14 +Relative budget ∆ +m (%) +40 +50 +60 +70 +Accuracy (%) +(c) Citeseer, Poisoning +0 +2 +4 +6 +8 +10 +12 +14 +Relative budget ∆ +m (%) +55 +60 +65 +70 +75 +Accuracy (%) +(d) Citeseer, Evasion +Figure F.2: Absolute variant of Fig. 4, showing relative budgets up to 15%. +GCN +Jaccard-GCN +SVD-GCN +RGCN +ProGNN +GNNGuard +GRAND +Soft-Median-GDC +0 +25 +50 +75 +100 +125 +150 +175 +200 +Relative budget +∆ +degree (%) +0 +20 +40 +60 +80 +Corr. pred. (%) +(a) Cora ML, Poisoning +0 +25 +50 +75 +100 +125 +150 +175 +200 +Relative budget +∆ +degree (%) +0 +20 +40 +60 +80 +Corr. pred. (%) +(b) Cora ML, Evasion +0 +25 +50 +75 +100 +125 +150 +175 +200 +Relative budget +∆ +degree (%) +0 +20 +40 +60 +80 +Corr. pred. (%) +(c) Citeseer, Poisoning +0 +25 +50 +75 +100 +125 +150 +175 +200 +Relative budget +∆ +degree (%) +0 +20 +40 +60 +80 +Corr. pred. (%) +(d) Citeseer, Evasion +Figure F.3: Absolute variant of Fig. 5, showing relative budgets up to 200%. +24 + +G +Ensemble transferability study +In Fig. 8, we transfer attacks found on an individual model to other models. It is natural to also assess +the strength of transfer attacks supplied by ensembles of models. In Fig. G.1, we address this question +for 2-ensembles. For poisoning, the combination of RGCN and ProGNN turns out to be (nearly) the +strongest in all cases, which is reasonable since both already form strong individual transfer attacks +as is evident in Fig. 8. For evasion, the differences are more subtle. +We also investigate 3-ensembles, but omit the plots due to their size. For poisoning, RGCN and +ProGNN now combined with Soft-Median-GDC remain the strongest transfer source, yet the im- +provement over the 2-ensemble is marginal. For evasion, there is still no clear winner. +GCN +Jaccard-GCN +SVD-GCN +RGCN +ProGNN +GNNGuard +GRAND +Soft-Median-GDC +Transfer to +GCN + Jaccard-GCN +GCN + SVD-GCN +GCN + RGCN +GCN + ProGNN +GCN + GNNGuard +GCN + GRAND +GCN + Soft-Median-GDC +Jaccard-GCN + SVD-GCN +Jaccard-GCN + RGCN +Jaccard-GCN + ProGNN +Jaccard-GCN + GNNGuard +Jaccard-GCN + GRAND +Jaccard-GCN + Soft-Median-GDC +SVD-GCN + RGCN +SVD-GCN + ProGNN +SVD-GCN + GNNGuard +SVD-GCN + GRAND +SVD-GCN + Soft-Median-GDC +RGCN + ProGNN +RGCN + GNNGuard +RGCN + GRAND +RGCN + Soft-Median-GDC +ProGNN + GNNGuard +ProGNN + GRAND +ProGNN + Soft-Median-GDC +GNNGuard + GRAND +GNNGuard + Soft-Median-GDC +GRAND + Soft-Median-GDC +Transfer from +.14 +.15 +.14 +.22 +.16 +.18 +.20 +.15 +.14 +.26 +.16 +.18 +.18 +.15 +.12 +.20 +.13 +.15 +.14 +.13 +.12 +.15 +.13 +.12 +.17 +.15 +.15 +.14 +.16 +.18 +.17 +.14 +.13 +.11 +.18 +.14 +.16 +.14 +.13 +.11 +.18 +.13 +.14 +.17 +.17 +.22 +.18 +.23 +.11 +.15 +.12 +.20 +.13 +.15 +.10 +.14 +.12 +.15 +.13 +.12 +.14 +.17 +.17 +.17 +.18 +.23 +.11 +.15 +.13 +.12 +.18 +.14 +.11 +.15 +.13 +.11 +.18 +.13 +.11 +.18 +.12 +.20 +.13 +.15 +.10 +.14 +.12 +.15 +.13 +.12 +.22 +.18 +.23 +.25 +.28 +.32 +.12 +.17 +.13 +.12 +.18 +.14 +.11 +.17 +.13 +.11 +.18 +.14 +.10 +.14 +.13 +.15 +.12 +.12 +.11 +.16 +.17 +.12 +.13 +.15 +.11 +.16 +.14 +.11 +.17 +.13 +.10 +.16 +.14 +.11 +.17 +.12 +.10 +.14 +.14 +.12 +.13 +.12 +.10 +.14 +.14 +.12 +.15 +.12 +.10 +.14 +.13 +.12 +.15 +.13 +.11 +.16 +.16 +.13 +.12 +.14 +.11 +.16 +.15 +.13 +.11 +.14 +.10 +.16 +.15 +.12 +.11 +.17 +(a) Poisoning +GCN +Jaccard-GCN +SVD-GCN +RGCN +ProGNN +GNNGuard +GRAND +Soft-Median-GDC +Transfer to +.28 +.28 +.27 +.36 +.36 +.40 +.31 +.28 +.27 +.39 +.36 +.40 +.31 +.27 +.27 +.39 +.33 +.40 +.31 +.27 +.28 +.38 +.36 +.40 +.31 +.25 +.28 +.27 +.36 +.40 +.31 +.24 +.28 +.27 +.39 +.40 +.31 +.27 +.28 +.27 +.38 +.35 +.26 +.30 +.29 +.36 +.39 +.42 +.25 +.28 +.28 +.36 +.33 +.41 +.26 +.28 +.30 +.36 +.39 +.41 +.26 +.25 +.30 +.29 +.39 +.42 +.26 +.25 +.30 +.29 +.36 +.41 +.26 +.27 +.30 +.28 +.36 +.36 +.26 +.34 +.29 +.40 +.33 +.42 +.28 +.36 +.32 +.38 +.40 +.42 +.38 +.34 +.41 +.38 +.45 +.47 +.37 +.43 +.34 +.37 +.44 +.44 +.29 +.35 +.33 +.32 +.39 +.37 +.26 +.34 +.28 +.38 +.33 +.41 +.26 +.33 +.25 +.29 +.33 +.42 +.26 +.34 +.24 +.29 +.40 +.41 +.26 +.34 +.27 +.29 +.38 +.33 +.28 +.33 +.25 +.32 +.40 +.42 +.28 +.36 +.24 +.32 +.38 +.42 +.28 +.34 +.28 +.32 +.38 +.36 +.37 +.34 +.22 +.34 +.36 +.44 +.29 +.33 +.24 +.33 +.32 +.37 +.29 +.35 +.23 +.32 +.32 +.39 +(b) Evasion +Figure G.1: Variant of Fig. 8 with ensembles of models as attack transfer sources. The color maps are +not matched across (a) and (b) for improved readability. +25 + +H +GCN and defense hyperparameters: original vs. tuned for adaptive +attacks +To allow for the fairest comparison possible, we tuned the hyperparameters for each model (including +GCN) towards maximizing both clean accuracy and adversarial robustness on a single random data +split. In Table H.1, we list all hyperparameter configurations. While we cannot run an exhaustive +search over all hyperparameter settings, we report substantial gains for most defenses and the GCN +in Fig. H.1. The only exceptions are GRAND, Soft-Median-GDC on Cora ML, and GNNGuard. For +GRAND, we do not report results for the default hyperparameters as they did not yield satisfactory +clean accuracy. Moreover, for Soft-Median-GDC on Cora ML and GNNGuard we were not able to +substantially improve over the default hyperparameters. +For the GCN, tuning is important to ensure that we have a fair and equally-well tuned baseline. A +GCN is the natural baseline since most defense methods propose slight modifications of a GCN or +additional steps to improve the robustness. For the defenses, tuning is vital since they were most +originally tuned w.r.t. non-adaptive attacks. In any case, the tuning should counterbalance slight +variations in the setup. +As stated in the introduction, each attack only provides an upper bound for the actual adversarial +robustness of a model (with fixed hyperparameters). A future attack of increased efficacy might lead +to a tighter estimate. Thus, when we empirically compare the defenses to a GCN, we only compare +upper bounds of the respective actual robustness. However, we attack the GCN with state-of-the-art +approaches that were developed by multiple researchers specifically for a GCN. Even though we also +tune the parameters of the adaptive attacks, we argue that the robustness estimate for a GCN is likely +tighter than our robustness estimate for the defenses. In summary, the tuning of hyperparameters +is necessary that we can fairly compare the robustness of multiple models, even though, we only +compare upper bounds of the true robustness. +26 + +GCN +Jaccard-GCN +SVD-GCN +RGCN +ProGNN +GNNGuard +GRAND +Soft-Median-GDC +Poisoning +Evasion +78 +80 +82 +84 +86 +Clean Accuracy (%) +0.00 +0.05 +0.10 +0.15 +0.20 +0.25 +0.30 +RAUC +(a) Global, Cora ML +68 +70 +72 +74 +76 +Clean Accuracy (%) +0.00 +0.01 +0.02 +0.03 +0.04 +0.05 +0.06 +(b) Global, Citeseer +78 +80 +82 +84 +86 +Clean Accuracy (%) +0.10 +0.15 +0.20 +0.25 +0.30 +0.35 +AUC +(c) Local, Cora ML +68 +70 +72 +74 +76 +Clean Accuracy (%) +0.10 +0.15 +0.20 +0.25 +0.30 +0.35 +0.40 +(d) Local, Citeseer +Figure H.1: Each defense’s clean accuracy vs. (R)AUC values of the strongest attacks, akin to +Fig. 6. Muted (semi-transparent) colors represent untuned defenses (except for Soft-Median-GDC on +Cora ML and GNNGuard), solid colors denote tuned defenses, and lines connect the two. Our tuned +defenses are almost always better than untuned variants w.r.t. both clean accuracy and robustness. +27 + +Table H.1: GCN and defense hyperparameters. +GCN +Tuned +Hidden +Dropout +Max epochs +Patience +LR +L2 reg. +× +1 × 16 +0.5 +3000 +50 +0.01 +0.0005 +✓ +1 × 64 +0.9 +3000 +50 +0.01 +0.001 +Jaccard-GCN +Tuned +Hidden +Dropout +ϵ +Max epochs +Patience +LR +L2 reg. +× +1 × 16 +0.5 +0.0 +3000 +200 +0.01 +0.0005 +✓ +1 × 64 +0.9 +0.0 +3000 +50 +0.01 +0.001 +SVD-GCN +Tuned +Hidden +Dropout +Rank +Max epochs +Patience +LR +L2 reg. +× +1 × 16 +0.5 +50 +3000 +200 +0.01 +0.0005 +✓ +1 × 64 +0.9 +50 +3000 +50 +0.01 +0.001 +RGCN +Tuned +Hidden +Dropout +ϵ +γ +Max epochs +Patience +LR +L2 reg. +β +× +1 × 16 +0.6 +1e-8 +1.0 +3000 +50 +0.01 +0.0005 +0.0005 +✓ +1 × 32 +0.6 +1e-8 +1.0 +3000 +50 +0.01 +0.01 +0.0005 +ProGNN +Tuned +Hidden +Dropout +Max epochs +Patience +LR +L2 reg. +τ +η +µ +β1 +β2 +β3 +β4 +× +Cora ML +1 × 16 +0.5 +3000 +50 +0.01 +0.0005 +2 +0.01 +0.9 +1.0 +0.001 +1.5 +0.0005 +Citeseer +1 × 16 +0.5 +3000 +50 +0.01 +0.0005 +2 +0.01 +0.9 +1.0 +0.0001 +1.5 +0.0005 +✓ +Cora ML +1 × 16 +0.5 +3000 +50 +0.01 +0.0005 +2 +0.01 +0.9 +1.0 +0.1 +10.0 +0.1 +Citeseer +1 × 16 +0.5 +3000 +50 +0.01 +0.0005 +2 +0.01 +0.9 +1.0 +0.2 +20.0 +0.2 +GNNGuard +Tuned +Hidden +Dropout +Pruning +ϵ +Max epochs +Patience +LR +L2 reg. +× +1 × 16 +0.5 +× +1e-6 +81 +n/a +0.01 +0.0005 +GRAND +Tuned +Hidden +Dropout +X dropout +δ +K +Max epochs +Patience +LR +L2 reg. +S +β +T +✓ +Cora ML +1 × 32 +0.5 +0.5 +0.5 +8 +3000 +50 +0.05 +0.0001 +4 +1.0 +0.5 +Citeseer +1 × 32 +0.2 +0.0 +0.5 +2 +3000 +50 +0.05 +0.0005 +2 +0.7 +0.3 +Soft-Median-GDC +Tuned +Hidden +Dropout +k +α +T +Max epochs +Patience +LR +L2 reg. +× +1 × 64 +0.5 +64 +0.15 +0.5 +3000 +50 +0.01 +0.001 +✓ +Citeseer +1 × 64 +0.5 +64 +0.25 +0.5 +3000 +50 +0.01 +0.001 +28 + +I +Comparison of success of attack approaches +In Fig. I.1 we report which of the global attack techniques generate the strongest attacks, and in +Fig. I.3, we break down every global attack attempt. Analogously, in Fig. I.2 and Fig. I.4, we report +which local attack techniques require the smallest budget to misclassify the target nodes. In Fig. I.3, +we additionally compare different loss types for global attacks. +In general, we can say that PGD is the dominating attack for global evasion. For poisoning, Meta-PGD +seems to be the strongest – slightly more successful than Metattack, though not in every case. Greedy +brute force dominates the local attacks, but for some defenses, PGD and Nettack have an edge. +FGA +PGD +Metattack w/ Adam +Metattack w/ SGD +Meta-PGD +0 +50 +100 +Cases supp. envelope +Soft-Median-GDC +GRAND +GNNGuard +ProGNN +RGCN +SVD-GCN +Jaccard-GCN +GCN +(a) Cora ML, Pois. +0 +50 +100 +Cases supp. envelope +(b) Citeseer, Pois. +0 +50 +100 +Cases supp. envelope +(c) Cora ML, Evas. +0 +50 +100 +Cases supp. envelope +(d) Citeseer, Evas. +Figure I.1: Number of global attack attempts which support the envelope curve over all attack attempts, +as introduced in Fig. 3. We observe that for evasion, PGD almost always yields the strongest attack, +while for poisoning, either Metattack, Meta-PGD, or both dominate. Using Adam instead of SGD to +train the defense nearly always worsens Metattack’s performance. +FGA +PGD +Nettack w/ surrogate +Nettack w/o surrogate +Greedy Brute Force +0 +200 +400 +600 +# Nodes misclass. first +Soft-Median-GDC +GRAND +GNNGuard +ProGNN +RGCN +SVD-GCN +Jaccard-GCN +GCN +(a) Cora ML, Pois. +0 +200 +400 +600 +# Nodes misclass. first +(b) Citeseer, Pois. +0 +200 +400 +600 +# Nodes misclass. first +(c) Cora ML, Evas. +0 +200 +400 +600 +# Nodes misclass. first +(d) Citeseer, Evas. +Figure I.2: Number of target nodes for which the respective local attack needs the least budget (among +all attacks) to misclassify them. When multiple attacks achieve the same lowest budget, the target +node is counted in parts towards each winning attack and drawn with a muted color. We observe +that greedy brute force is often the strongest attack; only sometimes, PGD and Nettack beat it on +some defenses, especially for poisoning. Using the defense’s weights instead of a surrogate model for +Nettack is rarely an improvement. Still, for the majority of target nodes, multiple attacks are equally +strong in terms of achieving the same lowest budget (tie). We do not run the greedy brute force attack +on Soft-Median-GDC due to the costly PPR calculation. +29 + +FGA +PGD +Metattack w/ Adam +Metattack w/ SGD +Meta-PGD +TLM loss +PM loss +MCE loss +0.1 +0.2 +0.3 +0.4 +0.5 +RAUC +Soft-Median-GDC +GRAND +GNNGuard +ProGNN +RGCN +SVD-GCN +Jaccard-GCN +GCN +(a) Cora ML, Poisoning +0.00 +0.05 +0.10 +0.15 +0.20 +RAUC +Soft-Median-GDC +GRAND +GNNGuard +ProGNN +RGCN +SVD-GCN +Jaccard-GCN +GCN +(b) Citeseer, Poisoning +0.1 +0.2 +0.3 +0.4 +0.5 +0.6 +RAUC +Soft-Median-GDC +GRAND +GNNGuard +ProGNN +RGCN +SVD-GCN +Jaccard-GCN +GCN +(c) Cora ML, Evasion +0.00 +0.05 +0.10 +0.15 +0.20 +0.25 +RAUC +Soft-Median-GDC +GRAND +GNNGuard +ProGNN +RGCN +SVD-GCN +Jaccard-GCN +GCN +(d) Citeseer, Evasion +Figure I.3: The RAUC of every global attack we have conducted. Attacks are color-coded by +principal technique, and markers indicate the attack loss. Muted colors represent attacks without +edge masking (Jaccard-GCN), our edge weighting trick (SVD-GCN), multiple PGD auxiliary models +(ProGNN), Meta-PGD initialization from ProGNN and unlimited unrolled epochs (GRAND), and +PGD initialization from GCN (Soft-Median-GDC). We observe that (1) the TLM and PM losses are +superior in almost all cases; (2) PGD attacks are best for evasion while Metattack and Meta-PGD +are unsuited; (3) Metattack with SGD and Meta-PGD are best for poisoning while Metattack w/ +Adam even falls behind the surprisingly strong evasion-poisoning transfer; (4) FGA is weak for each +defense apart from SVD-GCN; (5) the cited adaptions are beneficial as attacks with muted colors are +worse; (6) a strong adaptive attack is necessary to reach a low RAUC. +30 + +FGA +PGD +Nettack w/ surrogate +Nettack w/o surrogate +Greedy Brute Force +0.2 +0.3 +0.4 +0.5 +0.6 +0.7 +AUC +Soft-Median-GDC +GRAND +GNNGuard +ProGNN +RGCN +SVD-GCN +Jaccard-GCN +GCN +(a) Cora ML, Poisoning +0.2 +0.3 +0.4 +0.5 +0.6 +0.7 +AUC +Soft-Median-GDC +GRAND +GNNGuard +ProGNN +RGCN +SVD-GCN +Jaccard-GCN +GCN +(b) Citeseer, Poisoning +0.2 +0.3 +0.4 +0.5 +0.6 +0.7 +AUC +Soft-Median-GDC +GRAND +GNNGuard +ProGNN +RGCN +SVD-GCN +Jaccard-GCN +GCN +(c) Cora ML, Evasion +0.2 +0.3 +0.4 +0.5 +0.6 +0.7 +AUC +Soft-Median-GDC +GRAND +GNNGuard +ProGNN +RGCN +SVD-GCN +Jaccard-GCN +GCN +(d) Citeseer, Evasion +Figure I.4: The AUC of every local attack we have conducted. Attacks are color-coded by principal +technique. Muted colors have the same signification as in Fig. I.3. We observe that (1) greedy brute +force is often the best attack, closely followed by PGD, while FGA is not as strong; (2) Nettack can +rarely be made stronger by utilizing the target model’s weights instead of a surrogate model (red); (3) +many defenses successfully defend against Nettack; (4) against those defenses for which we have +adapted Nettack, it becomes much stronger (muted vs. normal green); (5) the adaptions are also +beneficial for other attacks, as those with muted colors are worse. +31 + +J +Sensitivity to random seed +0.15 +0.20 +0.25 +0.30 +RAUC +ProGNN Untuned +ProGNN +GCN Untuned +GCN +Same seed +Different seed w/ mul. aux. +Different seed +Figure J.1: Lowest RAUC achieved by global +evasion-poisoning transfer attacks on Cora +ML under the premise that the random seed +used by the victim is known respectively un- +known to the attacker. While not knowing +the seed is disadvantageous especially on +ProGNN, our attack using multiple auxiliary +models successfully compensates this issue. +When transferring perturbations from evasion to poi- +soning, a different random seed is used for training +the poisoned model than was used for the evasion +one. In Fig. J.1, we study using the example of GCN +and ProGNN whether poisoning success improves +when we instead assume the same seed is used. This +is indeed the case and turns out particularly strong +on tuned ProGNN. However, by using multiple aux- +iliary models during evasion as detailed in § 4 under +the ProGNN example subheading, we can substan- +tially reduce the dependence of the attack upon a +particular random seed and thereby improve attack +performance. +K +Robustness over node degree +We explore the behavior of nodes under attack de- +pending on their degree. In Fig. K.1, we show the +probability that a successfully misclassified node falls +into a certain degree range, broken down by relativ budget. +We cannot confirm the prevalent conjecture that global attacks tend to target low-degree nodes, as +they are easier to break. Our results show that all degree groups are misclassified uniformly over all +budgets. There is no clear preference for lower-degree nodes. +For local attacks, on the other hand, we indeed observe that the success rate of changing the predicted +class is independent of the node degree if and only if using a relative budget. For example, when +allowing a certain relative budget, e.g., 100% of the target node’s degree, we manage to misclassify +the same fraction of 1-degree target nodes (with absolute budget of 1) as 5-degree ones (with absolute +budget of 5). +1 +2 +3 +4 +5 +6 +7 +8 +9 +≥ 10 +1 +2 +3 +5 +8-10 +15-25 +0 +5 +10 +Rel. budget ∆ +m (%) +0.0 +0.2 +0.4 +0.6 +0.8 +1.0 +P(degree | misclass.) +(a) Global, Cora ML +0 +5 +10 +Rel. budget ∆ +m (%) +(b) Global, Citeseer +0 +100 +200 +Rel. budget +∆ +degree (%) +0.0 +0.2 +0.4 +0.6 +0.8 +1.0 +P(degree | misclass.) +(c) Local, Cora ML +0 +100 +200 +Rel. budget +∆ +degree (%) +(d) Local, Citeseer +Figure K.1: The probability that a misclassified node is in a certain degree range. More specifically, +for global attacks, that is which ratios of test set nodes from subsets with degree 1, 2, 3, ... , 9, ≥ 10 +are misclassified per budget, normalized s.t. the stacked results sum to 1 everywhere. For local attacks, +we show the amount of nodes from each target node set misclassified per budget, again normalized +s.t. the stack sums to 1. Results are averaged over all experiments conducted (including evasion and +poisoning) on tuned models. The dotted lines indicate standard deviation. We observe no substantial +systematic bias towards the misclassification of low-degree nodes. +32 + +L +Attack characteristics +Next, we present interesting patterns of the adversarial perturbations for each model/defense. We show +the (1) node degree, (2) closeness centrality, (3) homophily, (4) Jaccard similarity of node attributes, +and (5) the ratio of removed edges over the strongest edge perturbations in Fig. L.1. For statistics 1-4, +we consider the pairs of nodes that were affected by an adversarial edge flip (i.e., insertion or removal). +Here we average over the strongest attack found for each budget (without transferring attacks between +defenses). Thus, the values indicate what characteristics are important for strong, adaptive attacks. +GCN +Jaccard-GCN +SVD-GCN +RGCN +ProGNN +GNNGuard +GRAND +Soft-Median-GDC +Global +Local +1.98 +2.10 +19.9 +1.87 +2.03 +3.18 +2.03 +2.26 +4.26 +4.33 +19.9 +4.26 +4.19 +5.56 +4.35 +4.78 +(a) Node degree +Global +Local +.126 +.129 +.142 +.126 +.127 +.134 +.128 +.131 +.131 +.131 +.151 +.132 +.131 +.139 +.133 +.134 +(b) Closeness centrality +Global +Local +.023 +.024 +.061 +.014 +.043 +.068 +.021 +.121 +.027 +.031 +.041 +.030 +.016 +.142 +.056 +.181 +(c) Homophily +Global +Local +.028 +.037 +.025 +.026 +.032 +.095 +.022 +.034 +.030 +.038 +.028 +.028 +.026 +.081 +.024 +.045 +(d) Jaccard similarity +Global +Local +.001 +.001 +.001 +.001 +.006 +.012 +.003 +.016 +.023 +.026 +.020 +.029 +.010 +.139 +.056 +.173 +(e) Ratio of removed edges +Figure L.1: Various metrics characterizing the nature +of the adversarial edges from our strongest attacks, +which are those visible in Fig. I.1 and Fig. I.2, as +well as the nature of the nodes connected respectively +disconnected by them. +(1) Node degree. For global attacks, the de- +gree tends to be lower than the average degree +of the dataset as given in Table F.1. The higher +average degree for local attacks might be influ- +enced by the node selection. Interestingly, on +SVD-GCN attacks connect very high-degree +nodes, most likely because high-degree nodes +correspond to dimensions represented by the +most significant eigenvectors of A (see § 4 +Example 1 and § E.2). The attacks exploit the +sensitivity of SVD-GCN to perturbations of +high-degree nodes. This could hint towards +how adaptive attacks catastrophically break +SVD-GCN. +(2) Closeness centrality. The closeness cen- +trality of a particular node v is one over the +sum of distances from v to all other nodes in +the graph, multiplied by the total number of +nodes in the graph. Attacks against SVD-GCN +connect very central nodes, which probably +correlates with them having high degrees. In- +terestingly, also the perturbations for GNN- +Guard seem to be of slightly increased central- +ity. +(3) Homophily refers here to the fraction of +pairs of nodes that share the same class. Suc- +cessful adaptive attacks on Jaccard-GCN share +the same homophily as those on GCN, in- +dicating that the Jaccard coefficient is not +suited to filter heterophil edges. Attacks on +SVD-GCN, GNNGuard, and Soft-Median- +GDC have higher homophily than those on +GCN, hinting that these defenses successfully +filter some heterogeneous edges, forcing some +attacks to adapt. +(4) Jaccard similarity. As expected, attacks +on Jaccard-GCN have to compensate its filter +by picking edges with nonzero coefficient. Attacks against GNNGuard connect nodes with very +similar features, presumably to get past its cosine distance-based edge weighting. Curiously, attacks +against Soft-Median-GDC behave similarly, yet only in the local setting and less pronounced. This +is probably necessary to avoid that the new edges are weighted down as outliers by the robust +aggregation, which becomes less of an issue when perturbing a large amount of edges in the global +setting and thereby shifting what it means to be an outlier. Other defenses and especially GRAND +admit connecting nodes as or more dissimilar than is the case on GCN. +(5) Ratio of removed edges. It is clear to see that for all models, the adversarial attack mostly adds +new edges. This indicates that edge insertion is stronger than edge deletion. Strong adaptive attacks +on GNNGuard and Soft-Median-GDC seem to require the most edge deletions. Moreover, deletions +are of much greater importance for local attacks. +33 + +M +Spectral properties of adaptive attacks +Previous studies have shown that adversarial attacks tend to focus the high-frequency (i.e., less +significant) singular values of the adjacency matrix, both in the local [12] and global [30] setting. In +consequence, defenses that exploit this observation to subdue attacks have been proposed (including +SVD-GCN and ProGNN). This is a prime example of where (1) defenses were designed to circumvent +specific attack characteristics and (2) an intuitive explanation exists of why the defense should improve +robustness. However, our adaptive attacks have shown that neither (1) nor (2) entail actual robustness. +In the case of SVD-GCN, it seems like the model becomes even less robust. It is only natural to ask +whether our attacks exhibit spectral properties different from the high-frequency observation upon +which SVD-GCN is built. +In Fig. M.1, we show the spectra of adjacency matrices before and after attacking GCN and SVD-GCN +in various settings. Indeed, our adaptive attacks on SVD-GCN perturb more of the low frequencies +and less of the high frequencies compared to attacks on GCN. Even though such low frequency-heavy +perturbations are hypothesized to be “noticeable” [12, 30], it is unclear how this can be exploited in +practice without knowing the clean graph or the underlying distribution of the spectrum. In § A, we +give additional reasons why we disregard constraints beyond the L0 difference. +Fig. M.1 also shows that, in contrast to previous beliefs, effective attacks on a GCN may lie in the low- +frequency spectrum (see subplots a and c). This questions the strategy of dampening high-frequency +singular values to defend against attacks in the first place. +0 +5 +10 +15 +Singular Value +Clean +GCN +SVD-GCN +100 +101 +102 +103 +Order +0 +1 +2 +3 +4 +Singular Value Change +(a) Cora ML, FGA/PGD +100 +101 +102 +103 +Order +(b) Cora ML, Meta +100 +101 +102 +103 +Order +(c) Citeseer, FGA/PGD +100 +101 +102 +103 +Order +(d) Citeseer, Meta +Figure M.1: Singular value spectra of the adjacency matrix before and after perturbation via global +adaptive attacks with relative budget of 7.5% against GCN and SVD-GCN. Results are split into +native evasion attacks (via FGA and PGD) and native poisoning attacks (via Metattack and Meta- +PGD), and averaged in each group. The top row shows the absolute spectrum, and the bottom row the +difference to the clean spectrum. The order is plotted logarithmically. We observe that attacks against +SVD-GCN strongly perturb the low-order singular values, and it is evident from the relative plots +that high-order singular values are perturbed less compared to attacks against GCN. +34 + +N +On the scalability of adaptive attacks +In our main paper, we do not study adversarial robustness on larger graphs as (a) most defenses do +not scale well and (b) we do not want to distract from our finding that structure defense evaluations +are overly optimistic. Nevertheless, we consider scalability to be an important aspect for robustness +as it is relevant for many applications. As mentioned in § 7, Geisler et al. [17] already study adaptive +attacks scaled to large graphs. However, their work is focused on their own defense, and they only +consider evasion. For these reasons, we now briefly discuss adaptive attacks on larger graphs. +In Fig. N.1, we show an adaptive attack against “Cosine-GCN” on arXiv from the Open Graph +Benchmark [23] (169k nodes). Our Cosine-GCN defense is a natural equivalent of Jaccard-GCN [48] +for continuous features. Similarly to Jaccard-GCN on the smaller graphs, Cosine-GCN also comes +with some robustness w.r.t. a non-adaptive attack. However, once we apply an adaptive attack, it +performs actually slightly worse than the GCN baseline. +Scaling first order attacks. The biggest challenge is certainly that the number of elements in the +adjacency matrix scales quadratically with the number of nodes. One way to circumvent this “curse +of dimensionality” is to use randomization. For our adaptive attack, we adopt Projected Randomized +Block Coordinate Descent (PRBCD) [17]. PRBCD uses the same relaxation as PGD (see § 2 and +§ A). In each iteration of the attack, it considers only a random subset of edges for gradient update +and subsequent projection. Then, for the next iteration, PRBCD keeps edges of high weight and +randomly re-samples the edges of low weight. This way, the overhead remains constant in the block +size. Since PRBCD is a first-order attack, it is natively adaptive for differentiable models. +0.0 +0.5 +1.0 +1.5 +Relative budget ∆ +m (%) +50 +55 +60 +65 +70 +Accuracy (%) +(a) Poisoning +0.0 +0.5 +1.0 +1.5 +Relative budget ∆ +m (%) +MLP +GCN +Cosine-GCN +Adaptive +Cosine-GCN +Non-Adaptive +(b) Evasion +Figure N.1: Adversarial accuracy on the large arXiv dataset per budget for the scalable PRBCD attack +against a regular GCN and our Cosine-GCN (single random seed). We use a block size of 1 million +edges and run the attack for 200 epochs. Thereafter, we keep the best block for another 50 epochs +fixed. Poisoning is conducted by transferring perturbations from evasion. +Evasion vs. poisoning. Gradient-based poisoning attacks seem inherently more challenging since +we need to unroll the training. Nevertheless, as long as we can run an evasion attack, there is the +possibility to transfer the perturbed adjacency matrix to the poisoning setting. Here, we chose this +approach. Still, Zügner & Günnemann [66] show in their appendix that only very few training steps +are actually required for Metattack to be effective. Using a low number of training steps is therefore +something to consider to scale direct poisoning attacks on larger graphs. +35 + diff --git a/YNFRT4oBgHgl3EQf_jgG/content/tmp_files/load_file.txt b/YNFRT4oBgHgl3EQf_jgG/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..2c8226ece798efd65fa396dbc829832f8e136eb6 --- /dev/null +++ b/YNFRT4oBgHgl3EQf_jgG/content/tmp_files/load_file.txt @@ -0,0 +1,2314 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf,len=2313 +page_content='Are Defenses for Graph Neural Networks Robust?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Felix Mujkanovic1∗, Simon Geisler1∗, Stephan Günnemann1, Aleksandar Bojchevski2 1Dept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' of Computer Science & Munich Data Science Institute, Technical University of Munich 2CISPA Helmholtz Center for Information Security {f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='mujkanovic, s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='geisler, s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='guennemann}@tum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='de | bojchevski@cispa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='de Abstract A cursory reading of the literature suggests that we have made a lot of progress in de- signing effective adversarial defenses for Graph Neural Networks (GNNs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Yet, the standard methodology has a serious flaw – virtually all of the defenses are evaluated against non-adaptive attacks leading to overly optimistic robustness estimates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We perform a thorough robustness analysis of 7 of the most popular defenses spanning the entire spectrum of strategies, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=', aimed at improving the graph, the architecture, or the training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' The results are sobering – most defenses show no or only marginal improvement compared to an undefended baseline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We advocate using custom adaptive attacks as a gold standard and we outline the lessons we learned from successfully designing such attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Moreover, our diverse collection of perturbed graphs forms a (black-box) unit test offering a first glance at a model’s robustness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='1 1 Introduction The vision community learned a bitter lesson – we need specific carefully crafted attacks to properly evaluate the adversarial robustness of a defense.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Consequently, adaptive attacks are considered the gold standard [44].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' This was not always the case;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' until recently, most defenses were tested only against relatively weak static attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' The turning point was Carlini & Wagner [3]’s work showing that 10 methods for detecting adversarial attacks can be easily circumvented.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Shortly after, Athalye et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [1] showed that 7 out of the 9 defenses they studied can be broken since they (implicitly) rely on obfuscated gradients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' So far, this bitter lesson is completely ignored in the graph domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 72 74 76 78 Adversarial accuracy (%) Soft-Median-GDC GRAND ProGNN GCN RGCN GNNGuard Jaccard-GCN SVD-GCN (a) Global, Poisoning 75 80 Adversarial accuracy (%) (b) Global, Evasion 0 20 40 Correct predicitons (%) (c) Local, Poisoning 0 20 40 60 Correct predicitons (%) Adaptive attack Non- adaptive attack (d) Local, Evasion Figure 1: Adaptive attacks draw a different picture of robustness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' All defenses are less robust than reported, with an undefended GCN [33] outperforming some.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We show results on Cora ML for both poisoning (attack before training) and evasion (attack after training), and both global (attack the test set jointly) and local (attack individual nodes) setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' The perturbation budget is relative w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' the #edges for global attacks (5% evasion, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='5% poisoning) and w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' the degree for local attacks (100%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In (a)/(b) SVD-GCN is catastrophically broken – our adaptive attacks reach 24%/9% (not visible).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Note that our non-adaptive attacks are already stronger than what is typically used (see § 5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' ∗equal contribution 1 Project page: https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='cit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='tum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='de/daml/are-gnn-defenses-robust/ 36th Conference on Neural Information Processing Systems (NeurIPS 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='13694v1 [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='LG] 31 Jan 2023 Virtually no existing work that proposes an allegedly robust Graph Neural Network (GNN) evaluates against adaptive attacks, leading to overly optimistic robustness estimates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' To show the seriousness of this methodological flaw we categorize 49 works that propose a robust GNN and are published at major conferences/journals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We then choose one defense per category (usually the most highly cited).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Not surprisingly, we show that none of the assessed models are as robust as originally advertised in their respective papers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 1 we summarize the results for 7 of the most popular defenses, spanning the entire spectrum of strategies (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=', aimed at improving the graph, the architecture, or the training, see Table 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We see that in both local and global settings, as well as for both evasion and poisoning, the adversarial accuracy under our adaptive attacks is significantly smaller compared to the routinely used non- adaptive attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Even more troubling is that many of the defenses perform worse than an undefended baseline (a vanilla GCN [33]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Importantly, the 7 defenses are not cherry-picked.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We report the results for each defense we assessed and selected each defence before running any experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Adversarial robustness measures the local generalization capabilities of a model, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=', sensitivity to (bounded) worst-case perturbations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Certificates typically provide a lower bound on the actual robustness while attacks provide an upper bound.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Since stronger attacks directly translate into tighter bounds our goal is to design the strongest attack possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Our adaptive attacks have perfect knowledge of the model, the parameters, and the data, including all defensive measures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In contrast, non-adaptive attacks (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=', transferred from an undefended proxy or an attack lacking knowledge about defense measures) only show how good the defense is at suppressing a narrow subset of input perturbations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='2 Tramer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [44] showed that even adaptive attacks can be tricky to design with many subtle challenges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' The graph domain comes with additional challenges since graphs are typically sparse and discrete and the representation of any node depends on its neighborhood.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' For this reason, we describe the recurring themes, the lessons learned, and our systematic methodology for designing strong adaptive attacks for all examined models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Additionally, we find that defenses are sometimes sensitive to a common attack vector and transferring attacks can also be successful.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Thus, the diverse collection of perturbed adjacency matrices resulting from our attacks forms a (black-box) unit test that any truly robust model should pass before moving on to adaptive evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In summary: We survey and categorize 49 defenses published across prestigious machine learning venues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We design custom attacks for 7 defenses (14%), covering the spectrum of defense techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' All examined models forfeit a large fraction of previously reported robustness gains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We provide a transparent methodology and guidelines for designing strong adaptive attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Our collection of perturbed graphs can serve as a robustness unit test for GNNs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 2 Background and preliminaries We follow the most common setup and assume GNN [20, 33] classifiers fθ(A, X) that operate on a symmetric binary adjacency matrix A ∈ {0, 1}n×n with binary node features X ∈ {0, 1}n×d and node labels y ∈ {1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' , C}n where C is the number of classes, n is the number of nodes, and m the number of edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' A poisoning attack perturbs the graph (flips edges) prior to training, optimizing max ˜A∈Φ(A) ℓattack(fθ∗( ˜A, X), y) s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' θ∗ = arg min θ ℓtrain(fθ( ˜A, X), y) (1) where ℓattack is the attacker’s loss, which is possibly different from ℓtrain (see § 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In an evasion attack, θ∗ is kept fixed and obtained by training on the clean graph minθ ℓtrain(fθ(A, X), y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In both cases, the locality constraint Φ(A) enforces a budget ∆ by limiting the perturbation to an L0-ball around the clean adjacency matrix: ∥ ˜A − A∥0 ≤ 2∆.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Attacks on X also exist, however, this scenario is not considered by the vast majority of defenses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' For example, only one out of the seven examined ones also discusses feature perturbations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We refer to § D for more details on adaptive feature attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Threat model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Our attacks aim to either cause misclassification of the entire test set (global) or a single node (local).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' To obtain the strongest attack possible (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=', tightest robustness upper bound), we use white-box attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We do not constrain the attacker beyond a simple budget constraint that enforces a maximum number of perturbed edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' For our considerations on unnoticeability, see § A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 2 From a security perspective non-adaptive attacks (typically transfer attacks) are also relevant since a real-world adversary is unlikely to know everything about the model and the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 2 Greedy attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Attacking a GNN typically corresponds to solving a constrained discrete non- convex optimization problem that – evident by this work – is hard to solve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Commonly, approximate algorithms are used to to tackle these optimization problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' For example, the single-step Fast Gradient Attack (FGA) flips the edges whose gradient (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=', ∇Aℓtrain(fθ∗(A, X), y)) most strongly indicates so.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' On the other hand, Nettack [67] and Metattack [66] are greedy multi-step attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' The greedy approaches have the nice side-effect that an attack for a high budget ∆ directly gives all attacks for budgets lower than ∆.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' On the other hand, they tend to be relatively weaker.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Projected Gradient Descent (PGD).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Alternatively, PGD [53] has been applied to GNNs where the discrete adjacency matrix is relaxed to [0, 1]n×n during the gradient-based optimization and the resulting weighted change reflects the probability of flipping an edge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' After each gradient update, the changes are projected back such that the budget holds in expectation ∥E[ ˜A] − A∥0 ≤ 2∆.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Finally, multiple samples are obtained and the strongest perturbation ˜A is chosen that obeys the budget ∆.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' The biggest caveats while applying L0-PGD are the relaxation gap and limited scalability (see Geisler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [17] for a detailed discussion and a scalable alternative).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Evasion vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' poisoning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Evasion can be considered the easier setting from an attack perspective since the model is fixed fθ∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' For poisoning, on the other hand, the adjacency matrix is perturbed before training (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Two general strategies exist for poisoning attacks: (1) transfer a perturbed adjacency matrix from an evasion attack [67];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' or (2) attack directly by, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=', unrolling the training procedure to obtain gradients through training [66].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Xu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [53] propose to solve Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 1 with alternating optimization which was shown to be even weaker than the evasion transfer (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Note that evasion is particularly of interest for inductive learning and poisoning for transductive learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 3 Adversarial defenses We select the defenses s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' we capture the entire spectrum of methods improving robustness against structure perturbations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' For the selection, we extend the taxonomy proposed in [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We selected the subset without cherry-picking based on the criteria elaborated below before experimentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Taxonomy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' The top-level categories are improving the graph (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=', preprocessing), improving the training (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=', adversarial training or augmentations), and improving the architecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Many defenses for structure perturbations either fall into the category of improving the graph or adaptively weighting down edges through an improved architecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Thus, we introduce further subcategories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Similar to [21]’s discussion, unsupervised improvement of the graph finds clues in the node features and graph structure, while supervised improvement incorporates gradient information from the learning objective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Conversely, for adaptive edge weighting, we identify three prevalent approaches: rule- based (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=', using a simple metric), probabilistic (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=', modeling a latent distribution), and robust aggregations (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=', with guarantees).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We assign each defense to the most fitting taxon (details in § B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Selected defenses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' To evaluate a diverse set of defenses, we select one per leaf taxon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='3 We prioritize highly cited defenses published at renowned venues with publicly available code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We implement all defenses in one unified pipeline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We present the categorization of defenses and our selection in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Similarly to Tramer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [44], we exclude defenses in the “robust training” category (see § C for a discussion).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Two of the three models in the “miscellaneous” category report some improvement in robustness, but they are not explicitly designed for defense purposes so we exclude them from our study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Some works evaluate only against evasion [48], others only poisoning [12, 15, 58], and the rest tackle both [17, 30, 63].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In some cases the evaluation setting is not explicitly stated and inferred by us.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' For completeness, we consider each defense in all four settings (local/global and evasion/poisoning).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Next, we provide a short summary of the key ideas behind each defense (details in § E).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Improving the graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' The feature-based Jaccard-GCN [48] uses a preprocessing step to remove all edges between nodes whose features exhibit a Jaccard similarity below a certain threshold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' This was motivated by the homophily assumption which is violated by prior attacks that tend to insert edges between dissimilar nodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' The structure-based SVD-GCN [12] replaces the adjacency matrix with a low-rank approximation prior to plugging it into a regular GNN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' This defense was motivated by the observation that the perturbations from Nettack tend to disproportionately affect the high-frequency spectrum of the adjacency matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' The key idea in ProGNN [30] is to learn the graph structure by 3 The only exception is unsupervised graph improvement, as it contains two of the most popular approaches, which rely on orthogonal principles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' One filters edges based on the node features [48], the other uses a low-rank approximation of the adjacency matrix [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 3 Table 1: Categorization of selected defenses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Our taxonomy extends the one by Günnemann [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Taxonomy Selected Defenses Other Defenses Improving graph Unsupervised Jaccard-GCN [48] SVD-GCN [12] [10,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 26,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 50,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 59,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 60] Supervised ProGNN [30] [51,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 43,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 56] Improving training Robust training n/a (see § C) [6,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 9,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 14,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 22,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 27,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 28,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 41,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 52,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 53,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 54] Further training principles GRAND [15] [5,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 11,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 29,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 39,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 42,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 55,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 61,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 64,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 65] Improving architecture Adaptively weighting edges Rule-based GNNGuard [58] [31,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 36,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 37,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 57] Probabilistic RGCN [63] [8,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 13,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 24,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 25,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 38] Robust agg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Soft-Median-GDC [17] [7, 16, 47] Miscellaneous n/a (see above) [40, 46, 49] alternatingly optimizing the parameters of the GNN and the adjacency matrix (the edge weights).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' The loss for the latter includes the standard cross-entropy loss, the distance to the original graph, and three other objectives designed to promote sparsity, low rank, and feature smoothness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Improving the training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' GRAND [15] relies on random feature augmentations (zeroing features) coupled with neighbourhood augmentations ¯X = (AX + AAX + · · · ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' All randomly augmented copies of ¯X are passed through the same MLP that is trained with a consistency regularization loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Improving the architecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' GNNGuard [58] filters edges in each message passing aggregation via cosine-similarity (smoothed over layers).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In the first layer of RGCN [63] we learn a Gaussian distribution over the feature matrix and the subsequent layers then manipulate this distribution (instead of using point estimates).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' For the loss we then sample from the resulting distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In addition, in each layer, RGCN assigns higher/lower weights to features with low/high variance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Soft-Median-GDC [17] replaces the message passing aggregation function in GNNs (typically a weighted mean) with a more robust alternative by relaxing the median using differentiable sorting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Common themes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' One theme shared by some defenses is to first discover some property that can discriminate clean from adversarial edges (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=', high vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' low feature similarity), and then propose a strategy based on that property (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=', filter low similarity edges).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Often they analyze the edges from only a single attack such as Nettack [67].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' The obvious pitfall of this strategy is that the attacker can easily adapt by restricting the adversarial search space to edges that will bypass the defense’s (implicit) filter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Another theme is to add additional loss terms to promote some robustness objectives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Similarly, the attacker can incorporate the same terms in the attack loss to negate their influence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 4 Methodology: How to design strong adaptive attacks In this section, we describe our general methodology and the lessons we learned while designing adaptive attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We hope these guidelines can serve as a reference for testing new defenses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Step 1 – Understand how the defense works and categorize it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' For example, some defenses rely on preprocessing which filters out edges that meet certain criteria (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=', Jaccard-GCN [48]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Others introduce additional losses during training (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=', GRAND [15]) or change the architecture (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=', RGCN [63]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Different defenses might need different attacks or impose extra requirements on them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Step 2 – Probe for obvious weaknesses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Some examples include: (a) transfer adversarial edges from another (closely related) model (see also § 6);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' (b) use a gradient-free (black-box) attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' For example, in our local experiments, we use a Greedy Brute Force attack: in each step, it considers all possible single edge flips and chooses the one that contributes most to the attack objective (details in § A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Step 3 – Launch a gradient-based adaptive attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' For rapid prototyping, use a comparably cheap attack such as FGA, and later advance to stronger attacks like PGD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' For poisoning, strongly consider meta-gradient-based attacks like Metattack [66] that unroll the training procedure, as they almost always outperform just transferring perturbations from evasion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Unsurprisingly, we find that applying PGD [53] on the meta gradients often yields even stronger attacks than the greedy Metattack, and we refer to this new attack as Meta-PGD (details in § A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 4 Step 4 – Address gradient issues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Some defenses contain components that are non-differentiable, lead to exploding or vanishing gradients, or obfuscate the gradients [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' To circumvent these issues, potentially: (a) adjust the defense’s hyperparameters to retain numerical stability;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' (b) replace the offending component with a differentiable or stable counterpart, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=', substitute the low-rank ap- proximation of SVD-GCN [12] with a suitable differentiable alternative;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' or (c) remove components, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=', drop the “hard” filtering of edges done in the preprocessing of Soft-Median-GDC [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' These considerations also include poisoning attacks, where one also needs to pay attention to all components of the training procedure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' For example, we ignore the nuclear norm loss term in the training of ProGNN [30] to obtain the meta-gradient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Of course, keep the entire defense intact for its final evaluation on the found perturbations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Step 5 – Adjust the attack loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In previous works, the attack loss is often chosen to be the same as the training loss, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=', the cross-entropy (CE).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' This is suboptimal since CE is not consistent according to the definition by Tramer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [44] – higher loss values do not indicate a stronger attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Thus, we use a variant of the consistent Carlini-Wagner loss [4] for local attacks, namely the logit margin (LM), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=', the logit difference between the ground truth class and most-likely non-true class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' However, as discussed by Geisler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [17], for global attacks the mean LM across all target nodes is still suboptimal since it can “waste” budget on already misclassified nodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Their tanh logit margin (TLM) loss resolves this issue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' If not indicated otherwise, we either use TLM or the probability margin (PM) loss – a slight variant of LM that computes the margin after the softmax rather than before.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Step 6 – Tune the attack hyperparameters such as the number of PGD steps, the attack learning rate, the optimizer, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' For example, for Metattack we observed that using the Adam optimizer [32] can weaken the attack and replacing it with SGD can increase the effectiveness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Lessons learned.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We provide a detailed description of each adaptive attack and the necessary actions to make it as strong as possible in § E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Here, we highlight some important recurring challenges that should be kept in mind when designing adaptive attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' (1) Numerical issues, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=', due to division by tiny numbers can lead to weak attacks, and we typically resolve them via clamping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' (2) In some cases we observed that for PGD attacks it is beneficial to clip the gradients to stabilize the adversarial optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' (3) For a strong attack it is essential to tune its hyperparameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' (4) Relaxing non-differentiable components and deactivating operations that filter edges/embeddings based on a threshold in order to obtain gradients for every edge is an effective strategy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' (5) If the success of evasion-poisoning transfer depends on a fixed random initialization (see § J), it helps to use multiple clean auxiliary models trained with different random seeds for the PGD attack – in each PGD step we choose one model randomly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' (6) Components that make the optimization more difficult but barely help the defense can be safely deactivated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' (7) It is sometimes beneficial to control the randomness in the training loop of Meta-PGD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' (8) For Meta-PGD it can help to initialize the attack with non-zero perturbations and e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=', use the perturbed graph of a different attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Example 1 – SVD-GCN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' To illustrate the attack process (especially steps 3 and 4) we present a case study of how we construct an adaptive attack against SVD-GCN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Gradient-free attacks like Nettack do not work well here as they waste budget on adversarial edges which are filtered out by the low-rank approximation (LRA).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Moreover, to the demise of gradient-based attacks, the gradients of the adjacency matrix are very unstable due to the SVD and thus less useful.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Still, we start with a gradient-based attack as it is easier to adapt, specifically FGA, whose quick runtime enables rapid prototyping as it requires only a single gradient calculation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' To replace the LRA with a function whose gradients are better behaved, we first decompose the perturbed adjacency matrix ˜A = A + δA and, thus, only need gradients for δA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Next, we notice that the eigenvectors of A usually have few large components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Perturbations along those principal dimensions are representable by the eigenvectors, hence most likely are neither filtered out nor impact the eigenvectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Knowing this, we approximate the LRA in a tractable manner by element-wise multiplication of δA with weights that quantify how well an edge aligns with the principal dimensions (details in § E).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In short we replace LRA(A + δA) with LRA(A)+δA◦Weight(A), which admits useful gradients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' This approach carries over to other attacks such as Nettack – we can incorporate the weights into its score function to avoid selecting edges that will be filtered out.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Example 2 – ProGNN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' While we approached SVD-GCN with a theoretical insight, breaking a composite defense like ProGNN requires engineering and tinkering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' When attacking ProGNN with PGD and transferring the perturbations to poisoning we observe that the perturbations are only effective if the model is trained with the same random seed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' This over-sensitivity can be avoided by 5 employing lesson (5) in § 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' As ProGNN is very expensive to train due to its nuclear norm regularizer, we drop that term when training the set of auxiliary models without hurting attack strength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' For unrolling the training we again drop the nuclear norm regularizer since it is non-differentiable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Sometimes PGD does not find a state with high attack loss, which can be alleviated by random restarts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' As Meta-PGD optimization quickly stalls, we initialize it with a strong perturbation found by Meta-PGD on GCN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' All of these tricks combined are necessary to successfully attack ProGNN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Effort.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Breaking Jaccard-GCN (and SVD-GCN) required around half an hour (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' three days) of work for the initial proof of concept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Some other defenses require various adjustments that need to be developed over time, but reusing those can quickly break even challenging defenses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' It is difficult to quantify this effort, but it can be greatly accelerated by adopting our lessons learned in § 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In any case, we argue that authors proposing a new defense must put in reasonable effort to break it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 5 Evaluation of adaptive attacks First, we provide details on the experimental setup and used metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We then report the main results and findings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We refer to § A for details on the base attacks, including our Greedy Brute Force and Meta-PGD approaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We provide the code, configurations, and a collection of perturbed graphs on the project website linked on the first page.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Setup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We use the two most widely used datasets in the literature, namely Cora ML [2] and Cite- seer [19] (details in § F).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Unfortunately, larger datasets are barely possible since most defenses are not very scalable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Still, in § N, we discuss scalability and apply an adaptive attack to arXiv (170k nodes) [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We repeat the experiments for five different data splits (10% training, 10% validation, 80% testing) and report the means and variances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We use an internal cluster with Nvidia GTX 1080Ti GPUs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Most experiments can be reproduced within a few hours.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' However, the experiments with ProGNN and GRAND will likely require several GPU days.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Defense hyperparameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' When first attacking the defenses, we observed that many exhibit poor robustness using the hyperparameters provided by their authors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' To not accidentally dismiss a defense as non-robust, we tune the hyperparameters such that the clean accuracy remains constant but the robustness w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' adaptive attacks is improved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Still, we run all experiments on the untuned defenses as well to confirm we achieve this goal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In the same way, we also tune the GCN model, which we use as a reference to asses whether a defense has merit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We report the configurations and verify the success of our tuning in § H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Attacks and budget.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In the global setting, we run the experiments for budgets ∆ of up to 15% of the total number of edges in the dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Due to our (R)AUC metric (see below), we effectively focus on only the lower range of evaluated budgets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We apply FGA and PGD [53] for evasion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' For poisoning, we transfer the found perturbations and also run Metattack [66] and our Meta-PGD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Recall that where necessary, we adapt the attacks to the defenses as outlined in § 4 and detailed in § E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In the local setting, we first draw sets of 20 target nodes per split with degrees 1, 2, 3, 5, 8-10, and 15-25 respectively (total of 120 nodes).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' This enables us to study how the attacks affect different types of nodes – lower degree nodes are often conjectured to be less robust (see also § K).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We then run the experiments for relative budgets ∆ of up to 200% of the target node’s degree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' For example, if a node has 10 neighbors, and the budget ∆ = 70% then the attacker can change up to 10 · 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='7 = 7 edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' This commonly used setup ensures that we treat both low and high-degree nodes fairly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We use Nettack [67], FGA, PGD, and our greedy brute force attack for evasion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' For poisoning, we only transfer the found perturbations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Again, we adapt the attacks to the defenses if necessary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In alignment with our threat model, we evaluate each found perturbation by the test set accuracy it achieves (global) or the ratio of target nodes that remain correctly classified (local).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' For each budget, we choose the strongest attack among all attempts (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=', PGD, Metattack, Meta-PGD).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' This gives rise to an envelope curve as seen in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We also include lower budgets as attempts, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=', we enforce the envelope curve to be monotonically decreasing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We introduce a rich set of attack characteristics by also transferring the perturbations supporting the envelope curve to every other defense.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' These transfer attacks then also contribute to the final envelope curve of each defense, but in most cases their contribution is marginal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='2 RAUC Soft-Median-GDC GRAND ProGNN GCN RGCN GNNGuard Jaccard-GCN SVD-GCN (a) Global, Poisoning 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='4 RAUC (b) Global, Evasion 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='4 AUC (c) Local, Poisoning 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='4 AUC Adaptive attack Non- adaptive attack (d) Local, Evasion Figure 2: Adaptive vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' non-adaptive attacks with budget-agnostic (R)AUC on Cora ML (c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' SVD-GCN (b) is disastrously broken – our adaptive attacks reach <0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='02 (not visible).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' § F for Citeseer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Non-adaptive attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We call any attack “non-adaptive” that is not aware of any changes made to the model (including defense mechanisms).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Where we report results for a non-adaptive attack (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=', Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 1 or Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 2), we specifically refer to an attack performed on a (potentially linearlized) GCN with commonly used hyperparameters (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=', untuned).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We then apply the perturbed adjacency matrix to the actual defense.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In other words, we transfer the adversarial perturbation from a GCN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' For our local non-adaptive attack, we always use Nettack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In contrast, for our global non-adaptive attack, we apply all attacks listed above, and then transfer for each budget the attack which is strongest against the GCN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Due to this ensemble of attacks, our global non-adaptive attack is expected to be slightly stronger than the non-adaptive attacks in most other works.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 0 2 4 6 8 Relative budget ∆ m (%) 60 65 70 75 80 85 Accuracy (%) PGD Mettack Meta-PGD Envelope MLP RAUC Figure 3: The dotted lines show the test set accuracy per budget after three global poisoning attacks against a tuned GCN on Cora ML.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Taking the envelope gives the solid black robustness curve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' The dashed gray line denotes the accuracy of an MLP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' The shaded area is the RAUC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Area Under the Curve (AUC).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' An envelope curve gives us a detailed breakdown of the empirical robustness of a defense for different adversarial budgets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' However, it is difficult to compare different attacks and defenses by only visually comparing their curves in a figure (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=', see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Therefore, in addition to this breakdown per budget, we summarize robustness using the Area Under the Curve (AUC), which is independent of a specific choice of bud- get ∆ and also punishes defenses that achieve robustness by trading in too much clean accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Intuitively higher AUCs indicate more robust models, and conversely, lower AUCs indicate stronger attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' As our local attacks break virtually all target nodes within our conservative maximum budget (see § F), taking the AUC over all budgets conveniently measures how quick this occurs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' However, for global attacks, the test set accu- racy continues to decrease for unreasonably large budget, and it is unclear when to stop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' To avoid having to choose a maximum budget, we wish to stop when discarding the entire tainted graph becomes the better defense.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' This is fulfilled by the area between the envelope curve and the line signifying the accuracy of an MLP – a model that is oblivious to the graph structure, at the expense of a substantially lower clean accuracy than a GNN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We call this metric Relative AUC (RAUC) and illustrate it in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' More formally, RAUC(c) = � b0 0 (c(b) − aMLP)db s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' b ≶ b0 =⇒ c(b) ≷ aMLP where c(·) is a piecewise linear robustness per budget curve, and aMLP is the accuracy of the MLP baseline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We normalize the RAUC s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 0% is the performance of an MLP and 100% is the optimal score (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=', 100% accuracy).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Finding 1 – Our adaptive attacks lower robustness by 40% on average.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 2 we compare non-adaptive attacks, the current standard to evaluate defenses, with our adaptive attacks which we propose as a new standard.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' The achieved (R)AUC in each case drops on average by 40% (similarly for Citeseer, see § F).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In other words, the reported robustness in the original works proposing a defense is roughly 40% too optimistic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We confirm a statistically significant drop (p < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='05) with a one-sided t-test in 85% of all cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Considering adversarial accuracy for (small) fixed adversarial budget (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 1) instead of the summary (R)AUC over all budgets tells the same story: non-adaptive attacks are too weak to be reliable indicators of robustness and adaptive attacks massively shrink the alleged robustness gains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 7 0 2 4 6 Relative budget ∆ m (%) −4 −2 0 2 4 Accuracy (%) rel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' to GCN (a) Cora ML, Pois.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 0 5 10 15 Relative budget ∆ m (%) (b) Cora ML, Evas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 0 1 2 3 Relative budget ∆ m (%) (c) Citeseer, Pois.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 0 2 4 6 Relative budget ∆ m (%) MLP GCN Jaccard-GCN RGCN ProGNN GNNGuard GRAND Soft-Median-GDC (d) Citeseer, Evas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Figure 4: Difference (defense – undefended GCN) of adversarial accuracy for the strongest global attack per budget.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Almost half of the defenses perform worse than the GCN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We exclude SVD-GCN since it is catastrophically broken and plotting it would make the other defenses illegible (accuracy <24% already for a budget of 2% on Cora ML).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Absolute numbers in § F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Finding 2 – Structural robustness of GCN is not easily improved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 4 (global) and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 5 (local) we provide a more detailed view for different adversarial budgets and different graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' For easier comparison we show the accuracy relative to the undefended GCN baseline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Overall, the decline is substantial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Almost half of the examined defenses perform worse than GCN and most remaining defenses neither meaningfully improve nor lower the robustness (see also Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 1 and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' GRAND and Soft-Medoid-GCN retain robustness in some settings, but the gains are smaller than reported.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Finding 3 – Defense effectiveness depends on dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' As we can see in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 4 and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 5, our ability to circumvent specific defenses tends to depend on the dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' It appears that some defenses are more suited for different datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' For example, GRAND seems to be a good choice for Citeseer while it is not as strong on Cora ML.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' The results for local attacks (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 5) paint a similar picture, here we see that Cora ML is more difficult to defend.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' This points to another potentially problematic pitfall: most defenses are developed only using these two datasets as benchmarks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Is robustness even worse on other graphs?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We leave this question for future work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='0 82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='5 85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='0 Clean Accuracy (%) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='3 RAUC GCN Jaccard-GCN SVD-GCN RGCN ProGNN GNNGuard GRAND Soft-Median-GDC Poisoning Evasion Figure 6: Model accuracy vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' RAUC of the strongest global attacks on Cora ML.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We do not observe a robustness accu- racy trade-off, but even find models with higher accuracy to be more robust.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Finding 4 – No trade-off between accuracy and robust- ness for structure perturbations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Instead, Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 6 shows that defenses with high clean accuracy also exhibit high RAUC, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=', are more robust against our attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' This ap- pears to be in contrast to the image domain [45].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' However, we cannot exclude that future more powerful defenses might manifest this trade-off in the graph domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Finding 5 – Necessity of adaptive attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 7, we show two exemplary characteristics of how an adaptive attack bypasses defensive measures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' First, to attack SVD- GCN, it seems particularly effective to insert connections to high-degree nodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Second, for GNNGuard, GRAND and Soft-Median-GDC it is disproportionally helpful to 0 50 100 Relative budget ∆ degree (%) −20 0 20 40 Corr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' pred.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' (%) rel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' to GCN (a) Cora ML, Pois.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 0 50 100 Relative budget ∆ degree (%) (b) Cora ML, Evas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 0 50 100 Relative budget ∆ degree (%) (c) Citeseer, Pois.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 0 50 100 Relative budget ∆ degree (%) GCN Jaccard-GCN SVD-GCN RGCN ProGNN GNNGuard GRAND Soft-Median-GDC (d) Citeseer, Evas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Figure 5: Difference (defense – undefended GCN) of fraction of correct predictions for the strongest local attack per budget.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Most defenses show no or only marginal gain in robustness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' The dashed vertical line shows where 95% of nodes for a GCN are misclassified on average.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Abs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' numbers in § F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 8 GCN Jaccard-GCN SVD-GCN RGCN ProGNN GNNGuard GRAND Soft-Median-GDC Global Local 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='98 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='10 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='9 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='87 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='03 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='18 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='03 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='26 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='26 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='33 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='9 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='26 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='19 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='56 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='35 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='78 (a) Node degree GCN Jaccard-GCN SVD-GCN RGCN ProGNN GNNGuard GRAND Soft-Median-GDC .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='001 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='001 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='001 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='001 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='006 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='012 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='003 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='016 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='023 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='026 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='020 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='029 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='010 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='139 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='056 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='173 (b) Ratio of removed edges Figure 7: Exemplary metrics characterizing the attack vector our strongest attacks, which are those visible in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='1 and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We give a more elaborate study of attack characteristics in § L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' delete edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' These examples illustrate why the existence of a one-fits-all perturbation which circum- vents all possible defenses is unlikely.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Instead, an adaptive attack is necessary to properly assess a defense’s efficacy since different models are particularly susceptible to different perturbations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Additional analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' During this project, we generated a treasure trove of data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We perform a more in-depth analysis of our attacks in the appendix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' First, we study how node degree affects attacks (see § K).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' For local attacks, the required budget to misclassify a node is usually proportional to the node’s degree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Global attacks tend to be oblivious to degree and uniformly break nodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Next, we perform a breakdown of each defense in terms of the sensitivity to different attacks (see § I).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In short, global attacks are dominated by PGD for evasion and Metattack/Meta-PGD for poisoning with the PM or TLM loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' For local, our greedy brute-force is most effective, rarely beaten by PGD and Nettack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Finally, we analyze the properties of the adversarial edges in terms of various graph statistics such as edge centrality and frequency spectra (see § L § M).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 6 Robustness unit test Next we systematically study how well the attacks transfer between defenses, as introduced in the attacks and budget paragraph in § 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 8, we see that in 15 out of 16 cases the adaptive attack is the most effective strategy (see main diagonal).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' However for many defenses, there is often a source model or ensemble of source models (for the latter see § G) which forms a strong transfer attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' GCN Jaccard-GCN RGCN ProGNN GNNGuard GRAND Soft-Median-GDC SVD-GCN Transfer from GCN Jaccard-GCN RGCN ProGNN GNNGuard GRAND Soft-Median-GDC SVD-GCN Transfer to .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='12 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='14 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='11 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='10 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='22 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='12 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='11 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='51 .' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='15 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='12 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='32 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='14 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='12 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='55 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='15 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='17 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='17 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='14 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='29 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='16 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='15 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='02 (a) Poisoning GCN Jaccard-GCN RGCN ProGNN GNNGuard GRAND Soft-Median-GDC SVD-GCN Transfer from .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='21 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='26 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='26 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='28 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='38 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='37 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='42 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='42 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='42 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='47 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='44 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='29 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='55 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='28 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='30 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='29 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='29 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='25 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='25 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='28 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='02 (b) Evasion Figure 8: RAUC for the transfer of the strongest global adaptive attacks on Cora ML between models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' The columns contain the models for which the adaptive attacks were created.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' The rows contain the RAUC after the transfer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' With only one exception, adaptive attacks (diagonal) are most effective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 9 Motivated by the effectiveness of transfer attacks (especially if transferring from ProGNN [30]), we suggest this set of perturbed graphs to be used as a bare minimum robustness unit test: one can probe a new defense by testing against these perturbed graphs, and if there exists at least one that diminishes the robustness gains, we can immediately conclude that the defense is not robust in the worst-case – without the potentially elaborate process of designing a new adaptive attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We provide instructions on how to use this collection in the accompanying code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Nevertheless, we cannot stress enough that this collection does not replace a properly developed adaptive attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' For example, if one would come up with SVD-GCN and would use our collection (excluding the perturbed graphs for SVD-GCN) the unit test would partially pass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' However, as we can see in e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=', Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 2, SVD-GCN can be broken with an – admittedly very distinct – adaptive attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 7 Related work Excluding attacks on undefended GNNs, previous works studying adaptive attacks in the graph domain are scarce.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' The recently proposed graph robustness benchmark [62] also only studies transfer attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Such transfer attacks are so common in the graph domain that their usage is often not even explicitly stated, and we find that the perturbations are most commonly transferred from Nettack or Metattack (both use a linearized GCN).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Other times, the authors of a defense only state that they use PGD [53] (aka “topology attack”) without further explanations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In this case, the authors most certainly refer to a PGD transfer attack on a GCN proxy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' They almost never apply PGD to their actual defense, which would yield an adaptive attack (but possibly weak, see § 4 for guidance).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' An exception where the defense authors study an adaptive attack is SVD-GCN [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Their attack collects the edges flipped by Nettack in a difference matrix δA, replaces its most significant singular values and vectors with those from the clean adajcency matrix A, and finally adds it to A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Notably, this yields a dense continuous perturbed adjacency matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' While their SVD-GCN is susceptible to these perturbations, the results however do not appear as catastrophic as with our adaptive attacks, despite their severe violation of our threat model (see § 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Geisler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [17] are another exception where gradient-based greedy and PGD attacks are directly applied to their Soft-Median-GDC defense, making them adaptive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Still, our attacks manage to further reduce their robustness estimate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 8 Discussion We hope that the adversarial learning community for GNNs will reflect on the bitter lesson that evaluating adversarial robustness is not trivial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We show that on average adversarial robustness estimates are overstated by 40%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' To ease the transition into a more reliable regime of robustness evaluation for GNNs we share our recipe for successfully designing strong adaptive attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Using adaptive (white-box) attacks is also interesting from a security perspective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' If a model success- fully defends such strong attacks, it is less likely to have remaining attack vectors for a real-world adversary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Practitioners can use our methodology to evaluate their models in hope to avoid an arms race with attackers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Moreover, the white-box assumption lowers the chance that real-world adversaries can leverage our findings, as it is unlikely that they have perfect knowledge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We also urge for caution since the attacks only provide an upper bound (which with our attacks is now 40% tighter).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Nevertheless, we argue that the burden of proof that a defense is truly effective should lie with the authors proposing it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Following our methodology, the effort to design a strong adaptive attack is reduced, so we advocate for adaptive attacks as the gold-standard for future defenses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Acknowledgments and Disclosure of Funding This research was supported by the Helmholtz Association under the joint research school “Munich School for Data Science – MUDS“.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 10 References [1] Anish Athalye, Nicholas Carlini, and David Wagner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Obfuscated gradients give a false sense of security: Circumventing defenses to adversarial examples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In International Conference on Machine Learning, ICML, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [2] Aleksandar Bojchevski and Stephan Günnemann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Deep gaussian embedding of graphs: Unsuper- vised inductive learning via ranking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In International Conference on Learning Representations, ICLR, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [3] Nicholas Carlini and David Wagner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Adversarial examples are not easily detected: Bypassing ten detection methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In ACM Workshop on Artificial Intelligence and Security, AISec, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [4] Nicholas Carlini and David Wagner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Towards evaluating the robustness of neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In IEEE Symposium on Security and Privacy, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [5] Heng Chang, Yu Rong, Tingyang Xu, Yatao Bian, Shiji Zhou, Xin Wang, Junzhou Huang, and Wenwu Zhu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Not all low-pass filters are robust in graph convolutional networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In Advances in Neural Information Processing Systems, NeurIPS, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [6] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Chen, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Lin, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Xiong, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Wu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Zheng, and Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Xuan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Smoothing adversarial training for GNN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' IEEE Transactions on Computational Social Systems, 8(3), 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [7] Liang Chen, Jintang Li, Qibiao Peng, Yang Liu, Zibin Zheng, and Carl Yang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Understanding structural vulnerability in graph convolutional networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In International Joint Conference on Artificial Intelligence, IJCAI, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [8] Lingwei Chen, Xiaoting Li, and Dinghao Wu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Enhancing robustness of graph convolutional networks via dropping graph connections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases, ECML PKDD, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [9] Zhijie Deng, Yinpeng Dong, and Jun Zhu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Batch virtual adversarial training for graph convolu- tional networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In Workshop on Learning and Reasoning with Graph-Structured Representa- tions at the International Conference on Machine Learning, ICML, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [10] Dongsheng Duan, Lingling Tong, Yangxi Li, Jie Lu, Lei Shi, and Cheng Zhang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' AANE: Anomaly aware network embedding for anomalous link detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In IEEE International Conference on Data Mining, ICDM, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [11] Pantelis Elinas, Edwin V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Bonilla, and Louis Tiao.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Variational inference for graph convolu- tional networks in the absence of graph data and adversarial settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In Advances in Neural Information Processing Systems, NeurIPS, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [12] Negin Entezari, Saba A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Al-Sayouri, Amirali Darvishzadeh, and Evangelos E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Papalexakis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' All you need is low (rank): Defending against adversarial attacks on graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In ACM International Conference on Web Search and Data Mining, WSDM, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [13] Boyuan Feng, Yuke Wang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Wang, and Yufei Ding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Uncertainty-aware attention graph neural network for defending adversarial attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In AAAI Conference on Artificial Intelligence, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [14] Fuli Feng, Xiangnan He, Jie Tang, and Tat-Seng Chua.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Graph adversarial training: Dynamically regularizing based on graph structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' IEEE Transactions on Knowledge and Data Engineering, 33(6), 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [15] Wenzheng Feng, Jie Zhang, Yuxiao Dong, Yu Han, Huanbo Luan, Qian Xu, Qiang Yang, Evgeny Kharlamov, and Jie Tang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Graph random neural network for semi-supervised learning on graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In International Conference on Machine Learning, ICML, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [16] Simon Geisler, Daniel Zügner, and Stephan Günnemann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Reliable graph neural networks via robust aggregation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In Advances in Neural Information Processing Systems, NeurIPS, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [17] Simon Geisler, Tobias Schmidt, Hakan Sirin, Daniel Zügner, Aleksandar Bojchevski, and Stephan Günnemann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Robustness of graph neural networks at scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In Advances in Neural Information Processing Systems, NeurIPS, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 11 [18] Simon Geisler, Johanna Sommer, Jan Schuchardt, Aleksandar Bojchevski, and Stephan Günne- mann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Generalization of neural combinatorial solvers through the lens of adversarial robustness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In International Conference on Learning Representations, ICLR, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [19] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Lee Giles, Kurt D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Bollacker, and Steve Lawrence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' CiteSeer: An automatic citation indexing system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In ACM Conference on Digital Libraries, 1998.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [20] Justin Gilmer, Samuel S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Schoenholz, Patrick F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Riley, Oriol Vinyals, and George E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Dahl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Neural message passing for quantum chemistry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In International Conference on Machine Learning, ICML, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [21] Stephan Günnemann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Graph neural networks: Adversarial robustness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In Lingfei Wu, Peng Cui, Jian Pei, and Liang Zhao, editors, Graph Neural Networks: Foundations, Frontiers, and Applications, chapter 8, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Springer, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [22] Weibo Hu, Chuan Chen, Yaomin Chang, Zibin Zheng, and Yunfei Du.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Robust graph convo- lutional networks with directional graph adversarial training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Applied Intelligence, 51(11), 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [23] Weihua Hu, Matthias Fey, Marinka Zitnik, Yuxiao Dong, Hongyu Ren, Bowen Liu, Michele Catasta, and Jure Leskovec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Open graph benchmark: Datasets for machine learning on graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In Advances in Neural Information Processing Systems, NeurIPS, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [24] Vassilis N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Ioannidis and Georgios B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Giannakis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Edge dithering for robust adaptive graph convolutional networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In AAAI Conference on Artificial Intelligence, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [25] Vassilis N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Ioannidis, Antonio G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Marques, and Georgios B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Giannakis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Tensor graph con- volutional networks for multi-relational and robust learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' IEEE Transactions on Signal Processing, 68, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [26] Vassilis N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Ioannidis, Dimitris Berberidis, and Georgios B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Giannakis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Unveiling anomalous nodes via random sampling and consensus on graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [27] Hongwei Jin and Xinhua Zhang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Latent adversarial training of graph convolution networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In Workshop on Learning and Reasoning with Graph-Structured Representations at the Interna- tional Conference on Machine Learning, ICML, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [28] Hongwei Jin and Xinhua Zhang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Robust training of graph convolutional networks via latent perturbation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases, ECML PKDD, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [29] Ming Jin, Heng Chang, Wenwu Zhu, and Somayeh Sojoudi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Power up!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Robust graph convo- lutional network against evasion attacks based on graph powering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In AAAI Conference on Artificial Intelligence, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [30] Wei Jin, Yao Ma, Xiaorui Liu, Xianfeng Tang, Suhang Wang, and Jiliang Tang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Graph structure learning for robust graph neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In ACM International Conference on Knowledge Discovery and Data Mining, SIGKDD, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [31] Wei Jin, Tyler Derr, Yiqi Wang, Yao Ma, Zitao Liu, and Jiliang Tang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Node similarity preserving graph convolutional networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In ACM International Conference on Web Search and Data Mining, WSDM, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [32] Diederik P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Kingma and Jimmy Ba.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Adam: A method for stochastic optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In Interna- tional Conference on Learning Representations, ICLR, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [33] Thomas N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Kipf and Max Welling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Semi-supervised classification with graph convolutional networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In International Conference on Learning Representations, ICLR, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [34] Jintang Li, Tao Xie, Chen Liang, Fenfang Xie, Xiangnan He, and Zibin Zheng.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Adversarial attack on large scale graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' IEEE Transactions on Knowledge and Data Engineering, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [35] Yaxin Li, Wei Jin, Han Xu, and Jiliang Tang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Deeprobust: A pytorch library for adversarial attacks and defenses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' arXiv preprint arXiv:2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='06149, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 12 [36] Xiaorui Liu, Jiayuan Ding, Wei Jin, Han Xu, Yao Ma, Zitao Liu, and Jiliang Tang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Graph neural networks with adaptive residual.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In Advances in Neural Information Processing Systems, NeurIPS, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [37] Xiaorui Liu, Wei Jin, Yao Ma, Yaxin Li, Hua Liu, Yiqi Wang, Ming Yan, and Jiliang Tang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Elastic graph neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In International Conference on Machine Learning, ICML, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [38] Dongsheng Luo, Wei Cheng, Wenchao Yu, Bo Zong, Jingchao Ni, Haifeng Chen, and Xiang Zhang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Learning to drop: Robust graph neural network via topological denoising.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In ACM International Conference on Web Search and Data Mining, WSDM, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [39] Florence Regol, Soumyasundar Pal, Jianing Sun, Yingxue Zhang, Yanhui Geng, and Mark Coates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Node copying: A random graph model for effective graph sampling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Signal Processing, 192, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [40] Uday Shankar Shanthamallu, Jayaraman J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Thiagarajan, and Andreas Spanias.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Uncertainty- matching graph neural networks to defend against poisoning attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In AAAI Conference on Artificial Intelligence, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [41] Ke Sun, Zhouchen Lin, Hantao Guo, and Zhanxing Zhu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Virtual adversarial training on graph convolutional networks in node classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In Chinese Conference on Pattern Recognition and Computer Vision, PRCV, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [42] Xianfeng Tang, Yandong Li, Yiwei Sun, Huaxiu Yao, Prasenjit Mitra, and Suhang Wang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Trans- ferring robustness for graph neural network against poisoning attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In ACM International Conference on Web Search and Data Mining, WSDM, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [43] Shuchang Tao, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Shen, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Cao, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Hou, and Xueqi Cheng.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Adversarial immunization for certifiable robustness on graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In ACM International Conference on Web Search and Data Mining, WSDM, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [44] Florian Tramer, Nicholas Carlini, Wieland Brendel, and Aleksander Madry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' On adaptive attacks to adversarial example defenses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In Advances in Neural Information Processing Systems, NeurIPS, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [45] Dimitris Tsipras, Shibani Santurkar, Logan Engstrom, Alexander Turner, and Aleksander Madry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Robustness may be at odds with accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In International Conference on Learning Representations, ICLR, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [46] Haibo Wang, Chuan Zhou, Xin Chen, Jia Wu, Shirui Pan, and Jilong Wang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Graph stochastic neural networks for semi-supervised learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In Advances in Neural Information Processing Systems, NeurIPS, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [47] Yiwei Wang, Shenghua Liu, Minji Yoon, Hemank Lamba, Wei Wang, Christos Faloutsos, and Bryan Hooi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Provably robust node classification via low-pass message passing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In IEEE International Conference on Data Mining, ICDM, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [48] Huijun Wu, Chen Wang, Yuriy Tyshetskiy, Andrew Docherty, Kai Lu, and Liming Zhu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Adver- sarial examples for graph data: Deep insights into attack and defense.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In International Joint Conference on Artificial Intelligence, IJCAI, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [49] Tailin Wu, Hongyu Ren, Pan Li, and Jure Leskovec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Graph information bottleneck.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In Advances in Neural Information Processing Systems, NeurIPS, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [50] Yang Xiao, Jie Li, and Wengui Su.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' A lightweight metric defence strategy for graph neural networks against poisoning attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In International Conference on Information and Communi- cations Security, ICICS, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [51] Hui Xu, Liyao Xiang, Jiahao Yu, Anqi Cao, and Xinbing Wang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Speedup robust graph structure learning with low-rank information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In ACM International Conference on Information & Knowledge Management, CIKM, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [52] Jiarong Xu, Yang Yang, Junru Chen, Chunping Wang, Xin Jiang, Jiangang Lu, and Yizhou Sun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Unsupervised adversarially-robust representation learning on graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In AAAI Conference on Artificial Intelligence, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 13 [53] Kaidi Xu, Hongge Chen, Sijia Liu, Pin Yu Chen, Tsui Wei Weng, Mingyi Hong, and Xue Lin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Topology attack and defense for graph neural networks: An optimization perspective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In International Joint Conference on Artificial Intelligence, IJCAI, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [54] Kaidi Xu, Sijia Liu, Pin-Yu Chen, Mengshu Sun, Caiwen Ding, Bhavya Kailkhura, and Xue Lin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Towards an efficient and general framework of robust training for graph neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [55] Yuning You, Tianlong Chen, Yongduo Sui, Ting Chen, Zhangyang Wang, and Yang Shen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Graph contrastive learning with augmentations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In Advances in Neural Information Processing Systems, NeruIPS, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [56] Baoliang Zhang, Xiaoxin Guo, Zhenchuan Tu, and Jia Zhang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Graph alternate learning for robust graph neural networks in node classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Neural Computing and Applications, 34 (11), 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [57] Li Zhang and Haiping Lu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' A feature-importance-aware and robust aggregator for gcn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In ACM International Conference on Information & Knowledge Management, CIKM, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [58] Xiang Zhang and Marinka Zitnik.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' GNNGuard: Defending graph neural networks against adversarial attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In Advances in Neural Information Processing Systems, NeurIPS, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [59] Yingxue Zhang, Sakif Hossain Khan, and Mark Coates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Comparing and detecting adversarial attacks for graph deep learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In Workshop on Representation Learning on Graphs and Manifolds at the International Conference on Learning Representations, ICLR, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [60] Yingxue Zhang, Florence Regol, Soumyasundar Pal, Sakif Khan, Liheng Ma, and Mark Coates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Detection and defense of topological adversarial attacks on graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In International Conference on Artificial Intelligence and Statistics, AISTATS, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [61] Cheng Zheng, Bo Zong, Wei Cheng, Dongjin Song, Jingchao Ni, Wenchao Yu, Haifeng Chen, and Wei Wang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Robust graph representation learning via neural sparsification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In International Conference on Machine Learning, ICML, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [62] Qinkai Zheng, Xu Zou, Yuxiao Dong, Yukuo Cen, Da Yin, Jiarong Xu, Yang Yang, and Jie Tang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Graph robustness benchmark: Benchmarking the adversarial robustness of graph machine learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In Advances in Neural Information Processing Systems, NeurIPS, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [63] Dingyuan Zhu, Peng Cui, Ziwei Zhang, and Wenwu Zhu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Robust graph convolutional networks against adversarial attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In ACM International Conference on Knowledge Discovery and Data Mining, SIGKDD, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [64] Jun Zhuang and Mohammad Al Hasan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Defending graph convolutional networks against dynamic graph perturbations via bayesian self-supervision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In AAAI Conference on Artificial Intelligence, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [65] Jun Zhuang and Mohammad Al Hasan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' How does bayesian noisy self-supervision defend graph convolutional networks?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Neural Processing Letters, 54(4), 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [66] Daniel Zügner and Stephan Günnemann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Adversarial attacks on graph neural networks via meta learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In International Conference on Learning Representations, ICLR, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [67] Daniel Zügner, Amir Akbarnejad, and Stephan Günnemann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Adversarial attacks on neural networks for graph data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In ACM International Conference on Knowledge Discovery and Data Mining, SIGKDD, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Checklist 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' For all authors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' (a) Do the main claims made in the abstract and introduction accurately reflect the paper’s contributions and scope?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [Yes] (b) Did you describe the limitations of your work?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [Yes] See § 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 14 (c) Did you discuss any potential negative societal impacts of your work?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [Yes] See § 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' (d) Have you read the ethics review guidelines and ensured that your paper conforms to them?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [Yes] 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' If you are including theoretical results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' (a) Did you state the full set of assumptions of all theoretical results?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [N/A] (b) Did you include complete proofs of all theoretical results?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [N/A] 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' If you ran experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' (a) Did you include the code, data, and instructions needed to reproduce the main experi- mental results (either in the supplemental material or as a URL)?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [Yes] See § 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' (b) Did you specify all the training details (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=', data splits, hyperparameters, how they were chosen)?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [Yes] See § 5, § H and provided code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' (c) Did you report error bars (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=', with respect to the random seed after running ex- periments multiple times)?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [Yes] All experiments are repeated for five random data splits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' (d) Did you include the total amount of compute and the type of resources used (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=', type of GPUs, internal cluster, or cloud provider)?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [Yes] See beginning of § 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' If you are using existing assets (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=', code, data, models) or curating/releasing new assets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' (a) If your work uses existing assets, did you cite the creators?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [Yes] (b) Did you mention the license of the assets?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [No] (c) Did you include any new assets either in the supplemental material or as a URL?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [Yes] See beginning of § 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' (d) Did you discuss whether and how consent was obtained from people whose data you’re using/curating?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [N/A] (e) Did you discuss whether the data you are using/curating contains personally identifiable information or offensive content?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [N/A] 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' If you used crowdsourcing or conducted research with human subjects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' (a) Did you include the full text of instructions given to participants and screenshots, if applicable?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [N/A] (b) Did you describe any potential participant risks, with links to Institutional Review Board (IRB) approvals, if applicable?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [N/A] (c) Did you include the estimated hourly wage paid to participants and the total amount spent on participant compensation?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [N/A] 15 A Attacks overview In this section, we make the ensemble of attacks explicit and explain essential details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We then adapt these attack primitives to circumvent the defense mechanisms (see § E).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Global evasion attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' The goal of a global attack is to provoke the misclassification of a large fraction of nodes (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=', the test set) jointly, crafting a single perturbed adjacency matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' For evasion, we use (1) the Fast Gradient Attack (FGA) and (2) Projected Gradient Descent (PGD).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In FGA, we calculate the gradient towards the entries of the clean adjacency matrix ∇Aℓattack(fθ∗(A, X), y) and then flip the highest-ranked edges at once s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' we exhaust the budget ∆.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In contrast, PGD requires multiple gradient updates since it uses gradient ascent (see § 2 or explanation below for Meta-PGD).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We deviate from the PGD implementation of Xu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [53] is two ways: (I) we adapt the initialization of the perturbation before the first attack gradient descent step and (II) we adjust the final sampling of ˜A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' See below for more details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Global poisoning attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We either (a) transfer the perturbation ˜A found by evasion attack (1) or (2) and use it to poison training, or (b) differentiate through the training procedure by unrolling it, thereby obtaining a meta gradient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' The latter approach is taken by both (3) Metattack [66] and (4) our Meta-PGD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Metattack greedily flips a single edge in each iteration and then obtains a new meta gradient at the changed adjacency matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In Meta-PGD, we follow the same relaxation as Xu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [53] (see below as well as § 2) and obtain meta gradients at the relaxed adjacency matrices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In contrast to the greedy approach of Metattack, Meta-PGD is able to revise early decisions later on.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Meta-PGD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Next, we explain the details of Meta-PGD and we present the pseudo code for reference in Algorithm A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Recall that the discrete edges are relaxed {0, 1} → [0, 1] and that the “weight” of the perturbation reflects the probability of flipping the respective edge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Algorithm A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='1 Meta-PGD 1: Input: Adjacency matrix A, node features X, labels y, GNN fθ(·), loss ℓattack 2: Parameters: Budget ∆, iterations E, learning rates αt 3: Initialize P0 ∈ Rn×n 4: for t ∈ {1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' , E} do 5: Step P(t) ← P(t−1) + αt∇P(t−1) � ℓattack � f � A + P(t−1), X;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' θ = train(A + P(t−1), X, y) � , y �� 6: Projection P(t) ← Π∥E[A+P(t)]−A∥0≤2∆(P(t)) 7: Sample ˜A s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' ∥ ˜A − A∥0 ≤ 2∆ 8: Return ˜A In the first step of Meta-PGD, we initialize the perturbation (line 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In contrast to Xu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [53]’s suggestion, we find that initializing the perturbation with the zero matrix can cause convergence issues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Hence, we alternatively initialize the perturbation with ˜A from an attack on a different model (see also lesson learned #8 in § 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In each attack iteration, a gradient ascent step is performed on the relaxed perturbed adjacency matrix ˜A(t−1) = A + P(t−1) (line 5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' For obtaining the meta gradient through the training process, the training is unrolled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' For example, with vanilla gradient descent for training fθ(A, X) = f(A, X;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' θ), the meta gradient resolves to ∇P(t−1) � ℓattack � f � A + P(t−1), X;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' θ = θ0 − η Etrain � k=1 ∇θk−1ℓtrain[f(A + P(t−1), X;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' θ = θk−1), y] � , y �� (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='1) with number of training epochs Etrain, fixed training learning rate η, and parameters after (random) initialization θ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Notice that to obtain our variant of non-meta PGD, it suffices to replace the gradient computation in line 5 with ∇P(t−1) � ℓattack(fθ∗(A + P(t−1), X), y) � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Thereafter in line 6, the perturbation is projected such that in expectation the budget is obeyed, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=', Π∥E[A+P(t)]−A∥0≤2∆.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' First, the projection clips A + P(t−1) to be in [0, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' If the budget is violated after clipping, it solves arg min ˆP(t) ∥ˆP(t) − P(t)∥2 s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' A + ˆP(t) ∈ [0, 1]n×n and � |ˆP(t)| ≤ 2∆ (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='2) After the last iteration (line 7), each element of P(t) is interpreted as a probability and multiple perturbations are sampled accordingly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' The strongest drawn perturbed adjacency matrix (in terms of 16 attack loss) is chosen as ˜A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Specifically, in contrast to [53], we sample K = 100 potential solutions that all obey the budget ∆ and then choose the one that maximizes the attack loss ℓattack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Local attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' For local attacks we only run evasion attacks, and then transfer them to poisoning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' This is common practice (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=', see Zügner et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [67] or Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [34]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' The attacks we use are (1) FGA, (2) PGD, (3) Nettack [67], and a (4) Greedy Brute Force attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Nettack greedily flips the best edges considering a linearized GCN, whose weights are either specially trained or taken from the attacked defense.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In contrast, in each iteration, our Greedy Brute Force attack flips the current worst-case edge for the attacked model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' It determines the worst-case perturbation by evaluating the model for every single edge flip.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Notice that all examined models use two propagation steps, so we only consider all potential edges adjoining the target node or its neighbors4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Importantly, Greedy Brute Force is adaptive for any kind of model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Runtime-wise, the algorithm evaluates the attacked model O(∆nd) times with the number of nodes n and the degree of the target node d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We provide pseudo code in Algorithm A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Algorithm A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='2 Greedy Brute Force 1: Input: Target node i, adjacency matrix A, node features X, labels y, GNN fθ(·), loss ℓattack 2: Parameter: Budget ∆ 3: Initialize ˜A(0) = A 4: for t ∈ {1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' , ∆} do 5: for potential edge e adjoining i or any of i’s direct neighbors do 6: Flip edge ˜A(t) ← ˜A(t−1) ± e 7: Remember best ˜A(t) in terms of ℓattack(fθ∗( ˜A(t), X), y) 8: if node i is missclassifed then 9: Return ˜A(t) 10: Recover best ˜A(t) 11: Return ˜A∆ Unnoticeability typically serves as a proxy to ensure that the label of an instance (here node) has not changed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In the image domain, it is widely accepted that a sufficiently small perturbation of the input image w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' an Lp-norm is unnoticeable (and similarly for other threat models such as rotation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' For graphs the whole subject of unnoticeability is more nuanced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' The only constraint we use is the number of edge insertions/deletion, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=', an L0-ball around the clean adjacency matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' The only additional unnoticeability constraint proposed in the literature compares the clean and perturbed graph under a power law assumption on the node degrees [67].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' However, we do not include such a constraint since (1) the degree distribution is only one (arbitrary) property to distinguish two graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' (2) The degree distribution is a global property with an opaque relationship to the local class labels in node classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' (3) As demonstrated in Zügner & Günnemann [66], enforcing an indistinguishable degree distribution only has a negligible influence on attack efficacy, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=', their gradient-based/adaptive attack conveniently circumvents this measure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Thus, we argue that enforcing such a constraint is similar to an additional (weak) defense measure and is not the focus of this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Finally, since many defense (and attack) works in the literature considering node-classification (including the ones we study) also only use an L0-ball constraint as a proxy for unnoticeability, we do the same for improved consistency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Out of scope are also other domains, like combinatorial optimization, where unnoticeability is not required since the true label of the perturbed instance is known [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 4 Due to GCN-like normalization (see § E), the three-hop neighbors need to be considered to be exhaustive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' However, it is questionable if perturbing a neighbor three hops away is ever the strongest perturbation there is.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 17 B Defense taxonomy Next, we give further details behind our reasoning on how to categorize defenses for GNNs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Our taxonomy extends and largely follows Günnemann [21]’s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' The three main categories are improving the graph (§ B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='1), improving the training (§ B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='2), and improving the architecture (§ B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We assign each defense to the category that fits best, even though some defenses additionally include ideas fitting into other categories as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' For the assignment of defenses see Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='1 Improving the graph With this category, we refer to all kinds of preprocessing of the graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Alternatively, some approaches make the graph learnable with the goal of improved robustness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In summary, this category addresses changes that take place prior to the GNN (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=', any message passing).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We further distinguish (1) unsupervised and (2) supervised approaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Unsupervised.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Any improvements that are not entangled with a learning objective, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=', pure pre- processing, usually arising from clues found in the node features and graph structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' For example, Jaccard-GCN [48] filters out edges based on the Jaccard similarity of node features, while SVD- GCN [12] performs a low-rank approximation to filter out high-frequency perturbations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Most other approaches from this category exploit clues from features and structure simultaneously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Supervised.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' These graph improvements are entangled with the learning objective by making the adjacency matrix learnable, often accompanied by additional regularization terms that introduce expert assumptions about robustness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' For example, ProGNN [30] treats the adjacency matrix like a learnable parameter, and adds loss terms s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' it remains close to the original adjacency matrix and exhibits properties which are assumed about clean graphs like low-rankness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='2 Improving the training These approaches improve training – without changing the architecture – s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' the learned parameters θ∗ of the GNN exhibit improved robustness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In effect, the new training “nudges” a regular GNN towards being more robust.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We distinguish (1) robust training and (2) further training principles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Robust training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Alternative training schemes and losses which reward the correct classification of synthetic adversarial perturbations of the training data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' With this category, Günnemann [21] targets both straightforward adversarial training and losses stemming from certificates (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=', improving certifiable robustness).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Neither approach is interesting to us: the former is discussed in § C, and the latter targets provable robustness which does not lend itself to empirical evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Further training principles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' This category is distinct from robust training due to the lack of a clear mathematical definition of the training objective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' It mostly captures augmentations [15, 29, 39, 42, 61] or alternative training schemes [5, 11, 55, 64] that encourage robustness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' A simple example for such an approach is to pre-train the GNN weights on perturbed graphs [42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Another recurring theme is to use multiple models during training and then, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=', enforce consistency among them [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='3 Improving the architecture Even though there are some exceptions (see sub-category (2) miscellaneous), the recurring theme in this category is to somehow weight down the influence of some edges adaptively for each layer or message passing aggregation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We refer to this type of improved architecture with (1) adaptively weighting edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We further distinguish between approaches that are (a) rule-based, (b) probabilistic, or use (c) robust aggregation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Rule-based approaches typically use some metric [31, 58], alternative message passing [36, 37], or an auxiliary MLP [57] to filter out alleged adversarial edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Probabilistic approaches either work with distributions in the latent space [63], are built upon probabilistic principles like Bayesian uncertainty quantification [13], or integrate sampling into the architecture and hence apply it also at inference time [8, 24, 25, 38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Robust aggregation defenses replace the message passing aggregation (typically mean) with a more robust equivalent such as a trimmed mean, median, or soft median [7, 17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In relation to the trimmed mean, in this category we include also other related approaches that come with some guarantees based on their aggregation scheme Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 18 C On adversarial training defenses The most basic form of adversarial training for structure perturbations aims to solve: min θ max A′∈Φ(A) ℓ(fθ(A′, X), y) (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='1) Similarly to [44, 1, 4], we exclude defenses that build on adversarial training in our study for three reasons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' First, we observe that adversarial training requires knowing the clean A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' However, for poisoning, we would need to substitute A with an adversarially perturbed adjacency matrix ˜A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In this case, adversarial training aims to enforce adversarial generalization A′ ∈ Φ( ˜A) for the adversarially perturbed adjacency matrix ˜A – potentially even reinforcing the poisoning attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Second, an adaptive poisoning attack on adversarial training is very expensive as we need to unfold many adversarial attacks for a single training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Thus, designing truly adaptive poisoning attacks requires a considerable amount of resources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Scaling these attacks to such complicated training schemes is not the main objective of this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Third, adversarial training for structure perturbations on GNNs seems to be an unsolved question.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' So far, the robustness gains come from additional and orthogonal tricks such as self-training [53].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Hence, adversarial training for structure perturbations requires an entire paper on its own.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' D On defenses against feature perturbations As introduced in § 2, attacks may perturb the adjacency matrix A, the feature matrix X, or both.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' However, during our survey we found that few defenses tackle feature perturbations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Similarly, 6 out of the 7 defenses chosen by us mainly based on general popularity turn out to not consciously defend against feature perturbations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' The only exception is SVD-GCN [12], which also applies its low-rank approximation to the binary feature matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' However, the authors do not report robustness under feature-only attacks;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' instead, they only consider mixed structure and feature attacks found by Nettack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Given the strong bias of Nettack towards structure perturbations, we argue that their experimental results do not confirm feature robustness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Correspondingly, in preliminary experiments we were not able to achieve considerable robustness gains of SVD-GCN compared to an undefended GCN – even with non-adaptive feature perturbations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' If a non-adaptive attack is strong enough, there is not much merit in applying an adaptive attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' To reiterate, due to the apparent scarcity of defenses apt against feature attacks, we decided to focus our efforts on structure attacks and defenses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' However, new defenses considering feature perturbations should study robustness in the face of adaptive attacks – similarly to our work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In the following, we give some important hints for adaptive attacks using feature perturbations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We leave attacks that jointly consider feature and structure perturbations for future work due to the manifold open challenges, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=', balancing structure and feature perturbations in the budget quantity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Baseline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' To gauge the robustness of defenses w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' global attacks, we introduce the RAUC metric, which employs the accuracy of an MLP – which is perfectly robust w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' structure perturbations – to determine the maximally sensible budget to include in the summary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' As MLPs are however vulnerable to feature attacks, a different baseline model is required for this new setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We propose to resolve this issue by using a label propagation approach, which is oblivious to the node features and hence perfectly robust w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' feature perturbations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Perturbations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' The formulation of the set of admissible perturbations depends on what modality the data represents, which may differ between node features and graph edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Convenient choices for continuous features are l-p-norms;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' in other cases, more complicated formulations are more appropriate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Accordingly, one has to choose an appropriate constrained optimization scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 19 E Examined adversarial defenses In this section, we portray each defense and how we adapted the base attacks to each one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We refer to Table H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='1 for the used hyperparameter values for each defense.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We give the used attack parameters for a GCN below and refer to the provided code for the other defenses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' GCN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We employ an undefended GCN [33] as our baseline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' A GCN first adds self loops to the adjacency matrix A and subsequently applies GCN-normalization, thereby obtaining A′ = (D + I)− 1 2 (A + I)(D + I)− 1 2 with the diagonal degree matrix D ∈ Nn×n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Then, in each GCN layer it updates the hidden states H(l) = dropout(σ(A′H(l−1)W(l−1) + b(l−1))) where H(0) = X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We use the non-linear ReLU activation for intermediate layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Dropout is deactivated in the last layer and we refer to the output before softmax activation as logits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We use Adam [32] to learn the model’s parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We do not require special tricks since the GCN is fully differentiable and does not come with defensive measures to consider.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In fact, the off-the-shelf attacks we employ are tailored to a GCN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' For PGD, we use E = 200 iterations, K = 100 samples, and a base learning rate of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' For Meta-PGD, we only lower the base learning rate to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='01 and add gradient clipping to 1 (w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' global L2-norm).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' For Metattack with SGD instead of Adam for training the GCN, we use an SGD learning rate of 1 and restrict the training to Etrain = 100 epochs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='1 Jaccard-GCN Defense.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Additionally to a GCN, Jaccard-GCN [48] preprocesses the adjacency matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' It computes the Jaccard coefficient of the binarized features for the pair of nodes of every edge, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=', Jij = XiXj min{Xi+Xj,1}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Then edges are dropped where Jij ≤ ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Adaptive attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We do not need to adapt gradient-based attacks as the gradient is equal to zero for dropped edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Straightforwardly, we adapt Nettack to only consider non-dropped edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Analogously, we ignore these edges in the Greedy Brute Force attack for increased efficiency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='2 SVD-GCN Defense.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' SVD-GCN [12] preprocesses the adjacency matrix with a low-rank approximation (LRA) for a fixed rank r, utilizing the Singular Value Decomposition (SVD) A = UΣV⊤ ≈ UrΣrV⊤ r = Ar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Note that the LRA is performed on A before adding self-loops and GCN-normalization (see above).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Thereafter, the dense Ar is passed to the GCN as usual.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Since A is symmetric and positive semi- definite, we interchangeably refer to the singular values/vectors also as eigenvalues/eigenvectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Adaptive attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Unfortunately, the process of determining the singular vectors Ur and Vr is highly susceptible to small perturbations, and so is its gradient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Thus, we circumvent the need of differentiating the LRA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We now explain the approach from a geometrical perspective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Each row of A (or interchangeably column as A is symmetric) is interpreted as coordinates of a high-dimensional point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' The r most significant eigenvectors of A span an r-dimensional subspace, onto which the points are projected by the LRA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Adding or removing an adversarial edge (i, j) corresponds to moving the point Ai along dimension j, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=', Ai ± ej (vice-versa for Aj).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' As hinted at in § 4, the r most significant eigenvectors of A turn out to usually have few large components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Thus, the relevant subspace is mostly aligned with only few dimensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Changes along the highest-valued eigenvectors are consequently preserved by LRA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' To quantify how much exactly such a movement along a dimension j, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=', ej, is preserved, we project the movement itself onto the subspace and extract the projected vector’s j-th component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' More formally, we denote the projection matrix onto the subspace as P = �r k=0 vkvT k where vk are the eigenvectors of A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We now score each dimension j with (Pej)j = Pjj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Since the adjacency matrix is symmetric and rows and columns are hence exchangeable, we then symmetrize the scores Wij = (Pii + Pjj)/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Finally, we decompose the perturbed adjacency matrix ˜A = A + δA and, thus, only need gradients for δA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Using the approach sketched above, we now replace LRA(A + δA) ≈ LRA(A) + δA ◦ W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 20 The weights W can also be incorporated into the Greedy Brute Force attack by dropping edges with weight < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='2 and, for efficient early stopping, sort edges to try in order of descending weight.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Similarly, Nettack’s score function sstruct(i, j) – which attains positive and negative values, while W is positive – can be wrapped to s′ struct(i, j) = log(exp(sstruct(i, j)) ◦ W) = sstruct(i, j) + log W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Note that we assume that the direction of the eigenvectors remains roughly equal after perturbing the adjacency matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In practice, we find this assumption to be true.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Intuitively, a change along the dominant eigenvectors should even reinforce their significance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='3 RGCN Defense.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' The implementations of R(obust)GCN provided by the authors5 and in the widespread DeepRobust [35] library6 are both consistent, but diverge slightly from the paper [63].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We use and now present RGCN according to those reference implementations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Principally, RGCN models the hidden states as Gaussian vectors with diagonal variance instead of sharp vectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In addition to GCN’s A′, a second A′′ = (D + I)−1(A + I)(D + I)−1 is prepared to propagate the variances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' The mean and variance of this hidden Gaussian distribution are initialized as M(0) = V(0) = X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Each layer first computes an intermediate distributions given by ˆM(l) = elu(dropout(M(l−1))W(l−1) M ) and ˆV(l) = relu(dropout(V(l−1))W(l−1) V ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Then, attention coefficients α(l) = e−γ ˆV(l) are calculated with the aim to subdue high-variance dimensions (where exponentiation is element-wise and γ is a hyperparameter).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' The final distributions are obtained with M(l) = A′ ˆM′(l) ◦ α(l).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Note the absence of bias terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' After the last layer, point estimates are sampled from the distributions via the reparameterization trick, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=', scalars are sampled from a standard Gaussian and arranged in a matrix R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' These samples are then used to obtain the logits via M(L) + R ◦ (V(L) + ϵ) 1 2 (where the square root applies element-wise and ϵ is a hyperparameter).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Adam is the default optimizer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' The loss is extended with the regularizer β � i KL(N( ˆM(1) i , diag( ˆV(1) i ))∥N(0, I)) (where β is a hyperparameter).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Adaptive attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' A direct gradient attack suffices for a strong adaptive attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Only when unrolling the training procedure for Metattack and Meta-PGD, we increase hyperparameter ϵ from 10−8 to 10−2 to retain numerical stability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='4 ProGNN Defense.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We use and present Pro(perty)GNN [30] exactly following the implementation provided by the authors in their DeepRobust [35] library6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' ProGNN learns an alternative adjacency matrix S that is initialized with A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' A regular GCN – which, as usual, adds self-loops and applies GCN-normalization – is trained using S, which is simultaneously updated in every τ-th epoch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' For that, first a gradient descent step is performed on S with learning rate η and momentum µ towards minimizing the principal training loss alongside two regularizers that measure deviation β1∥S − A∥2 F and feature smoothness β2 2 � i,j Sij∥ Xi √di − Xj √ dj ∥2 (where di = � j Sij + 10−3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Next, the singular value decomposition UΣVT of the updated S is computed, and S is again updated to be U max(0, Σ − ηβ3)VT to promote low-rankness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Thereafter, S is again updated to be sgn(S) ◦ max(0, |S| − ηβ4) to promote sparsity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Finally, the epoch’s resulting S is obtained by clamping its elements between 0 and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Adaptive attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Designing an adaptive attack for ProGNN proved to be a challenging endeavor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We describe the collection of tricks in § 4’s Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='5 GNNGuard Defense.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We closely follow the authors’ implementation7 as it deviates from the formal definitions in the paper [58].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' GNNGuard adopts a regular GCN and, before each layer, it adaptively weights down alleged adversarial edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Thus, each layer has a unique propagation matrix A(l) that is used instead of A′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 5 https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='com/ZW-ZHANG/RobustGCN 6 https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='com/DSE-MSU/DeepRobust 7 https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='com/mims-harvard/GNNGuard 21 GNNGuard’s rule-based edge reweighting can be clustered into four consecutive steps: (1) the edges are reweighted based on the pair-wise cosine similarity C(l) ij = H(l−1) i H(l−1) j ∥H(l−1) i ∥∥H(l−1) j ∥ according to S(l) = A ◦ C(l) ◦ I[C(l) ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='1], where edges with too dissimilar node embeddings are removed (see Iverson bracket I[C(l) ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='1]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Then, (2) the matrix is rescaled Γ(l) ij = S(l) ij /s(l) i with s(l) i = � j S(l) ij For stability, if s(l) i < ϵ, s(l) i is set to 1 (here ϵ is a small constant).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Next, (3) self-loops are added and Γ(l) is non-linarily transformed according to ˆΓ(l) = exp̸=0(Γ(l) +diag 1/1 + d(l)), where exp̸=0 only operates on nonzero elements and d(l) i = ∥Γ(l) i ∥0 is the row-wise number of nonzero entries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Last, (4) the result is smoothed over the layers with Ω(l) = σ(ρ)Ω(l−1) + (1 − σ(ρ))ˆΓ(l) with learnable parameter ρ and sigmoid function σ(·).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' The resulting reweighted adjacency matrix Ω(l) is then GCN-normalized (without adding self-loops) and passed on to a GCN layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Note that steps (1) to (3) are excluded from back-propagation during training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' When comparing with the GNNGuard paper, one notices that among other deviations, we have omitted learnable edge pruning because it is disabled in the reference implementation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Adaptive attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' The hyperparameter ϵ must be increased from 10−6 to 10−2 during the attack to retain numerical stability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In contrast to the reference implementation but as stated above, it is important to place the hard filtering step I[C(l) ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='1] for S(l) s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' the gradient calculation w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' A is not suppressed for these entries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='6 GRAND Defense.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' The Graph Random Neural Network (GRAND) [15] model is the only defense from our selection that is not based on a GCN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' First, A is endowed with self-loops and GCN-normalized to obtain A′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Also, each row of X is l1-normalized, yielding X′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Next, rows from X′ are randomly dropped with probability δ during training to generate a random augmentation, and X′ is scaled by 1 − δ during inference to compensate, thereby obtaining ˆX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Those preprocessed node features are then propagated multiple times along the graph to get X = 1 K+1 �K k=0 A′k ˆX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Finally, dropout is applied once to X, and the result is plugged into a 2-layer MLP with dropout and ReLU activation to obtain class probabilities Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' The authors also propose an alternative architecture using a GCN instead of an MLP, however, we do not explore this option since the MLP version is superior according to their own results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' GRAND is trained with Adam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' The training loss comprises the mean of the cross-entropy losses of S model evaluations, thereby incorporating multiple random augmentations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Additionally, a consistency regularizer is added to enforce similar class probabilities across all evaluations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' More formally, first the probabilities are averaged across all evaluations: Z = 1 S �S s=1 Z(s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Next, each node’s categorical distribution is sharpened according to a temperature hyperparameter T, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=', Z ′ ij = Z 1 T ij /� c Z 1 T ic .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' The final regularizer penalizes the distance between the class probabilities and the sharpened averaged distributions, namely β S �S s=1 ∥Z(s) − Z ′∥2 F .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Adaptive attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' When unrolling the training procedure for Metattack and Meta-PGD, to reduce the memory footprint, we reduce the number of random augmentations per epoch to 1, and we use a manual gradient calculation for the propagation operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We also initialize Meta-PGD with a strong perturbation found by Meta-PGD on ProGNN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Otherwise, the attack has issues finding a perturbation with high loss;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' it presumably stalls in a local optimum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' It is surprising that “only” initializing from GCN instead of ProGNN does not give a satisfyingly strong attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Finally, we use the same random seed for every iteration of Metattack and Meta-PGD, as otherwise the constantly changing random graph augmentations make the optimization very noisy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='7 Soft-Median-GDC Defense.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' The Soft-Median-GDC [17] deviates in two ways from a GCN: (1) it uses Personalized Page Rank (PPR) with restart probability α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='15 to further preprocess the adjacency matrix after adding self-loops and applying GCN-normalization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' The result is then sparsified using a row-wise top-k operation (k = 64).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' (2) the message passing aggregation is replaced with a robust estimator 22 called Soft-Median.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' From the perspective of node i, a GCN uses the message passing aggregation H(l) i = AiH(l−1) which can be interpreted as a weighted mean/sum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In Soft-Median-GDC, the “weights” Ai are replaced with a scaled version of Ai ◦ softmax (−c/T √ d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Here the vector c denotes the distance between hidden embedding of a neighboring node to the neighborhood-specific weighted dimension-wise median: ci = ∥ Median(Ai, H(l−1)) − H(l−1) i ∥.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' To keep the scale, these weights are scaled s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' they sum up to � Ai.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Adaptive attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' During gradient-based attacks, we adjust the c of every node s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' it now captures the distance to all other nodes, not only neighbors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' This of course modifies the values of c, but is necessary to obtain a nonzero gradient w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' to all candidate edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We initialize PGD with a strong perturbation found by a similar attack on GCN, and initialize Meta-PGD with a perturbation from a similar attack on ProGNN (as with GRAND, using an attack against GCN as a base would be insufficient here).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' F Evaluation of adaptive attacks In Table F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='1, we summarize the variants of the datasets we use, both of which we have precisely extracted from Nettack’s code8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='1, we complement Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 2 and compare the (R)AUC of all defenses on Citeseer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' The robustness estimates for the defenses on Citeseer are also much lower as originally reported.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' For completeness, we give absolute envelope curve plots for all settings and datasets as well as for higher budgets in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='2 and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='3 (compare with Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 4 and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Table F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='1: Statistics of the datasets we used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We measure homophily as the fraction of edges which connect nodes of the same class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Dataset Nodes Undirected Edges Features Classes Avg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Degree Homophily Cora ML [2] 2485 5069 1433 7 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='08 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='804 Citeseer [19] 2110 3668 3703 6 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='477 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='736 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='02 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='04 RAUC Soft-Median-GDC GRAND RGCN ProGNN GCN GNNGuard Jaccard-GCN SVD-GCN (a) Global, Poisoning 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='15 RAUC (b) Global, Evasion 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='4 AUC (c) Local, Poisoning 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='6 AUC Adaptive attack Non- adaptive attack (d) Local, Evasion Figure F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='1: Variant of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 2 for Citeseer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 8 https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='com/danielzuegner/nettack 23 MLP GCN Jaccard-GCN SVD-GCN RGCN ProGNN GNNGuard GRAND Soft-Median-GDC 0 2 4 6 8 10 12 14 Relative budget ∆ m (%) 40 50 60 70 80 Accuracy (%) (a) Cora ML,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Poisoning 0 2 4 6 8 10 12 14 Relative budget ∆ m (%) 60 65 70 75 80 85 Accuracy (%) (b) Cora ML,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Evasion 0 2 4 6 8 10 12 14 Relative budget ∆ m (%) 40 50 60 70 Accuracy (%) (c) Citeseer,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Poisoning 0 2 4 6 8 10 12 14 Relative budget ∆ m (%) 55 60 65 70 75 Accuracy (%) (d) Citeseer,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Evasion Figure F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='2: Absolute variant of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 4, showing relative budgets up to 15%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' GCN Jaccard-GCN SVD-GCN RGCN ProGNN GNNGuard GRAND Soft-Median-GDC 0 25 50 75 100 125 150 175 200 Relative budget ∆ degree (%) 0 20 40 60 80 Corr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' pred.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' (%) (a) Cora ML, Poisoning 0 25 50 75 100 125 150 175 200 Relative budget ∆ degree (%) 0 20 40 60 80 Corr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' pred.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' (%) (b) Cora ML, Evasion 0 25 50 75 100 125 150 175 200 Relative budget ∆ degree (%) 0 20 40 60 80 Corr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' pred.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' (%) (c) Citeseer, Poisoning 0 25 50 75 100 125 150 175 200 Relative budget ∆ degree (%) 0 20 40 60 80 Corr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' pred.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' (%) (d) Citeseer, Evasion Figure F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='3: Absolute variant of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 5, showing relative budgets up to 200%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 24 G Ensemble transferability study In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 8, we transfer attacks found on an individual model to other models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' It is natural to also assess the strength of transfer attacks supplied by ensembles of models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='1, we address this question for 2-ensembles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' For poisoning, the combination of RGCN and ProGNN turns out to be (nearly) the strongest in all cases, which is reasonable since both already form strong individual transfer attacks as is evident in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' For evasion, the differences are more subtle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We also investigate 3-ensembles, but omit the plots due to their size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' For poisoning, RGCN and ProGNN now combined with Soft-Median-GDC remain the strongest transfer source, yet the im- provement over the 2-ensemble is marginal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' For evasion, there is still no clear winner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='GCN ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='Jaccard-GCN ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='SVD-GCN ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='RGCN ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='ProGNN ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='GNNGuard ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='GRAND ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='Soft-Median-GDC ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='Transfer to ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='GCN + Jaccard-GCN ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='GCN + SVD-GCN ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='GCN + RGCN ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='GCN + ProGNN ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='GCN + GNNGuard ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='GCN + GRAND ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='GCN + Soft-Median-GDC ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='Jaccard-GCN + SVD-GCN ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='Jaccard-GCN + RGCN ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='Jaccard-GCN + ProGNN ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='Jaccard-GCN + GNNGuard ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='Jaccard-GCN + GRAND ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='Jaccard-GCN + Soft-Median-GDC ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='SVD-GCN + RGCN ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='SVD-GCN + ProGNN ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='SVD-GCN + GNNGuard ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='SVD-GCN + GRAND ' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='ProGNN + GRAND ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='ProGNN + Soft-Median-GDC ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='GNNGuard + GRAND ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='GNNGuard + Soft-Median-GDC ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='GRAND + Soft-Median-GDC ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='Transfer from ' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='32 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='39 (b) Evasion Figure G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='1: Variant of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 8 with ensembles of models as attack transfer sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' The color maps are not matched across (a) and (b) for improved readability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 25 H GCN and defense hyperparameters: original vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' tuned for adaptive attacks To allow for the fairest comparison possible, we tuned the hyperparameters for each model (including GCN) towards maximizing both clean accuracy and adversarial robustness on a single random data split.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In Table H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='1, we list all hyperparameter configurations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' While we cannot run an exhaustive search over all hyperparameter settings, we report substantial gains for most defenses and the GCN in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' The only exceptions are GRAND, Soft-Median-GDC on Cora ML, and GNNGuard.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' For GRAND, we do not report results for the default hyperparameters as they did not yield satisfactory clean accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Moreover, for Soft-Median-GDC on Cora ML and GNNGuard we were not able to substantially improve over the default hyperparameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' For the GCN, tuning is important to ensure that we have a fair and equally-well tuned baseline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' A GCN is the natural baseline since most defense methods propose slight modifications of a GCN or additional steps to improve the robustness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' For the defenses, tuning is vital since they were most originally tuned w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' non-adaptive attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In any case, the tuning should counterbalance slight variations in the setup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' As stated in the introduction, each attack only provides an upper bound for the actual adversarial robustness of a model (with fixed hyperparameters).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' A future attack of increased efficacy might lead to a tighter estimate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Thus, when we empirically compare the defenses to a GCN, we only compare upper bounds of the respective actual robustness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' However, we attack the GCN with state-of-the-art approaches that were developed by multiple researchers specifically for a GCN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Even though we also tune the parameters of the adaptive attacks, we argue that the robustness estimate for a GCN is likely tighter than our robustness estimate for the defenses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In summary, the tuning of hyperparameters is necessary that we can fairly compare the robustness of multiple models, even though, we only compare upper bounds of the true robustness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 26 GCN Jaccard-GCN SVD-GCN RGCN ProGNN GNNGuard GRAND Soft-Median-GDC Poisoning Evasion 78 80 82 84 86 Clean Accuracy (%) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='30 RAUC (a) Global, Cora ML 68 70 72 74 76 Clean Accuracy (%) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='02 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='03 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='04 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='06 (b) Global, Citeseer 78 80 82 84 86 Clean Accuracy (%) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='30 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='35 AUC (c) Local, Cora ML 68 70 72 74 76 Clean Accuracy (%) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='30 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='35 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='40 (d) Local, Citeseer Figure H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='1: Each defense’s clean accuracy vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' (R)AUC values of the strongest attacks, akin to Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Muted (semi-transparent) colors represent untuned defenses (except for Soft-Median-GDC on Cora ML and GNNGuard), solid colors denote tuned defenses, and lines connect the two.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Our tuned defenses are almost always better than untuned variants w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' both clean accuracy and robustness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 27 Table H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='1: GCN and defense hyperparameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' GCN Tuned Hidden Dropout Max epochs Patience LR L2 reg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' × 1 × 16 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='5 3000 50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='0005 ✓ 1 × 64 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='9 3000 50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='001 Jaccard-GCN Tuned Hidden Dropout ϵ Max epochs Patience LR L2 reg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' × 1 × 16 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='0 3000 200 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='0005 ✓ 1 × 64 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='9 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='0 3000 50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='001 SVD-GCN Tuned Hidden Dropout Rank Max epochs Patience LR L2 reg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' × 1 × 16 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='5 50 3000 200 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='0005 ✓ 1 × 64 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='9 50 3000 50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='001 RGCN Tuned Hidden Dropout ϵ γ Max epochs Patience LR L2 reg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' β × 1 × 16 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='6 1e-8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='0 3000 50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='0005 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='0005 ✓ 1 × 32 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='6 1e-8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='0 3000 50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='0005 ProGNN Tuned Hidden Dropout Max epochs Patience LR L2 reg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' τ η µ β1 β2 β3 β4 × Cora ML 1 × 16 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='5 3000 50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='0005 2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='9 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='001 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='0005 Citeseer 1 × 16 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='5 3000 50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='0005 2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='9 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='0001 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='0005 ✓ Cora ML 1 × 16 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='5 3000 50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='0005 2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='9 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='1 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='1 Citeseer 1 × 16 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='5 3000 50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='0005 2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='9 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='2 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='2 GNNGuard Tuned Hidden Dropout Pruning ϵ Max epochs Patience LR L2 reg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' × 1 × 16 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='5 × 1e-6 81 n/a 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='0005 GRAND Tuned Hidden Dropout X dropout δ K Max epochs Patience LR L2 reg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' S β T ✓ Cora ML 1 × 32 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='5 8 3000 50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='0001 4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='5 Citeseer 1 × 32 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='5 2 3000 50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='0005 2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='3 Soft-Median-GDC Tuned Hidden Dropout k α T Max epochs Patience LR L2 reg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' × 1 × 64 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='5 64 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='5 3000 50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='001 ✓ Citeseer 1 × 64 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='5 64 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='5 3000 50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='001 28 I Comparison of success of attack approaches In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='1 we report which of the global attack techniques generate the strongest attacks, and in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='3, we break down every global attack attempt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Analogously, in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='2 and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='4, we report which local attack techniques require the smallest budget to misclassify the target nodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='3, we additionally compare different loss types for global attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In general, we can say that PGD is the dominating attack for global evasion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' For poisoning, Meta-PGD seems to be the strongest – slightly more successful than Metattack, though not in every case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Greedy brute force dominates the local attacks, but for some defenses, PGD and Nettack have an edge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' FGA PGD Metattack w/ Adam Metattack w/ SGD Meta-PGD 0 50 100 Cases supp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' envelope Soft-Median-GDC GRAND GNNGuard ProGNN RGCN SVD-GCN Jaccard-GCN GCN (a) Cora ML, Pois.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 0 50 100 Cases supp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' envelope (b) Citeseer, Pois.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 0 50 100 Cases supp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' envelope (c) Cora ML, Evas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 0 50 100 Cases supp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' envelope (d) Citeseer, Evas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Figure I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='1: Number of global attack attempts which support the envelope curve over all attack attempts, as introduced in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We observe that for evasion, PGD almost always yields the strongest attack, while for poisoning, either Metattack, Meta-PGD, or both dominate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Using Adam instead of SGD to train the defense nearly always worsens Metattack’s performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' FGA PGD Nettack w/ surrogate Nettack w/o surrogate Greedy Brute Force 0 200 400 600 # Nodes misclass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' first Soft-Median-GDC GRAND GNNGuard ProGNN RGCN SVD-GCN Jaccard-GCN GCN (a) Cora ML, Pois.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 0 200 400 600 # Nodes misclass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' first (b) Citeseer, Pois.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 0 200 400 600 # Nodes misclass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' first (c) Cora ML, Evas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 0 200 400 600 # Nodes misclass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' first (d) Citeseer, Evas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Figure I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='2: Number of target nodes for which the respective local attack needs the least budget (among all attacks) to misclassify them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' When multiple attacks achieve the same lowest budget, the target node is counted in parts towards each winning attack and drawn with a muted color.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We observe that greedy brute force is often the strongest attack;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' only sometimes, PGD and Nettack beat it on some defenses, especially for poisoning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Using the defense’s weights instead of a surrogate model for Nettack is rarely an improvement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Still, for the majority of target nodes, multiple attacks are equally strong in terms of achieving the same lowest budget (tie).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We do not run the greedy brute force attack on Soft-Median-GDC due to the costly PPR calculation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 29 FGA PGD Metattack w/ Adam Metattack w/ SGD Meta-PGD TLM loss PM loss MCE loss 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='5 RAUC Soft-Median-GDC GRAND GNNGuard ProGNN RGCN SVD-GCN Jaccard-GCN GCN (a) Cora ML, Poisoning 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='20 RAUC Soft-Median-GDC GRAND GNNGuard ProGNN RGCN SVD-GCN Jaccard-GCN GCN (b) Citeseer, Poisoning 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='6 RAUC Soft-Median-GDC GRAND GNNGuard ProGNN RGCN SVD-GCN Jaccard-GCN GCN (c) Cora ML, Evasion 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='25 RAUC Soft-Median-GDC GRAND GNNGuard ProGNN RGCN SVD-GCN Jaccard-GCN GCN (d) Citeseer, Evasion Figure I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='3: The RAUC of every global attack we have conducted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Attacks are color-coded by principal technique, and markers indicate the attack loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Muted colors represent attacks without edge masking (Jaccard-GCN), our edge weighting trick (SVD-GCN), multiple PGD auxiliary models (ProGNN), Meta-PGD initialization from ProGNN and unlimited unrolled epochs (GRAND), and PGD initialization from GCN (Soft-Median-GDC).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We observe that (1) the TLM and PM losses are superior in almost all cases;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' (2) PGD attacks are best for evasion while Metattack and Meta-PGD are unsuited;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' (3) Metattack with SGD and Meta-PGD are best for poisoning while Metattack w/ Adam even falls behind the surprisingly strong evasion-poisoning transfer;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' (4) FGA is weak for each defense apart from SVD-GCN;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' (5) the cited adaptions are beneficial as attacks with muted colors are worse;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' (6) a strong adaptive attack is necessary to reach a low RAUC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 30 FGA PGD Nettack w/ surrogate Nettack w/o surrogate Greedy Brute Force 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='7 AUC Soft-Median-GDC GRAND GNNGuard ProGNN RGCN SVD-GCN Jaccard-GCN GCN (a) Cora ML, Poisoning 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='7 AUC Soft-Median-GDC GRAND GNNGuard ProGNN RGCN SVD-GCN Jaccard-GCN GCN (b) Citeseer, Poisoning 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='7 AUC Soft-Median-GDC GRAND GNNGuard ProGNN RGCN SVD-GCN Jaccard-GCN GCN (c) Cora ML, Evasion 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='7 AUC Soft-Median-GDC GRAND GNNGuard ProGNN RGCN SVD-GCN Jaccard-GCN GCN (d) Citeseer, Evasion Figure I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='4: The AUC of every local attack we have conducted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Attacks are color-coded by principal technique.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Muted colors have the same signification as in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We observe that (1) greedy brute force is often the best attack, closely followed by PGD, while FGA is not as strong;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' (2) Nettack can rarely be made stronger by utilizing the target model’s weights instead of a surrogate model (red);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' (3) many defenses successfully defend against Nettack;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' (4) against those defenses for which we have adapted Nettack, it becomes much stronger (muted vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' normal green);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' (5) the adaptions are also beneficial for other attacks, as those with muted colors are worse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 31 J Sensitivity to random seed 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='30 RAUC ProGNN Untuned ProGNN GCN Untuned GCN Same seed Different seed w/ mul.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' aux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Different seed Figure J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='1: Lowest RAUC achieved by global evasion-poisoning transfer attacks on Cora ML under the premise that the random seed used by the victim is known respectively un- known to the attacker.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' While not knowing the seed is disadvantageous especially on ProGNN, our attack using multiple auxiliary models successfully compensates this issue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' When transferring perturbations from evasion to poi- soning, a different random seed is used for training the poisoned model than was used for the evasion one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='1, we study using the example of GCN and ProGNN whether poisoning success improves when we instead assume the same seed is used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' This is indeed the case and turns out particularly strong on tuned ProGNN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' However, by using multiple aux- iliary models during evasion as detailed in § 4 under the ProGNN example subheading, we can substan- tially reduce the dependence of the attack upon a particular random seed and thereby improve attack performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' K Robustness over node degree We explore the behavior of nodes under attack de- pending on their degree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='1, we show the probability that a successfully misclassified node falls into a certain degree range, broken down by relativ budget.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We cannot confirm the prevalent conjecture that global attacks tend to target low-degree nodes, as they are easier to break.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Our results show that all degree groups are misclassified uniformly over all budgets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' There is no clear preference for lower-degree nodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' For local attacks, on the other hand, we indeed observe that the success rate of changing the predicted class is independent of the node degree if and only if using a relative budget.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' For example, when allowing a certain relative budget, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=', 100% of the target node’s degree, we manage to misclassify the same fraction of 1-degree target nodes (with absolute budget of 1) as 5-degree ones (with absolute budget of 5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 1 2 3 4 5 6 7 8 9 ≥ 10 1 2 3 5 8-10 15-25 0 5 10 Rel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' budget ∆ m (%) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='0 P(degree | misclass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=') (a) Global, Cora ML 0 5 10 Rel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' budget ∆ m (%) (b) Global, Citeseer 0 100 200 Rel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' budget ∆ degree (%) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='0 P(degree | misclass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=') (c) Local, Cora ML 0 100 200 Rel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' budget ∆ degree (%) (d) Local, Citeseer Figure K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='1: The probability that a misclassified node is in a certain degree range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' More specifically, for global attacks, that is which ratios of test set nodes from subsets with degree 1, 2, 3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' , 9, ≥ 10 are misclassified per budget, normalized s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' the stacked results sum to 1 everywhere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' For local attacks, we show the amount of nodes from each target node set misclassified per budget, again normalized s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' the stack sums to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Results are averaged over all experiments conducted (including evasion and poisoning) on tuned models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' The dotted lines indicate standard deviation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We observe no substantial systematic bias towards the misclassification of low-degree nodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 32 L Attack characteristics Next, we present interesting patterns of the adversarial perturbations for each model/defense.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We show the (1) node degree, (2) closeness centrality, (3) homophily, (4) Jaccard similarity of node attributes, and (5) the ratio of removed edges over the strongest edge perturbations in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' For statistics 1-4, we consider the pairs of nodes that were affected by an adversarial edge flip (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=', insertion or removal).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Here we average over the strongest attack found for each budget (without transferring attacks between defenses).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Thus, the values indicate what characteristics are important for strong, adaptive attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' GCN Jaccard-GCN SVD-GCN RGCN ProGNN GNNGuard GRAND Soft-Median-GDC Global Local 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='98 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='10 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='9 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='87 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='03 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='18 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='03 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='26 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='26 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='33 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='9 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='26 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='19 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='56 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='35 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='78 (a) Node degree Global Local .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='126 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='129 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='142 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='126 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='127 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='134 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='128 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='131 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='131 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='131 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='151 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='132 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='131 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='139 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='133 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='134 (b) Closeness centrality Global Local .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='023 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='024 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='061 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='014 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='043 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='068 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='021 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='121 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='027 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='031 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='041 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='030 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='016 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='142 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='056 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='181 (c) Homophily Global Local .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='028 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='037 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='025 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='026 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='032 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='095 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='022 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='034 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='030 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='038 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='028 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='028 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='026 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='081 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='024 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='045 (d) Jaccard similarity Global Local .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='001 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='001 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='001 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='001 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='006 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='012 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='003 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='016 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='023 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='026 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='020 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='029 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='010 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='139 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='056 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='173 (e) Ratio of removed edges Figure L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='1: Various metrics characterizing the nature of the adversarial edges from our strongest attacks, which are those visible in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='1 and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='2, as well as the nature of the nodes connected respectively disconnected by them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' (1) Node degree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' For global attacks, the de- gree tends to be lower than the average degree of the dataset as given in Table F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' The higher average degree for local attacks might be influ- enced by the node selection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Interestingly, on SVD-GCN attacks connect very high-degree nodes, most likely because high-degree nodes correspond to dimensions represented by the most significant eigenvectors of A (see § 4 Example 1 and § E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' The attacks exploit the sensitivity of SVD-GCN to perturbations of high-degree nodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' This could hint towards how adaptive attacks catastrophically break SVD-GCN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' (2) Closeness centrality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' The closeness cen- trality of a particular node v is one over the sum of distances from v to all other nodes in the graph, multiplied by the total number of nodes in the graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Attacks against SVD-GCN connect very central nodes, which probably correlates with them having high degrees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In- terestingly, also the perturbations for GNN- Guard seem to be of slightly increased central- ity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' (3) Homophily refers here to the fraction of pairs of nodes that share the same class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Suc- cessful adaptive attacks on Jaccard-GCN share the same homophily as those on GCN, in- dicating that the Jaccard coefficient is not suited to filter heterophil edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Attacks on SVD-GCN, GNNGuard, and Soft-Median- GDC have higher homophily than those on GCN, hinting that these defenses successfully filter some heterogeneous edges, forcing some attacks to adapt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' (4) Jaccard similarity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' As expected, attacks on Jaccard-GCN have to compensate its filter by picking edges with nonzero coefficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Attacks against GNNGuard connect nodes with very similar features, presumably to get past its cosine distance-based edge weighting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Curiously, attacks against Soft-Median-GDC behave similarly, yet only in the local setting and less pronounced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' This is probably necessary to avoid that the new edges are weighted down as outliers by the robust aggregation, which becomes less of an issue when perturbing a large amount of edges in the global setting and thereby shifting what it means to be an outlier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Other defenses and especially GRAND admit connecting nodes as or more dissimilar than is the case on GCN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' (5) Ratio of removed edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' It is clear to see that for all models, the adversarial attack mostly adds new edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' This indicates that edge insertion is stronger than edge deletion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Strong adaptive attacks on GNNGuard and Soft-Median-GDC seem to require the most edge deletions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Moreover, deletions are of much greater importance for local attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 33 M Spectral properties of adaptive attacks Previous studies have shown that adversarial attacks tend to focus the high-frequency (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=', less significant) singular values of the adjacency matrix, both in the local [12] and global [30] setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In consequence, defenses that exploit this observation to subdue attacks have been proposed (including SVD-GCN and ProGNN).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' This is a prime example of where (1) defenses were designed to circumvent specific attack characteristics and (2) an intuitive explanation exists of why the defense should improve robustness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' However, our adaptive attacks have shown that neither (1) nor (2) entail actual robustness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In the case of SVD-GCN, it seems like the model becomes even less robust.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' It is only natural to ask whether our attacks exhibit spectral properties different from the high-frequency observation upon which SVD-GCN is built.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='1, we show the spectra of adjacency matrices before and after attacking GCN and SVD-GCN in various settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Indeed, our adaptive attacks on SVD-GCN perturb more of the low frequencies and less of the high frequencies compared to attacks on GCN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Even though such low frequency-heavy perturbations are hypothesized to be “noticeable” [12, 30], it is unclear how this can be exploited in practice without knowing the clean graph or the underlying distribution of the spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In § A, we give additional reasons why we disregard constraints beyond the L0 difference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='1 also shows that, in contrast to previous beliefs, effective attacks on a GCN may lie in the low- frequency spectrum (see subplots a and c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' This questions the strategy of dampening high-frequency singular values to defend against attacks in the first place.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 0 5 10 15 Singular Value Clean GCN SVD-GCN 100 101 102 103 Order 0 1 2 3 4 Singular Value Change (a) Cora ML, FGA/PGD 100 101 102 103 Order (b) Cora ML, Meta 100 101 102 103 Order (c) Citeseer, FGA/PGD 100 101 102 103 Order (d) Citeseer, Meta Figure M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='1: Singular value spectra of the adjacency matrix before and after perturbation via global adaptive attacks with relative budget of 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='5% against GCN and SVD-GCN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Results are split into native evasion attacks (via FGA and PGD) and native poisoning attacks (via Metattack and Meta- PGD), and averaged in each group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' The top row shows the absolute spectrum, and the bottom row the difference to the clean spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' The order is plotted logarithmically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We observe that attacks against SVD-GCN strongly perturb the low-order singular values, and it is evident from the relative plots that high-order singular values are perturbed less compared to attacks against GCN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 34 N On the scalability of adaptive attacks In our main paper, we do not study adversarial robustness on larger graphs as (a) most defenses do not scale well and (b) we do not want to distract from our finding that structure defense evaluations are overly optimistic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Nevertheless, we consider scalability to be an important aspect for robustness as it is relevant for many applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' As mentioned in § 7, Geisler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' [17] already study adaptive attacks scaled to large graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' However, their work is focused on their own defense, and they only consider evasion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' For these reasons, we now briefly discuss adaptive attacks on larger graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='1, we show an adaptive attack against “Cosine-GCN” on arXiv from the Open Graph Benchmark [23] (169k nodes).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Our Cosine-GCN defense is a natural equivalent of Jaccard-GCN [48] for continuous features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Similarly to Jaccard-GCN on the smaller graphs, Cosine-GCN also comes with some robustness w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' a non-adaptive attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' However, once we apply an adaptive attack, it performs actually slightly worse than the GCN baseline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Scaling first order attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' The biggest challenge is certainly that the number of elements in the adjacency matrix scales quadratically with the number of nodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' One way to circumvent this “curse of dimensionality” is to use randomization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' For our adaptive attack, we adopt Projected Randomized Block Coordinate Descent (PRBCD) [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' PRBCD uses the same relaxation as PGD (see § 2 and § A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' In each iteration of the attack, it considers only a random subset of edges for gradient update and subsequent projection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Then, for the next iteration, PRBCD keeps edges of high weight and randomly re-samples the edges of low weight.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' This way, the overhead remains constant in the block size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Since PRBCD is a first-order attack, it is natively adaptive for differentiable models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='5 Relative budget ∆ m (%) 50 55 60 65 70 Accuracy (%) (a) Poisoning 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='5 Relative budget ∆ m (%) MLP GCN Cosine-GCN Adaptive Cosine-GCN Non-Adaptive (b) Evasion Figure N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content='1: Adversarial accuracy on the large arXiv dataset per budget for the scalable PRBCD attack against a regular GCN and our Cosine-GCN (single random seed).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' We use a block size of 1 million edges and run the attack for 200 epochs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Thereafter, we keep the best block for another 50 epochs fixed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Poisoning is conducted by transferring perturbations from evasion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Evasion vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' poisoning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Gradient-based poisoning attacks seem inherently more challenging since we need to unroll the training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Nevertheless, as long as we can run an evasion attack, there is the possibility to transfer the perturbed adjacency matrix to the poisoning setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Here, we chose this approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Still, Zügner & Günnemann [66] show in their appendix that only very few training steps are actually required for Metattack to be effective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' Using a low number of training steps is therefore something to consider to scale direct poisoning attacks on larger graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} +page_content=' 35' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YNFRT4oBgHgl3EQf_jgG/content/2301.13694v1.pdf'} diff --git a/YtE0T4oBgHgl3EQfmwGE/content/tmp_files/2301.02503v1.pdf.txt b/YtE0T4oBgHgl3EQfmwGE/content/tmp_files/2301.02503v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..4e48c211932d5ea438d5faf63052530752d28e1f --- /dev/null +++ b/YtE0T4oBgHgl3EQfmwGE/content/tmp_files/2301.02503v1.pdf.txt @@ -0,0 +1,2651 @@ +DESY-22-211 +Systematic study of one-loop realizations of d = 7 long-range +0νββ decay operators +Ping-Tao Chen1∗, Gui-Jun Ding1†, Chang-Yuan Yao2,3‡ +1Department of Modern Physics, University of Science and Technology of China, +Hefei, Anhui 230026, China +2School of Physics, Nankai University, Tianjin 300071, China +3Deutsches Elektronen-Synchrotron DESY, Notkestr. 85, 22607 Hamburg, Germany +Abstract +We study the systematical one-loop decomposition of the dimension-7 long-range +0νββ decay operators. We find that there are 3 genuine one-loop topologies and 8 +diagrams. The procedure to determine the SM quantum number assignments for both +internal and external fields is presented. The Majorana neutrino mass in long-range +0νββ models is discussed. We also present a one-loop 0νββ decay model which pro- +duces Majorana neutrino mass at three-loop level. The phenomenological predictions +for light neutrino mass and 0νββ decay half-life time including both mass mechanism +and long-range contribution are studied. +∗E-mail: chenpt@mail.ustc.edu.cn +†E-mail: dinggj@ustc.edu.cn +‡E-mail: yaocy@nankai.edu.cn +arXiv:2301.02503v1 [hep-ph] 6 Jan 2023 + +Contents +1 +Introduction +2 +2 +Effective operators for long-range 0νββ decay +4 +3 +Systematical one-loop decomposition +6 +3.1 +One-loop topologies for long-range 0νββ decay operators . . . . . . . . . . . +6 +3.2 +Constructing diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . +7 +3.3 +The approach of generating models . . . . . . . . . . . . . . . . . . . . . . . +11 +3.3.1 +Attaching external fields . . . . . . . . . . . . . . . . . . . . . . . . . +11 +3.3.2 +U(1)Y quantum number assignments . . . . . . . . . . . . . . . . . . +15 +3.3.3 +SU(2)L quantum number assignments +. . . . . . . . . . . . . . . . . +18 +3.3.4 +SU(3)C quantum number assignments +. . . . . . . . . . . . . . . . . +23 +3.3.5 +Constructing long-range 0νββ decay models . . . . . . . . . . . . . . +23 +3.3.6 +Genuine one-loop models . . . . . . . . . . . . . . . . . . . . . . . . . +24 +4 +Neutrino mass in long-range 0νββ decay models +27 +5 +An example model of one-loop 0νββ decay +28 +5.1 +Prediction for neutrino mass +. . . . . . . . . . . . . . . . . . . . . . . . . . +30 +5.2 +Half-life time of 0νββ decay . . . . . . . . . . . . . . . . . . . . . . . . . . . +33 +6 +Summary and conclusions +36 +1 +Introduction +The nature of neutrinos and the origin of neutrino mass are great puzzles in particle physics. +In order to accommodate the tiny neutrino masses, one has to extend the standard model(SM). +Without extending the gauge symmetry of SM and introducing additional global symmetry, +the light neutrinos prefer to be Majorana particles. If neutrinos are Dirac particles, the +corresponding Yukawa couplings would be as small as about 10−12 and certain gauge/global +symmetry such as UB−L(1) is necessary to forbid the Majorana mass terms of right-handed +neutrinos. At present, we still don’t know whether neutrinos are Majorana or Dirac particles. +It is well known that the search for the Standard Model (SM) forbidden neutrinoless double- +beta (0νββ) decay is the most practical way to probe the Majorana nature of neutrinos. +0νββ decay is a transition from a parent nucleus (A, Z) to a daughter nucleus (A, Z + 2) +with two electrons accompanied but no neutrinos emitted. Obviously, the lepton number +is violated by two units in 0νββ decay, hence the searches for 0νββ decay are searches for +lepton-number violation whose observation would demonstrate the breaking of a global con- +servation law of the SM. It is usually assumed that the 0νββ decay is induced by exchange +of light Majorana neutrinos between two charged current vertices, then the decay rate is +proportional to the square of the effective Majorana neutrino mass mββ = �3 +i=1 U 2 +eimi where +Uei denotes the element of the lepton mixing matrix and mi are the light neutrino masses. +2 + +This is the so-called mass mechanism. The current most stringent constraints on the 0νββ +decay half-life in 136Xe is provided by the KamLAND-Zen experiment [1]: +T1/2(136Xe) > 2.3 × 1026yr +(1) +at 90% confidence level. This corresponds to upper limits on the effective Majorana neutrino +mass in the range 36 meV ≤ |mββ| ≤ 156 meV, where the uncertainties mainly arise from the +nuclear matrix elements in different nuclear models. Conversely, if 0νββ decay is observed, +neutrinos must be Majorana particles [2]. However, the 0νββ decay could also be induced +by other new physics effects beyond that of Majorana neutrino masses. +In general, the +possible mechanism of 0νββ decay can be categorized into two classes: the short-range +contributions [3] and the long-range contributions [4]. The short-range part of the 0νββ +decay amplitude is mediated by the exchange of heavy particles with masses larger than 100 +MeV [3], and it is described by a set of dimension-9 operators at leading order [3, 5]. The +ultraviolet completions of the short-range operators of 0νββ decay has been systematically +studied at both tree level [6] and one-loop level [7]. The long-range contributions are induced +by the exchange of a light neutrino between two nucleons. If the interaction vertices of both +nucleons are the SM charged current interactions, it is exactly the mass mechanism. The +long-range contribution to the 0νββ decay can appear in new physics models with lepton +number violation (LNV), such as the R-parity violating supersymmetric models [8–12], the +left-right symmetric models [13–16] and the leptoquark models [17–19]. The 0νββ decay +rate including both short-range and long-range parts has been studied in the framework of +effective field theory [20,21]. +The long-range 0νββ decay can be described by dimension-7 lepton number violating +operators [4,22], the complete tree-level decomposition of these dimension-7 operators which +induce momentum enhanced contributions to long-range 0νββ decay has been discussed in +Ref. [23]. In the present work, we shall give a systematical and complete classification of +all models contributing to the d = 7 operators at one-loop level. The procedures to attach +external fields and determine the SM quantum numbers of internal fields are presented. +Certain quantum number assignments are excluded by the absence of tree-level diagrams +in a genuine one-loop 0νββ decay model. +The long-range 0νββ decay operators violate +lepton number by two units, consequently the mediators of any 0νββ decay model can +generate Majorana neutrino mass. The long-range contribution of one-loop is expected to +be subdominant to the mass mechanism without fine tuning of parameter values if the +neutrino mass is produced at tree or one-loop level. For models with two-loop or higher-loop +level neutrino mass, the long-range contribution can be comparable to or dominant over the +mass mechanism. +The rest of this paper is organized as follows. We present the effective operators for long- +range 0νββ decay below and above the electroweak (EW) scale in section 2. The strategy of +decomposing the long-range 0νββ decay operators at one-loop level is studied in section 3, +and we give the procedures of generating the topologies and diagrams and models for long- +range 0νββ decay. The relation between long-range 0νββ decay model and neutrino mass +is discussed in section 4. Dominance of the one-loop long-range contribution over the mass +mechanism requires that neutrino mass should be generated at two-loop and higher loop +levels. We study one example of a one-loop model in detail in section 5, and we discuss +the constraints imposed by the half-life times of the isotopes 76Ge and 136Xe. Finally, we +3 + +summarize and present our conclusions in section 6. +2 +Effective operators for long-range 0νββ decay +At low energy below the electroweak scale, the most general Lagrangian for the long-range +0νββ decay can be written as [4,22]: +Leff = GF +√ +2 +� +�jµ +V −AJV −A,µ + +� +α,β̸=V −A +ϵβ +αjβJα +� +� , +(2) +where the effective coupling constants ϵβ +α are scaled with respect to the SM charged current +strength GF/ +√ +2. The leptonic (hadronic) currents jβ (Jα) are defined as: +Jµ +V ±A = uγµ(1 ± γ5)d , +jµ +V ±A = eγµ(1 ± γ5)ν , +JS±P = u(1 ± γ5)d , +jS±P = e(1 ± γ5)ν , +Jµν +TR/L = uγµν(1 ± γ5)d , +jµν +TR/L = eγµν(1 ± γ5)ν , +(3) +with γµν = i +2[γµ, γν] and ν ≡ νL + νc +L, where νc +L = CνL +T is the charge conjugation field of +left-handed neutrino and C is the charge conjugation matrix. We can see that all currents +involving operators proportional to (1 + γ5) will pick the component νC +L and consequently +they would violate lepton number by two units. In Eq. (2), one should sum over all possible +contractions of leptonic and hadronic currents allowed by Lorentz-invariance, in other words, +all possible combinations of Lorentz indices α, β should be considered. Notice the identity +jµν +TRJTLµν = jµν +TLJTRµν = 0, consequently there are only ten independent operators in Eq. (3) +for the long-range 0νββ decays. +The long-range part of 0νββ decay is induced by the exchange of a light neutrino between +two point-like vertices. If both interaction vertices are the SM charged current interactions, +it yields the mass mechanism. If both interaction vertices are new physics contributions +parameterized by Eq. (2), the corresponding amplitudes would be quadratic in ϵβ +α and they +are too small to be negligible. In the present work, we shall be concerned with the case that +only one vertex arises from the new physics beyond SM and the other one is the SM charged +current interaction, as shown in figure 1. Then the 0νββ decay amplitude is proportional to +the time-ordered product of the Lagrangian of the two interaction vertices +� +d4x +� +d4y G2 +F +2 ϵβ +α T +� +jβ(x)Jα(x)jµ +V −A(y)JV −A,µ(y) +� +. +(4) +If the non-SM lepton current jβ is left-handed with β = (S − P), TL, lepton number +violation arises from the Majorana mass terms of light neutrinos. Then the light neutrino +mass in the numerator of the neutrino propagator would be picked out by the chiral projection +operator 1 ± γ5, consequently the resulting amplitude would be proportional to ϵβ +α⟨mν⟩ +which is subdominant to the mass mechanism contribution, where ⟨mν⟩ is the effective +Majorana neutrino mass. On the other hand, if the lepton current jβ is right-handed with +β = (S + P), (V + A), TR, the lepton number is violated at the new interaction vertex, +and the term p/ will be projected out from the numerator of the neutrino propagator, where +4 + +GF +GF +e +d +u +⟨H0⟩ +⟨H0⟩ +e +u +d +(a) +ν +ν +GF +e +d +u +⟨H0⟩ +e +u +d +(b) +ν +Figure 1: The mass mechanism (left panel) and long-range contributions (right panel) to +the 0νββ decay rate, where the black dot denotes the SM effective four-fermion interaction, +while the slashed circle stands for the effective vertex of the neutrino masses (left panel) +and the long-range 0νββ operator (right panel) arising from new physics. Here we do not +show the diagram with two new physics vertices, since the corresponding contribution is +suppressed. +the neutrino momentum is of order O(100) MeV. As a result, the long-range amplitude is +proportional to ϵβ +αp and it could be comparable to the standard mass mechanism. In the +following sections, we shall study the ultraviolet completion of the lepton number violating +long-range 0νββ decay operators with right-handed leptonic current: jS+PJS+P, jS+PJS−P, +jµ +V +AJV +A,µ, jµ +V +AJV −A,µ and jµν +TRJTR,µν. +These five operators satisfy the electromagnetic +U(1) gauge symmetry, but they are not invariant under the action of the SM gauge group +SU(3)C × SU(2)L × U(1)Y . They arise from the following dimension-7 SM gauge invariant +operators [5,23,24], +O1 ≡ ϵikϵjl(ℓc +iℓj)(dRQk)Hl , +O2 ≡ ϵikϵjl(ℓc +iγµνℓj)(dRγµνQk)Hl , +O3 ≡ ϵjk(ℓc +iℓj)(Q +iuR)Hk , +O4 ≡ (ℓc +iγµeR)(dRγµuR)ϵijHj , +(5) +where i, j, k, l = 1, 2 are the indices of the SU(2)L gauge group, ℓ = (νeL, eL)T and Q = +(uL, dL)T denote the first generation of lepton and quark doublet respectively, uR, dR and eR +are the first generation of right-handed quark and lepton singlets, H is the SM Higgs doublet. +After the electroweak symmetry breaking by the vacuum expectation value (VEV) of the +Higgs field, the operators O1, O2, O3 and O4 give rise to the low energy long-range 0νββ +decay operators j† +S+PJ† +S+P, jµν† +TR J† +TR,µν, j† +S+PJ† +S−P and jµ† +V +AJ† +V +A,µ respectively. Notice that +the remaining long-range operator jµ +V +AJV −A,µ is generated by the following dimension-9 SM +effective operator [25] +O5 = ϵimϵkn(ℓc +iγµeR)(Q +jγµQk)HmHjHn , +(6) +which leads to 0νββ decay at higher dimension, we will not discuss this scenario in our +current work. Including the lepton flavor indices in Eq. (5), one can obtain all independent +5 + +dimension-7 lepton number violating operators without derivative [23]: +O1(α, β) ≡ ϵikϵjl(ℓc +αiℓβj)(dRQk)Hl , +O2(α, β) ≡ ϵikϵjl(ℓc +αiγµνℓβj)(dRγµνQk)Hl , +O3(α, β) ≡ ϵjk(ℓc +αiℓβj)(Q +iuR)Hk , +O4(α, β) ≡ (ℓc +αiγµeRβ)(dRγµuR)ϵijHj , +(7) +besides ϵikϵjl(ℓc +αiℓβj)HkHl(H†H) which is the famous Weinberg operator with the addition +H†H. Here α and β are lepton flavor indices. In the following we will study the one-loop +decomposition of the 0νββ decay operators in Eq. (5) and the relation with light neutrino +mass. +3 +Systematical one-loop decomposition +In the following, we will use the diagrammatic method [26,27] to find out all possible one- +loop decomposition of the dimension seven long-range 0νββ decay operators in Eq. (5). +This method has been used to decompose the neutrino mass operators for both Majorana +neutrinos [28–30] and Dirac neutrinos [31–34]. Firstly, we identify the one-loop topologies +with five external legs by using only 3-point vertices and 4-point vertices. The topologies +of tadpole and self-energies are eliminated. In the next step, we promote topologies to dia- +grams by specifying the Lorentz nature (spinor or scalar) of each internal and external lines. +Renormalizability and Lorenz invariance require the diagrams contain only the interaction +vertices of the type fermion-fermion-scalar, scalar-scalar-scalar or scalar-scalar-scalar-scalar. +A topology can lead to a few number of Feynman diagrams, because there are usually sev- +eral possible assignments of quark fields, lepton fields and Higgs field to the five external +legs. Furthermore, each interaction vertex should be invariant under the SM gauge group +SU(3)C ×SU(2)L ×U(1)Y such that one can constrain the quantum numbers of the internal +fermion and scalar fields. If the gauge quantum numbers of all internal fields are specified for +a diagram, the corresponding UV completion will be called a model, and the gauge invari- +ant interactions involving the beyond SM fields can be read out straightforwardly. Notice +that the SM gauge quantum numbers of the new fields can be unambiguously fixed in the +tree-level realizations, while there are infinite possible quantum number assignments to the +fields running in the loop. In the following, we will consider the scenarios that new fields +are singlets, doublets or triplets of SU(2)L, and the results for the higher dimensional rep- +resentations can be derived in a similar way. Regarding SU(3)C assignment for the fields, +the low-dimensional representations up to octet are considered for illustration. +3.1 +One-loop topologies for long-range 0νββ decay operators +As shown in Eq. (5), we see the dimension-7 long-range 0νββ decay operators involve two +quark fields, two lepton fields and a Higgs doublet. Using our own codes unpublicized yet, +we plot the connected one-loop topologies with five external legs, and we find there are +37 one-loop topologies. However, most of the topologies are of no interest to us, we can +exclude a lot of them at the topology level. The first step is to exclude all the topologies +6 + +with tadpoles and self-energy, because the models generated from these topologies always +have divergent parts in their loop integrals, and there should be a lower order counter term +required by renormalizability. +Then there are 16 topologies left. +Since we are working on the operators with four +fermions and one scalar, some topologies need non-renormalizable interactions to accommo- +date these external lines. As a consequence, these topologies should be discarded and they +are shown in figure 3 for completeness. At this point we are left with 7 different topologies. +We intend to identify the topologies and diagrams as well as the models for which the lead- +ing order contribution to 0νββ decay arises at one-loop level, and the tree-level contribution +is absent without the need to introduce extra symmetry. These topologies, diagrams and +models will be considered genuine. If a diagram has a sub-diagram with a loop and three +external legs, then the three-point vertex without the loop is also compatible with the sym- +metry. In other words, any internal loop (or loop) with three legs can be compressed into +a three-point vertex. Thus the corresponding one-loop diagram must be accompanied by +the more important tree-level diagram, and consequently it is non-genuine and should be +discarded. The topologies with compressible one-loop sub-diagram are displayed in figure 4 +for completeness, they can be regarded as extensions of the tree-level topology, where one +of the vertices is generated at one-loop. Discarding the compressible topologies in figure 4, +there remain only 3 genuine topologies shown in figure 2. We also display the unique tree- +level topology in figure 2, and the systematic decomposition of tree-level 0νββ decay model +dominated by long-range contribution has been studied in Ref. [23]. In the present work, we +also provide the tree-level decomposition, since these results are necessary when determining +the genuineness of a one-loop model. +3.2 +Constructing diagrams +We proceed to specify the Lorentz nature (fermion or scalar) of both external and internal +lines of each topology. The SM invariant 0νββ decay operators in Eq. (5) involve two quark +fields, two lepton fields and a Higgs field. There are several options for the assignments of +the four fermions and one scalar to the five external legs for each topology. After considering +all possible external leg assignments, we insert the fermion or scalar into internal lines one +by one and Lorentz invariance implies that each vertex must contain an even number of +fermions. The UV completion models are required to be renormalizable so that the dimen- +sion of each interaction vertex should be less than or equal to 4. As a consequence, only +the renormalizable scalar-scalar-scalar, fermion-fermion-scalar and scalar-scalar-scalar-scalar +interactions can be used. As shown in figure 5, we find there are 8 independent one-loop +diagrams arising from the genuine topologies of figure 2. After the electroweak symmetry +breaking, the couplings to external Higgs field lead to chirality flip of fermion field or scalar +mixing. The external Higgs field with vacuum expectation value insertion can be removed. +Hence the 8 diagrams in figure 5 get reduced to only 3 diagrams in mass basis, as shown in +figure 6, these diagrams will be useful when we calculate the 0νββ decay rate. +7 + +NL-0-1 +Tree level +NL-1-1 +One loop +NL-1-2 +NL-1-3 +Figure 2: The tree-level and one-loop topologies that can lead to genuine models of long- +range 0νββ decays. +8 + +Figure 3: The one-loop topologies that always lead to non-renormalizable diagrams. +Figure 4: The one-loop topologies leading to non-genuine finite or divergent diagrams, the +internal loop with three legs can be compressed into a three-point vertex. +9 + +NL-0-1-1 +Tree level +NL-0-1-2 +NL-1-1-1 +One-loop level +NL-1-2-1 +NL-1-2-2 +NL-1-2-3 +NL-1-2-4 +NL-1-2-5 +NL-1-3-1 +NL-1-3-2 +Figure 5: List of genuine diagrams for long-range 0νββ decay up to one-loop level. +10 + +NLM-1 +NLM-2 +NLM-3 +Figure 6: The genuine one-loop diagrams for long-range 0νββ decay in the mass basis. +Notice that the external leg of Higgs is removed after electroweak symmetry breaking. +3.3 +The approach of generating models +The next step is to generate models based on the 8 genuine diagrams listed in figure 5. +We need to specify how each internal line transforms under the SM gauge group SU(3)C × +SU(2)L × U(1)Y . We firstly attach the fields of the effective operators to external lines of +the diagram. Subsequently imposing gauge invariance of the interaction vertices, we can +determine the possible quantum numbers of the messenger fields. In the following, we give +the details of generating models. +3.3.1 +Attaching external fields +The effective operators O1,2,3,4 of long-range 0νββ decay can be classified into three categories +according to the fields involved, as summarized in table 1, where the conjugate operators +are considered to accommodate our convention. We see that O1 and O2 are composed of the +same fields, therefore they share the same routine of UV completion. Generally both of them +are generated in a concrete UV model after integrating out the heavy fields. Each operator +class in table 1 involves different external legs, as a result, the UV completions of these +three classes should be performed separately based on the diagrams given in figure 5. In the +following, we take the diagram NL-1-1-1 with operator O4 as an example to illustrate the +external field assignment. One can decompose the 0νββ decay operators for other diagrams +in the same fashion. The full results are collected in the attached Mathematica file [35]. +Name +0νββ decay operators +External fields +NL1 +O† +1, O† +2 +ℓ, ℓ, Q, dR, H† +NL2 +O† +3 +ℓ, ℓ, Q, ¯uR, H† +NL3 +O† +4 +ℓ, ¯eR, ¯uR, dR, H† +Table 1: The fields involved in the 0νββ decay operators, the hermitian conjugate operators +are used to accommodate our convention. +The operator O† +4 is constituted by the fields ℓ, ¯eR, ¯uR, dR and H†, which can be freely +assigned to the external legs. However, the lepton and quark fields in the SM are chiral fields +11 + +in weak basis, consequently, for certain attachment of external fields, Lorentz invariance +requires vector mediators otherwise the vertex would be vanishing. +As far as we know, +vector bosons should be the gauge bosons of certain gauge symmetry and their masses are +generated through the spontaneous breaking of the extended gauge symmetry. Thus the +new gauge bosons require extending both the SM gauge group and scalar field content. In +the present work, we would like to preserve the SM gauge group SU(3)C × SU(2)L × U(1)Y +that has been tested by lots of experiments from low energy to TeV scale. Hence the cases +of vector mediators will not be considered1. Let us consider the attachment of external legs +at the vertex A of diagram NL-1-1-1, as shown in figure 7. Lorentz invariance implies that +4 out of the 6 possible assignments need new vector mediators, and consequently they are +discarded. Moreover, one can freely attach the fields to all the external lines, and some +attachments are superfluous. In order to identify the redundant ones, we should consider +permutations of vertices and compare the different couplings. If two different attachments +are related with each other through permutation of vertices, they will be essentially the same +one. After attaching all the fields of the operator O† +4 to the external lines of the diagram NL- +1-1-1, we find there are only two possible assignments shown in figure 8. Following the above +procedure, we have found out all the possible independent external fields attachments for the +genuine diagrams in figure 5 , and the same procedure can be applied to all other 0νββ decay +operators. Our results are summarized in table 2, table 3 and table 4. Once the external +lines are specified, the SM quantum numbers of the internal fields can be determined. See +the following sections for details. +E5 +E1 +E2 +E4 +E3 +I1 +I3 +I2 +I4 +Operator Diagram E1 E2 E3 E4 E5 Operator Diagram E1 E2 E3 E4 E5 +NL1 +NL-1-1-1 +ℓ dR ℓ Q H† +NL2 +NL-1-1-1 ¯uR Q ℓ +ℓ H† +Q ℓ +ℓ dR H† +ℓ +ℓ ¯uR Q H† +Q dR ℓ +ℓ H† +NL3 +NL-1-1-1 ¯uR ¯eR ℓ dR H† +ℓ +ℓ Q dR H† +ℓ dR ¯eR ¯uR H† +Table 2: The possible external field attachments for the topology NL-1-1, where the external +and internal fields are labelled as Ei and Ii respectively. +1The scalar mediators can also be the SM gauge bosons if they transforms as (1, 3, 0) or (1, 1, 0) under +the SM gauge group SU(3)C × SU(2)L × U(1)Y and the relevant fermion-fermion-vector interaction is +allowed by the chirality of external fermions. We would like to mention that the results for vectors can be +straightforwardly derived from the corresponding ones for scalars. However, the interaction vertices and the +propagator of a massive vector boson are different from those of a scalar, the vector mediator and scalar +mediator lead to different contributions. +12 + +NL-1-1-1 +A +uR +eL +dR +eL +eL +eR +uR +eR +dR +eR +uR +dR +Figure 7: Attach the fields of the 0νββ decay operator O† +4 to the external lines of the diagram +NL-1-1-1 at the vertex A. On the right side, the dashed lines stand for scalar fields while +the wavy lines denote vector fields. Note that the chirality of the external fermions fixes the +mediator to be either vector or scalar boson. +H +uR +eR +dR +ℓ +NL3-1-1-1-1 +S1 +S2 +F1 +S3 +H +ℓ +dR +uR +eR +NL3-1-1-1-2 +S1 +S2 +F1 +S3 +Figure 8: Attach external fields of NL3 to the diagram NL-1-1-1. After attaching external +fields, we change the notation “NL-” to corresponding operator notation “NL3-”. +13 + +E4 +E5 +E3 +E1 +E2 +I4 +I5 +I2 +I3 +I1 +Operator Diagram E1 E2 E3 E4 E5 Operator Diagram E1 E2 E3 E4 E5 +NL1 +NL-1-2-1 +NL-1-2-5 +ℓ +ℓ Q H† dR +NL2 +NL-1-2-1 +NL-1-2-5 +ℓ +ℓ ¯uR H† Q +ℓ Q ℓ H† dR +Q ¯uR ℓ H† ℓ +dR ℓ Q H† ℓ +NL-1-2-2 +NL-1-2-4 +ℓ +ℓ H† ¯uR Q +dR Q ℓ H† ℓ +ℓ +ℓ H† Q ¯uR +NL-1-2-2 +NL-1-2-4 +Q ℓ H† ℓ dR +Q ¯uR H† ℓ +ℓ +dR ℓ H† ℓ Q +NL3 +NL-1-2-1 +NL-1-2-5 +dR ℓ ¯uR H† ¯eR +ℓ +ℓ H† Q dR +¯eR ¯uR ℓ H† dR +dR ℓ H† Q ℓ +NL-1-2-2 +NL-1-2-4 +dR ℓ H† ¯eR ¯uR +ℓ +ℓ H† dR Q +dR ℓ H† ¯uR ¯eR +ℓ Q H† dR ℓ +¯uR ¯eR H† ℓ dR +dR Q H† ℓ +ℓ +¯eR ¯uR H† dR ℓ +Continued on next page +14 + +Operator Diagram E1 E2 E3 E4 E5 Operator Diagram E1 E2 E3 E4 E5 +NL1 +NL-1-2-3 +H† ℓ Q +ℓ dR +NL3 +NL-1-2-3 +H† ¯eR ¯uR ℓ dR +H† ℓ dR ℓ Q +H† ¯eR dR ℓ ¯uR +H† Q ℓ +ℓ dR +H† ¯uR ¯eR ℓ dR +H† Q dR ℓ +ℓ +H† ¯uR dR ℓ ¯eR +H† dR ℓ +ℓ Q +H† dR ¯eR ℓ ¯uR +H† dR Q +ℓ +ℓ +H† dR ¯uR ℓ ¯eR +H† ℓ +ℓ +Q dR +H† ℓ ¯uR ¯eR dR +H† ℓ dR Q ℓ +H† ℓ dR ¯eR ¯uR +H† dR ℓ +Q ℓ +H† ¯uR ℓ ¯eR dR +H† ℓ +ℓ dR Q +H† ¯uR dR ¯eR ℓ +H† ℓ Q dR ℓ +H† dR ℓ ¯eR ¯uR +H† Q ℓ dR ℓ +H† dR ¯uR ¯eR ℓ +NL2 +NL-1-2-3 +H† ℓ ¯uR ℓ Q +H† ℓ ¯eR ¯uR dR +H† ℓ Q +ℓ ¯uR +H† ℓ dR ¯uR ¯eR +H† ¯uR ℓ +ℓ Q +H† ¯eR ℓ ¯uR dR +H† ¯uR Q +ℓ +ℓ +H† ¯eR dR ¯uR ℓ +H† Q ℓ +ℓ ¯uR +H† dR ℓ ¯uR ¯eR +H† Q ¯uR ℓ +ℓ +H† dR ¯eR ¯uR ℓ +H† ℓ +ℓ ¯uR Q +H† ℓ ¯eR dR ¯uR +H† ℓ Q ¯uR ℓ +H† ℓ ¯uR dR ¯eR +H† Q ℓ ¯uR ℓ +H† ¯eR ℓ dR ¯uR +H† ℓ +ℓ +Q ¯uR +H† ¯eR ¯uR dR ℓ +H† ℓ ¯uR Q ℓ +H† ¯uR ℓ dR ¯eR +H† ¯uR ℓ +Q ℓ +H† ¯uR ¯eR dR ℓ +Table 3: The possible external field attachments for the topology NL-1-2, where the external +and internal fields are labelled as Ei and Ii respectively. +3.3.2 +U(1)Y quantum number assignments +For any given diagram with external field attachments specified, one can straightforwardly +determine the hypercharges of the internal messenger fields from of the U(1)Y invariance +at each vertex. Since a plenty of diagrams are involved, we would like to determine the +U(1)Y quantum numbers at the topology level rather than at the diagram level. Notice that +the hypercharge Y of a field is related to its electric charge Q via the Gell-Mann-Nishijima +formula Q = T3 + Y , where T3 is the third component of the weak isospin. For the topology +15 + +E5 +E1 +E2 +E3 +E4 +I5 +I1 +I2 +I3 +I4 +Operator Diagram E1 E2 E3 E4 E5 Operator Diagram E1 E2 E3 E4 E5 +NL1 +NL-1-3-1 +NL-1-3-2 +H† Q ℓ dR ℓ +NL3 +NL-1-3-1 +NL-1-3-2 +H† ¯uR ¯eR dR ℓ +H† dR ℓ Q ℓ +H† dR ¯eR ¯uR ℓ +H† ℓ Q dR ℓ +H† ¯eR ¯uR dR ℓ +H† dR Q ℓ +ℓ +H† dR ¯uR ¯eR ℓ +H† Q dR ℓ +ℓ +H† ¯eR dR ¯uR ℓ +H† dR ℓ +ℓ Q +H† ¯uR dR ¯eR ℓ +NL2 +NL-1-3-1 +NL-1-3-2 +H† ¯uR ℓ Q ℓ +H† ¯uR ℓ dR ¯eR +H† Q ℓ ¯uR ℓ +H† dR ℓ ¯uR ¯eR +H† ℓ ¯uR Q ℓ +H† dR ¯uR ℓ ¯eR +H† Q ¯uR ℓ +ℓ +H† ¯uR dR ℓ ¯eR +H† ¯uR Q ℓ +ℓ +H† dR ℓ ¯eR ¯uR +H† Q ℓ +ℓ ¯uR +H† dR ¯eR ℓ ¯uR +Table 4: The possible external field attachments for the topology NL-1-3, where the external +and internal fields are labelled as Ei and Ii respectively. +16 + +NL-1-1, the equations of hypercharge conservation are given by +YE1 + YI1 − YI2 = 0, +YE2 + YI2 + YI3 = 0, +YE5 − YI1 − YI3 − YI4 = 0, +YE3 + YE4 + YI4 = 0 , +(8) +where the labels Ei and Ii represent the external and internal fields respectively, the diagram +can be found in table 2. The solution to the above equations leads to the following constraints +on the hypercharge: +YI1 = α, +YI2 = YE1 + α, +YI3 = −YE1 − YE2 − α, +YI4 = −YE3 − YE4 , +(9) +where α is an arbitrary real parameter and it parameterizes the hypercharge flow in the loop. +A definite value of α should be taken in a concrete model. For the second one-loop topology +NL-1-2 as shown in table 3, conservation of hypercharge at each vertex implies +YE1 + YE2 + YI1 = 0, +YI1 + YI2 + YI5 = 0, +YE3 + YI2 + YI3 = 0, +YE4 − YI3 − YI4 = 0, +YE5 + YI4 + YI5 = 0 . +(10) +The solution to the above system of equations leads to the following constraints on hyper- +charge: +YI1 = −YE1 − YE2, +YI2 = α, +YI3 = −YE3 − α, +YI4 = YE3 + YE4 + α, +YI5 = −YE1 − YE2 − α . +(11) +Similar to previous case, the hypercharge is not unambiguously fixed, and the arbitrariness +is encoded in the real free parameter α. For the last topology NL-1-3 with labels defined in +table 4, the gauge invariance under U(1)Y leads to the following constraints +YE1 − YI1 − YI5 = 0, +YE2 + YI1 + YI2 = 0, +YE3 − YI2 + YI3 = 0, +YE4 − YI3 − YI4 = 0, +YE5 + YI4 + YI5 = 0 , +(12) +and the solution is given by +YI1 = α, +YI2 = −YE2 − α, +YI3 = −YE2 − YE3 − α, +YI4 = −YE1 − YE5 + α, +YI5 = YE1 − α , +(13) +We summarize the above results for the hypercharge values of the internal fields in table 5. +Once the assignment of external legs is specified for any given diagram, one can straight- +forwardly extract the hypercharges of the mediators by using the general results collected in +table 5. Taking the diagram NL3-1-1-1-1 as an example, we have the external fields E1 = ¯uR, +E2 = ¯eR, E3 = ℓ, E4 = dR and E5 = H†, thus the hypercharges of messenger fields are fixed +to be +YS1 = α, +YF1 = −2 +3 + α, +YS2 = −1 +3 − α, +YS3 = −1 +6 , +(14) +where YuR = 2 +3, YeR = −1, Yℓ = −1 +2, YdR = −1 +3 and YH = 1 +2 have been used. Similarly, we +have E1 = ℓ, E2 = dR, E3 = ¯eR, E4 = ¯uR and E5 = H† for the diagram NL3-1-1-1-2 and +consequently the hypercharge can be determined as follows, +YS1 = α, +YF1 = 1 +2 + α, +YS2 = −1 +6 − α, +YS3 = −1 +3 . +(15) +17 + +Topology +YI1 +YI2 +YI3 +YI4 +YI5 +NL-1-1 +α +YE1 + α −YE1 − YE2 − α +−YE3 − YE4 +\ +NL-1-2 −YE1 − YE2 +α +−YE3 − α +YE3 + YE4 + α −YE1 − YE2 − α +NL-1-3 +α +−YE2 − α −YE2 − YE3 − α −YE1 − YE5 + α +YE1 − α +Table 5: The hypercharge of each internal line for the three renormalizable topologies of +long-range 0νββ decay, and the conventions for the hypercharge flows are shown in tables 2, +3 and 4. +3.3.3 +SU(2)L quantum number assignments +Once the attachment of external legs to the fields of 0νββ decay operators is finished, as +summarized in table 2, table 3 and table 4, the SU(2)L transformation of the each external +line can be read off directly. We would like to mention that ℓ, Q and H are SU(2)L dou- +blets while eR, uR and dR are SU(2)L singlets, and the complex conjugate of any SU(2)L +irreducible representation is equivalent to itself. If focusing on the SU(2)L transformation of +the external lines and ignoring other properties, from table 2 we can see that there are only +4 different SU(2)L assignments of external legs for the topology NL-1-1. Renormalizability +fixes possible vertices to be only three and four point interactions. The trilinear couplings +can be of the types fermion-fermion-scalar (FFS) or scalar-scalar-scalar (SSS), and the 4- +point vertex can only be the scalar-scalar-scalar-scalar (SSSS) interaction. Accordingly, the +interaction Lagrangian can be written as F 1F2S, S1S2S3 and S1S2S3S4 respectively, the +SU(2)L invariance gives the following constraints: +F 1F2S +: +nF1 ⊗ nF2 ⊗ nS ⊃ 1 , +S1S2S3 +: +nS1 ⊗ nS2 ⊗ nS3 ⊃ 1 , +S1S2S3S4 +: +nS1 ⊗ nS2 ⊗ nS3 ⊗ nS4 ⊃ 1 , +(16) +where nX denotes the SU(2)L representation under which the X field transforms. +The +SU(2)L quantum number assignments for the internal fields can be determined by solving +the constraint of Eq. (16) at each interaction vertex. There are generally an infinite number +of possible SU(2)L quantum numbers assignments to the internal particles except the tree- +level diagrams. In the following, we will only consider singlet, doublet and triplet of SU(2)L +for illustration, and extension to high dimensional representations is straightforward. We +use the Mathematica group package GroupMath [36] to efficiently determine the SU(2)L +assignments. The results of SU(2)L quantum number assignments for the topology NL-1- +1 are listed in table 6. The SU(2)L assignments for the other two topologies NL-1-2 and +NL-1-3 can be determined in a similar way, and the results are listed in table 7 and table 8 +respectively. +18 + +E5 +E1 +E2 +E4 +E3 +I1 +I3 +I2 +I4 +E1 E2 E3 E4 E5 I1 I2 I3 I4 E1 E2 E3 E4 E5 I1 I2 I3 I4 +SU(2)L +2 +1 +2 +2 +2 +2 1 1 1 +2 +2 +2 +1 +2 +2 1 2 2 +2 1 1 3 +2 3 2 2 +1 2 2 1 +3 2 3 2 +1 2 2 3 +1 +1 +2 +1 +2 +1 1 1 2 +3 2 2 1 +2 2 2 2 +3 2 2 3 +3 3 3 2 +2 3 3 1 +2 +1 +1 +1 +2 +2 1 1 1 +2 3 3 3 +1 2 2 1 +2 +2 +2 +1 +2 1 2 1 2 +3 2 2 1 +1 2 3 2 +2 3 3 1 +SU(3)C +1 +3 +1 +¯3 +1 +¯3 ¯3 1 3 +1 +¯3 +1 +3 +1 +3 3 1 ¯3 +3 3 3 3 +1 1 3 ¯3 +¯6 ¯6 3 3 +8 8 3 ¯3 +1 1 ¯3 3 +¯3 ¯3 ¯3 ¯3 +8 8 ¯3 3 +6 6 ¯3 ¯3 +3 3 ¯6 3 +8 8 ¯6 ¯3 +8 8 6 3 +¯3 ¯3 6 ¯3 +¯3 ¯3 8 3 +3 3 8 ¯3 +6 6 8 3 +¯6 ¯6 8 ¯3 +¯3 +3 +1 +1 +1 +1 ¯3 1 1 +1 +1 +¯3 +3 +1 +1 1 1 1 +¯3 3 3 1 +¯3 ¯3 3 1 +¯3 ¯6 3 1 +¯3 ¯3 3 8 +3 1 ¯3 1 +6 6 ¯6 1 +3 8 ¯3 1 +6 6 ¯6 8 +6 3 ¯6 1 +8 8 8 1 +¯6 8 6 1 +8 8 8 8 +8 ¯3 8 1 +8 6 8 1 +Table 6: The independent SU(2)L and SU(3)C quantum number assignments for the topol- +ogy NL-1-1, where Ei and Ii denote the external fields and internal fields respectively. Other +assignments are related to these in the table through permutations of external and internal +lines. +19 + +E4 +E5 +E3 +E1 +E2 +I4 +I5 +I2 +I3 +I1 +E1 E2 E3 E4 E5 I1 I2 I3 I4 I5 E1 E2 E3 E4 E5 I1 I2 I3 I4 I5 +SU(2)L +2 +2 +2 +2 +1 +1 1 2 1 1 +2 +2 +2 +1 +2 +1 2 2 2 1 +3 3 2 1 1 +3 1 2 2 3 +1 2 1 2 2 +1 2 1 1 2 +3 2 1 2 2 +3 2 1 1 2 +1 2 3 2 2 +1 2 3 3 2 +3 2 3 2 2 +3 2 3 3 2 +3 1 2 3 3 +1 3 2 2 3 +1 3 2 3 3 +3 3 2 2 3 +3 3 2 3 3 +1 +1 +2 +2 +1 +1 1 2 1 1 +2 +2 +1 +1 +1 +1 1 1 1 1 +1 2 1 2 2 +1 2 2 2 2 +1 2 3 2 2 +3 2 2 2 2 +1 3 2 3 3 +1 3 3 3 3 +1 +2 +2 +1 +1 +2 1 2 2 2 +3 3 3 3 3 +2 2 1 1 1 +1 +2 +2 +2 +2 +2 1 2 1 2 +2 2 3 3 3 +2 1 2 3 2 +2 3 2 2 2 +2 2 1 2 3 +1 +1 +2 +1 +2 +1 1 2 2 1 +2 2 3 2 3 +1 2 1 1 2 +1 +2 +1 +2 +1 2 1 1 2 2 +1 2 3 3 2 +2 3 3 2 2 +1 3 2 2 3 +Continued on next page +20 + +E1 E2 E3 E4 E5 I1 I2 I3 I4 I5 E1 E2 E3 E4 E5 I1 I2 I3 I4 I5 +SU(3)C +1 +1 +¯3 +1 +3 +1 1 3 ¯3 1 +1 +¯3 +1 +1 +3 +3 ¯3 3 ¯3 1 +1 ¯3 ¯3 3 3 +3 3 ¯3 3 3 +1 ¯3 6 ¯6 3 +3 ¯6 6 ¯6 3 +1 3 1 1 ¯3 +3 1 1 1 ¯3 +1 3 8 8 ¯3 +3 8 8 8 ¯3 +1 6 ¯3 3 ¯6 +3 3 ¯3 3 ¯6 +1 ¯6 8 8 6 +3 8 8 8 6 +1 8 3 ¯3 8 +3 ¯3 3 ¯3 8 +1 8 ¯6 6 8 +3 6 ¯6 6 8 +3 +1 +¯3 +1 +1 +¯3 1 3 ¯3 3 +1 +1 +3 +¯3 +1 +1 1 ¯3 1 1 +¯3 3 1 1 1 +1 ¯3 1 ¯3 3 +¯3 3 8 8 8 +1 ¯3 8 ¯3 3 +¯3 ¯3 ¯3 3 ¯3 +1 3 3 3 ¯3 +¯3 ¯3 6 ¯6 6 +1 3 ¯6 3 ¯3 +¯3 ¯6 8 8 8 +1 6 8 6 ¯6 +¯3 6 ¯3 3 ¯3 +1 ¯6 3 ¯6 6 +¯3 8 3 ¯3 3 +1 8 ¯3 8 8 +¯3 8 ¯6 6 ¯6 +1 8 6 8 8 +3 +1 +1 +¯3 +1 +¯3 1 1 ¯3 3 +1 +¯3 +1 +3 +1 +3 1 1 3 ¯3 +¯3 3 ¯3 8 8 +3 3 ¯3 ¯3 3 +¯3 ¯3 3 3 ¯3 +3 3 ¯3 6 ¯6 +¯3 ¯3 3 ¯6 6 +3 ¯3 3 8 8 +¯3 ¯6 6 8 8 +3 6 ¯6 8 8 +1 +1 +1 +3 +¯3 +1 1 1 3 1 +3 +¯3 +1 +1 +1 +1 1 1 1 1 +1 3 ¯3 ¯3 ¯3 +1 3 ¯3 3 ¯3 +1 3 ¯3 6 ¯3 +8 3 ¯3 3 ¯3 +1 ¯3 3 1 3 +1 ¯6 6 ¯6 6 +1 ¯3 3 8 3 +8 ¯6 6 ¯6 6 +1 ¯6 6 ¯3 6 +1 8 8 8 8 +1 6 ¯6 8 ¯6 +8 8 8 8 8 +1 8 8 3 8 +1 8 8 ¯6 8 +Table 7: The independent SU(2)L and SU(3)C quantum number assignments for the topol- +ogy NL-1-2, where Ei and Ii denote the external fields and internal fields respectively. Other +assignments are related to these in the table through permutations of external and internal +lines. +21 + +E5 +E1 +E2 +E3 +E4 +I5 +I1 +I2 +I3 +I4 +E1 E2 E3 E4 E5 I1 I2 I3 I4 I5 E1 E2 E3 E4 E5 I1 I2 I3 I4 I5 +SU(2)L +2 +2 +2 +2 +1 +2 1 2 1 1 +2 +2 +1 +1 +1 +2 1 1 1 1 +2 1 2 3 3 +1 2 2 2 2 +1 2 1 2 2 +3 2 2 2 2 +3 2 1 2 2 +2 3 3 3 3 +3 2 3 2 2 +1 +2 +1 +2 +1 +2 1 1 2 2 +2 3 2 1 1 +1 2 2 1 1 +2 3 2 3 3 +3 2 2 3 3 +2 3 3 2 2 +SU(3)C 1 +1 +¯3 +1 +3 +1 1 3 ¯3 1 +1 +1 +1 ¯3 +3 +1 1 1 ¯3 1 +¯3 3 ¯3 3 3 +¯3 3 3 3 3 +¯3 3 6 ¯6 3 +¯3 3 3 ¯6 3 +3 ¯3 1 1 ¯3 +3 ¯3 ¯3 1 ¯3 +3 ¯3 8 8 ¯3 +3 ¯3 ¯3 8 ¯3 +6 ¯6 ¯3 3 ¯6 +6 ¯6 ¯6 3 ¯6 +¯6 6 8 8 6 +¯6 6 6 8 6 +8 8 3 ¯3 8 +8 8 8 ¯3 8 +8 8 ¯6 6 8 +8 8 8 6 8 +Table 8: The independent SU(2)L and SU(3)C quantum number assignments for the topol- +ogy NL-1-3, where Ei and Ii denote the external fields and internal fields respectively. Other +assignments are related to these in the table through permutations of external and internal +lines. +22 + +3.3.4 +SU(3)C quantum number assignments +All the long-range 0νββ decay operators involve one quark, one anti-quark, two lepton +fields and one Higgs field. The quark is in the irreducible representations 3, and the anti- +quark is in the conjugate triplet representation ¯3 of SU(3)C while leptons and Higgs are +invariant under the SU(3)C group. Hence two external fields transform as 3 and ¯3 and +the remaining three external fields are trivial singlets of SU(3)C. +It is remarkable that +one can assign SU(3)C quantum numbers of external legs at the topology level without +specifying the field property of each line. +As regard the topology NL-1-1, the external +field E5 is attached to a four-point vertex, consequently it can only be the Higgs scalar +field. We can see there are only four independent SU(3)C assignments to the external legs, +without loss of generality we can choose (E1, E2, E3, E4, E5) ∼ (1, 3, 1, ¯3, 1), (¯3, 3, 1, 1, 1), +(1, ¯3, 1, 3, 1) and (1, 1, ¯3, 3, 1), as shown in table 6. Other assignments are redundant and they +are related to these four representative ones by permutating external fields. For instance, +the assignment (E1, E2, E3, E4, E5) ∼ (1, 3, ¯3, 1, 1) is equivalent to (E1, E2, E3, E4, E5) ∼ +(1, 3, 1, ¯3, 1) since there is a E3, E4 permutation symmetry in the topology. Similarly there +are eight different SU(3)C assignments to the external fields of the topology NL-1-2, as listed +in table 7. Regarding the last topology NL-1-3, the five external lines attach at the vertices of +a pentagon, and the two colored ones can be adjacent or spaced. Consequently it is sufficient +to consider only two kinds of SU(3)C assignments displayed in table 8. Then we proceed +to assign SU(3)C quantum numbers to each internal line. Similar to Eq. (16) for SU(2)L, +one should determine whether SU(3)C invariant contractions can be formed at the vertices +by using the technique of Young diagrams [37], and this task can be made much easier with +the help of the Mathematica package GroupMath [36]. Analogous to the case of SU(2)L and +U(1)Y , there are in principle endless SU(3)C representation assignments consistent with the +SM gauge invariance at one-loop level. We present the SU(3)C quantum numbers of the +internal fields for the three topologies NL-1-1, NL-1-2 and NL-1-3 in table 6, table 7 and +table 8 respectively, where only the lower-dimensional SU(3)C representations 1, 3, ¯3, 6, ¯6 +and 8 are used. +3.3.5 +Constructing long-range 0νββ decay models +Using the results of sections 3.3.2, 3.3.3 and 3.3.4, one can construct explicit UV models +for 0νββ decay by assigning the SM SU(3)C × SU(2)L × U(1)Y quantum numbers to the +internal fields. The first step is to choose a diagram, here we take NL-1-1-1 as an example. +The second step is to attach fields to the external legs, see table 2 for different possibilities. +We choose the first kind of attachment for the operator NL3, and it yields the diagrams +shown in the left panel of figure 8. The third step is to determine the U(1)Y charges of the +messenger fields by using table 5. The U(1)Y charges of external fields read as +YE1 = YuR = −2 +3 , YE2 = YeR = 1 , YE3 = Yℓ = 1 +2 , YE4 = YdR = −1 +3 , YE5 = YH† = −1 +2 . (17) +As a consequence, the U(1)Y charges of the internal fields are determined to be +YI1 = α , +YI2 = −2 +3 + α , +YI3 = −1 +3 − α , +YI4 = 5 +6 . +(18) +23 + +H +uR +eR +dR +ℓ +NL3-1-1-1-1-1 +1 +1 +1 +2 +2 +1 +1 +1 +2 +H +uR +eR +dR +ℓ +NL3-1-1-1-1-2 +2 +2 +2 +2 +2 +1 +1 +1 +2 +H +uR +eR +dR +ℓ +NL3-1-1-1-1-3 +3 +3 +3 +2 +2 +1 +1 +1 +2 +Figure 9: Assignments of the SU(2)L quantum numbers for the diagram NL3-1-1-1-1. +The fourth step is the assignment of the SU(2)L quantum numbers. The external fields +transform as (E1, E2, E3, E4, E5) ∼ (1, 1, 2, 1, 2) under SU(2)L. From table 6 we see that +the SU(2)L transformation of the mediators can be (I1, I2, I3, I4) ∼ (1, 1, 1, 2), (2, 2, 2, 2), +(3, 3, 3, 2), these three SU(2)L assignments are displayed in figure 9. The last step is to +determine the SU(3)C quantum numbers of messenger fields. The SU(3)C transformations +of external legs are (E1, E2, E3, E4, E5) = (¯3, 1, 1, 3, 1). There is no such assignment in table 6 +at first glance. However, one can exchange E1 and E2 as well as I1 and I3 at topology level, +consequently we can consider the assignment (E1, E2, E3, E4, E5) ∼ (1, ¯3, 1, 3, 1) instead. +Then we see from table 6 that the internal fields can transform as (I1, I2, I3, I4) ∼ (1, 3, 3, ¯3), +(3, 1, 1, ¯3), (3, 8, 8, ¯3), (¯3, ¯3, ¯3, ¯3), (¯3, 6, 6, ¯3), (¯6, 8, 8, ¯3), (6, ¯3, ¯3, ¯3), (8, 3, 3, ¯3) and (8, ¯6, ¯6, ¯3) +under SU(3)C, as shown in figure 10. In this way, we can find the possible UV completions +for all the long-range 0νββ decay operators. +3.3.6 +Genuine one-loop models +Numerous one-loop models for long-range 0νββ decays can be generated through a series +of steps described in previous sections, however, some of them are not the leading-order +contribution to the long-range 0νββ decays. A one-loop model is the dominant contribution +if and only if the combination of fields participating in the model can not generate more +important tree-level contributions to 0νββ decay. +Such kind of models would be called +genuine models, for which the tree-level diagrams are automatically absent without the need +of invoking additional symmetries. If the lower order contributions can not be forbidden +without extra symmetry, the model would be non-genuine. We can determine the genuineness +of each model by comparing its field content with that of the tree-level models one by +one. Since the quantum numbers of the mediators of the tree-level 0νββ decay models are +unambiguously fixed, genuineness of a one-loop model generally excludes certain value of the +hypercharge parameter α. +We take the model NL3-1-1-1-2-2-1 for illustration, the Feynman diagram is shown in +figure 11, in which we have introduced the notation CY +L to label the quantum numbers of a +field, where C refers to the SU(3)C representation, L refers to the SU(2)L transformation, +and Y stands for U(1)Y charge. When the hypercharge parameter α = 1 +3, we see that the +mediators S2(S3) and F as well as the associated interactions allow to generate the tree-level +models NL1-0-1-2-2-1-1, NL3-0-1-2-3-1-1 which are the more important ones. +Therefore +the genuineness of the one-loop model NL3-1-1-1-2-2-1 requires α ̸= 1 +3. The condition of +24 + +H +uR +eR +dR +ℓ +NL3-1-1-1-1-X-1 +1 +3 +3 +1 +¯3 +3 +1 +3 +1 +H +uR +eR +dR +ℓ +NL3-1-1-1-1-X-2 +3 +1 +1 +1 +¯3 +3 +1 +3 +1 +H +uR +eR +dR +ℓ +NL3-1-1-1-1-X-3 +3 +8 +8 +1 +¯3 +3 +1 +3 +1 +H +uR +eR +dR +ℓ +NL3-1-1-1-1-X-4 +¯3 +¯3 +¯3 +1 +¯3 +3 +1 +3 +1 +H +uR +eR +dR +ℓ +NL3-1-1-1-1-X-5 +¯3 +6 +6 +1 +¯3 +3 +1 +3 +1 +H +uR +eR +dR +ℓ +NL3-1-1-1-1-X-6 +¯6 +8 +8 +1 +¯3 +3 +1 +3 +1 +H +uR +eR +dR +ℓ +NL3-1-1-1-1-X-7 +6 +¯3 +¯3 +1 +¯3 +3 +1 +3 +1 +H +uR +eR +dR +ℓ +NL3-1-1-1-1-X-8 +8 +3 +3 +1 +¯3 +3 +1 +3 +1 +H +uR +eR +dR +ℓ +NL3-1-1-1-1-X-9 +8 +¯6 +¯6 +1 +¯3 +3 +1 +3 +1 +Figure 10: Assignments of the SU(3)C quantum numbers for the diagram NL3-1-1-1-1-X, +where X=1, 2, 3 stands for the possible SU(2)L quantum number assignments shown in +figure 9. +25 + +H +dR +ℓ +uR +eR +S1 : 1−1/6−α +2 +S2 : ¯3α +1 +NL3-1-1-1-2-2-1 +F : ¯31/2+α +2 +S3 : 3−1/3 +1 +α = 1 +3 +α = 1 +3 +ℓ +uR +eR +dR +H +NL3-0-1-2-3-1-1 +S3 (S∗ +2) +F +ℓ +Q +ℓ +dR +H +NL1-0-1-2-2-1-1 +S3 (S∗ +2) +F +Figure 11: One example of the non-genuine model NL3-1-1-1-2-2-1, and the messenger fields +F, S2 and S3 can lead to the tree-level contributions NL1-0-1-2-2-1-1 and NL3-0-1-2-3-1-1 +in the case of α = +1 +3. +Notice that the mediators F, S2 and S3 will also lead to tree- +level contributions NL1-0-1-2-2-1-1, NL3-0-1-2-3-1-1, NL3-0-1-1-3-1-1 when the hypercharge +parameter α = ±1. The quantum numbers are given in the notation CY +L , where C refers to +the SU(3)C transformation, L refers to the SU(2)L transformation, and Y stands for U(1)Y +charge. +26 + +genuineness has been considered for each possible one-loop decomposition of the 0νββ decay +operators, and the full results are listed in the attachment [35]. +4 +Neutrino mass in long-range 0νββ decay models +u +u +d +d +e +e +W +W +ν +ν +⟨H0⟩ +u +d +e +ν +W +ν +Figure 12: The black box diagrams for neutrino masses from 0νββ decay effective vertices. +The diagram in the left panel can generate Majorana neutrino masses if 0νββ decay is +observed, while the diagram in the right panel can generate Majorana neutrino masses from +the long-range 0νββ decay operator. In the UV decomposition of the current work, the +effective vertex of the long-range 0νββ operator is realized by a one-loop diagram, which +means the neutrino masses are generated at most at three-loop level. +The black box theorem shows that, one can obtain the Majorana neutrino masses by +connecting the quark and charged lepton legs in these 0νββ decay effective operators with +the SM interactions [2], the schematic black box diagram is shown in left panel of figure 12. +Since the long-range 0νββ decay operators violate lepton number by two units, we can +similarly get another black box diagram for Majorana neutrino mass from the long-range +0νββ effective vertex, which is shown in the right panel of figure 12. Consequently, any 0νββ +decay model will always generate a non-zero Majorana neutrino mass. In current work, the +effective 0νββ decay operator in the black box diagram is realized at the one-loop level. +The tree-level contribution is forbidden in order to maintain the genuineness of the one-loop +model, so the black box is realized at most at the three-loop level in our UV models. The +fields introduced in the one-loop 0νββ decay model can also generate neutrino mass. In some +cases, these fields can result in a lower loop-level model for neutrino mass, then the three-loop +diagram in the black box is the higher order contribution. In other words, one can construct +neutrino mass diagrams by using the SM fields and the mediators that appear in one-loop +renormalizable long-range 0νββ decay models at most at three-loop level. Indeed, as shown +below, any decomposition of the long-range 0νββ decay operators contains automatically +the particle content and interactions such that Majorana neutrino masses can be generated. +Given the quantum numbers of mediators and the SM fields, one can use the Mathematica +package Sym2Int [38, 39] to generate all renormalizable interactions consistent with SM +gauge symmetry. Subsequently we import these interactions to the package qgraf [40] to +generate all possible leading-order neutrino mass diagrams. We take the one-loop model +NL2-1-3-1-1-3-1 for example, the leading order contribution to neutrino masses arises at +one-loop and two-loop level for α = −1/2 and α = −2/3 respectively, as shown in figure 13. +Since the black box theorem implies that any contributions to the 0νββ decay always induce +Majorana neutrino masses, thus the contribution of the mass mechanism always exists in any +0νββ model. For models in which neutrino masses are generated at tree or one-loop level, +27 + +one generally expects that the one-loop long-range contribution is subdominant to the mass +mechanism, if the values of the model parameters are not severely fine-tuned. The long-range +contribution and the mass mechanism can be comparable in certain parameter space for the +one-loop 0νββ decay decomposition with two-loop or three-loop neutrino masses. Hence +both tree and one-loop contributions to neutrino mass should be forbidden in a genuine +one-loop model of long-range 0νββ decay, thus certain values of the hypercharge would be +excluded. +uR +H +ℓ +Q +ℓ +NL2-1-3-1-1-3-1 +S1 : 1−α +2 +S2 : 11/2−α +1 +F1 : 1−α +2 +S3 : 31/6+α +1 +F2 : 32/3+α +2 +α = − 3 +2 +α = − 1 +2 +H +ℓ +ℓ +H +eR +ℓ +S2 +S1 +H +ℓ +ℓ +H +uR +S3 +S1 +S2 +F1 +Q +F2 +Figure 13: The neutrino mass generation in the 0νββ decay model NL2-1-3-1-1-3-1. One +sees that the mechanism producing neutrino mass depends on the value of the hypercharge +parameter α. +5 +An example model of one-loop 0νββ decay +In this section, we shall present a one-loop model for long-range 0νββ decay. This model +only contains two new scalar fields S1, S2 and a new vector-like fermion F which transform +28 + +dR +H +ℓ +eR +uR +NL3-1-3-2-7-1-4 +eR : 1−1 +1 +ℓ : 1−1/2 +2 +S1 : 11 +1 +F : 12 +1 +S2 : 3−4/3 +1 +ν +e +d +u +e +S1 +F +S2 +Figure 14: The example model NL3-1-3-2-7-1-4 of one-loop 0νββ decay. After electroweak +symmetry breaking, the corresponding Feynman diagram is shown in the right panel. For +this model, the neutrino mass is generated at three-loop level, as shown in figure 15 and +figure 16. +under the SM gauge group as +S1 ∼ (1, 1, 1) , +S2 ∼ (3, 1, −4/3) , +F ∼ (1, 1, 2) +(19) +in the notation of (SU(3)C, SU(2)L, U(1)Y ). Notice that we assume there is only one gen- +eration of the fermion field F. Then we can read out the following SM gauge invariant +Lagrangian Lint among the SM fields and new fields: +Lint =yIαβℓαiτ 2ℓc +βS∗ +1 + yIIαβec +R,αdR,βS∗ +2 + yIIIαuR,αFS2 + yIV αFec +R,αS1 + h.c. ++ mFFF + +2 +� +i=1 +m2 +SiS† +i Si + +2 +� +i=1 +ξiH†HS† +i Si + +2 +� +i,j=1 +ζijS† +i SiS† +jSj , +(20) +which can generate the one-loop diagram for long-range 0νββ decay shown in figure 14. +We see that the coupling yI is antisymmetric on the flavor indices, i.e., yIαβ = −yIβα. It is +important to note that the lepton fields inside the loop can be second or the third generation, +while the external lepton fields can only be from the first generation. +After electroweak symmetry breaking, the diagram NL3-1-3-2-7-1-4 reduces to the Feyn- +man diagram displayed in the right panel of figure 14. With the interaction Lagrangian +in Eq. (20), we can straightforwardly calculate this Feynman diagram, and find that the +following effective operator is generated +GF +√ +2ϵV +A +V +Ajµ +V +AJµ,V +A , +(21) +29 + +where jµ +V +A and Jµ,V +A are defined in Eq. (2), and the coefficient ϵV +A +V +A is given by +ϵV +A +V +A = +√ +2 yIeτyIIτdyIIIuyIV emτ +64π2GFm3 +F +D +� m2 +τ +m2 +F +, 1, m2 +S1 +m2 +F +, m2 +S2 +m2 +F +� +, +(22) +The function D(x1, x2, x3, x4) is the loop integral and it is given by +D(x1, x2, x3, x4) = 1 +iπ2 +� +d4p +1 +� +p2 − x1 +� � +p2 − x2 +� � +p2 − x3 +� � +p2 − x4 +� += +x1 (1 − ln x1) +(x1 − x2) (x1 − x3) (x1 − x4) + +x2 (1 − ln x2) +(x2 − x1) (x2 − x3) (x2 − x4) ++ +x3 (1 − ln x3) +(x3 − x1) (x3 − x2) (x3 − x4) + +x4 (1 − ln x4) +(x4 − x1) (x4 − x2) (x4 − x3) . +(23) +5.1 +Prediction for neutrino mass +With the three new fields in Eq. (19) and the relevant interactions, we find that the leading +order contributions to the neutrino mass arise at three-loop level, and the corresponding +Feynman diagrams are shown in figure 15 and figure 16. From the diagram of figure 15 +after electroweak symmetry breaking, we see that the neutrino masses are really generated +through the black box diagram shown in the right panel of figure 12. We recall that in +the mass mechanism of 0νββ decay, the decay amplitude is proportional to the effective +Majorana mass mββ with +mββ = +� +i +U 2 +eimi , +(24) +where Uei denote the elements of the neutrino mixing matrix and mi refer to the light +neutrino mass. It is known that the effective neutrino mass mββ is exactly the (ee) entry of +the Majorana neutrino mass matrix in the charged lepton diagonal basis. +It is remarkable that all the diagrams in figure 16 generate neutrino mass matrices with +vanishing diagonal entries, while the diagrams in figure 15 can produce non-zero diagonal +elements of the neutrino mass matrix. As a consequence, the contributions of figure 16 to the +0νββ decay via mass mechanism are negligible, and it is sufficient to focus on the diagrams +in figure 15. After the electroweak symmetry breaking, figure 15 produces neutrino masses +and the dominant contribution arises from the exchange of the heavy top quark, bottom +quark and tau. From the bottom panel of figure 15, one can straightforwardly calculate the +expression of the neutrino mass matrix element as follows +(mν)αβ = +3g2 +(16π2)3Vtb y∗ +IIτby∗ +IIIt +mτmbmtmeβ +m2 +WmF +� +� +�y∗ +Iατy∗ +IV βM +� +� m2 +b +m2 +F +, +m2 +eβ +m2 +F +, m2 +W +m2 +F +, m2 +τ +m2 +F +, m2 +S1 +m2 +F +, m2 +t +m2 +F +, 1, m2 +S2 +m2 +F +� +� + (α ↔ β) +� +� +� , +(25) +where g is the gauge coupling constant of SU(2)L, Vtb is the (33) entry of the Cabibbo- +Kobayashi-Maskawa (CKM) quark mixing matrix, and M denotes a three-loop integral, +M (x1, x2, x3, x4, x5, x6, x7, x8) +30 + +ℓ +H +ℓ +H +ℓ +eR +dR +Q +uR +H +eR +S1 +F +S2 +Above EW scale: +ℓ +H +ℓ +H +ℓ +eR +dR +Q +uR +H +eR +S1 +F +S2 +ναL +νβL +τ +b +t +W +eβ +S1 +F +S2 +Below EW scale: +Figure 15: The diagrams for the neutrino masses in the example model NL3-1-3-2-7-1-4 of +long-range 0νββ decay, which can generate non-zero diagonal entries of the neutrino mass +matrix. +31 + +ℓ +ℓ +H +H +ℓ +W +H +Q +dR +S2 +eR +S1 +F +uR +ℓ +ℓ +H +H +ℓ +W +H +Q +uR +S2 +F +S1 +eR +dR +ℓ +H +ℓ +H +ℓ +eR +H +Q +dR +S2 +eR +S1 +F +uR +ℓ +H +ℓ +H +ℓ +eR +H +Q +uR +S2 +F +S1 +eR +dR +ℓ +ℓ +H +H +ℓ +W +Q +uR +S2 +F +S1 +eR +dR +Q +Figure 16: The diagrams for the neutrino masses in the example model NL3-1-3-2-7-1-4 of +long-range 0νββ decay, for which the diagonal entries of the neutrino mass matrix is vanish- +ing. Notice that the inner loops can not be compressed to tree-level renormalizable vertices +due to the antisymmetric nature of some SU(2)L contractions and the chiral structure of the +SM. +32 + += +� 1 +iπ2 +�3 � +d4k1d4k2d4k3 +� +4x3 − k2 +2 +� +1 +k2 +1 − x1 +1 +k2 +2 − x2 +1 +k2 +2 − x3 +1 +k2 +3 − x4 +1 +k2 +3 − x5 +1 +(k1 − k2)2 − x6 +1 +(k2 − k3)2 − x7 +1 +(k3 − k1)2 − x8 +. +(26) +Once the masses of the new fields are specified, the three-loop integrals M can be computed +numerically [41,42]. +5.2 +Half-life time of 0νββ decay +The neutrinoless double beta decay has been discussed in the framework of effective field +theory [20], and the contribution of lepton number violating operator up to dimension seven +have been studied. The inverse half-life time of the 0νββ decay can be generally expressed +as [20] +T −1 +1/2 = +g4 +A +� +� +�G01|Aν|2 + 4G02|AE|2 + 2G04 +� +|Ame|2 + Re +� +A∗ +meAν +�� ++ G09|AM|2 +−2G03 Re +� +AνA∗ +E + 2AmeA∗ +E +� ++ G06 Re (AνA∗ +M) +� +� +� , +(27) +where Aν, AE, Ame, AM depend on nuclear matrix elements and Wilson coefficients of +the ∆L = 2 operators, and their explicit expressions given in Ref. [20] are a bit lengthy. +Moreover, G0i are phase space factors and gA is the well-known unquenched axial coupling, +we adopt the values of G0i and gA listed in Ref. [20]. +As shown in previous section, the mediators of the long-range 0νββ decay model can +generate non-vanishing light neutrino masses at three-loop level. Therefore both the long- +range mechanism and the mass mechanism contribute to the 0νββ decay, and these two +contributions should be added coherently. The effective Majorana mass mββ in mass mech- +anism leads to non-vanishing Aν, and the Wilson coefficient ϵV +A +V +A in Eq. (21) gives rise to +the parameters AE and Ame, +Aν = mββ +me +V 2 +udMν, +AE = VudϵV +A +V +AME,R, +Ame = VudϵV +A +V +AMme,R , +(28) +where me is the mass of electron, Vud refers to the (11) entry of the CKM matrix, Mν,ME,R +and Mme,R are the nuclear matrix elements and one should reply on certain nuclear models +to calculate their values. Hence the half-life of 0νββ decay in our model can be reduced to +T −1 +1/2 += +g4 +A +� +G01|Aν|2 + 4G02|AE|2 + 2G04|Ame|2 ++2G04|Ame| |Aν| cos φ − 2G03 +� +|Aν||AE| cos φ + 2|Ame| |AE| +� � +, +(29) +where φ denotes the relative phase between mββ and ϵV +A +V +A. We show the constraints of the +current and forthcoming 0νββ decay experiments on the effective Majorana neutrino mass +33 + +|mββ| and the long-range coupling |ϵV +A +V +A| in figure 17, where the values of phase space factor +and nuclear matrix elements are adopted from Refs. [20,43]. +It is known that the neutrino mass is tightly constrained by the Planck measurements +of the cosmic microwave background anisotropies. Assuming the standard minimal ΛCDM +model and combining with baryon acoustic oscillation measurements, the most stringent +bound on neutrino mass is � +i mνi < 0.12 eV at 95% confidence level from the Planck +collaboration [44]. +Considering the values of the neutrino mass squared differences and +mixing angles measured by the neutrino oscillation experiments [45], one can obtain that +the effective Majorana neutrino mass is in the region: |mββ| ≤ 31.12 meV for normal ordering +(NO) neutrino mass spectrum and 18.62 meV ≤ |mββ| ≤ 51.14 meV for inverted ordering +(IO) neutrino mass, which are shown as vertical white bands in figure 17. +The highlighted areas in figure 17 denote the allowed regions by the current limits and +future sensitivities of the 0νββ decay half-life of the isotopes 76Ge and 136Xe, where the +relative phase φ freely varies in the range 0 ≤ φ < 2π. The next generation tonne-scale +experiments of 0νββ decay would greatly increase the sensitivity by approximately two +orders of magnitude, therefore the constraint on the parameter space would be improved +considerably, as can be seen from figure 17. We notice that the constraint imposed by 136Xe +is more stringent than that of 76Ge. It is remarkable that the inverted ordering neutrino +mass could potentially be excluded in the future when the experimental data of neutrino +oscillation and Planck are taken into account. +We proceed to discuss the relative size of the long-range mechanism and mass mechanism +to the decay rate. As an estimation of order of magnitude, we assume that the new fields +have the same mass mS1 = mS2 = mF = M and the new couplings in the Lagrangian of +Eq. (20) have the same size yIαβ = yIIαβ = yIIIα = yIV α ≡ yeff which are taken to be real. +From the expression of the neutrino mass matrix elements given in Eqs. (25), we see that +the effective Majorana mass could scale as +mββ ∼ +6g2 +(16π2)3Vtb y4 +eff +mτmbmtme +m2 +WM +, +(30) +where M is the characteristic mass scale of new particles. Consequently the contribution of +the mass mechanism to the 0νββ decay is proportional to y8 +eff/M 2, i.e., +MC = g4 +AG01|Aν|2 ∼ g4 +AG01 +V 4 +ud|Mν|2 +m2 +e +� +6g2 Vtby4 +eff +(16π2)3 +mτmbmtme +m2 +W M +�2 +∼ 5 × 10−27 yr−1 · y8 +eff +�1GeV +M +�2 +. +(31) +Moreover, the Wilson coefficient ϵV +A +V +A of the long-range operator in Eq. (22) scales as +ϵV +A +V +A ∼ +√ +2 y4 +effmτ +64π2GFM 3 . +(32) +Hence the long-range contribution is proportional to y8 +eff/M 6, +LC = g4 +A +� +4G02|AE|2 + 2G04|Ame|2 − 4G03|Ame| |AE| +� +∼ g4 +A +� +4G02|ME,R|2 + 2G04|Mme,R|2 − 4G03|ME,R| |Mme,R| +� +V 2 +ud +� √ +2y4 +effmτ +64π2GFM 3 +�2 +34 + +0 +20 +40 +60 +80 +100 120 140 +0 +0.5 +1.0 +1.5 +2.0 +2.5 +|mββ|[meV] +|ϵV+A +V+A|[10-7] +IO +0 +20 +40 +60 +80 +100 120 140 +0 +0.5 +1.0 +1.5 +2.0 +2.5 +|mββ|[meV] +|ϵV+A +V+A|[10-7] +NO +T1/2 +Xe≥2.30×1026yr +T1/2 +Xe≥1.35×1028yr +T1/2 +Ge≥1.80×1026yr +T1/2 +Ge≥1.30×1028yr +0 +20 +40 +60 +80 +100 120 140 +0 +0.5 +1.0 +1.5 +2.0 +2.5 +|mββ|[meV] +|ϵV+A +V+A|[10-7] +IO +0 +20 +40 +60 +80 +100 120 140 +0 +0.5 +1.0 +1.5 +2.0 +2.5 +|mββ|[meV] +|ϵV+A +V+A|[10-7] +NO +Figure 17: +Constraints on the effective neutrino mass |mββ| and the long-range coupling +|ϵV +A +V +A|. In the top panels, the highlighted regions represent the parameter space allowed by +the current bounds T1/2(136Xe) > 2.3 × 1026 yr [1] and the future sensitivities T1/2(136Xe) > +1.35 × 1028 yr [46]. Similarly the bottom panels display the parameter space allowed by +the current bounds T1/2(76Ge) > 1.8 × 1026 yr [47] and the future sensitivities T1/2(76Ge) > +1.3×1028 yr [48]. The vertical white bands denote the generally allowed region of mββ for NO +and IO neutrino mass spectrum when the experimental data of both neutrino oscillation [45] +and Planck [44] are considered. +35 + +∼ 10−8 yr−1 · y8 +eff +�1GeV +M +�6 +. +(33) +We see that the long-range contribution is comparable to the mass mechanism (i.e., LC/MC∼ +1) for the new particle mass M ∼ O(20) TeV. The long-range contribution dominates over +the mass mechanism with LC/MC≫ 1 for M < 20 TeV, while the mass mechanism is +dominant in the mass range M > 20 TeV. We plot the ratio of long-range contribution to +mass mechanism with respect to the mass M in figure 18. We see the ratio LC/MC decreases +with the new physics mass scale M. +76Ge +136Xe +1 +101 +102 +103 +10-6 +10-4 +10-2 +1 +102 +104 +106 +M[TeV] +LC/MC +Figure 18: The ratio of the long-range mechanism to the mass mechanism. In the figure, +LC= g4 +A +� +4G02|AE|2 + 2G04|Ame|2 − 4G03|Ame| |AE| +� +denotes the long-range contribution to +0νββ decay, and MC=g4 +AG01|Aν|2 is the mass mechanism contribution to 0νββ decay. The +horizontal dash line, representing LC/MC = 1, indicates that the long-range contribution is +equal to that of the mass mechanism. The values of phase space factors and nuclear matrix +elements used in this figure are taken from [20,43]. +In figure 19, we plot the regions of the parameters yeff and M compatible with the +current bounds and future sensitivities of 0νββ decay search in the isotopes 136Xe and 76Ge. +We see that there are still sizable parameter space in which the long-range contribution is +dominant. +6 +Summary and conclusions +A lot of neutrino oscillation experiments have established that neutrinos have tiny masses, +but the nature of neutrinos is still unknown. If neutrinos are Majorana particles, the light +36 + +2 +4 +6 +8 +10 +0 +1 +2 +3 +4 +5 +M[TeV] +yeff +2 +4 +6 +8 +10 +0 +1 +2 +3 +4 +5 +M[TeV] +yeff +T1/2 +Xe≥2.30×1026yr +T1/2 +Ge≥1.80×1026yr +T1/2 +Xe≥1.35×1028yr +T1/2 +Ge≥1.30×1028yr +Figure 19: The constraint on the effective coupling yeff and new particle mass M by the +0νββ decay of 136Xe and 76Ge, where the highlighted regions are allowed by the 0νββ decay +search. The horizontal grey band is excluded by the perturbative constraint yeff ≤ +√ +4π. +neutrino exchange between two charged current interaction vertices can leads to 0νββ decay. +This is the so-called mass mechanism, it is not a priori guaranteed to be the dominant +contribution in all models. The different possibilities mediating 0νββ decay can be generally +classified as short-range mechanism, long-rang mechanism and mass mechanism. +In the +present work, we have performed a systematical decomposition of the dimension-7 long- +range 0νββ decay operators at one-loop level. +After removing the non-renormalizable topologies and the non-genuine topologies which +are one-loop corrections to the tree-level UV completions, we find that there are only 3 +genuine one-loop topologies shown in figure 2. Subsequently we specify the Lorentz nature of +both internal and external fields, these 3 topologies give rise to 8 diagrams in the electroweak +basis, as displayed in figure 5. +In combination with the possible SM quantum number +assignments listed in tables 5, 6, 7, 8 for the each line, one can construct novel one-loop +0νββ decay models. Our results can serve as a guide for the construction of one-loop 0νββ +decay models and for the study of the phenomenology of these models at colliders or high +luminosity facilities. +The long-range 0νββ decay operators violate lepton number by two unit, consequently +the mediators of 0νββ decay models generally generate Majorana neutrino masses, as shown +in the black box diagram in the right panel of figure 12. One expects that the long-range +0νββ decay models of one-loop can give the dominant contribution to the decay ampli- +tude in certain parameter space if the neutrino mass is generated at two-loop and higher +levels, otherwise the long-range contribution should be subdominant to the mass mecha- +nism. Therefore both tree-level and one-loop level contributions to neutrino mass should be +forbidden in a genuine one-loop model of long-range 0νββ decay, consequently certain SM +37 + +quantum number assignments for the internal fields are excluded. +Furthermore, we present an example of one-loop 0νββ decay model with three-loop neu- +trino masses. This example requires two new scalar fields and a color singlet vector-like +fermion. +The predictions for the neutrino mass and 0νββ decay are studied. +The con- +straints on the couplings and new physics scale from the 0νββ decay search in the isotopes +76Ge and 136Xe are discussed. In this model, the long-range contribution is dominant over +the mass mechanism for the new particle mass M < 20 TeV, while the mass mechanism is +dominant in the mass range M > 20 TeV. Thus we expect this model could be tested at the +LHC, or at least LHC can constrain the new messenger fields. +Acknowledgements +PTC and GJD are supported by the National Natural Science Foundation of China un- +der Grant Nos. 11975224, 11835013. CYY is supported in part by the Grants No. NSFC- +11975130, No. NSFC-12035008, No. NSFC-12047533, the Helmholtz-OCPC International +Postdoctoral Exchange Fellowship Program, the National Key Research and Development +Program of China under Grant No. 2017YFA0402200, the China Postdoctoral Science Foun- +dation under Grant No. 2018M641621, and the Deutsche Forschungsgemeinschaft (DFG, +German Research Foundation) under Germany’s Excellence Strategy — EXC 2121 “Quan- +tum Universe” —390833306. +References +[1] KamLAND-Zen Collaboration, S. Abe et al., “First Search for the Majorana Nature +of Neutrinos in the Inverted Mass Ordering Region with KamLAND-Zen,” +arXiv:2203.02139 [hep-ex]. +[2] J. Schechter and J. W. F. Valle, “Neutrinoless Double beta Decay in SU(2) x U(1) +Theories,” Phys. Rev. D 25 (1982) 2951. +[3] H. Päs, M. Hirsch, H. V. Klapdor-Kleingrothaus, and S. G. Kovalenko, “A +superformula for neutrinoless double beta decay II: The short range part,” Physics +Letters B 498 no. 1-2, (Jan., 2001) 35–39, arXiv:hep-ph/0008182. +[4] H. Päs, M. Hirsch, H. V. Klapdor-Kleingrothaus, and S. G. Kovalenko, “Towards a +superformula for neutrinoless double beta decay,” Physics Letters B 453 no. 3-4, +(May, 1999) 194–198, arXiv:hep-ph/9804374. +[5] K. S. Babu and C. N. Leung, “Classification of effective neutrino mass operators,” +Nuclear Physics B 619 no. OSU-HEP-01-02, UDHEP-02-01, (2001) 667–689, +arXiv:hep-ph/0106054. +[6] F. Bonnet, M. Hirsch, T. Ota, and W. Winter, “Systematic decomposition of the +neutrinoless double beta decay operator,” Journal of High Energy Physics 2013 no. 3, +(Mar., 2013) 55, arXiv:1212.3045. +38 + +[7] P.-T. Chen, G.-J. Ding, and C.-Y. Yao, “Decomposition of d = 9 short-range 0νββ +decay operators at one-loop level,” JHEP 12 (2021) 169, arXiv:2110.15347 +[hep-ph]. +[8] R. N. Mohapatra, “New Contributions to Neutrinoless Double beta Decay in +Supersymmetric Theories,” Phys. Rev. D 34 (1986) 3457–3461. +[9] M. Hirsch, H. V. Klapdor-Kleingrothaus, and S. G. Kovalenko, “New constraints on +R-parity broken supersymmetry from neutrinoless double beta decay,” Phys. Rev. +Lett. 75 (1995) 17–20. +[10] M. Hirsch, H. V. Klapdor-Kleingrothaus, and S. G. Kovalenko, “Supersymmetry and +neutrinoless double beta decay,” Phys. Rev. D 53 (1996) 1329–1348, +arXiv:hep-ph/9502385. +[11] K. S. Babu and R. N. Mohapatra, “New vector - scalar contributions to neutrinoless +double beta decay and constraints on R-parity violation,” Phys. Rev. Lett. 75 (1995) +2276–2279, arXiv:hep-ph/9506354. +[12] H. Pas, M. Hirsch, and H. V. Klapdor-Kleingrothaus, “Improved bounds on SUSY +accompanied neutrinoless double beta decay,” Phys. Lett. B 459 (1999) 450–454, +arXiv:hep-ph/9810382. +[13] R. N. Mohapatra and G. Senjanovic, “Neutrino Masses and Mixings in Gauge Models +with Spontaneous Parity Violation,” Phys. Rev. D 23 (1981) 165. +[14] F. F. Deppisch, T. E. Gonzalo, S. Patra, N. Sahu, and U. Sarkar, “Double beta decay, +lepton flavor violation, and collider signatures of left-right symmetric models with +spontaneous D-parity breaking,” Phys. Rev. D 91 no. 1, (2015) 015018, +arXiv:1410.6427 [hep-ph]. +[15] D. Borah, A. Dasgupta, and S. Patra, “Neutrinoless double beta decay in minimal +left–right symmetric model with universal seesaw,” Int. J. Mod. Phys. A 33 no. 35, +(2018) 1850198, arXiv:1706.02456 [hep-ph]. +[16] G. Li, M. Ramsey-Musolf, and J. C. Vasquez, “Left-Right Symmetry and Leading +Contributions to Neutrinoless Double Beta Decay,” Phys. Rev. Lett. 126 no. 15, +(2021) 151801, arXiv:2009.01257 [hep-ph]. +[17] M. Hirsch, H. V. Klapdor-Kleingrothaus, and S. G. Kovalenko, “New leptoquark +mechanism of neutrinoless double beta decay,” Phys. Rev. D 54 (1996) R4207–R4210, +arXiv:hep-ph/9603213. +[18] S. Choubey, M. Duerr, M. Mitra, and W. Rodejohann, “Lepton Number and Lepton +Flavor Violation through Color Octet States,” JHEP 05 (2012) 017, arXiv:1201.3031 +[hep-ph]. +[19] B. Brahmachari and E. Ma, “Neutrinoless double beta decay with negligible neutrino +mass,” Phys. Lett. B 536 (2002) 259–262, arXiv:hep-ph/0202262. +39 + +[20] V. Cirigliano, W. Dekens, J. de Vries, M. L. Graesser, and E. Mereghetti, +“Neutrinoless double beta decay in chiral effective field theory: Lepton number +violation at dimension seven,” JHEP 12 no. LA-UR-17-27799, NIKHEF-2017-039, +(2017) 082, arXiv:1708.09390 [hep-ph]. +[21] V. Cirigliano, W. Dekens, J. de Vries, M. L. Graesser, and E. Mereghetti, “A +neutrinoless double beta decay master formula from effective field theory,” JHEP 12 +(2018) 097, arXiv:1806.02780 [hep-ph]. +[22] F. F. Deppisch, M. Hirsch, and H. Päs, “Neutrinoless Double Beta Decay and Physics +Beyond the Standard Model,” Journal of Physics G: Nuclear and Particle Physics 39 +no. 12, (Dec., 2012) 124007, arXiv:1208.0727. +[23] J. Helo, M. Hirsch, and T. Ota, “Long-range contributions to double beta decay +revisited,” JHEP 06 (2016) 006, arXiv:1602.03362 [hep-ph]. +[24] L. Lehman, “Extending the Standard Model Effective Field Theory with the Complete +Set of Dimension-7 Operators,” Physical Review D 90 no. 12, (Dec., 2014) 125023, +arXiv:1410.4193. +[25] Y. Liao and X.-D. Ma, “An explicit construction of the dimension-9 operator basis in +the standard model effective field theory,” JHEP 11 (2020) 152, arXiv:2007.08125 +[hep-ph]. +[26] S. Antusch, J. P. Baumann, and E. Fernandez-Martinez, “Non-Standard Neutrino +Interactions with Matter from Physics Beyond the Standard Model,” Nucl. Phys. B +810 (2009) 369–388, arXiv:0807.1003 [hep-ph]. +[27] M. B. Gavela, D. Hernandez, T. Ota, and W. Winter, “Large gauge invariant +non-standard neutrino interactions,” Phys. Rev. D 79 (2009) 013007, +arXiv:0809.3451 [hep-ph]. +[28] F. Bonnet, M. Hirsch, T. Ota, and W. Winter, “Systematic study of the d=5 Weinberg +operator at one-loop order,” JHEP 07 (2012) 153, arXiv:1204.5862 [hep-ph]. +[29] D. Aristizabal Sierra, A. Degee, L. Dorame, and M. Hirsch, “Systematic classification +of two-loop realizations of the Weinberg operator,” JHEP 03 (2015) 040, +arXiv:1411.7038 [hep-ph]. +[30] R. Cepedello, R. M. Fonseca, and M. Hirsch, “Systematic classification of three-loop +realizations of the Weinberg operator,” JHEP 10 (2018) 197, arXiv:1807.00629 +[hep-ph]. [Erratum: JHEP 06, 034 (2019)]. +[31] C.-Y. Yao and G.-J. Ding, “Systematic Study of One-Loop Dirac Neutrino Masses and +Viable Dark Matter Candidates,” Phys. Rev. D 96 no. 9, (2017) 095004, +arXiv:1707.09786 [hep-ph]. [Erratum: Phys.Rev.D 98, 039901 (2018)]. +[32] C.-Y. Yao and G.-J. Ding, “Systematic analysis of Dirac neutrino masses from a +dimension five operator,” Phys. Rev. D 97 no. 9, (2018) 095042, arXiv:1802.05231 +[hep-ph]. +40 + +[33] S. Centelles Chuliá, R. Cepedello, E. Peinado, and R. Srivastava, “Systematic +classification of two loop d = 4 Dirac neutrino mass models and the Diracness-dark +matter stability connection,” JHEP 10 (2019) 093, arXiv:1907.08630 [hep-ph]. +[34] S. Jana, P. Vishnu, and S. Saad, “Minimal realizations of Dirac neutrino mass from +generic one-loop and two-loop topologies at d = 5,” JCAP 04 (2020) 018, +arXiv:1910.09537 [hep-ph]. +[35] P.-T. Chen, G.-J. Ding, and C.-Y. Yao, Supplementary material: Decomposition of +d = 7 long-range 0νββ decay operators at one-loop level, 2023 (accessed January 9, +2023). http: +//staff.ustc.edu.cn/~dinggj/supplementary_materials/Long_range_0nbb.zip. +[36] R. M. Fonseca, “GroupMath: A Mathematica package for group theory calculations,” +Computer Physics Communications 267 (Oct., 2021) 108085, arXiv:2011.01764 +[hep-ph, physics:hep-th]. +[37] Particle Data Group Collaboration, R. L. Workman, “Review of Particle Physics,” +PTEP 2022 (2022) 083C01. +[38] R. M. Fonseca, “The Sym2Int program: Going from symmetries to interactions,” +Journal of Physics: Conference Series 873 (July, 2017) 012045, arXiv:1703.05221. +[39] R. M. Fonseca, “Enumerating the operators of an effective field theory,” Physical +Review D 101 no. 3, (Feb., 2020) 035040, arXiv:1907.12584 [hep-ph, +physics:hep-th]. +[40] P. Nogueira, “Automatic feynman graph generation,” Journal of Computational +Physics 105 no. IFM-7-91, (1993) 279–289. +[41] S. P. Martin and D. G. Robertson, “Evaluation of the general 3-loop vacuum Feynman +integral,” Phys. Rev. D 95 no. 1, (2017) 16008, arXiv:1610.07720 [hep-ph]. +[42] A. Freitas, “Three-loop vacuum integrals with arbitrary masses,” J. High Energy +Phys. 2016 no. 11, (Nov., 2016) 145, arXiv:1609.09159. +[43] J. Hyvärinen and J. Suhonen, “Nuclear matrix elements for 0νββ decays with light or +heavy Majorana-neutrino exchange,” Phys. Rev. C 91 no. 2, (2015) 024613. +[44] Planck Collaboration, N. Aghanim et al., “Planck 2018 results. VI. Cosmological +parameters,” Astron. Astrophys. 641 (2020) A6, arXiv:1807.06209 [astro-ph.CO]. +[Erratum: Astron.Astrophys. 652, C4 (2021)]. +[45] I. Esteban, M. C. Gonzalez-Garcia, M. Maltoni, T. Schwetz, and A. Zhou, “The fate +of hints: updated global analysis of three-flavor neutrino oscillations,” JHEP 09 +(2020) 178, arXiv:2007.14792 [hep-ph]. +[46] nEXO Collaboration, G. Adhikari et al., “nEXO: neutrinoless double beta decay +search beyond 1028 year half-life sensitivity,” J. Phys. G 49 no. 1, (2022) 015104, +arXiv:2106.16243 [nucl-ex]. +41 + +[47] GERDA Collaboration, M. Agostini et al., “Final Results of GERDA on the Search +for Neutrinoless Double-β Decay,” Phys. Rev. Lett. 125 no. 25, (2020) 252502, +arXiv:2009.06079 [nucl-ex]. +[48] LEGEND Collaboration, N. Abgrall et al., “The Large Enriched Germanium +Experiment for Neutrinoless ββ Decay: LEGEND-1000 Preconceptual Design +Report,” arXiv:2107.11462 [physics.ins-det]. +42 + diff --git a/YtE0T4oBgHgl3EQfmwGE/content/tmp_files/load_file.txt b/YtE0T4oBgHgl3EQfmwGE/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..bdbca4e0550bfd5bc8a9c7067c9df267ba67d60a --- /dev/null +++ b/YtE0T4oBgHgl3EQfmwGE/content/tmp_files/load_file.txt @@ -0,0 +1,1806 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf,len=1805 +page_content='DESY-22-211 Systematic study of one-loop realizations of d = 7 long-range 0νββ decay operators Ping-Tao Chen1∗, Gui-Jun Ding1†, Chang-Yuan Yao2,3‡ 1Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China 2School of Physics, Nankai University, Tianjin 300071, China 3Deutsches Elektronen-Synchrotron DESY, Notkestr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 85, 22607 Hamburg, Germany Abstract We study the systematical one-loop decomposition of the dimension-7 long-range 0νββ decay operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' We find that there are 3 genuine one-loop topologies and 8 diagrams.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' The procedure to determine the SM quantum number assignments for both internal and external fields is presented.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' The Majorana neutrino mass in long-range 0νββ models is discussed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' We also present a one-loop 0νββ decay model which pro- duces Majorana neutrino mass at three-loop level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' The phenomenological predictions for light neutrino mass and 0νββ decay half-life time including both mass mechanism and long-range contribution are studied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' ∗E-mail: chenpt@mail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='ustc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='cn †E-mail: dinggj@ustc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='cn ‡E-mail: yaocy@nankai.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='cn arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='02503v1 [hep-ph] 6 Jan 2023 Contents 1 Introduction 2 2 Effective operators for long-range 0νββ decay 4 3 Systematical one-loop decomposition 6 3.' 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+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 6 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='2 Constructing diagrams .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='6 Genuine one-loop models .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 24 4 Neutrino mass in long-range 0νββ decay models 27 5 An example model of one-loop 0νββ decay 28 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='1 Prediction for neutrino mass .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 30 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='2 Half-life time of 0νββ decay .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 33 6 Summary and conclusions 36 1 Introduction The nature of neutrinos and the origin of neutrino mass are great puzzles in particle physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' In order to accommodate the tiny neutrino masses, one has to extend the standard model(SM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Without extending the gauge symmetry of SM and introducing additional global symmetry, the light neutrinos prefer to be Majorana particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' If neutrinos are Dirac particles, the corresponding Yukawa couplings would be as small as about 10−12 and certain gauge/global symmetry such as UB−L(1) is necessary to forbid the Majorana mass terms of right-handed neutrinos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' At present, we still don’t know whether neutrinos are Majorana or Dirac particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' It is well known that the search for the Standard Model (SM) forbidden neutrinoless double- beta (0νββ) decay is the most practical way to probe the Majorana nature of neutrinos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 0νββ decay is a transition from a parent nucleus (A, Z) to a daughter nucleus (A, Z + 2) with two electrons accompanied but no neutrinos emitted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Obviously, the lepton number is violated by two units in 0νββ decay, hence the searches for 0νββ decay are searches for lepton-number violation whose observation would demonstrate the breaking of a global con- servation law of the SM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' It is usually assumed that the 0νββ decay is induced by exchange of light Majorana neutrinos between two charged current vertices, then the decay rate is proportional to the square of the effective Majorana neutrino mass mββ = �3 i=1 U 2 eimi where Uei denotes the element of the lepton mixing matrix and mi are the light neutrino masses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 2 This is the so-called mass mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' The current most stringent constraints on the 0νββ decay half-life in 136Xe is provided by the KamLAND-Zen experiment [1]: T1/2(136Xe) > 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='3 × 1026yr (1) at 90% confidence level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' This corresponds to upper limits on the effective Majorana neutrino mass in the range 36 meV ≤ |mββ| ≤ 156 meV, where the uncertainties mainly arise from the nuclear matrix elements in different nuclear models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Conversely, if 0νββ decay is observed, neutrinos must be Majorana particles [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' However, the 0νββ decay could also be induced by other new physics effects beyond that of Majorana neutrino masses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' In general, the possible mechanism of 0νββ decay can be categorized into two classes: the short-range contributions [3] and the long-range contributions [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' The short-range part of the 0νββ decay amplitude is mediated by the exchange of heavy particles with masses larger than 100 MeV [3], and it is described by a set of dimension-9 operators at leading order [3, 5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' The ultraviolet completions of the short-range operators of 0νββ decay has been systematically studied at both tree level [6] and one-loop level [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' The long-range contributions are induced by the exchange of a light neutrino between two nucleons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' If the interaction vertices of both nucleons are the SM charged current interactions, it is exactly the mass mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' The long-range contribution to the 0νββ decay can appear in new physics models with lepton number violation (LNV), such as the R-parity violating supersymmetric models [8–12], the left-right symmetric models [13–16] and the leptoquark models [17–19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' The 0νββ decay rate including both short-range and long-range parts has been studied in the framework of effective field theory [20,21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' The long-range 0νββ decay can be described by dimension-7 lepton number violating operators [4,22], the complete tree-level decomposition of these dimension-7 operators which induce momentum enhanced contributions to long-range 0νββ decay has been discussed in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' In the present work, we shall give a systematical and complete classification of all models contributing to the d = 7 operators at one-loop level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' The procedures to attach external fields and determine the SM quantum numbers of internal fields are presented.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Certain quantum number assignments are excluded by the absence of tree-level diagrams in a genuine one-loop 0νββ decay model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' The long-range 0νββ decay operators violate lepton number by two units, consequently the mediators of any 0νββ decay model can generate Majorana neutrino mass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' The long-range contribution of one-loop is expected to be subdominant to the mass mechanism without fine tuning of parameter values if the neutrino mass is produced at tree or one-loop level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' For models with two-loop or higher-loop level neutrino mass, the long-range contribution can be comparable to or dominant over the mass mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' The rest of this paper is organized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' We present the effective operators for long- range 0νββ decay below and above the electroweak (EW) scale in section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' The strategy of decomposing the long-range 0νββ decay operators at one-loop level is studied in section 3, and we give the procedures of generating the topologies and diagrams and models for long- range 0νββ decay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' The relation between long-range 0νββ decay model and neutrino mass is discussed in section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Dominance of the one-loop long-range contribution over the mass mechanism requires that neutrino mass should be generated at two-loop and higher loop levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' We study one example of a one-loop model in detail in section 5, and we discuss the constraints imposed by the half-life times of the isotopes 76Ge and 136Xe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Finally, we 3 summarize and present our conclusions in section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 2 Effective operators for long-range 0νββ decay At low energy below the electroweak scale, the most general Lagrangian for the long-range 0νββ decay can be written as [4,22]: Leff = GF √ 2 � �jµ V −AJV −A,µ + � α,β̸=V −A ϵβ αjβJα � � , (2) where the effective coupling constants ϵβ α are scaled with respect to the SM charged current strength GF/ √ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' The leptonic (hadronic) currents jβ (Jα) are defined as: Jµ V ±A = uγµ(1 ± γ5)d , jµ V ±A = eγµ(1 ± γ5)ν , JS±P = u(1 ± γ5)d , jS±P = e(1 ± γ5)ν , Jµν TR/L = uγµν(1 ± γ5)d , jµν TR/L = eγµν(1 ± γ5)ν , (3) with γµν = i 2[γµ, γν] and ν ≡ νL + νc L, where νc L = CνL T is the charge conjugation field of left-handed neutrino and C is the charge conjugation matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' We can see that all currents involving operators proportional to (1 + γ5) will pick the component νC L and consequently they would violate lepton number by two units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' In Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' (2), one should sum over all possible contractions of leptonic and hadronic currents allowed by Lorentz-invariance, in other words, all possible combinations of Lorentz indices α, β should be considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Notice the identity jµν TRJTLµν = jµν TLJTRµν = 0, consequently there are only ten independent operators in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' (3) for the long-range 0νββ decays.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' The long-range part of 0νββ decay is induced by the exchange of a light neutrino between two point-like vertices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' If both interaction vertices are the SM charged current interactions, it yields the mass mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' If both interaction vertices are new physics contributions parameterized by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' (2), the corresponding amplitudes would be quadratic in ϵβ α and they are too small to be negligible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' In the present work, we shall be concerned with the case that only one vertex arises from the new physics beyond SM and the other one is the SM charged current interaction, as shown in figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Then the 0νββ decay amplitude is proportional to the time-ordered product of the Lagrangian of the two interaction vertices � d4x � d4y G2 F 2 ϵβ α T � jβ(x)Jα(x)jµ V −A(y)JV −A,µ(y) � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' (4) If the non-SM lepton current jβ is left-handed with β = (S − P), TL, lepton number violation arises from the Majorana mass terms of light neutrinos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Then the light neutrino mass in the numerator of the neutrino propagator would be picked out by the chiral projection operator 1 ± γ5, consequently the resulting amplitude would be proportional to ϵβ α⟨mν⟩ which is subdominant to the mass mechanism contribution, where ⟨mν⟩ is the effective Majorana neutrino mass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' On the other hand,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' if the lepton current jβ is right-handed with β = (S + P),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' (V + A),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' TR,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' the lepton number is violated at the new interaction vertex,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' and the term p/ will be projected out from the numerator of the neutrino propagator,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' where 4 GF GF e d u ⟨H0⟩ ⟨H0⟩ e u d (a) ν ν GF e d u ⟨H0⟩ e u d (b) ν Figure 1: The mass mechanism (left panel) and long-range contributions (right panel) to the 0νββ decay rate,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' where the black dot denotes the SM effective four-fermion interaction,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' while the slashed circle stands for the effective vertex of the neutrino masses (left panel) and the long-range 0νββ operator (right panel) arising from new physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Here we do not show the diagram with two new physics vertices, since the corresponding contribution is suppressed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' the neutrino momentum is of order O(100) MeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' As a result, the long-range amplitude is proportional to ϵβ αp and it could be comparable to the standard mass mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' In the following sections, we shall study the ultraviolet completion of the lepton number violating long-range 0νββ decay operators with right-handed leptonic current: jS+PJS+P, jS+PJS−P, jµ V +AJV +A,µ, jµ V +AJV −A,µ and jµν TRJTR,µν.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' These five operators satisfy the electromagnetic U(1) gauge symmetry, but they are not invariant under the action of the SM gauge group SU(3)C × SU(2)L × U(1)Y .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' They arise from the following dimension-7 SM gauge invariant operators [5,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='23,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='24],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' O1 ≡ ϵikϵjl(ℓc iℓj)(dRQk)Hl ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' O2 ≡ ϵikϵjl(ℓc iγµνℓj)(dRγµνQk)Hl ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' O3 ≡ ϵjk(ℓc iℓj)(Q iuR)Hk ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' O4 ≡ (ℓc iγµeR)(dRγµuR)ϵijHj ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' (5) where i,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' j,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' k,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' l = 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 2 are the indices of the SU(2)L gauge group,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' ℓ = (νeL,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' eL)T and Q = (uL,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' dL)T denote the first generation of lepton and quark doublet respectively,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' uR,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' dR and eR are the first generation of right-handed quark and lepton singlets,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' H is the SM Higgs doublet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' After the electroweak symmetry breaking by the vacuum expectation value (VEV) of the Higgs field, the operators O1, O2, O3 and O4 give rise to the low energy long-range 0νββ decay operators j† S+PJ† S+P, jµν† TR J† TR,µν, j† S+PJ† S−P and jµ† V +AJ† V +A,µ respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Notice that the remaining long-range operator jµ V +AJV −A,µ is generated by the following dimension-9 SM effective operator [25] O5 = ϵimϵkn(ℓc iγµeR)(Q jγµQk)HmHjHn , (6) which leads to 0νββ decay at higher dimension, we will not discuss this scenario in our current work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Including the lepton flavor indices in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' (5), one can obtain all independent 5 dimension-7 lepton number violating operators without derivative [23]: O1(α, β) ≡ ϵikϵjl(ℓc αiℓβj)(dRQk)Hl , O2(α, β) ≡ ϵikϵjl(ℓc αiγµνℓβj)(dRγµνQk)Hl , O3(α, β) ≡ ϵjk(ℓc αiℓβj)(Q iuR)Hk , O4(α, β) ≡ (ℓc αiγµeRβ)(dRγµuR)ϵijHj , (7) besides ϵikϵjl(ℓc αiℓβj)HkHl(H†H) which is the famous Weinberg operator with the addition H†H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Here α and β are lepton flavor indices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' In the following we will study the one-loop decomposition of the 0νββ decay operators in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' (5) and the relation with light neutrino mass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 3 Systematical one-loop decomposition In the following, we will use the diagrammatic method [26,27] to find out all possible one- loop decomposition of the dimension seven long-range 0νββ decay operators in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' (5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' This method has been used to decompose the neutrino mass operators for both Majorana neutrinos [28–30] and Dirac neutrinos [31–34].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Firstly, we identify the one-loop topologies with five external legs by using only 3-point vertices and 4-point vertices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' The topologies of tadpole and self-energies are eliminated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' In the next step, we promote topologies to dia- grams by specifying the Lorentz nature (spinor or scalar) of each internal and external lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Renormalizability and Lorenz invariance require the diagrams contain only the interaction vertices of the type fermion-fermion-scalar, scalar-scalar-scalar or scalar-scalar-scalar-scalar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' A topology can lead to a few number of Feynman diagrams, because there are usually sev- eral possible assignments of quark fields, lepton fields and Higgs field to the five external legs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Furthermore, each interaction vertex should be invariant under the SM gauge group SU(3)C ×SU(2)L ×U(1)Y such that one can constrain the quantum numbers of the internal fermion and scalar fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' If the gauge quantum numbers of all internal fields are specified for a diagram, the corresponding UV completion will be called a model, and the gauge invari- ant interactions involving the beyond SM fields can be read out straightforwardly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Notice that the SM gauge quantum numbers of the new fields can be unambiguously fixed in the tree-level realizations, while there are infinite possible quantum number assignments to the fields running in the loop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' In the following, we will consider the scenarios that new fields are singlets, doublets or triplets of SU(2)L, and the results for the higher dimensional rep- resentations can be derived in a similar way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Regarding SU(3)C assignment for the fields, the low-dimensional representations up to octet are considered for illustration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='1 One-loop topologies for long-range 0νββ decay operators As shown in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' (5), we see the dimension-7 long-range 0νββ decay operators involve two quark fields, two lepton fields and a Higgs doublet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Using our own codes unpublicized yet, we plot the connected one-loop topologies with five external legs, and we find there are 37 one-loop topologies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' However, most of the topologies are of no interest to us, we can exclude a lot of them at the topology level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' The first step is to exclude all the topologies 6 with tadpoles and self-energy, because the models generated from these topologies always have divergent parts in their loop integrals, and there should be a lower order counter term required by renormalizability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Then there are 16 topologies left.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Since we are working on the operators with four fermions and one scalar, some topologies need non-renormalizable interactions to accommo- date these external lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' As a consequence, these topologies should be discarded and they are shown in figure 3 for completeness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' At this point we are left with 7 different topologies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' We intend to identify the topologies and diagrams as well as the models for which the lead- ing order contribution to 0νββ decay arises at one-loop level, and the tree-level contribution is absent without the need to introduce extra symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' These topologies, diagrams and models will be considered genuine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' If a diagram has a sub-diagram with a loop and three external legs, then the three-point vertex without the loop is also compatible with the sym- metry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' In other words, any internal loop (or loop) with three legs can be compressed into a three-point vertex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Thus the corresponding one-loop diagram must be accompanied by the more important tree-level diagram, and consequently it is non-genuine and should be discarded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' The topologies with compressible one-loop sub-diagram are displayed in figure 4 for completeness, they can be regarded as extensions of the tree-level topology, where one of the vertices is generated at one-loop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Discarding the compressible topologies in figure 4, there remain only 3 genuine topologies shown in figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' We also display the unique tree- level topology in figure 2, and the systematic decomposition of tree-level 0νββ decay model dominated by long-range contribution has been studied in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' In the present work, we also provide the tree-level decomposition, since these results are necessary when determining the genuineness of a one-loop model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='2 Constructing diagrams We proceed to specify the Lorentz nature (fermion or scalar) of both external and internal lines of each topology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' The SM invariant 0νββ decay operators in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' (5) involve two quark fields, two lepton fields and a Higgs field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' There are several options for the assignments of the four fermions and one scalar to the five external legs for each topology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' After considering all possible external leg assignments, we insert the fermion or scalar into internal lines one by one and Lorentz invariance implies that each vertex must contain an even number of fermions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' The UV completion models are required to be renormalizable so that the dimen- sion of each interaction vertex should be less than or equal to 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' As a consequence, only the renormalizable scalar-scalar-scalar, fermion-fermion-scalar and scalar-scalar-scalar-scalar interactions can be used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' As shown in figure 5, we find there are 8 independent one-loop diagrams arising from the genuine topologies of figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' After the electroweak symmetry breaking, the couplings to external Higgs field lead to chirality flip of fermion field or scalar mixing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' The external Higgs field with vacuum expectation value insertion can be removed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Hence the 8 diagrams in figure 5 get reduced to only 3 diagrams in mass basis, as shown in figure 6, these diagrams will be useful when we calculate the 0νββ decay rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 7 NL-0-1 Tree level NL-1-1 One loop NL-1-2 NL-1-3 Figure 2: The tree-level and one-loop topologies that can lead to genuine models of long- range 0νββ decays.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 8 Figure 3: The one-loop topologies that always lead to non-renormalizable diagrams.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Figure 4: The one-loop topologies leading to non-genuine finite or divergent diagrams, the internal loop with three legs can be compressed into a three-point vertex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 9 NL-0-1-1 Tree level NL-0-1-2 NL-1-1-1 One-loop level NL-1-2-1 NL-1-2-2 NL-1-2-3 NL-1-2-4 NL-1-2-5 NL-1-3-1 NL-1-3-2 Figure 5: List of genuine diagrams for long-range 0νββ decay up to one-loop level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 10 NLM-1 NLM-2 NLM-3 Figure 6: The genuine one-loop diagrams for long-range 0νββ decay in the mass basis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Notice that the external leg of Higgs is removed after electroweak symmetry breaking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='3 The approach of generating models The next step is to generate models based on the 8 genuine diagrams listed in figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' We need to specify how each internal line transforms under the SM gauge group SU(3)C × SU(2)L × U(1)Y .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' We firstly attach the fields of the effective operators to external lines of the diagram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Subsequently imposing gauge invariance of the interaction vertices, we can determine the possible quantum numbers of the messenger fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' In the following, we give the details of generating models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='1 Attaching external fields The effective operators O1,2,3,4 of long-range 0νββ decay can be classified into three categories according to the fields involved, as summarized in table 1, where the conjugate operators are considered to accommodate our convention.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' We see that O1 and O2 are composed of the same fields, therefore they share the same routine of UV completion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Generally both of them are generated in a concrete UV model after integrating out the heavy fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Each operator class in table 1 involves different external legs, as a result, the UV completions of these three classes should be performed separately based on the diagrams given in figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' In the following, we take the diagram NL-1-1-1 with operator O4 as an example to illustrate the external field assignment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' One can decompose the 0νββ decay operators for other diagrams in the same fashion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' The full results are collected in the attached Mathematica file [35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Name 0νββ decay operators External fields NL1 O† 1, O† 2 ℓ, ℓ, Q, dR, H† NL2 O† 3 ℓ, ℓ, Q, ¯uR, H† NL3 O† 4 ℓ, ¯eR, ¯uR, dR, H† Table 1: The fields involved in the 0νββ decay operators, the hermitian conjugate operators are used to accommodate our convention.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' The operator O† 4 is constituted by the fields ℓ, ¯eR, ¯uR, dR and H†, which can be freely assigned to the external legs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' However, the lepton and quark fields in the SM are chiral fields 11 in weak basis, consequently, for certain attachment of external fields, Lorentz invariance requires vector mediators otherwise the vertex would be vanishing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' As far as we know, vector bosons should be the gauge bosons of certain gauge symmetry and their masses are generated through the spontaneous breaking of the extended gauge symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Thus the new gauge bosons require extending both the SM gauge group and scalar field content.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' In the present work, we would like to preserve the SM gauge group SU(3)C × SU(2)L × U(1)Y that has been tested by lots of experiments from low energy to TeV scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Hence the cases of vector mediators will not be considered1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Let us consider the attachment of external legs at the vertex A of diagram NL-1-1-1, as shown in figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Lorentz invariance implies that 4 out of the 6 possible assignments need new vector mediators, and consequently they are discarded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Moreover, one can freely attach the fields to all the external lines, and some attachments are superfluous.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' In order to identify the redundant ones, we should consider permutations of vertices and compare the different couplings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' If two different attachments are related with each other through permutation of vertices, they will be essentially the same one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' After attaching all the fields of the operator O† 4 to the external lines of the diagram NL- 1-1-1, we find there are only two possible assignments shown in figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Following the above procedure, we have found out all the possible independent external fields attachments for the genuine diagrams in figure 5 , and the same procedure can be applied to all other 0νββ decay operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Our results are summarized in table 2, table 3 and table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Once the external lines are specified, the SM quantum numbers of the internal fields can be determined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' See the following sections for details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' E5 E1 E2 E4 E3 I1 I3 I2 I4 Operator Diagram E1 E2 E3 E4 E5 Operator Diagram E1 E2 E3 E4 E5 NL1 NL-1-1-1 ℓ dR ℓ Q H† NL2 NL-1-1-1 ¯uR Q ℓ ℓ H† Q ℓ ℓ dR H† ℓ ℓ ¯uR Q H† Q dR ℓ ℓ H† NL3 NL-1-1-1 ¯uR ¯eR ℓ dR H† ℓ ℓ Q dR H† ℓ dR ¯eR ¯uR H† Table 2: The possible external field attachments for the topology NL-1-1, where the external and internal fields are labelled as Ei and Ii respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 1The scalar mediators can also be the SM gauge bosons if they transforms as (1, 3, 0) or (1, 1, 0) under the SM gauge group SU(3)C × SU(2)L × U(1)Y and the relevant fermion-fermion-vector interaction is allowed by the chirality of external fermions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' We would like to mention that the results for vectors can be straightforwardly derived from the corresponding ones for scalars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' However, the interaction vertices and the propagator of a massive vector boson are different from those of a scalar, the vector mediator and scalar mediator lead to different contributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 12 NL-1-1-1 A uR eL dR eL eL eR uR eR dR eR uR dR Figure 7: Attach the fields of the 0νββ decay operator O† 4 to the external lines of the diagram NL-1-1-1 at the vertex A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' On the right side, the dashed lines stand for scalar fields while the wavy lines denote vector fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Note that the chirality of the external fermions fixes the mediator to be either vector or scalar boson.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' H uR eR dR ℓ NL3-1-1-1-1 S1 S2 F1 S3 H ℓ dR uR eR NL3-1-1-1-2 S1 S2 F1 S3 Figure 8: Attach external fields of NL3 to the diagram NL-1-1-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' After attaching external fields, we change the notation “NL-” to corresponding operator notation “NL3-”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='13 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='E4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='E5 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='E3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='E1 ' metadata={'source': 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metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='H† ℓ Q ¯uR ℓ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='H† ℓ ¯uR dR ¯eR ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='H† Q ℓ ¯uR ℓ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='H† ¯eR ℓ dR ¯uR ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='H† ℓ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='ℓ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='Q ¯uR ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='H† ¯eR ¯uR dR ℓ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='H† ℓ ¯uR Q ℓ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='H† ¯uR ℓ dR ¯eR ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='H† ¯uR ℓ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='Q ℓ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='H† ¯uR ¯eR dR ℓ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='Table 3: The possible external field attachments for the topology NL-1-2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' where the external and internal fields are labelled as Ei and Ii respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='2 U(1)Y quantum number assignments For any given diagram with external field attachments specified, one can straightforwardly determine the hypercharges of the internal messenger fields from of the U(1)Y invariance at each vertex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Since a plenty of diagrams are involved, we would like to determine the U(1)Y quantum numbers at the topology level rather than at the diagram level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Notice that the hypercharge Y of a field is related to its electric charge Q via the Gell-Mann-Nishijima formula Q = T3 + Y , where T3 is the third component of the weak isospin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' For the topology ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='15 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='E5 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='E1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='E2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='E3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='E4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='I5 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='I1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='I2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='I3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='I4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='Operator Diagram E1 E2 E3 E4 E5 Operator Diagram E1 E2 E3 E4 E5 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='NL1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='NL-1-3-1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='NL-1-3-2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='H† Q ℓ dR ℓ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='NL3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='NL-1-3-1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='NL-1-3-2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='H† ¯uR ¯eR dR ℓ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='H† dR ℓ Q ℓ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='H† dR ¯eR ¯uR ℓ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='H† ℓ Q dR ℓ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='H† ¯eR ¯uR dR ℓ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='H† dR Q ℓ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='ℓ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='H† dR ¯uR ¯eR ℓ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='H† Q dR ℓ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='ℓ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='H† ¯eR dR ¯uR ℓ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='H† dR ℓ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='ℓ Q ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='H† ¯uR dR ¯eR ℓ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='NL2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='NL-1-3-1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='NL-1-3-2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='H† ¯uR ℓ Q ℓ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='H† ¯uR ℓ dR ¯eR ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='H† Q ℓ ¯uR ℓ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='H† dR ℓ ¯uR ¯eR ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='H† ℓ ¯uR Q ℓ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='H† dR ¯uR ℓ ¯eR ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='H† Q ¯uR ℓ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='ℓ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='H† ¯uR dR ℓ ¯eR ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='H† ¯uR Q ℓ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='ℓ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='H† dR ℓ ¯eR ¯uR ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='H† Q ℓ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='ℓ ¯uR ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='H† dR ¯eR ℓ ¯uR ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='Table 4: The possible external field attachments for the topology NL-1-3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' where the external and internal fields are labelled as Ei and Ii respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 16 NL-1-1, the equations of hypercharge conservation are given by YE1 + YI1 − YI2 = 0, YE2 + YI2 + YI3 = 0, YE5 − YI1 − YI3 − YI4 = 0, YE3 + YE4 + YI4 = 0 , (8) where the labels Ei and Ii represent the external and internal fields respectively, the diagram can be found in table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' The solution to the above equations leads to the following constraints on the hypercharge: YI1 = α, YI2 = YE1 + α, YI3 = −YE1 − YE2 − α, YI4 = −YE3 − YE4 , (9) where α is an arbitrary real parameter and it parameterizes the hypercharge flow in the loop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' A definite value of α should be taken in a concrete model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' For the second one-loop topology NL-1-2 as shown in table 3, conservation of hypercharge at each vertex implies YE1 + YE2 + YI1 = 0, YI1 + YI2 + YI5 = 0, YE3 + YI2 + YI3 = 0, YE4 − YI3 − YI4 = 0, YE5 + YI4 + YI5 = 0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' (10) The solution to the above system of equations leads to the following constraints on hyper- charge: YI1 = −YE1 − YE2, YI2 = α, YI3 = −YE3 − α, YI4 = YE3 + YE4 + α, YI5 = −YE1 − YE2 − α .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' (11) Similar to previous case, the hypercharge is not unambiguously fixed, and the arbitrariness is encoded in the real free parameter α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' For the last topology NL-1-3 with labels defined in table 4, the gauge invariance under U(1)Y leads to the following constraints YE1 − YI1 − YI5 = 0, YE2 + YI1 + YI2 = 0, YE3 − YI2 + YI3 = 0, YE4 − YI3 − YI4 = 0, YE5 + YI4 + YI5 = 0 , (12) and the solution is given by YI1 = α, YI2 = −YE2 − α, YI3 = −YE2 − YE3 − α, YI4 = −YE1 − YE5 + α, YI5 = YE1 − α , (13) We summarize the above results for the hypercharge values of the internal fields in table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Once the assignment of external legs is specified for any given diagram, one can straight- forwardly extract the hypercharges of the mediators by using the general results collected in table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Taking the diagram NL3-1-1-1-1 as an example, we have the external fields E1 = ¯uR, E2 = ¯eR, E3 = ℓ, E4 = dR and E5 = H†, thus the hypercharges of messenger fields are fixed to be YS1 = α, YF1 = −2 3 + α, YS2 = −1 3 − α, YS3 = −1 6 , (14) where YuR = 2 3, YeR = −1, Yℓ = −1 2, YdR = −1 3 and YH = 1 2 have been used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Similarly, we have E1 = ℓ, E2 = dR, E3 = ¯eR, E4 = ¯uR and E5 = H† for the diagram NL3-1-1-1-2 and consequently the hypercharge can be determined as follows, YS1 = α, YF1 = 1 2 + α, YS2 = −1 6 − α, YS3 = −1 3 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' (15) 17 Topology YI1 YI2 YI3 YI4 YI5 NL-1-1 α YE1 + α −YE1 − YE2 − α −YE3 − YE4 \\ NL-1-2 −YE1 − YE2 α −YE3 − α YE3 + YE4 + α −YE1 − YE2 − α NL-1-3 α −YE2 − α −YE2 − YE3 − α −YE1 − YE5 + α YE1 − α Table 5: The hypercharge of each internal line for the three renormalizable topologies of long-range 0νββ decay, and the conventions for the hypercharge flows are shown in tables 2, 3 and 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='3 SU(2)L quantum number assignments Once the attachment of external legs to the fields of 0νββ decay operators is finished, as summarized in table 2, table 3 and table 4, the SU(2)L transformation of the each external line can be read off directly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' We would like to mention that ℓ, Q and H are SU(2)L dou- blets while eR, uR and dR are SU(2)L singlets, and the complex conjugate of any SU(2)L irreducible representation is equivalent to itself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' If focusing on the SU(2)L transformation of the external lines and ignoring other properties, from table 2 we can see that there are only 4 different SU(2)L assignments of external legs for the topology NL-1-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Renormalizability fixes possible vertices to be only three and four point interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' The trilinear couplings can be of the types fermion-fermion-scalar (FFS) or scalar-scalar-scalar (SSS), and the 4- point vertex can only be the scalar-scalar-scalar-scalar (SSSS) interaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Accordingly, the interaction Lagrangian can be written as F 1F2S, S1S2S3 and S1S2S3S4 respectively, the SU(2)L invariance gives the following constraints: F 1F2S : nF1 ⊗ nF2 ⊗ nS ⊃ 1 , S1S2S3 : nS1 ⊗ nS2 ⊗ nS3 ⊃ 1 , S1S2S3S4 : nS1 ⊗ nS2 ⊗ nS3 ⊗ nS4 ⊃ 1 , (16) where nX denotes the SU(2)L representation under which the X field transforms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' The SU(2)L quantum number assignments for the internal fields can be determined by solving the constraint of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' (16) at each interaction vertex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' There are generally an infinite number of possible SU(2)L quantum numbers assignments to the internal particles except the tree- level diagrams.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' In the following, we will only consider singlet, doublet and triplet of SU(2)L for illustration, and extension to high dimensional representations is straightforward.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' We use the Mathematica group package GroupMath [36] to efficiently determine the SU(2)L assignments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' The results of SU(2)L quantum number assignments for the topology NL-1- 1 are listed in table 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' The SU(2)L assignments for the other two topologies NL-1-2 and NL-1-3 can be determined in a similar way, and the results are listed in table 7 and table 8 respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='18 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='E5 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='E1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='E2 ' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='6 6 ¯6 1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='3 8 ¯3 1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='6 6 ¯6 8 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='6 3 ¯6 1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='8 8 8 1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='¯6 8 6 1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='8 8 8 8 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='8 ¯3 8 1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='8 6 8 1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='Table 6: The independent SU(2)L and SU(3)C quantum number assignments for the topol- ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='ogy NL-1-1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' where Ei and Ii denote the external fields and internal fields respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Other assignments are related to these in the table through permutations of external and internal lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='19 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='E4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='E5 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='E3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='E1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='E2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='I4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='I5 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='I2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='I3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='I1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='E1 E2 E3 E4 E5 I1 I2 I3 I4 I5 E1 E2 E3 E4 E5 I1 I2 I3 I4 I5 ' 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='1 3 ¯3 6 ¯3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='8 3 ¯3 3 ¯3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='1 ¯3 3 1 3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='1 ¯6 6 ¯6 6 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='1 ¯3 3 8 3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='8 ¯6 6 ¯6 6 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='1 ¯6 6 ¯3 6 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='1 8 8 8 8 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='1 6 ¯6 8 ¯6 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='8 8 8 8 8 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='1 8 8 3 8 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='1 8 8 ¯6 8 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='Table 7: The independent SU(2)L and SU(3)C quantum number assignments for the topol- ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='ogy NL-1-2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' where Ei and Ii denote the external fields and internal fields respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Other assignments are related to these in the table through permutations of external and internal lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='21 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='E5 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='E1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='E2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='E3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='E4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='I5 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='I1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='I2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='I3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='I4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='E1 E2 E3 E4 E5 I1 I2 I3 I4 I5 E1 E2 E3 E4 E5 I1 I2 I3 I4 I5 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='SU(2)L ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='2 1 2 1 1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='2 1 1 1 1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='2 1 2 3 3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='1 2 2 2 2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='1 2 1 2 2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='3 2 2 2 2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='3 2 1 2 2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='2 3 3 3 3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='3 2 3 2 2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='2 1 1 2 2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='2 3 2 1 1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='1 2 2 1 1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='2 3 2 3 3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='3 2 2 3 3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='2 3 3 2 2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='SU(3)C 1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='¯3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='1 1 3 ¯3 1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='1 ¯3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='1 1 1 ¯3 1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='¯3 3 ¯3 3 3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='¯3 3 3 3 3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='¯3 3 6 ¯6 3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='¯3 3 3 ¯6 3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='3 ¯3 1 1 ¯3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='3 ¯3 ¯3 1 ¯3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='3 ¯3 8 8 ¯3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='3 ¯3 ¯3 8 ¯3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='6 ¯6 ¯3 3 ¯6 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='6 ¯6 ¯6 3 ¯6 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='¯6 6 8 8 6 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='¯6 6 6 8 6 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='8 8 3 ¯3 8 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='8 8 8 ¯3 8 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='8 8 ¯6 6 8 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='8 8 8 6 8 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='Table 8: The independent SU(2)L and SU(3)C quantum number assignments for the topol- ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='ogy NL-1-3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' where Ei and Ii denote the external fields and internal fields respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Other assignments are related to these in the table through permutations of external and internal lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 22 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='4 SU(3)C quantum number assignments All the long-range 0νββ decay operators involve one quark, one anti-quark, two lepton fields and one Higgs field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' The quark is in the irreducible representations 3, and the anti- quark is in the conjugate triplet representation ¯3 of SU(3)C while leptons and Higgs are invariant under the SU(3)C group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Hence two external fields transform as 3 and ¯3 and the remaining three external fields are trivial singlets of SU(3)C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' It is remarkable that one can assign SU(3)C quantum numbers of external legs at the topology level without specifying the field property of each line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' As regard the topology NL-1-1, the external field E5 is attached to a four-point vertex, consequently it can only be the Higgs scalar field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' We can see there are only four independent SU(3)C assignments to the external legs, without loss of generality we can choose (E1, E2, E3, E4, E5) ∼ (1, 3, 1, ¯3, 1), (¯3, 3, 1, 1, 1), (1, ¯3, 1, 3, 1) and (1, 1, ¯3, 3, 1), as shown in table 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Other assignments are redundant and they are related to these four representative ones by permutating external fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' For instance, the assignment (E1, E2, E3, E4, E5) ∼ (1, 3, ¯3, 1, 1) is equivalent to (E1, E2, E3, E4, E5) ∼ (1, 3, 1, ¯3, 1) since there is a E3, E4 permutation symmetry in the topology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Similarly there are eight different SU(3)C assignments to the external fields of the topology NL-1-2, as listed in table 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Regarding the last topology NL-1-3, the five external lines attach at the vertices of a pentagon, and the two colored ones can be adjacent or spaced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Consequently it is sufficient to consider only two kinds of SU(3)C assignments displayed in table 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Then we proceed to assign SU(3)C quantum numbers to each internal line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Similar to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' (16) for SU(2)L, one should determine whether SU(3)C invariant contractions can be formed at the vertices by using the technique of Young diagrams [37], and this task can be made much easier with the help of the Mathematica package GroupMath [36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Analogous to the case of SU(2)L and U(1)Y , there are in principle endless SU(3)C representation assignments consistent with the SM gauge invariance at one-loop level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' We present the SU(3)C quantum numbers of the internal fields for the three topologies NL-1-1, NL-1-2 and NL-1-3 in table 6, table 7 and table 8 respectively, where only the lower-dimensional SU(3)C representations 1, 3, ¯3, 6, ¯6 and 8 are used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='5 Constructing long-range 0νββ decay models Using the results of sections 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='2, 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='3 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='4, one can construct explicit UV models for 0νββ decay by assigning the SM SU(3)C × SU(2)L × U(1)Y quantum numbers to the internal fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' The first step is to choose a diagram, here we take NL-1-1-1 as an example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' The second step is to attach fields to the external legs, see table 2 for different possibilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' We choose the first kind of attachment for the operator NL3, and it yields the diagrams shown in the left panel of figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' The third step is to determine the U(1)Y charges of the messenger fields by using table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' The U(1)Y charges of external fields read as YE1 = YuR = −2 3 , YE2 = YeR = 1 , YE3 = Yℓ = 1 2 , YE4 = YdR = −1 3 , YE5 = YH† = −1 2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' (17) As a consequence, the U(1)Y charges of the internal fields are determined to be YI1 = α , YI2 = −2 3 + α , YI3 = −1 3 − α , YI4 = 5 6 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' (18) 23 H uR eR dR ℓ NL3-1-1-1-1-1 1 1 1 2 2 1 1 1 2 H uR eR dR ℓ NL3-1-1-1-1-2 2 2 2 2 2 1 1 1 2 H uR eR dR ℓ NL3-1-1-1-1-3 3 3 3 2 2 1 1 1 2 Figure 9: Assignments of the SU(2)L quantum numbers for the diagram NL3-1-1-1-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' The fourth step is the assignment of the SU(2)L quantum numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' The external fields transform as (E1, E2, E3, E4, E5) ∼ (1, 1, 2, 1, 2) under SU(2)L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' From table 6 we see that the SU(2)L transformation of the mediators can be (I1, I2, I3, I4) ∼ (1, 1, 1, 2), (2, 2, 2, 2), (3, 3, 3, 2), these three SU(2)L assignments are displayed in figure 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' The last step is to determine the SU(3)C quantum numbers of messenger fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' The SU(3)C transformations of external legs are (E1, E2, E3, E4, E5) = (¯3, 1, 1, 3, 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' There is no such assignment in table 6 at first glance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' However, one can exchange E1 and E2 as well as I1 and I3 at topology level, consequently we can consider the assignment (E1, E2, E3, E4, E5) ∼ (1, ¯3, 1, 3, 1) instead.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Then we see from table 6 that the internal fields can transform as (I1, I2, I3, I4) ∼ (1, 3, 3, ¯3), (3, 1, 1, ¯3), (3, 8, 8, ¯3), (¯3, ¯3, ¯3, ¯3), (¯3, 6, 6, ¯3), (¯6, 8, 8, ¯3), (6, ¯3, ¯3, ¯3), (8, 3, 3, ¯3) and (8, ¯6, ¯6, ¯3) under SU(3)C, as shown in figure 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' In this way, we can find the possible UV completions for all the long-range 0νββ decay operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='6 Genuine one-loop models Numerous one-loop models for long-range 0νββ decays can be generated through a series of steps described in previous sections, however, some of them are not the leading-order contribution to the long-range 0νββ decays.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' A one-loop model is the dominant contribution if and only if the combination of fields participating in the model can not generate more important tree-level contributions to 0νββ decay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Such kind of models would be called genuine models, for which the tree-level diagrams are automatically absent without the need of invoking additional symmetries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' If the lower order contributions can not be forbidden without extra symmetry, the model would be non-genuine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' We can determine the genuineness of each model by comparing its field content with that of the tree-level models one by one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Since the quantum numbers of the mediators of the tree-level 0νββ decay models are unambiguously fixed, genuineness of a one-loop model generally excludes certain value of the hypercharge parameter α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' We take the model NL3-1-1-1-2-2-1 for illustration, the Feynman diagram is shown in figure 11, in which we have introduced the notation CY L to label the quantum numbers of a field, where C refers to the SU(3)C representation, L refers to the SU(2)L transformation, and Y stands for U(1)Y charge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' When the hypercharge parameter α = 1 3, we see that the mediators S2(S3) and F as well as the associated interactions allow to generate the tree-level models NL1-0-1-2-2-1-1, NL3-0-1-2-3-1-1 which are the more important ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Therefore the genuineness of the one-loop model NL3-1-1-1-2-2-1 requires α ̸= 1 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' The condition of ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='24 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='H ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='uR ' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='Figure 10: Assignments of the SU(3)C quantum numbers for the diagram NL3-1-1-1-1-X,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' where X=1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 3 stands for the possible SU(2)L quantum number assignments shown in figure 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 25 H dR ℓ uR eR S1 : 1−1/6−α 2 S2 : ¯3α 1 NL3-1-1-1-2-2-1 F : ¯31/2+α 2 S3 : 3−1/3 1 α = 1 3 α = 1 3 ℓ uR eR dR H NL3-0-1-2-3-1-1 S3 (S∗ 2) F ℓ Q ℓ dR H NL1-0-1-2-2-1-1 S3 (S∗ 2) F Figure 11: One example of the non-genuine model NL3-1-1-1-2-2-1, and the messenger fields F, S2 and S3 can lead to the tree-level contributions NL1-0-1-2-2-1-1 and NL3-0-1-2-3-1-1 in the case of α = 1 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Notice that the mediators F, S2 and S3 will also lead to tree- level contributions NL1-0-1-2-2-1-1, NL3-0-1-2-3-1-1, NL3-0-1-1-3-1-1 when the hypercharge parameter α = ±1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' The quantum numbers are given in the notation CY L , where C refers to the SU(3)C transformation, L refers to the SU(2)L transformation, and Y stands for U(1)Y charge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 26 genuineness has been considered for each possible one-loop decomposition of the 0νββ decay operators, and the full results are listed in the attachment [35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 4 Neutrino mass in long-range 0νββ decay models u u d d e e W W ν ν ⟨H0⟩ u d e ν W ν Figure 12: The black box diagrams for neutrino masses from 0νββ decay effective vertices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' The diagram in the left panel can generate Majorana neutrino masses if 0νββ decay is observed, while the diagram in the right panel can generate Majorana neutrino masses from the long-range 0νββ decay operator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' In the UV decomposition of the current work, the effective vertex of the long-range 0νββ operator is realized by a one-loop diagram, which means the neutrino masses are generated at most at three-loop level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' The black box theorem shows that, one can obtain the Majorana neutrino masses by connecting the quark and charged lepton legs in these 0νββ decay effective operators with the SM interactions [2], the schematic black box diagram is shown in left panel of figure 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Since the long-range 0νββ decay operators violate lepton number by two units, we can similarly get another black box diagram for Majorana neutrino mass from the long-range 0νββ effective vertex, which is shown in the right panel of figure 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Consequently, any 0νββ decay model will always generate a non-zero Majorana neutrino mass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' In current work, the effective 0νββ decay operator in the black box diagram is realized at the one-loop level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' The tree-level contribution is forbidden in order to maintain the genuineness of the one-loop model, so the black box is realized at most at the three-loop level in our UV models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' The fields introduced in the one-loop 0νββ decay model can also generate neutrino mass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' In some cases, these fields can result in a lower loop-level model for neutrino mass, then the three-loop diagram in the black box is the higher order contribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' In other words, one can construct neutrino mass diagrams by using the SM fields and the mediators that appear in one-loop renormalizable long-range 0νββ decay models at most at three-loop level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Indeed, as shown below, any decomposition of the long-range 0νββ decay operators contains automatically the particle content and interactions such that Majorana neutrino masses can be generated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Given the quantum numbers of mediators and the SM fields, one can use the Mathematica package Sym2Int [38, 39] to generate all renormalizable interactions consistent with SM gauge symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Subsequently we import these interactions to the package qgraf [40] to generate all possible leading-order neutrino mass diagrams.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' We take the one-loop model NL2-1-3-1-1-3-1 for example, the leading order contribution to neutrino masses arises at one-loop and two-loop level for α = −1/2 and α = −2/3 respectively, as shown in figure 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Since the black box theorem implies that any contributions to the 0νββ decay always induce Majorana neutrino masses, thus the contribution of the mass mechanism always exists in any 0νββ model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' For models in which neutrino masses are generated at tree or one-loop level, 27 one generally expects that the one-loop long-range contribution is subdominant to the mass mechanism, if the values of the model parameters are not severely fine-tuned.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' The long-range contribution and the mass mechanism can be comparable in certain parameter space for the one-loop 0νββ decay decomposition with two-loop or three-loop neutrino masses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Hence both tree and one-loop contributions to neutrino mass should be forbidden in a genuine one-loop model of long-range 0νββ decay, thus certain values of the hypercharge would be excluded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' uR H ℓ Q ℓ NL2-1-3-1-1-3-1 S1 : 1−α 2 S2 : 11/2−α 1 F1 : 1−α 2 S3 : 31/6+α 1 F2 : 32/3+α 2 α = − 3 2 α = − 1 2 H ℓ ℓ H eR ℓ S2 S1 H ℓ ℓ H uR S3 S1 S2 F1 Q F2 Figure 13: The neutrino mass generation in the 0νββ decay model NL2-1-3-1-1-3-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' One sees that the mechanism producing neutrino mass depends on the value of the hypercharge parameter α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 5 An example model of one-loop 0νββ decay In this section, we shall present a one-loop model for long-range 0νββ decay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' This model only contains two new scalar fields S1, S2 and a new vector-like fermion F which transform 28 dR H ℓ eR uR NL3-1-3-2-7-1-4 eR : 1−1 1 ℓ : 1−1/2 2 S1 : 11 1 F : 12 1 S2 : 3−4/3 1 ν e d u e S1 F S2 Figure 14: The example model NL3-1-3-2-7-1-4 of one-loop 0νββ decay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' After electroweak symmetry breaking, the corresponding Feynman diagram is shown in the right panel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' For this model, the neutrino mass is generated at three-loop level, as shown in figure 15 and figure 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' under the SM gauge group as S1 ∼ (1, 1, 1) , S2 ∼ (3, 1, −4/3) , F ∼ (1, 1, 2) (19) in the notation of (SU(3)C, SU(2)L, U(1)Y ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Notice that we assume there is only one gen- eration of the fermion field F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Then we can read out the following SM gauge invariant Lagrangian Lint among the SM fields and new fields: Lint =yIαβℓαiτ 2ℓc βS∗ 1 + yIIαβec R,αdR,βS∗ 2 + yIIIαuR,αFS2 + yIV αFec R,αS1 + h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' + mFFF + 2 � i=1 m2 SiS† i Si + 2 � i=1 ξiH†HS† i Si + 2 � i,j=1 ζijS† i SiS† jSj , (20) which can generate the one-loop diagram for long-range 0νββ decay shown in figure 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' We see that the coupling yI is antisymmetric on the flavor indices, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=', yIαβ = −yIβα.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' It is important to note that the lepton fields inside the loop can be second or the third generation, while the external lepton fields can only be from the first generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' After electroweak symmetry breaking, the diagram NL3-1-3-2-7-1-4 reduces to the Feyn- man diagram displayed in the right panel of figure 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' With the interaction Lagrangian in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' (20), we can straightforwardly calculate this Feynman diagram, and find that the following effective operator is generated GF √ 2ϵV +A V +Ajµ V +AJµ,V +A , (21) 29 where jµ V +A and Jµ,V +A are defined in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' (2),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' and the coefficient ϵV +A V +A is given by ϵV +A V +A = √ 2 yIeτyIIτdyIIIuyIV emτ 64π2GFm3 F D � m2 τ m2 F ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' m2 S1 m2 F ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' m2 S2 m2 F � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' (22) The function D(x1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' x2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' x3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' x4) is the loop integral and it is given by D(x1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' x2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' x3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' x4) = 1 iπ2 � d4p 1 � p2 − x1 � � p2 − x2 � � p2 − x3 � � p2 − x4 � = x1 (1 − ln x1) (x1 − x2) (x1 − x3) (x1 − x4) + x2 (1 − ln x2) (x2 − x1) (x2 − x3) (x2 − x4) + x3 (1 − ln x3) (x3 − x1) (x3 − x2) (x3 − x4) + x4 (1 − ln x4) (x4 − x1) (x4 − x2) (x4 − x3) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' (23) 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='1 Prediction for neutrino mass With the three new fields in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' (19) and the relevant interactions, we find that the leading order contributions to the neutrino mass arise at three-loop level, and the corresponding Feynman diagrams are shown in figure 15 and figure 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' From the diagram of figure 15 after electroweak symmetry breaking, we see that the neutrino masses are really generated through the black box diagram shown in the right panel of figure 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' We recall that in the mass mechanism of 0νββ decay, the decay amplitude is proportional to the effective Majorana mass mββ with mββ = � i U 2 eimi , (24) where Uei denote the elements of the neutrino mixing matrix and mi refer to the light neutrino mass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' It is known that the effective neutrino mass mββ is exactly the (ee) entry of the Majorana neutrino mass matrix in the charged lepton diagonal basis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' It is remarkable that all the diagrams in figure 16 generate neutrino mass matrices with vanishing diagonal entries, while the diagrams in figure 15 can produce non-zero diagonal elements of the neutrino mass matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' As a consequence, the contributions of figure 16 to the 0νββ decay via mass mechanism are negligible, and it is sufficient to focus on the diagrams in figure 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' After the electroweak symmetry breaking, figure 15 produces neutrino masses and the dominant contribution arises from the exchange of the heavy top quark, bottom quark and tau.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' From the bottom panel of figure 15,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' one can straightforwardly calculate the expression of the neutrino mass matrix element as follows (mν)αβ = 3g2 (16π2)3Vtb y∗ IIτby∗ IIIt mτmbmtmeβ m2 WmF � � �y∗ Iατy∗ IV βM � � m2 b m2 F ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' m2 eβ m2 F ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' m2 W m2 F ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' m2 τ m2 F ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' m2 S1 m2 F ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' m2 t m2 F ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' m2 S2 m2 F � � + (α ↔ β) � � � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' (25) where g is the gauge coupling constant of SU(2)L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Vtb is the (33) entry of the Cabibbo- Kobayashi-Maskawa (CKM) quark mixing matrix,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' and M denotes a three-loop integral,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' M (x1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' x2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' x3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' x4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' x5,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' x6,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' x7,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' x8) 30 ℓ H ℓ H ℓ eR dR Q uR H eR S1 F S2 Above EW scale: ℓ H ℓ H ℓ eR dR Q uR H eR S1 F S2 ναL νβL τ b t W eβ S1 F S2 Below EW scale: Figure 15: The diagrams for the neutrino masses in the example model NL3-1-3-2-7-1-4 of long-range 0νββ decay,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' which can generate non-zero diagonal entries of the neutrino mass matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 31 ℓ ℓ H H ℓ W H Q dR S2 eR S1 F uR ℓ ℓ H H ℓ W H Q uR S2 F S1 eR dR ℓ H ℓ H ℓ eR H Q dR S2 eR S1 F uR ℓ H ℓ H ℓ eR H Q uR S2 F S1 eR dR ℓ ℓ H H ℓ W Q uR S2 F S1 eR dR Q Figure 16: The diagrams for the neutrino masses in the example model NL3-1-3-2-7-1-4 of long-range 0νββ decay, for which the diagonal entries of the neutrino mass matrix is vanish- ing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Notice that the inner loops can not be compressed to tree-level renormalizable vertices due to the antisymmetric nature of some SU(2)L contractions and the chiral structure of the SM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 32 = � 1 iπ2 �3 � d4k1d4k2d4k3 � 4x3 − k2 2 � 1 k2 1 − x1 1 k2 2 − x2 1 k2 2 − x3 1 k2 3 − x4 1 k2 3 − x5 1 (k1 − k2)2 − x6 1 (k2 − k3)2 − x7 1 (k3 − k1)2 − x8 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' (26) Once the masses of the new fields are specified, the three-loop integrals M can be computed numerically [41,42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='2 Half-life time of 0νββ decay The neutrinoless double beta decay has been discussed in the framework of effective field theory [20], and the contribution of lepton number violating operator up to dimension seven have been studied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' The inverse half-life time of the 0νββ decay can be generally expressed as [20] T −1 1/2 = g4 A � � �G01|Aν|2 + 4G02|AE|2 + 2G04 � |Ame|2 + Re � A∗ meAν �� + G09|AM|2 −2G03 Re � AνA∗ E + 2AmeA∗ E � + G06 Re (AνA∗ M) � � � , (27) where Aν, AE, Ame, AM depend on nuclear matrix elements and Wilson coefficients of the ∆L = 2 operators, and their explicit expressions given in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' [20] are a bit lengthy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Moreover, G0i are phase space factors and gA is the well-known unquenched axial coupling, we adopt the values of G0i and gA listed in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' As shown in previous section, the mediators of the long-range 0νββ decay model can generate non-vanishing light neutrino masses at three-loop level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Therefore both the long- range mechanism and the mass mechanism contribute to the 0νββ decay, and these two contributions should be added coherently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' The effective Majorana mass mββ in mass mech- anism leads to non-vanishing Aν, and the Wilson coefficient ϵV +A V +A in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' (21) gives rise to the parameters AE and Ame, Aν = mββ me V 2 udMν, AE = VudϵV +A V +AME,R, Ame = VudϵV +A V +AMme,R , (28) where me is the mass of electron, Vud refers to the (11) entry of the CKM matrix, Mν,ME,R and Mme,R are the nuclear matrix elements and one should reply on certain nuclear models to calculate their values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Hence the half-life of 0νββ decay in our model can be reduced to T −1 1/2 = g4 A � G01|Aν|2 + 4G02|AE|2 + 2G04|Ame|2 +2G04|Ame| |Aν| cos φ − 2G03 � |Aν||AE| cos φ + 2|Ame| |AE| � � , (29) where φ denotes the relative phase between mββ and ϵV +A V +A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' We show the constraints of the current and forthcoming 0νββ decay experiments on the effective Majorana neutrino mass 33 |mββ| and the long-range coupling |ϵV +A V +A| in figure 17, where the values of phase space factor and nuclear matrix elements are adopted from Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' [20,43].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' It is known that the neutrino mass is tightly constrained by the Planck measurements of the cosmic microwave background anisotropies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Assuming the standard minimal ΛCDM model and combining with baryon acoustic oscillation measurements, the most stringent bound on neutrino mass is � i mνi < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='12 eV at 95% confidence level from the Planck collaboration [44].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Considering the values of the neutrino mass squared differences and mixing angles measured by the neutrino oscillation experiments [45], one can obtain that the effective Majorana neutrino mass is in the region: |mββ| ≤ 31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='12 meV for normal ordering (NO) neutrino mass spectrum and 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='62 meV ≤ |mββ| ≤ 51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='14 meV for inverted ordering (IO) neutrino mass, which are shown as vertical white bands in figure 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' The highlighted areas in figure 17 denote the allowed regions by the current limits and future sensitivities of the 0νββ decay half-life of the isotopes 76Ge and 136Xe, where the relative phase φ freely varies in the range 0 ≤ φ < 2π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' The next generation tonne-scale experiments of 0νββ decay would greatly increase the sensitivity by approximately two orders of magnitude, therefore the constraint on the parameter space would be improved considerably, as can be seen from figure 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' We notice that the constraint imposed by 136Xe is more stringent than that of 76Ge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' It is remarkable that the inverted ordering neutrino mass could potentially be excluded in the future when the experimental data of neutrino oscillation and Planck are taken into account.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' We proceed to discuss the relative size of the long-range mechanism and mass mechanism to the decay rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' As an estimation of order of magnitude, we assume that the new fields have the same mass mS1 = mS2 = mF = M and the new couplings in the Lagrangian of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' (20) have the same size yIαβ = yIIαβ = yIIIα = yIV α ≡ yeff which are taken to be real.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' From the expression of the neutrino mass matrix elements given in Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' (25), we see that the effective Majorana mass could scale as mββ ∼ 6g2 (16π2)3Vtb y4 eff mτmbmtme m2 WM , (30) where M is the characteristic mass scale of new particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Consequently the contribution of the mass mechanism to the 0νββ decay is proportional to y8 eff/M 2, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=', MC = g4 AG01|Aν|2 ∼ g4 AG01 V 4 ud|Mν|2 m2 e � 6g2 Vtby4 eff (16π2)3 mτmbmtme m2 W M �2 ∼ 5 × 10−27 yr−1 · y8 eff �1GeV M �2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' (31) Moreover, the Wilson coefficient ϵV +A V +A of the long-range operator in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' (22) scales as ϵV +A V +A ∼ √ 2 y4 effmτ 64π2GFM 3 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' (32) Hence the long-range contribution is proportional to y8 eff/M 6, LC = g4 A � 4G02|AE|2 + 2G04|Ame|2 − 4G03|Ame| |AE| � ∼ g4 A � 4G02|ME,R|2 + 2G04|Mme,R|2 − 4G03|ME,R| |Mme,R| � V 2 ud � √ 2y4 effmτ 64π2GFM 3 �2 34 0 20 40 60 80 100 120 140 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='5 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='5 |mββ|[meV] |ϵV+A V+A|[10-7] IO 0 20 40 60 80 100 120 140 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='5 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='5 |mββ|[meV] |ϵV+A V+A|[10-7] NO T1/2 Xe≥2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='30×1026yr T1/2 Xe≥1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='35×1028yr T1/2 Ge≥1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='80×1026yr T1/2 Ge≥1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='30×1028yr 0 20 40 60 80 100 120 140 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='5 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='5 |mββ|[meV] |ϵV+A V+A|[10-7] IO 0 20 40 60 80 100 120 140 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='5 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='5 |mββ|[meV] |ϵV+A V+A|[10-7] NO Figure 17: Constraints on the effective neutrino mass |mββ| and the long-range coupling |ϵV +A V +A|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' In the top panels, the highlighted regions represent the parameter space allowed by the current bounds T1/2(136Xe) > 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='3 × 1026 yr [1] and the future sensitivities T1/2(136Xe) > 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='35 × 1028 yr [46].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Similarly the bottom panels display the parameter space allowed by the current bounds T1/2(76Ge) > 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='8 × 1026 yr [47] and the future sensitivities T1/2(76Ge) > 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='3×1028 yr [48].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' The vertical white bands denote the generally allowed region of mββ for NO and IO neutrino mass spectrum when the experimental data of both neutrino oscillation [45] and Planck [44] are considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 35 ∼ 10−8 yr−1 · y8 eff �1GeV M �6 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' (33) We see that the long-range contribution is comparable to the mass mechanism (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=', LC/MC∼ 1) for the new particle mass M ∼ O(20) TeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' The long-range contribution dominates over the mass mechanism with LC/MC≫ 1 for M < 20 TeV, while the mass mechanism is dominant in the mass range M > 20 TeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' We plot the ratio of long-range contribution to mass mechanism with respect to the mass M in figure 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' We see the ratio LC/MC decreases with the new physics mass scale M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 76Ge 136Xe 1 101 102 103 10-6 10-4 10-2 1 102 104 106 M[TeV] LC/MC Figure 18: The ratio of the long-range mechanism to the mass mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' In the figure, LC= g4 A � 4G02|AE|2 + 2G04|Ame|2 − 4G03|Ame| |AE| � denotes the long-range contribution to 0νββ decay, and MC=g4 AG01|Aν|2 is the mass mechanism contribution to 0νββ decay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' The horizontal dash line, representing LC/MC = 1, indicates that the long-range contribution is equal to that of the mass mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' The values of phase space factors and nuclear matrix elements used in this figure are taken from [20,43].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' In figure 19, we plot the regions of the parameters yeff and M compatible with the current bounds and future sensitivities of 0νββ decay search in the isotopes 136Xe and 76Ge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' We see that there are still sizable parameter space in which the long-range contribution is dominant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 6 Summary and conclusions A lot of neutrino oscillation experiments have established that neutrinos have tiny masses, but the nature of neutrinos is still unknown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' If neutrinos are Majorana particles, the light 36 2 4 6 8 10 0 1 2 3 4 5 M[TeV] yeff 2 4 6 8 10 0 1 2 3 4 5 M[TeV] yeff T1/2 Xe≥2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='30×1026yr T1/2 Ge≥1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='80×1026yr T1/2 Xe≥1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='35×1028yr T1/2 Ge≥1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='30×1028yr Figure 19: The constraint on the effective coupling yeff and new particle mass M by the 0νββ decay of 136Xe and 76Ge, where the highlighted regions are allowed by the 0νββ decay search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' The horizontal grey band is excluded by the perturbative constraint yeff ≤ √ 4π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' neutrino exchange between two charged current interaction vertices can leads to 0νββ decay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' This is the so-called mass mechanism, it is not a priori guaranteed to be the dominant contribution in all models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' The different possibilities mediating 0νββ decay can be generally classified as short-range mechanism, long-rang mechanism and mass mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' In the present work, we have performed a systematical decomposition of the dimension-7 long- range 0νββ decay operators at one-loop level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' After removing the non-renormalizable topologies and the non-genuine topologies which are one-loop corrections to the tree-level UV completions, we find that there are only 3 genuine one-loop topologies shown in figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Subsequently we specify the Lorentz nature of both internal and external fields, these 3 topologies give rise to 8 diagrams in the electroweak basis, as displayed in figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' In combination with the possible SM quantum number assignments listed in tables 5, 6, 7, 8 for the each line, one can construct novel one-loop 0νββ decay models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Our results can serve as a guide for the construction of one-loop 0νββ decay models and for the study of the phenomenology of these models at colliders or high luminosity facilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' The long-range 0νββ decay operators violate lepton number by two unit, consequently the mediators of 0νββ decay models generally generate Majorana neutrino masses, as shown in the black box diagram in the right panel of figure 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' One expects that the long-range 0νββ decay models of one-loop can give the dominant contribution to the decay ampli- tude in certain parameter space if the neutrino mass is generated at two-loop and higher levels, otherwise the long-range contribution should be subdominant to the mass mecha- nism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Therefore both tree-level and one-loop level contributions to neutrino mass should be forbidden in a genuine one-loop model of long-range 0νββ decay, consequently certain SM 37 quantum number assignments for the internal fields are excluded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Furthermore, we present an example of one-loop 0νββ decay model with three-loop neu- trino masses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' This example requires two new scalar fields and a color singlet vector-like fermion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' The predictions for the neutrino mass and 0νββ decay are studied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' The con- straints on the couplings and new physics scale from the 0νββ decay search in the isotopes 76Ge and 136Xe are discussed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' In this model, the long-range contribution is dominant over the mass mechanism for the new particle mass M < 20 TeV, while the mass mechanism is dominant in the mass range M > 20 TeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Thus we expect this model could be tested at the LHC, or at least LHC can constrain the new messenger fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Acknowledgements PTC and GJD are supported by the National Natural Science Foundation of China un- der Grant Nos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 11975224, 11835013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' CYY is supported in part by the Grants No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' NSFC- 11975130, No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' NSFC-12035008, No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' NSFC-12047533, the Helmholtz-OCPC International Postdoctoral Exchange Fellowship Program, the National Key Research and Development Program of China under Grant No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 2017YFA0402200, the China Postdoctoral Science Foun- dation under Grant No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 2018M641621, and the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy — EXC 2121 “Quan- tum Universe” —390833306.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' References [1] KamLAND-Zen Collaboration, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Abe et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=', “First Search for the Majorana Nature of Neutrinos in the Inverted Mass Ordering Region with KamLAND-Zen,” arXiv:2203.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='02139 [hep-ex].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' [2] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Schechter and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Valle, “Neutrinoless Double beta Decay in SU(2) x U(1) Theories,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' D 25 (1982) 2951.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' [3] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Päs, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Hirsch, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Klapdor-Kleingrothaus, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Kovalenko, “A superformula for neutrinoless double beta decay II: The short range part,” Physics Letters B 498 no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 1-2, (Jan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=', 2001) 35–39, arXiv:hep-ph/0008182.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' [4] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Päs, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Hirsch, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Klapdor-Kleingrothaus, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Kovalenko, “Towards a superformula for neutrinoless double beta decay,” Physics Letters B 453 no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 3-4, (May, 1999) 194–198, arXiv:hep-ph/9804374.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' [5] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Babu and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Leung, “Classification of effective neutrino mass operators,” Nuclear Physics B 619 no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' OSU-HEP-01-02, UDHEP-02-01, (2001) 667–689, arXiv:hep-ph/0106054.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' [6] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Bonnet, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Hirsch, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Ota, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Winter, “Systematic decomposition of the neutrinoless double beta decay operator,” Journal of High Energy Physics 2013 no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 3, (Mar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=', 2013) 55, arXiv:1212.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='3045.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 38 [7] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='-T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Chen, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Ding, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Yao, “Decomposition of d = 9 short-range 0νββ decay operators at one-loop level,” JHEP 12 (2021) 169, arXiv:2110.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='15347 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' [8] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Mohapatra, “New Contributions to Neutrinoless Double beta Decay in Supersymmetric Theories,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' D 34 (1986) 3457–3461.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' [9] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Hirsch, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Klapdor-Kleingrothaus, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Kovalenko, “New constraints on R-parity broken supersymmetry from neutrinoless double beta decay,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 75 (1995) 17–20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' [10] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Hirsch, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Klapdor-Kleingrothaus, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Kovalenko, “Supersymmetry and neutrinoless double beta decay,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' D 53 (1996) 1329–1348, arXiv:hep-ph/9502385.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' [11] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Babu and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Mohapatra, “New vector - scalar contributions to neutrinoless double beta decay and constraints on R-parity violation,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 75 (1995) 2276–2279, arXiv:hep-ph/9506354.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' [12] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Pas, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Hirsch, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Klapdor-Kleingrothaus, “Improved bounds on SUSY accompanied neutrinoless double beta decay,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' B 459 (1999) 450–454, arXiv:hep-ph/9810382.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' [13] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Mohapatra and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Senjanovic, “Neutrino Masses and Mixings in Gauge Models with Spontaneous Parity Violation,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' D 23 (1981) 165.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' [14] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Deppisch, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Gonzalo, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Patra, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Sahu, and U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Sarkar, “Double beta decay, lepton flavor violation, and collider signatures of left-right symmetric models with spontaneous D-parity breaking,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' D 91 no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 1, (2015) 015018, arXiv:1410.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='6427 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' [15] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Borah, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Dasgupta, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Patra, “Neutrinoless double beta decay in minimal left–right symmetric model with universal seesaw,” Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' A 33 no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 35, (2018) 1850198, arXiv:1706.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='02456 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' [16] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Li, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Ramsey-Musolf, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Vasquez, “Left-Right Symmetry and Leading Contributions to Neutrinoless Double Beta Decay,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 126 no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 15, (2021) 151801, arXiv:2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='01257 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' [17] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Hirsch, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Klapdor-Kleingrothaus, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Kovalenko, “New leptoquark mechanism of neutrinoless double beta decay,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' D 54 (1996) R4207–R4210, arXiv:hep-ph/9603213.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' [18] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Choubey, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Duerr, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Mitra, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Rodejohann, “Lepton Number and Lepton Flavor Violation through Color Octet States,” JHEP 05 (2012) 017, arXiv:1201.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='3031 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' [19] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Brahmachari and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Ma, “Neutrinoless double beta decay with negligible neutrino mass,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' B 536 (2002) 259–262, arXiv:hep-ph/0202262.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 39 [20] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Cirigliano, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Dekens, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' de Vries, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Graesser, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Mereghetti, “Neutrinoless double beta decay in chiral effective field theory: Lepton number violation at dimension seven,” JHEP 12 no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' LA-UR-17-27799, NIKHEF-2017-039, (2017) 082, arXiv:1708.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='09390 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' [21] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Cirigliano, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Dekens, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' de Vries, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Graesser, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Mereghetti, “A neutrinoless double beta decay master formula from effective field theory,” JHEP 12 (2018) 097, arXiv:1806.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='02780 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' [22] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Deppisch, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Hirsch, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Päs, “Neutrinoless Double Beta Decay and Physics Beyond the Standard Model,” Journal of Physics G: Nuclear and Particle Physics 39 no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 12, (Dec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=', 2012) 124007, arXiv:1208.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='0727.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' [23] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Helo, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Hirsch, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Ota, “Long-range contributions to double beta decay revisited,” JHEP 06 (2016) 006, arXiv:1602.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='03362 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' [24] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Lehman, “Extending the Standard Model Effective Field Theory with the Complete Set of Dimension-7 Operators,” Physical Review D 90 no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 12, (Dec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=', 2014) 125023, arXiv:1410.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='4193.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' [25] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Liao and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='-D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Ma, “An explicit construction of the dimension-9 operator basis in the standard model effective field theory,” JHEP 11 (2020) 152, arXiv:2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='08125 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' [26] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Antusch, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Baumann, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Fernandez-Martinez, “Non-Standard Neutrino Interactions with Matter from Physics Beyond the Standard Model,” Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' B 810 (2009) 369–388, arXiv:0807.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='1003 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' [27] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Gavela, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Hernandez, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Ota, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Winter, “Large gauge invariant non-standard neutrino interactions,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' D 79 (2009) 013007, arXiv:0809.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='3451 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' [28] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Bonnet, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Hirsch, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Ota, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Winter, “Systematic study of the d=5 Weinberg operator at one-loop order,” JHEP 07 (2012) 153, arXiv:1204.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='5862 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' [29] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Aristizabal Sierra, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Degee, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Dorame, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Hirsch, “Systematic classification of two-loop realizations of the Weinberg operator,” JHEP 03 (2015) 040, arXiv:1411.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='7038 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' [30] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Cepedello, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Fonseca, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Hirsch, “Systematic classification of three-loop realizations of the Weinberg operator,” JHEP 10 (2018) 197, arXiv:1807.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='00629 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' [Erratum: JHEP 06, 034 (2019)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' [31] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Yao and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Ding, “Systematic Study of One-Loop Dirac Neutrino Masses and Viable Dark Matter Candidates,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' D 96 no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 9, (2017) 095004, arXiv:1707.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='09786 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' [Erratum: Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='D 98, 039901 (2018)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' [32] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Yao and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Ding, “Systematic analysis of Dirac neutrino masses from a dimension five operator,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' D 97 no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 9, (2018) 095042, arXiv:1802.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='05231 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 40 [33] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Centelles Chuliá, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Cepedello, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Peinado, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Srivastava, “Systematic classification of two loop d = 4 Dirac neutrino mass models and the Diracness-dark matter stability connection,” JHEP 10 (2019) 093, arXiv:1907.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='08630 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' [34] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Jana, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Vishnu, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Saad, “Minimal realizations of Dirac neutrino mass from generic one-loop and two-loop topologies at d = 5,” JCAP 04 (2020) 018, arXiv:1910.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='09537 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' [35] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='-T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Chen, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Ding, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Yao, Supplementary material: Decomposition of d = 7 long-range 0νββ decay operators at one-loop level, 2023 (accessed January 9, 2023).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' http: //staff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='ustc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='cn/~dinggj/supplementary_materials/Long_range_0nbb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='zip.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' [36] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Fonseca, “GroupMath: A Mathematica package for group theory calculations,” Computer Physics Communications 267 (Oct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=', 2021) 108085, arXiv:2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='01764 [hep-ph, physics:hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' [37] Particle Data Group Collaboration, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Workman, “Review of Particle Physics,” PTEP 2022 (2022) 083C01.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' [38] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Fonseca, “The Sym2Int program: Going from symmetries to interactions,” Journal of Physics: Conference Series 873 (July, 2017) 012045, arXiv:1703.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='05221.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' [39] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Fonseca, “Enumerating the operators of an effective field theory,” Physical Review D 101 no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 3, (Feb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=', 2020) 035040, arXiv:1907.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='12584 [hep-ph, physics:hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' [40] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Nogueira, “Automatic feynman graph generation,” Journal of Computational Physics 105 no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' IFM-7-91, (1993) 279–289.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' [41] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Martin and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Robertson, “Evaluation of the general 3-loop vacuum Feynman integral,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' D 95 no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 1, (2017) 16008, arXiv:1610.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='07720 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' [42] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Freitas, “Three-loop vacuum integrals with arbitrary masses,” J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' High Energy Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 2016 no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 11, (Nov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=', 2016) 145, arXiv:1609.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='09159.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' [43] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Hyvärinen and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Suhonen, “Nuclear matrix elements for 0νββ decays with light or heavy Majorana-neutrino exchange,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' C 91 no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 2, (2015) 024613.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' [44] Planck Collaboration, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Aghanim et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=', “Planck 2018 results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Cosmological parameters,” Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 641 (2020) A6, arXiv:1807.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='06209 [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='CO].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' [Erratum: Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 652, C4 (2021)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' [45] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Esteban, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Gonzalez-Garcia, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Maltoni, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Schwetz, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Zhou, “The fate of hints: updated global analysis of three-flavor neutrino oscillations,” JHEP 09 (2020) 178, arXiv:2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='14792 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' [46] nEXO Collaboration, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Adhikari et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=', “nEXO: neutrinoless double beta decay search beyond 1028 year half-life sensitivity,” J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' G 49 no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 1, (2022) 015104, arXiv:2106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='16243 [nucl-ex].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 41 [47] GERDA Collaboration, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Agostini et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=', “Final Results of GERDA on the Search for Neutrinoless Double-β Decay,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 125 no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 25, (2020) 252502, arXiv:2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='06079 [nucl-ex].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' [48] LEGEND Collaboration, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' Abgrall et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=', “The Large Enriched Germanium Experiment for Neutrinoless ββ Decay: LEGEND-1000 Preconceptual Design Report,” arXiv:2107.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='11462 [physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content='ins-det].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} +page_content=' 42' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/YtE0T4oBgHgl3EQfmwGE/content/2301.02503v1.pdf'} diff --git a/Z9AyT4oBgHgl3EQf9vq-/content/tmp_files/2301.00881v1.pdf.txt b/Z9AyT4oBgHgl3EQf9vq-/content/tmp_files/2301.00881v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..8148430d4162b80d9604eeb4596f515cef7cb6a6 --- /dev/null +++ b/Z9AyT4oBgHgl3EQf9vq-/content/tmp_files/2301.00881v1.pdf.txt @@ -0,0 +1,1524 @@ +Draft version January 4, 2023 +Typeset using LATEX twocolumn style in AASTeX631 +PHANGS-JWST First Results: The Dust Filament Network of NGC 628 and its Relation to Star +Formation Activity +David A. Thilker +,1 Janice C. Lee +,2 Sinan Deger +,3, 4 Ashley T. Barnes +,5 Frank Bigiel +,5 +M´ed´eric Boquien +,6 Yixian Cao +,7 M´elanie Chevance +,8, 9 Daniel A. Dale +,10 Oleg V. Egorov +,8, 11 +Simon C. O. Glover +,12 Kathryn Grasha +,13 Jonathan D. Henshaw +,14, 15 Ralf S. Klessen +,12, 16 +Eric Koch +,17 J. M. Diederik Kruijssen +,9 Adam K. Leroy +,18 Ryan A. Lessing +,1 Sharon E. Meidt +,19 +Francesca Pinna +,20 Miguel Querejeta +,21 Erik Rosolowsky +,22 Karin M. Sandstrom +,23 +Eva Schinnerer +,24 Rowan J. Smith +,25 Elizabeth J. Watkins +,8 Thomas G. Williams +,24 +Gagandeep S. Anand +,26 Francesco Belfiore +,27 Guillermo A. Blanc +,28, 29 Rupali Chandar +,30 +Enrico Congiu +,29 Eric Emsellem +,31, 32 Brent Groves +,33, 13 Kathryn Kreckel +,8 Kirsten L. Larson +,34 +Daizhong Liu +,35 Ismael Pessa +,24, 36 and Bradley C. Whitmore +26 +ABSTRACT +PHANGS-JWST mid-infrared (MIR) imaging of nearby spiral galaxies has revealed ubiquitous fil- +aments of dust emission in intricate detail. We present a pilot study to systematically map the dust +filament network (DFN) at multiple scales between 25–400 pc in NGC 628. MIRI images at 7.7, 10, 11.3 +and 21µm of NGC 628 are used to generate maps of the filaments in emission, while PHANGS-HST +B-band imaging yields maps of dust attenuation features. We quantify the correspondence between +filaments traced by MIR thermal continuum / polycyclic aromatic hydrocarbon (PAH) emission and +filaments detected via extinction / scattering of visible light; the fraction of MIR flux contained in +the DFN; and the fraction of HII regions, young star clusters and associations within the DFN. We +examine the dependence of these quantities with the physical scale at which the DFN is extracted. +With our highest resolution DFN maps (25 pc filament width), we find that filaments in emission and +attenuation are co-spatial in 40% of sight lines, often exhibiting detailed morphological agreement; +that ∼30% of the MIR flux is associated with the DFN; and that 75–80% of HII regions and 60% of +star clusters younger than 5 Myr are contained within the DFN. However, the DFN at this scale is +anti-correlated with looser associations of stars identified using PHANGS-HST near-UV imaging. We +discuss the impact of these findings for studies of star formation and the ISM, and the broad range of +new investigations enabled with multi-scale maps of the DFN. +Keywords: Interstellar medium (847), Interstellar filaments (842), Interstellar dust (846), Dust contin- +uum emission (412), Extinction (505), Star formation (1569), Star forming regions (1565) +1. INTRODUCTION +Two +overwhelming +impressions +from +inspecting +JWST images of nearby galaxies are the sheer number +of resolved stars seen in the near-IR (NIR) andthe stun- +ning degree of structured, filamentary mid-IR (MIR) +emission originating from small dust grains and poly- +cyclic aromatic hydrocarbons (PAHs) in the interstel- +lar medium (ISM). JWST provides the spatial resolu- +Corresponding author: David A. Thilker +dthilker@jhu.edu +tion necessary to cleanly decompose the observed MIR +dust emission into filament features, discrete compact +sources, and a diffuse component throughout the Local +Volume (d ≲11 Mpc) and beyond, as could only pre- +viously be done in the Local Group (Hinz et al. 2004; +Barmby et al. 2006; Verley et al. 2007, 2009). This is of +astrophysical importance not only because dust plays a +central role in enabling star formation, but also hides the +youngest clusters and star-forming regions from view at +short wavelengths. In HST optical multi-color imaging +of star-forming galaxies, dust lanes stand out as highly +structured attenuation features (La Vigne et al. 2006; +arXiv:2301.00881v1 [astro-ph.GA] 2 Jan 2023 + +ID2 +Dong et al. 2016) occasionally punctuated by H ii re- +gions and clusters that have pierced the veil of their +dusty natal molecular cloud. +The observation of such abundant organized extra- +galactic structure in dust emission and attenuation is +tantalising because studies of the cold gas and dust in +the Milky Way have revealed filaments (Jackson et al. +2010) of length >100 pc that have even been dubbed +the ‘bones’ of the Milky Way’s cold ISM (Goodman +et al. 2014; Ragan et al. 2014; Zucker et al. 2015; +Soler et al. 2020). +Indeed, much recent work in the +Milky Way points towards a view of the cold, dusty +star-forming medium that is filamentary and multi-scale +(Hacar et al. 2022; Pineda et al. 2022; Zucker et al. +2018), very different from the classical ‘spherical molec- +ular cloud’. Filamentary structure even persists at sub- +pc, cloud-substructure scales (e.g. Andr´e et al. 2010, +2014) though, in the Local Volume extragalactic con- +text, we are limited to studying larger filaments (akin +to those of Syed et al. 2022). The shift to a filament- +centered paradigm implies that criteria for stability and +fragmentation change, becoming a mass per unit length +threshold rather than a more traditional Jeans mass ar- +gument. All this filamentary structure seeds star forma- +tion and determines the rate and efficiency of collapse, +and defines the medium that the stellar feedback is sub- +sequently driven into, thereby determining how feedback +drives the baryon cycle within galaxies. +A revolution in our view of the dust structure in +nearby galaxies is underway, having overcome the bar- +rier of resolution with the combined capabilities of +JWST and HST . This enhanced extragalactic perspec- +tive is a critical advance we can now quantify entire +filament networks on scales ranging from the size of in- +dividual GMCs up to morphological features dominat- +ing entire galaxies and reveal their intimate connection +with respect to star formation, feedback, and dynami- +cal mechanisms. This new era of dusty ISM cartogra- +phy will leverage representative galaxy samples to pro- +vide systematic answers to: +how the prevalence and +properties of these filamentary features may depend on +galactic environment; whether they universally form the +backbone of the cold ISM, through comparison to CO +maps; and how the joint dust and molecular gas distri- +bution is related to structures like spiral arms and bars, +contrasted to high-resolution pc-scale UV+IR tracers +of star formation activity from HST and JWST . Crit- +ically, the new observations can be directly compared +to state-of-the-art galaxy simulations (e.g. Smith et al. +2014, 2020; Duarte-Cabral et al. 2015; Duarte-Cabral & +Dobbs 2017; Tress et al. 2020; Treß et al. 2021; Jeffreson +et al. 2020). +JWST resolution and depth are sufficient to re- +cover filamentary dust emission features, at GMC- +scales, analogous to those of the Milky Way in galax- +ies out to the distance of the Virgo cluster. This let- +ter focuses on NGC 628 (also known as Messier 74, +‘The Phantom Galaxy’) an archetypal face-on SA(s)c +galaxy +Buta +et +al. +(2015). +NGC 628 +is +nearby +(d = 9.84±0.03 Mpc; Anand et al. 2021a,b), star-forming +(SFR = 1.8 ± 0.45 M⊙yr−1), massive (M∗ = 2.2 ± 0.56 × +1010 M⊙) and viewed at low inclination (i ∼ 9◦ ± 12◦, +Lang et al. 2020). NGC 628 is part of a broader sample +of 19 “main sequence” star-forming galaxies for which +systematic, uniform surveys with HST (Lee et al. 2022), +ALMA (Leroy et al. 2021) VLT-MUSE (Emsellem et al. +2022) and now JWST (Lee et al. in prep.) have been +carried out by the PHANGS (Physics at High Angular +resolution in Nearby GalaxieS) collaboration.1 +2. DATA +2.1. PHANGS-JWST imaging +NGC 628 is one of the initial targets observed for the +PHANGS-JWST Cycle 1 Treasury project (GO 2107, +PI J. Lee). +Our observations of NGC 628 target the +central region (Rgal ≲ 5 kpc) of the star-forming disk, +to overlap areas where HST , ALMA, and MUSE data +have been obtained.2 +The dataset includes imaging +with NIRCam (F200W, F300M, F335M and F360M) +and MIRI (F770W, F1000W, F1130W and F2100W). +Photospheric emission from resolved stellar populations +is major component in the four NIRCam bands (except- +ing F335M which primarily probes the 3.3µm PAH fea- +ture), whereas MIRI traces the ISM (both PAHs and +hot, small dust grains). +Resolution varies from 0.066 +to 0.12′′(NIRCam) and 0.25 to 0.67′′(MIRI). For MIRI, +this corresponds to 12–32 pc at the distance of NGC 628. +A detailed description of the PHANGS-JWST observa- +tions and data reduction is presented by Lee et al. (in +prep.). Here, we focus on MIRI imaging, deferring anal- +ysis of filamentary structure seen in the 3.3µm PAH +feature to future work in anticipation of improved as- +trometric alignment among the PHANGS-JWST NIR- +Cam and MIRI imaging. Of particular importance to +the analysis in Sec. 4.2 is the sky background adopted +for the MIRI data. We use background-corrected images +which have been tied to the sky level measured in wide- +field Spitzer and WISE archival imaging, as described in +1 https://sites.google.com/view/phangs/home +2 Footprint maps of the HST , ALMA, and MUSE observations are +available at https://archive.stsci.edu/hlsp/phangs-hst. Science- +ready PHANGS-HST images are also available for download. + +3 +Figure 1. +Left: +Pre-processed B-band HST image, filtered to remove compact positive sources but retain small nega- +tive/concave morphological features. Center: Filament masks for visible attenuation (blue) and MIR emission (red) extracted +at scale of 25 pc. Areas of overlap appear magenta. Right: JWST /MIRI F770W image. North is up, East is left, and the field +of view spans 7.3 kpc from top to bottom. The figure only shows a portion of the area observed with JWST . The entire image +may be seen in Figs. 5 and A1–A4. +the Appendix of Leroy et al. (in prep.). The MIRI back- +ground levels are currently uncertain by ±0.1 MJy sr−1. +2.2. PHANGS-HST imaging +The HST NUV-U-B-V-I (F275W, F336W, F435W, +F555W, F814W) observations of the central NGC 628 +disk we use were obtained by LEGUS (GO 13364, +Calzetti et al. 2015) using WFC3/UVIS for NUV and +U, and by R. Chandar (GO 10402) using ACS/WFC +for B, V and I. All data were reprocessed by PHANGS- +HST. Full details are given in (Lee et al. 2022). The +ACS/WFC B-band images we use to identify dust lanes +in attenuation have resolution (∼ 0.09′′, 4.3 pc), approx- +imately 2.5× finer than MIRI F770W. +2.3. MUSE H ii region catalog +We use the nebular catalog of H ii regions derived +from the integral field unit (IFU) spectroscopy of the +PHANGS-MUSE survey Emsellem et al. (2022). +For +NGC 628, the ”convolved, optimized” resolution in +PHANGS-MUSE DR 2.2 is 0.92′′, corresponding to a +spatial resolution of 44 pc. +Santoro et al. (2022) and +Groves et al. (subm.) +used PHANGS-MUSE data to +create a catalog of H ii regions and provide fluxes cor- +rected for Milky Way and internal extinction. +Only +star-forming regions classified using the BPT diagram +(Baldwin et al. 1981) are retained in our analysis. +2.4. HST stellar association and cluster catalogs +PHANGS-HST resolved stellar photometry has been +used to identify and characterize stellar associations +as summarized in (Lee et al. 2022) and described in +detail by Larson et al. (subm.). +Stellar clusters in +NGC 628 have been studied by Thilker et al. (2022). +PHANGS-HST catalogs are publicly available3. +For +both associations and clusters, fluxes for the five avail- +able HST bands were measured (using upper-limits in +non-detected photometric bands) and then age, mass +and reddening were estimated4 via fitting of observed +SEDs (Turner et al. 2021) to solar metallicity stellar +population models using cigale (Boquien et al. 2019). +We use the PHANGS-HST associations catalog based +on local over-densities of NUV point-like detections at a +scale of 32 pc for our analysis. The stellar associations +have ages ranging up to ∼102 Myr. We use a subset +3 https://archive.stsci.edu/hlsp/phangs-cat +4 Degeneracy between age and reddening is apparent for a subset +of objects, and could be more relevant in our dust filaments. + +4 +Figure 2. +Blue markings represent sight lines with +attenuation-only, magenta markings represent areas of over- +lap of between attenuation and emission, and red markings +account for sight lines with emission-only. Top: F770W. Bot- +tom: F2100W. Results generated for cumulative masks are +shown with points and sloping lines. +We disregard scales +> 200 pc (shown faded in the plot) because the filament +masks become unreliable (in the case of attenuation) or re- +dundant with smaller scale features (for emission). The first +bar of the F770W plot (25 pc) presents the measurement for +masks shown in Fig. 1. +selected to have age less than five Myr in order to limit +the population to the most recent star formation activ- +ity. Clusters for our analysis were also selected with the +same upper limit on age. +3. DUST FILAMENT ANALYSIS +3.1. Filament extraction +We identify dust filaments using FilFinder (Koch +& Rosolowsky 2015). +This code applies an adaptive +thresholding algorithm and graph-based medial skele- +ton analysis to isolate and then characterize filaments. +Thresholding is conducted over local neighborhoods, al- +Figure 3. +Top: For F770W, the fraction of pixels cov- +ered by a dust filament mask (emission or absorption) or left +unassigned to a dust filament. +Scales we elect to exclude +from the filament network (see text) are shown faded in the +plot. Bottom: Same, for F2100W. +lowing for the extraction of structure over a large dy- +namic range both in intensity and spatial scale (the lat- +ter when the code is run multiple times with different pa- +rameter choices). The potential effect of bright sources +interspersed in the web of filaments is mitigated by an +arctan intensity transform before thresholding. We use +a slightly modified version of FilFinder in which the +arctan transformed image is convolved to the filament +extraction scale before each run. In the current analy- +sis we only utilize the filament masks produced by the +code, leaving FilFinder’s skeleton analysis capabilities +for future work. +We +apply +FilFinder +independently +to +the +background-corrected image in each MIRI band and +to a pre-processed version of the B-band HST image (in +which attenuation features are most evident compared +to NUV, U, V, and I). + +Attenuation-only / Both / Emission-only +F770W +1.0 +0.8 +0.6 +0.4 +0.2 +0.0 +2535　50　70 100 140 200 280 400 +Filament extraction scale (pc)Attenuation-only / Both / Emission-only +F2100W +1.0 +0.8 +0.6 +0.4 +0.2 +0.0 +25 35　50 70 100 140 200 280 400 +Filament extraction scale (pc)F770W +100 +No filament (%) +80 +60 +Any Filament, [ +40 +20 +0 +25 +35 50 70 100 140 200 280 400 +Filament extraction scale (pc)F2100W +100 +No filament (%) +80 +60 +Any Filament, [ +40 +20 +0 +25 +35　50 70 100 140 200 280 400 +Filament extraction scale (pc)5 +For pre-processing the HST image, multi-scale median +filtering is used to suppress peak-like features over a +range in scale, while retaining small scale dips (concave +areas). Our specific filtering method follows from Hov- +ersten et al. (2011). At each pixel the output value is +assigned to be that location’s minimum in a stack of cir- +cular median filtered images. Filter kernel diameters are +taken from a ladder of physical scales (starting at the +resolution limit and proceeding up to 32 pc). The result +is that confusion by bright stars and stellar clusters is +greatly reduced, emphasizing the dust lane structures. +Fig. 1 (left) and Fig. 6 (left) show the pre-processed im- +age. FilFinder nominally operates by finding positive +filamentary features above the background. before pass- +ing the pre-processed B-band image to FilFinder, we +invert the sense of the intensity (subtracting the image +from a constant value equal to the maximum in the field +of view) +For both attenuation and emission, we use FilFinder +to identify potential filaments with narrow dimension +(width) starting at 25 pc then stepping by factors of +√ +2 +(0.15 dex) up to 400 pc (25, 35, 50, 70, 100, 140, 200, +280, 400 pc). The minimum scale of 25 pc corresponds to +approximately twice the PSF FWHM of MIRI F770W. +For F2100W analysis, we begin at the 35 pc scale due +to the larger F2100W PSF. FilFinder parameters are +set as follows: size thresh = 6πw2, adapt thresh = 2w, +glob thresh = 2σ above sky level, smooth size = 0.5w, +fill hole size = 0.5w2, where w is the extraction scale (in +pixels) and σ is the standard deviation noise level ex- +pected in the arctan transformed, convolved images. +In addition to the filament masks generated for ex- +traction at specific scales, we also produce masks repre- +senting the union of filaments detected cumulatively at +different scales. For these cumulative masks, we sum the +individual masks (for scales less than or equal to the cur- +rent scale) and then flatten the result, such that it has +a value of one anywhere a constituent scale contributes +filament coverage. The cumulative summed mask before +flattening is also retained, as it highlights the multi-scale +nature of the filament network. Appendix A presents +individual scale and cumulative multi-scale masks for +F770W, F2100W, and HST B-band as a Figure Set. +The wide range of scales initially allowed for fila- +ment extraction is exploratory. +In the second half of +Sec. 4.1), we argue that all emission and attenuation fil- +ament masks for scales > 200 pc not be used, although +we do include them in plots allowing for the reader to +make their own. +3.2. DFN characterization +For Sec. 4.1, we measure filament mask overlap cate- +gorizing each pixel as belonging to one of four classes: +(1) attenuation filament only, (2) emission filament only, +(3) both attenuation and emission filaments, or (4) no +filamentary features detected. Note that the sight line +fractions we report in Sec. 4.1 for classes (1)-(3) are nor- +malized to the total count of pixels with any detected +filamentary feature, rather than the total count of pixels +in the image. It is beyond the scope of the current study +to quantify the dependence of pixel classes on the depth +of the imaging – however, given the pervasive character +of the detected filament network, we suggest that at least +the F770W, F1000W, and F1130W observations are sen- +sitive enough to make this a moot point. Our F2100W +data is about 2× less sensitive in absolute terms of lim- +iting surface brightness, σI [MJy sr−1], and also suffers +from a similar loss in resolution compared to F770W. +These factors likely contribute to loss of some smaller +scale filamentary structure in the F2100W imaging. +Sec. 4.2 (flux fractions) requires local estimation of +the diffuse emission to obtain background-subtracted +filament flux. +the photutils (Bradley et al. 2022) +background2D code, supplying filament masks to indi- +cate which pixels the procedure should ignore. A mesh +of bins (each having size two-thirds the filament extrac- +tion scale) is defined, and the mode of unmasked pixels +is determined in each bin. These mesh modes are me- +dian filtered with a 3×3 boxcar (ignoring bins with too +many pixels masked as within a filament) and the result- +ing values are interpolated across the image grid. from +the input image and non-filament pixels are set to zero. +Integrating this result gives the background subtracted +flux of the filament structures, which is then divided +by the total flux in the MIRI footprint to obtain flux +fractions. +4. RESULTS +Figure 1 illustrates the dust lanes seen as deficits of +visible light (left) and dust emission filaments detected +in MIR emission (right). Plotted for a single extraction +scale (25 pc), the central panel emphasizes the detailed +coincidence between these two tracers of dust (blue = +attenuation, red = emission) in the interstellar medium, +with magenta indicating overlap. +It is clear that the +dust filament network (DFN) occupies a large fraction +of sight lines and contributes a significant fraction of the +MIR luminosity. Knots of emission from star-forming re- +gions are generally distributed throughout the filaments. +In this section, we quantify each of these statements. +Here we show results only for F770W and F2100W, +as the filament masks and measured quantities based on + +6 +F1000W and F1130W are consistent with F770W. Any +notable differences are discussed. +4.1. Contrasting views of the dust filament network +We start by highlighting the consistency between fil- +amentary attenuation (dust lane) features and web-like +MIR dust emission to illustrate the potential of using +HST -detected features as a high resolution proxy for the +dense dusty ISM morphology (and perhaps even molec- +ular gas5). +Fig. 2 shows the results of filament overlap analysis. +For the PAH-dominated bands (F770W, F1130W) and +10µm thermal emission traced by F1000W, in the top +panel of Fig. 2, we find that the percentage of sight +lines in common between visible attenuation and MIR +emission filaments is nearly 40%, at 25 pc and declines +smoothly with increasing scale (filament width). This +decline is due to more area becoming traced by attenua- +tion only for larger individual filament extraction scales. +The percentage of emission-only filament sight lines de- +clines a small amount from 25 pc to 200 pc. Overlap +statistics generated on the basis of cumulative multi- +scale masks show a different picture, in which the per- +centage of attenuation plus emission sight lines grows +with scale from just over 40% at 35 pc to 55% up to +200 pc. +This is a consequence of different extraction +scale masks picking up varied portions of the overall +web-like DFN. We return to this point further in the +current subsection (see Fig. 4 and Fig. 5). +In the bottom panel of Fig. 2, we show the overlap +for F2100W emission filaments with the dust lanes from +HST . At 21µm the percentage is 24% for 35 pc indi- +vidual extraction scale, substantially less than for the +three other bands, declining to ∼16% for 200 pc. For +all separate scales, attenuation-only sight lines amount +to more than 65% and emission-only ≲10%. Given that +the attenuation filament mask remains constant F770W +and F2100W, this could suggest that either we are sen- +sitivity limited for F2100W or the filamentary emis- +sion detected in 21µm imaging is less consistently recov- +ered into coherent structures. The latter interpretation +is supported by mask inspection in the figures of Ap- +pendix A, and by the fact that the morphology of the +F2100W image is more dominated by compact sources +(e.g. IR-bright star-forming regions, see Hassani et al. +in prep.) +than F770W, F1000W, and F1130W. This +serves as a reminder that we are tracing warm (140 K) +dust at 21µm, whereas the dust attenuation provides +a more complete inventory with respect to dust over a +5 The association between the DFN structures and 12CO(2-1)- +traced molecular gas will be investigated in a future study. +wide range of [cooler] temperatures. Nevertheless, the +overlap with the 200 pc cumulative multi-scale mask is +40% (only ∼1/3 less than for F770W). +In summary, the 40% level of pixel-by-pixel agreement +of the attenuation and emission filament masks at 25 pc +and the trend for the greatest agreement on the small- +est scales that the correspondence may be even tighter +if smaller physical scales are probed, such as in Local +Group galaxies. We stress that, although 40% overlap +may sound low, inspection of Fig. 1 shows that the de- +tailed morphology (e.g. extent, shape) of filaments that +are detected in attenuation and dust emission is fre- +quently rather well-matched. We also note that regions +of the filament network only found as dust emission are +expected due to line-of-sight effects: some filaments will +be positioned on the ‘back’ side of the face-on galaxy +disk, and could account for the majority of ‘emission- +only’ areas. Some attenuation-only regions also lie in +false-negatives for MIR dust emission on the scale of in- +terest, or lie in relatively MIR-faint, intermediate surface +brightness regions of the visible galaxy disk. False nega- +tives occur when a MIRI filament structure has a width +that is somewhat different than the visible attenuation +feature, or when scale-matched emission in the region is +biased against detection at the scale of interest (e.g. a +filament centered between brighter neighboring emission +features spaced by about the width of the FilFinder +adaptive thresholding box). +Figure 3 shows the division of sight lines between those +associated to a dust filament (here, either attenuation +or emission) and those that do not lie in a filament for +the particular extraction scale. The plots show very lit- +tle change between bands. We find that approximately +50–55% of sight lines are attributed to dust filaments +for scales 25–100 pc with no variation due to extrac- +tion scale, then a mild increase at larger scales (to ∼60– +65% for 200 pc). Cumulative multi-scale mask measure- +ments of the dust filament sight line fraction (dots and +lines in Fig. 3) steadily rise across the 25–200 pc range, +despite the constancy for individual extraction scales +smaller than 140 pc. Our filament masks are detecting +a morphologically diverse dusty ISM, Though beyond +the scope of this paper, it will be important to investi- +gate if the component is increasingly atomic-dominated +compared to narrower filaments. +Figure 4 illustrates the tendency for dust filament +masks to capture different morphological features when +extracted using varied scales. In particular, we show the +JWST F770W image in the top panel and HST B-band +in the bottom panel. Using red and blue lines, overplot- +ted on each of the images is a contour boundary of the +25 pc mask (dashed thin line) and 200 pc mask (solid + +7 +Figure 4. +Top: JWST F770W image. Dust emission filament mask boundaries are shown for: 25 pc dashed, thin red; 200 pc, +thick red; and cumulative 400 pc, dashed thin yellow. Bottom: B-band F435W HST image, with attenuation filament mask +coverage of 25 pc dashed, thin blue; 200 pc, thick blue. The scale bar in each panel is 1 kpc in length + +、8 +Figure 5. +JWST F770W image of NGC 628, overplotted +with the contours showing the coverage of multi-scale masks. +The maximum scale is as follows: green, 100 pc; yellow, +140 pc; red, 200 pc; cyan, 280 pc; magenta, 400 pc. +We +adopt 200 pc as a preferred value. The scale bar corresponds +to 1 kpc +thick line), with the variety of mask corresponding to +the dust detection property of each image (emission on +top, attenuation on bottom). +Many of the single ex- +traction scale 25 pc dust filaments are very long, with +l >1 kpc and have rather high aspect ratio. However, +there are also frequent cases of the 25 pc masks (dashed +thin lines) only including localized substructure within +larger coherent filaments left unjoined by small scale ex- +traction. This selective property of the filament identi- +fication outcome can be seen in spiral arms (markedly +less so in interarm regions) and in both emission and at- +tenuation. Conversely, the 200 pc filament masks (solid +thick lines) often entirely exclude areas with a significant +population of narrow GMC-scale width filaments. We +note that the 200 pc attenuation filament mask recov- +ers continuous spiral structure more effectively than the +F770W emission mask of the same scale. Additionally, +Fig. 4 demonstrates that the recovered dust attenuation +features can be quite modest in terms of apparent A(B). +Inspection in the peripheral areas of the HST panel nev- +ertheless suggests the majority of such filaments are real. +On the JWST image, we also plot a contour representing +the cumulative (up to 400 pc) emission filament mask +(dashed thin yellow). The 25 pc and 200 pc filament +structures alone do not include all portions of the DFN, +especially in dust emission. The yellow contour shows +how using a cumulative mask addresses this issue, link- +ing many smaller scale components. Using cumulative +masks with large upper scales can excessively broaden +the extent of filaments, and hence we urge caution in +the choice of the upper limit on multi-scale integration. +Fig. 5 provides empirical justification for maximum +scale on the basis of emission. The figure plots cumu- +lative F770W mask boundaries for different maximum +scales, starting at 100 pc (green), running through 140, +200, 280 pc (yellow, red, cyan), up to 400 pc (magenta). +The top layer contour (100 pc, green) already struc- +ture of the DFN, but several regions of seemingly con- +tiguous filamentary emission remain disconnected either +internally or to the network. By looking at other col- +ored contours emerging from under the green bound- +ary, one can infer how adding progressively larger scales +changes the network. The 200 pc cumulative mask (red) +appears to provide reliable recovery of all filamentary +emission structures without undue peripheral excess, al- +though 140 pc and 280 pc are probably also acceptable. +HST B-band filament extraction at 280 and 400 pc oc- +casionally confuses interarm gaps as attenuation. Such +large (> 200 pc) scales also push the limit of what can +be considered a filament in the sense of forming via tur- +bulent Jeans scale gravitational instabilities (see Meidt +et al. in prep.). +Fig. 6 presents a zoomed in view of a region east- +southeast of the galaxy center, showing the filtered B- +band data in comparison to an unprocessed version of +the same image and to F1000W data from JWST . Con- +tours of the 25 pc B-band and F1000W filaments are +overplotted. +This figure visually emphasizes the 40% +sight line overlap and morphological agreement at this +scale. +Fig. 6 also demonstrates feasibility to probe +even smaller scales in visible dust lanes across the en- +tire PHANGS-HST sample. Significant substructuring +(down to the ∼ 5 pc WFC3/UVIS resolution limit in +NGC 628) in attenuation of the features detected as dust +emission filaments at 25 pc scales is apparent. We fur- +ther expect HST to detect additional small scale fila- +ments beyond the limit of MIRI – several super nar- +row attenuation filaments without corresponding larger +scale intensity depression are apparent in other regions +of NGC 628. +Finally, Fig. 6 demonstrates that with +HST we will be able to reveal candidate features we +nickname ‘dust motes’ (examples marked with yellow +circles), essentially compact (≲ 10 pc), dark clouds we +cannot cleanly identify solely with JWST due to confu- + +9 +Figure 6. +Left: Subsection of our pre-processed B-band image, overlaid with contours corresponding to the filament masks +generated at 25 pc resolution in emission, red, and absorption, blue. Center: Unprocessed B-band image Right: JWST F1000W +image, also with the filament mask contours shown. Yellow circles surround three example dust motes. There are many more +in the field shown, left unmarked. Green circles surround three example candidate dusty stars, others are not marked. Circles +are 1′′ in diameter, equivalent to 48 pc at the distance of NGC 628 +sion with point-like dusty extreme AGB stars (Thilker +et al. in prep.) lying outside the emission filament net- +work (examples marked with green circles) in the short +wavelength MIRI images. These dust motes could be +individual molecular clouds in relative isolation. Their +size is comparable to the Taurus Molecular Cloud, al- +though Taurus is star-forming whereas the motes may +often be quiescent. A better Milky Way might be the +smallest scale clouds found in the 3D extinction maps of +e.g. Leike et al. (2020). Dust mote clouds are challeng- +ing to confirm with MIRI, but appear in the HST B- +band images before any pre-processing (Fig. 6 center). +PHANGS-JWST F335M 3.3µm PAH imaging (Sand- +strom et al. in prep.; Rodriguez et al. in prep.) +and +forthcoming PHANGS-HST Hα imaging (GO 17126, PI +R. Chandar) may prove useful to further vet dust can- +didates as a class. +4.2. Fraction of flux in MIR filament network +The relative amount of structured and unstructured +(diffuse) dust in a galaxy is fundamental metric of ISM +morphology and offers a basis for comparison with sim- +ulations that aim to understand the impact of factors +such as stellar feedback and dynamical influences (e.g. +Smith et al. 2020). As noted in Sec. 4.3, this observable +is also relevant to star formation rate (SFR) estimation. +We measure the fraction of flux contained within the ex- +tracted filaments compared to the total flux in the im- +age. As the filaments are brighter than their surround- +ings, this requires that we establish a local background +estimate at all locations in the image, which we do us- +ing the procedure given in Sec. 3. Figure 7 presents our +results concerning flux fraction as a function of filament +extraction scale. +We find that at the smallest independent extraction +scales considered (25 pc for F770W, F1000W, F1130W; +35 pc for F2100W), the background-subtracted filament +flux fractions are nearly 30% except for F2100W at +≈ 20%. The flux fraction is essentially constant versus +extraction scale for F770W, F1000, and F1130W, but +peaks at 35 pc and 200 pc for F2100W. The F2100W +flux fractions are always significantly less than all three +shorter wavelength MIRI bands. +Given the present +residual ± 0.1 MJy sr−1 uncertainty in the background +level of our MIRI images (see Sec. 2.1 and Leroy et al. +in prep.), we assess the impact this has on filament flux +fractions, by offsetting the image intensities by the un- +certainty in a positive and negative sense. Dashes over- +plotted on the bars of Fig. 7 indicate the resulting per- +turbed fractions. +Cumulative multi-scale mask filament flux fraction re- +sults are also shown in Fig. 7, indicated by the solid +lines and dots. As expected, the fraction increases as +progressively more individual masks are combined and +the maximum allowed extraction scale is increased. For +our choice of maximum scale (200 pc) the background- +subtracted filament flux is in the range 55% to 60% of +the total F770W, F1000W, and F1130W flux in the field. +At the same cumulative scale, the F2100W measurement +is 43%. Scatter due to uncertainty in background level + +10 +Figure 7. +Top: +Filament flux fraction in F770W ex- +pressed as percentage, with individual filament extraction +scales plotted as pink bars, and cumulative multi-scale re- +sults as solid lines and points. The faded region is shown +for completeness, although we adopt a maximum cumula- +tive scale of 200 pc. Horizontal dashes on each bar indicate +the one-sigma uncertainty of the flux fraction measurements, +obtained by perturbing the sky level in accord with the post- +pipeline calibration described by Leroy et al. (in prep.), Lee +et al. (in prep.). Dotted lines show the one-sigma range due +to uncertainty of cumulative flux fractions. Bottom: Same, +but for F2100W. +is also checked for cumulative values, and shown with +dotted lines on Fig. 7. +The impact is notably larger +than for individual scales, but is generally less than sys- +tematic uncertainty due to our choice of maximum scale +included in the DFN cumulative mask. +We note that if diffuse emission is neglected, rather +than subtracted away as in our analysis, the inte- +grated flux from the filament network becomes 40-100% +higher boosting the cumulative filament flux fractions to +∼80% for F770W, F1000W, and F1130W and 60% for +F2100W. +4.3. Linking the dust filament network to star +formation activity +The results of Sec. 4.2 confirm that more than half +of the MIR flux from NGC 628 originates in the intri- +cately structured filament network, with the only excep- +tion being for F2100W (43%). This outcome is what we +anticipated based on previous work for nearby galaxies +(Liu et al. 2011; Leroy et al. 2012; Crocker et al. 2013; +Calzetti 2013; Boquien et al. 2016; Kumari et al. 2020; +Belfiore et al. in prep.). It reinforces the necessity of +correcting the integrated MIR luminosity of a galaxy +for the presence of inherently diffuse emission heated by +older stellar populations, when using MIR to measure +current SFR (Lonsdale Persson & Helou 1987; Boquien +et al. 2016). One of the goals of PHANGS-JWST is to +clarify systematics of this correction. We can position- +ally test the linkage of the DFN to age-dated markers +of star formation events, checking whether all regions +of the filament network can be attributed to heating by +current star formation or if some filamentary structure +is effectively quiescent and should be removed alongside +diffuse emission when estimating SFR. Put differently, +perhaps only filamentary structure up to a certain max- +imum scale, or down to a limiting dust surface density, +is directly linked to the youngest stellar populations. +We take a first step toward the goal above by cross- +correlating the filament masks with the PHANGS- +MUSE H ii regions, plus PHANGS-HST young (≤ +5 Myr) clusters and associations, described in Sec. 2. +With these populations, we measure unweighted inclu- +sion fractions (number of objects contained within the +filament mask divided by the total count in the image +footprint) and also tracer-weighted inclusion fractions +(summing weights corresponding to SFR rather than ob- +ject counts). For weighting we use extinction corrected +L(Hα), effectively unobscured SFR, for H ii region popu- +lations; and M∗ / age ≈ effective SFR(5 Myr) for young +clusters and associations. +Fig. 8 plots the measured inclusion fractions for each +of the test populations. We begin by making general +comments about Fig. 8 which are applicable to all pan- +els. +We find that the inclusion fractions (at individ- +ual scales or cumulatively) are consistently maximized +for H ii regions but decline slightly when using young +clusters and dramatically using young associations, re- +gardless of scale or band. The inclusion fraction mea- +sured at individual filament extraction scales for H ii +regions and young clusters (≤ 5 Myr), decline from a +maximum at 25 pc until reaching 70–100 pc. For as- +sociations, there is far weaker, if any, dependence on +scale over the same range, but an apparent enhancement +at 140–200 pc scales. The random inclusion fractions + +F770W +100 +Filament flux fraction (as %) +80 +60 +40 +20 +0 +25 +35　5070 100 140 200 280 400 +Filament extraction scale (pc)F2100W +100 +Filament flux fraction (as %) +80 +60 +40 +20 +0 +25 +35　50　70 100 140 200 280 400 +Filament extraction scale (pc)11 +Figure 8. +Top: Filament inclusion fractions for various star formation event tracers (H ii regions, young clusters, young multi- +scale associations) versus the dust emission filament extraction scale. Bars indicate results for each individual extraction scale, +whereas lines and points indicate the cumulative filament mask measurements. Inclusion fractions for randomly distributed +points are shown with inset bars and dotted lines. Bottom: SFR-weighted inclusion fractions. +for unweighted measurements (top panels) provide fur- +ther insight. They indicate strong correlation between +dust emission filaments and H ii regions / young clusters, +moderate anti-correlation of associations with filaments +at scales <100 pc, and increasingly strong correlation +of associations with the DFN for extraction scales of +100, 140, and 200 pc. +For measurements made with +cumulative masks, the inclusion fractions (unweighted +and weighted) increase with scale as would be expected. +The slope of the cumulative curves in Fig. 8 (top) is +consistent with the scale dependence of the random- +ized control, showing the influence of significant multi- +scale mask covering fraction, but normalization is sig- +nificantly higher (excess over random 20 ± 5 σ for H ii +regions, 3–6σ for young clusters) except for associa- +tions. For associations, the small scale signal of anti- +correlation dominates until our cumulative measurement +finally reaches random equivalence by 200 pc. +The SFR-weighted inclusion fractions Fig. 8 (bottom) +are perhaps more physically relevant to the questions +raised at the start of this Section. +Remarkably, our +measurements show about 75% of the SF traced by +H ii regions is occurring within the 25 pc scale of the +F770W filament network (bottom left), whereas the +peak SFR-weighted inclusion fraction for F2100W is +∼45% (at 35 pc, bottom right). We find the single scale +SFR-weighted inclusion fractions are highest overall for +F1130W and F1000W at nearly 80% for 25 pc filament +extraction (not shown). Perhaps the most striking mea- +surement linking the dust emission filaments to current +star formation is the attainment of ∼ 95% SFR-weighted +inclusion by our uppermost cumulative scale, 200 pc, for + +Unweighted,F770w +100 +Hll regions +Clusters <5 Myr +% +80 +Associations <5 Myr +Inclusion fraction (as +60 +40 +20 +0 +25 +3550 70 100 140 200 280 400 +Filament extraction scale (pc)Unweighted, F2100w +100 +Hll regions +Clusters <5 Myr +% +80 +Associations<5 Myr +(as +Inclusion fraction ( +60 +40 +20 +0 +25 +3550　70 100 140 200 280 400 +Filament extraction scale (pc)SFR-weiahted. F77oW +100 +SFR-weighted incl. fraction (as %) +Hll regions +Clusters <5 Myr +80 +Associations <5 Myr +60 +40 +20 +0 +25 +35　5070　100 140 200 280 400 +Filament extraction scale (pc)SFR-weighted, F2100w +100 +SFR-weighted incl. fraction (as %) +Hll regions +Clusters <5 Myr +80 +Associations <5 Myr +60 +40 +20 +0 +25 +35　50　70100140 200 280 400 +Filament extraction scale (pc)12 +each of F770W, F1000W and F1130W when using the +multi-scale masks, and 72% for F2100W. +We anticipated seeing a reduction in inclusion frac- +tion for stellar associations, since, although the associ- +ations are young, they are star formation events that +have evolved from clusters via disruption/dissolution or +were initially formed unbound, and either way seem +more likely to have already cleared their environment +of dust. However, the anti-correlation observed at small +scales is an unexpected demonstration that such feed- +back actively helps to sculpt the dust into bubble/shell +structures (e.g. Watkins et al. in prep.; Barnes et al. +subm.). +Work is currently underway to obtain a catalog +of PHANGS-ALMA GMCs associated with embed- +ded (t ∼ 0 Myr) star formation, indicated by compact +F2100W sources coincident with a GMC (Lessing et al. +in prep.). When ready, we will compare our dust emis- +sion filaments to that population. We emphasize that +the F2100W source population does not drive the identi- +fication of filaments at 21µm due to FilFinder’s trans- +formation of the image intensity scale. +5. SUMMARY AND FUTURE WORK +This paper presents initial exploratory analysis of +PHANGS-JWST+HST imaging for NGC 628 revealing +its extensive dust filament network (DFN) as seen in +both MIR emission and visible attenuation. Our pilot +investigation offers insight into extragalactic ISM struc- +ture at small scales rarely probed by other tracers, in- +cluding atomic and molecular gas, with an emphasis on +quantifying filaments and associated star formation ac- +tivity. +Conclusions from our study are as follows: +1. At the smallest extraction scale currently consid- +ered (25 pc filament width), the agreement of in- +dependently constructed attenuation and emission +filament masks is 40%. More so, the detailed mor- +phology of filaments that are detected in both ways +is frequently rather well-matched with only minor +deviations in shape or extent. We find evidence for +emission-only filaments (and portions of filaments) +likely on the ‘back side’ of the galaxy disk, but also +a less well-understood set of attenuation-only fila- +ments that requires further characterization. +2. No single extraction scale (filament width) pro- +vides a complete inventory of all filamentary dust +emission structures. +Our masks are detecting a +morphologically diverse dusty ISM, spanning from +very compact filaments to ultimately constitut- +ing spiral arm features. +We anticipate that the +molecular fraction probably declines with increas- +ing scale in this hierarchy, but require higher reso- +lution observations of atomic gas in order to check +this. +3. HST reveals candidate features we nickname ‘dust +motes’ which are comparatively isolated (lying +outside the DFN) and appear as compact (≲ +10 pc), dark clouds essentially unrecoverable with +JWST /MIRI alone due to confusion with dusty +stellar point sources. They could trace largely qui- +escent individual molecular clouds. Regardless of +whether candidate ‘dust motes’ are ultimately ver- +ified as a bona fide population, HST is capable of +probing substructure in dust filaments at smaller +scales than MIRI. +4. Approximately one-third of the total MIR flux in +F770W, F1000W, F1130W bands is contained in +the 25 pc scale mask of the emission filament net- +work, using diffuse background subtracted mea- +surements. The flux fraction determined for the +200 pc limited cumulative multi-scale filament +mask is 55–60% in the same bands. The F2100W +filament flux fractions are significantly less than +the others, with a cumulative measurement of +∼ 45%. This is in-line with Leroy et al. (in prep.) +who showed that F2100W correlates less well with +CO than the other MIRI bands and that it is not +as clean of a tracer of column density. +5. Our filament inclusion fraction analysis shows that +75–80% of the current star formation traced by H ii +regions is occurring within the 25 pc scale of the +filament network. The analogous measurement for +young (<5 Myr) clusters is slightly more than 60%. +Integrated over cumulative scales up to 200 pc, the +H ii region fraction exceeds 95%. Similar analy- +sis demonstrates moderate anti-correlation of as- +sociations younger than 5 Myr with dust filaments +at scales <100 pc then a reversal to increasingly +strong association-filament correlation for extrac- +tion scales of 100, 140, and 200 pc. +Expansion and further development of our work to +the remaining PHANGS-JWST galaxies will: (a) pro- +vide the clarity of an external and diversified perspec- +tive which is absent from Galactic studies, and which +can allow quantification of trends, (b) enable compari- +son to increasingly detailed simulations, which can iso- +late the effects of different ISM structuring mechanisms, +(c) constrain the dependence of opacity on dust grain +properties, and eventually (d) firmly quantify the di- +vision of MIR emission between currently star-forming + +13 +and evolved stellar populations (related to the work +of Belfiore et al. in prep.), with complete accounting +of unobscured and embedded star formation (Rodriguez +et al. in prep.; Hassani et al. in prep.). The union of +JWST and HST dust tracing also motivates targeting +for focused high-resolution ALMA follow-up mapping of +dense gas. We further emphasize that ngVLA and/or +SKA is required to obtain sensitive H i imaging at the +substantially better than 6′′ resolution that is needed +to constrain ISM phase changes within the filamentary +structures we study. +We plan the following practical improvements to our +work in the near term. +Attenuation (dust lane) fea- +tures will be identified on the basis of the complete +multi-wavelength PHANGS-HST dataset and at sub- +MIRI-resolution scales. +We will study the integrated +SED of the filament network versus scale, and use Fil- +Finder capabilities to generate catalogs of filament sub- +structures with measured properties (such as length, as- +pect ratio, curvature, flux, mass per unit length) plus +molecular-cloud-linked quantities (velocity gradient, CO +velocity dispersion, virial parameter) when a GMC is +found to be co-spatial. Such cataloged properties will +be ripe for comparison to equivalent quantities measured +from simulations. We will assess whether or not embed- +ded star-forming regions tend to be located at the in- +tersection of filament spines, as they do in simulations. +of dust emission and attenuation filament network sub- +structures versus physical condition metrics (e.g. Sun +et al. 2022) of the local (∼kpc-scale) environment. +ACKNOWLEDGEMENTS +This work was carried out as part of the PHANGS +collaboration. +Based on observations made with the +NASA/ESA/CSA JWST and Hubble Space Telescopes. +The data were obtained from the Mikulski Archive for +Space Telescopes at the Space Telescope Science Insti- +tute, which is operated by the Association of Univer- +sities for Research in Astronomy, Inc., under NASA +contract NAS 5-03127 for JWST and NASA contract +NAS 5-26555 for HST. The JWST observations are +associated with program 2107, and those from HST +with program 15454 Based on observations collected at +the European Southern Observatory under ESO pro- +grammes 094.C-0623 (PI: Kreckel), 095.C-0473, 098.C- +0484 (PI: Blanc), 1100.B-0651 (PHANGS-MUSE; PI: +Schinnerer), as well as 094.B-0321 (MAGNUM; PI: +Marconi), 099.B-0242, 0100.B-0116, 098.B-0551 (MAD; +PI: Carollo) and 097.B-0640 (TIMER; PI: Gadotti). +We acknowledge the usage of the SAO/NASA Astro- +physics Data System6. +D.A.T. acknowledges fund- +ing support from STScI via JWST-GO-02107.002-A. +E.W.K. acknowledges support from the Smithsonian In- +stitution as a Submillimeter Array (SMA) Fellow and +the Natural Sciences and Engineering Research Coun- +cil of Canada. J.M.D.K. gratefully acknowledges fund- +ing from the European Research Council (ERC) under +the European Union’s Horizon 2020 research and inno- +vation programme via the ERC Starting Grant MUS- +TANG (grant agreement number 714907). COOL Re- +search DAO is a Decentralized Autonomous Organiza- +tion supporting research in astrophysics aimed at un- +covering our cosmic origins. E.J.W. acknowledges the +funding provided by the Deutsche Forschungsgemein- +schaft (DFG, German Research Foundation) – Project- +ID 138713538 – SFB 881 (“The Milky Way System”, +subproject P1). M.C. gratefully acknowledges funding +from the DFG through an Emmy Noether Research +Group (grant number CH2137/1-1). +M.B. acknowl- +edges support from FONDECYT regular grant 1211000 +and by the ANID BASAL project FB210003. T.G.W. +and E.S. acknowledge funding from the European Re- +search Council (ERC) under the European Union’s Hori- +zon 2020 research and innovation programme (grant +agreement No. +694343). +E.R. acknowledges the sup- +port of the Natural Sciences and Engineering Re- +search Council of Canada (NSERC), funding reference +number RGPIN-2022-03499. +F.B. would like to ac- +knowledge funding from the European Research Coun- +cil (ERC) under the European Union’s Horizon 2020 +research and innovation programme (grant agreement +No.726384/Empire) K.G. is supported by the Australian +Research Council through the Discovery Early Career +Researcher Award (DECRA) Fellowship DE220100766 +funded by the Australian Government. +K.G. is sup- +ported by the Australian Research Council Centre of +Excellence for All Sky Astrophysics in 3 Dimensions +(ASTRO 3D), through project number CE170100013. +R.S.K. acknowledges financial support from the Euro- +pean Research Council via the ERC Synergy Grant +“ECOGAL” (project ID 855130), from the Deutsche +Forschungsgemeinschaft (DFG) via the Collaborative +Research Center “The Milky Way System” (SFB 881 +– funding ID 138713538 – subprojects A1, B1, B2 and +B8) and from the Heidelberg Cluster of Excellence (EXC +2181 - 390900948) “STRUCTURES”, funded by the +German Excellence Strategy. +R.S.K. also thanks the +German Ministry for Economic Affairs and Climate Ac- +tion for funding in the project “MAINN” (funding ID +6 http://www.adsabs.harvard.edu + +14 +50OO2206). +G.A.B. acknowledges the support from +ANID Basal project FB210003. +M.Q. acknowledges +support from the Spanish grant PID2019-106027GA- +C44, funded by MCIN/AEI/10.13039/501100011033. +E.C. acknowledges support from ANID Basal projects +ACE210002 and FB210003. S.D. is supported by fund- +ing from the European Research Council (ERC) under +the European Union’s Horizon 2020 research and innova- +tion programme (grant agreement no. 101018897 Cos- +micExplorer). +K.K. and O.E. gratefully acknowledge +funding from DFG in the form of an Emmy Noether Re- +search Group (grant number KR4598/2-1, PI Kreckel). +Facilities: +HST , JWST , VLT:Yepun +Software: +astropy (Astropy Collaboration et al. +2013, +2018), +numpy +(Harris +et +al. +2020), +mat- +plotlib (Hunter 2007) and FilFinder (v1.7.2; Koch +& Rosolowsky 2015) +APPENDIX +A. DUST FILAMENT MASKS VERSUS BAND AND EXTRACTION SCALE +In to permit examination of the extracted dust filaments with respect to the JWST and HST data, we present the +filament masks as a Figure Set. They are displayed first for F770W, then F2100W, and lastly HST B-band. We show +the filaments as transparent colored areas on the associated JWST or HST image. For each band, we present all of the +individual scale filament masks in order of increasing extraction scale, followed by the cumulative multi-scale masks. +Fig. Set 1. +Dust filament masks +REFERENCES +Anand, G. S., Rizzi, L., Tully, R. B., et al. 2021a, AJ, 162, +80, doi: 10.3847/1538-3881/ac0440 +Anand, G. S., Lee, J. C., Van Dyk, S. D., et al. 2021b, +MNRAS, 501, 3621, doi: 10.1093/mnras/staa3668 +Andr´e, P., Di Francesco, J., Ward-Thompson, D., et al. +2014, in Protostars and Planets VI, ed. H. Beuther, R. S. +Klessen, C. P. Dullemond, & T. Henning, 27, +doi: 10.2458/azu uapress 9780816531240-ch002 +Andr´e, P., Men’shchikov, A., Bontemps, S., et al. 2010, +A&A, 518, L102, doi: 10.1051/0004-6361/201014666 +Astropy Collaboration, Robitaille, T. P., Tollerud, E. J., +et al. 2013, A&A, 558, A33, +doi: 10.1051/0004-6361/201322068 +Astropy Collaboration, Price-Whelan, A. M., Sip˝ocz, B. M., +et al. 2018, AJ, 156, 123, doi: 10.3847/1538-3881/aabc4f +Baldwin, J. A., Phillips, M. M., & Terlevich, R. 1981, +PASP, 93, 5, doi: 10.1086/130766 +Barmby, P., Ashby, M. L. N., Bianchi, L., et al. 2006, +ApJL, 650, L45, doi: 10.1086/508626 +Barnes, A., Watkins, E., et al. subm., ApJL +Belfiore, F., et al. in prep., A&A +Boquien, M., Burgarella, D., Roehlly, Y., et al. 2019, A&A, +622, A103, doi: 10.1051/0004-6361/201834156 +Boquien, M., Kennicutt, R., Calzetti, D., et al. 2016, A&A, +591, A6, doi: 10.1051/0004-6361/201527759 +Bradley, L., Sip˝ocz, B., Robitaille, T., et al. 2022, +astropy/photutils: 1.5.0, 1.5.0, Zenodo, Zenodo, +doi: 10.5281/zenodo.6825092 +Buta, R. J., Sheth, K., Athanassoula, E., et al. 2015, ApJS, +217, 32, doi: 10.1088/0067-0049/217/2/32 +Calzetti, D. 2013, in Secular Evolution of Galaxies, ed. +J. Falc´on-Barroso & J. H. Knapen, 419 +Calzetti, D., Lee, J. C., Sabbi, E., et al. 2015, AJ, 149, 51, +doi: 10.1088/0004-6256/149/2/51 +Crocker, A. F., Calzetti, D., Thilker, D. A., et al. 2013, +ApJ, 762, 79, doi: 10.1088/0004-637X/762/2/79 +Dong, H., Li, Z., Wang, Q. D., et al. 2016, MNRAS, 459, +2262, doi: 10.1093/mnras/stw778 +Duarte-Cabral, A., Acreman, D. M., Dobbs, C. L., et al. +2015, MNRAS, 447, 2144, doi: 10.1093/mnras/stu2586 +Duarte-Cabral, A., & Dobbs, C. L. 2017, MNRAS, 470, +4261, doi: 10.1093/mnras/stx1524 +Emsellem, E., Schinnerer, E., Santoro, F., et al. 2022, +A&A, 659, A191, doi: 10.1051/0004-6361/202141727 +Goodman, A. A., Alves, J., Beaumont, C. N., et al. 2014, +ApJ, 797, 53, doi: 10.1088/0004-637X/797/1/53 +Groves, B., et al. subm., MNRAS +Hacar, A., Clark, S., Heitsch, F., et al. 2022, arXiv e-prints, +arXiv:2203.09562. https://arxiv.org/abs/2203.09562 +Harris, C. R., Millman, K. J., van der Walt, S. J., et al. +2020, Nature, 585, 357, doi: 10.1038/s41586-020-2649-2 +Hassani, H., et al. in prep., ApJL +Hinz, J. L., Rieke, G. H., Gordon, K. D., et al. 2004, ApJS, +154, 259, doi: 10.1086/422558 +Hoversten, E. A., Gronwall, C., Vanden Berk, D. E., et al. +2011, AJ, 141, 205, doi: 10.1088/0004-6256/141/6/205 + +15 +Figure A1. +JWST F770W image with extracted emission filaments (25 pc scale) shown as transparent colored areas. The +image is oriented with North up and East left. The complete figure set (44 images) is available in the online journal +Hunter, J. D. 2007, Computing in Science & Engineering, 9, +90, doi: 10.1109/MCSE.2007.55 +Jackson, J. M., Finn, S. C., Chambers, E. T., Rathborne, +J. M., & Simon, R. 2010, ApJL, 719, L185, +doi: 10.1088/2041-8205/719/2/L185 +Jeffreson, S. M. R., Kruijssen, J. M. D., Keller, B. W., +Chevance, M., & Glover, S. C. O. 2020, MNRAS, 498, +385, doi: 10.1093/mnras/staa2127 +Koch, E. W., & Rosolowsky, E. W. 2015, MNRAS, 452, +3435, doi: 10.1093/mnras/stv1521 +Kumari, N., Irwin, M. J., & James, B. L. 2020, A&A, 634, +A24, doi: 10.1051/0004-6361/201732467 +La Vigne, M. A., Vogel, S. N., & Ostriker, E. C. 2006, ApJ, +650, 818, doi: 10.1086/506589 +Lang, P., Meidt, S. E., Rosolowsky, E., et al. 2020, ApJ, +897, 122, doi: 10.3847/1538-4357/ab9953 + +F770W 25pc +15°49' +48' +Declination (ICRS) +47' +46° +45° +1h36m48s +45s +42s +39s +36s +Right Ascension (iCRS)16 +Figure A2. +JWST F770W image with extracted emission filaments (cumulative up to 200 pc scale) shown as transparent +colored areas. The image is oriented with North up and East left. The complete figure set (44 images) is available in the online +journal +Larson, K., et al. subm., MNRAS +Lee, J., et al. in prep., ApJL +Lee, J. C., Whitmore, B. C., Thilker, D. A., et al. 2022, +ApJS, 258, 10, doi: 10.3847/1538-4365/ac1fe5 +Leike, R. H., Glatzle, M., & Enßlin, T. A. 2020, A&A, 639, +A138, doi: 10.1051/0004-6361/202038169 +Leroy, A., et al. in prep., ApJL +Leroy, A. K., Bigiel, F., de Blok, W. J. G., et al. 2012, AJ, +144, 3, doi: 10.1088/0004-6256/144/1/3 +Leroy, A. K., Hughes, A., Liu, D., et al. 2021, ApJS, 255, +19, doi: 10.3847/1538-4365/abec80 +Lessing, R., Thilker, D. A., et al. in prep., MNRAS +Liu, G., Koda, J., Calzetti, D., Fukuhara, M., & Momose, +R. 2011, ApJ, 735, 63, doi: 10.1088/0004-637X/735/1/63 + +F770W up to 200pc +15°49' +48' +Declination (ICRS) +47' +46° +45° +1h36m48s +45s +42s +39s +36s +Right Ascension (iCRS)17 +Figure A3. +JWST F2100W image with extracted emission filaments (35 pc scale) shown as transparent colored areas. The +image is oriented with North up and East left. The complete figure set (44 images) is available in the online journal +Lonsdale Persson, C. J., & Helou, G. 1987, ApJ, 314, 513, +doi: 10.1086/165082 +Meidt, S., et al. in prep., ApJL +Pineda, J. E., Arzoumanian, D., Andr´e, P., et al. 2022, +arXiv e-prints, arXiv:2205.03935. +https://arxiv.org/abs/2205.03935 +Ragan, S. E., Henning, T., Tackenberg, J., et al. 2014, +A&A, 568, A73, doi: 10.1051/0004-6361/201423401 +Rodriguez, J., et al. in prep., ApJL +Sandstrom, K., et al. in prep., ApJL +Santoro, F., Kreckel, K., Belfiore, F., et al. 2022, A&A, 658, +A188, doi: 10.1051/0004-6361/202141907 +Smith, R. J., Glover, S. C. O., Clark, P. C., Klessen, R. S., +& Springel, V. 2014, MNRAS, 441, 1628, +doi: 10.1093/mnras/stu616 + +F2100W 35pc +15°49' +48' +Declination (ICRS) +471 +46° +45° +1h36m48s +45s +42s +39s +36s +Right Ascension (iCRS)18 +Figure A4. +JWST F2100W image with extracted emission filaments (cumulative up to 200 pc scale) shown as transparent +colored areas. The image is oriented with North up and East left. The complete figure set (44 images) is available in the online +journal +Smith, R. J., Treß, R. G., Sormani, M. C., et al. 2020, +MNRAS, 492, 1594, doi: 10.1093/mnras/stz3328 +Soler, J. D., Beuther, H., Syed, J., et al. 2020, A&A, 642, +A163, doi: 10.1051/0004-6361/202038882 +Sun, J., Leroy, A. K., Rosolowsky, E., et al. 2022, AJ, 164, +43, doi: 10.3847/1538-3881/ac74bd +Syed, J., Soler, J. D., Beuther, H., et al. 2022, A&A, 657, +A1, doi: 10.1051/0004-6361/202141265 +Thilker, D. A., Whitmore, B. C., Lee, J. C., et al. 2022, +MNRAS, 509, 4094, doi: 10.1093/mnras/stab3183 +Thilker, D. A., et al. in prep., MNRAS +Tress, R. G., Sormani, M. C., Glover, S. C. O., et al. 2020, +MNRAS, 499, 4455, doi: 10.1093/mnras/staa3120 + +F2100W,up to 200pc +15°49' +48' +Declination (ICRS) +47' +46° +45° +1h36m48s +45s +42s +39s +36s +Right Ascension (iCRS)19 +Figure A5. +HST B-band (F435W) image with extracted attenuation filaments (25 pc scale) shown as transparent colored +areas. The image is oriented with North up and East left. The complete figure set (44 images) is available in the online journal +Treß, R. G., Sormani, M. C., Smith, R. J., et al. 2021, +MNRAS, 505, 5438, doi: 10.1093/mnras/stab1683 +Turner, J. A., Dale, D. A., Lee, J. C., et al. 2021, MNRAS, +502, 1366, doi: 10.1093/mnras/stab055 +Verley, S., Corbelli, E., Giovanardi, C., & Hunt, L. K. 2009, +A&A, 493, 453, doi: 10.1051/0004-6361:200810566 +Verley, S., Hunt, L. K., Corbelli, E., & Giovanardi, C. 2007, +A&A, 476, 1161, doi: 10.1051/0004-6361:20078179 +Watkins, E., et al. in prep., ApJL +Zucker, C., Battersby, C., & Goodman, A. 2015, ApJ, 815, +23, doi: 10.1088/0004-637X/815/1/23 +—. 2018, ApJ, 864, 153, doi: 10.3847/1538-4357/aacc66 + +HST F435W 25pc +15°49' +48' +Declination (ICRS) +47' +46° +45° +1h36m48s +45s +42s +39s +36s +Right Ascension (iCRS)20 +Figure A6. +HST B-band (F435W) image with extracted attenuation filaments (cumulative up to 200 pc scale) shown as +transparent colored areas. The image is oriented with North up and East left. The complete figure set (44 images) is available +in the online journal + +HST F435W up to 200pc +15°49' +48' +Declination (ICRS) +47' +46° +45° +1h36m48s +45s +42s +39s +36s +Right Ascension (iCRS)All Authors and Affiliations +David A. Thilker +,1 Janice C. Lee +,2 Sinan Deger +,3, 4 Ashley T. Barnes +,5 Frank Bigiel +,5 +M´ed´eric Boquien +,6 Yixian Cao +,7 M´elanie Chevance +,8, 9 Daniel A. Dale +,10 Oleg V. Egorov +,8, 11 +Simon C. O. Glover +,12 Kathryn Grasha +,13 Jonathan D. Henshaw +,14, 15 Ralf S. Klessen +,12, 16 +Eric Koch +,17 J. M. Diederik Kruijssen +,9 Adam K. Leroy +,18 Ryan A. Lessing +,1 Sharon E. Meidt +,19 +Francesca Pinna +,20 Miguel Querejeta +,21 Erik Rosolowsky +,22 Karin M. Sandstrom +,23 +Eva Schinnerer +,24 Rowan J. Smith +,25 Elizabeth J. Watkins +,8 Thomas G. Williams +,24 +Gagandeep S. Anand +,26 Francesco Belfiore +,27 Guillermo A. Blanc +,28, 29 Rupali Chandar +,30 +Enrico Congiu +,29 Eric Emsellem +,31, 32 Brent Groves +,33, 13 Kathryn Kreckel +,8 Kirsten L. Larson +,34 +Daizhong Liu +,35 Ismael Pessa +,24, 36 and Bradley C. Whitmore +26 +1Department of Physics and Astronomy, The Johns Hopkins University, Baltimore, MD 21218, USA +2Gemini Observatory/NSF’s NOIRLab, 950 N. Cherry Avenue, Tucson, AZ, 85719, USA +3California Institute of Technology, 1200 E. California Blvd., MC 249-17, Pasadena, CA 91125, USA +4The Oskar Klein Centre for Cosmoparticle Physics, Department of Physics, Stockholm University, AlbaNova, Stockholm, SE-106 91, +Sweden +5Argelander-Institut f¨ur Astronomie, Universit¨at Bonn, Auf dem H¨ugel 71, 53121 Bonn, Germany +6Centro de Astronom´ıa (CITEVA), Universidad de Antofagasta, Avenida Angamos 601, Antofagasta, Chile +7Max-Planck-Institut f¨ur Extraterrestrische Physik (MPE), Giessenbachstr. 1, D-85748 Garching, Germany +8Astronomisches Rechen-Institut, Zentrum f¨ur Astronomie der Universit¨at Heidelberg, M¨onchhofstraße 12-14, D-69120 Heidelberg, +Germany +9Cosmic Origins Of Life (COOL) Research DAO, coolresearch.io +10Department of Physics and Astronomy, University of Wyoming, Laramie, WY 82071, USA +11Sternberg Astronomical Institute, Lomonosov Moscow State University, Universitetsky pr. 13, 119234 Moscow, Russia +12Universit¨at Heidelberg, Zentrum f¨ur Astronomie, Institut f¨ur Theoretische Astrophysik, Albert-Ueberle-Str 2, D-69120 Heidelberg, +Germany +13Research School of Astronomy and Astrophysics, Australian National University, Canberra, ACT 2611, Australia +14Astrophysics Research Institute, Liverpool John Moores University, 146 Brownlow Hill, Liverpool L3 5RF, UK +15Max-Planck-Institut f¨ur Astronomie, K¨onigstuhl 17, D-69117 Heidelberg, Germany +16Universit¨at Heidelberg, Interdisziplin¨ares Zentrum f¨ur Wissenschaftliches Rechnen, Im Neuenheimer Feld 205, D-69120 Heidelberg, +Germany +17Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA +18Department of Astronomy, The Ohio State University, 140 West 18th Avenue, Columbus, Ohio 43210, USA +19Sterrenkundig Observatorium, Universiteit Gent, Krijgslaan 281 S9, B-9000 Gent, Belgium +20Max-Planck-Institut f¨ur Astronomie, K¨onigstuhl 17, D-69117 Heidelberg, Germany +21Observatorio Astron´omico Nacional (IGN), C/Alfonso XII, 3, E-28014 Madrid, Spain +22Department of Physics, University of Alberta, Edmonton, AB T6G 2E1, Canada +23Center for Astrophysics and Space Sciences, Department of Physics, University of California, +San Diego, 9500 Gilman Drive, La Jolla, CA 92093, USA +24Max-Planck-Institut f¨ur Astronomie, K¨onigstuhl 17, D-69117, Heidelberg, Germany +25Jodrell Bank center for Astrophysics, Department of Physics and Astronomy, University of Manchester, Oxford Road, Manchester M13 +9PL, UK +26Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA +27INAF – Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, I-50157, Firenze, Italy +28Observatories of the Carnegie Institution for Science, 813 Santa Barbara Street, Pasadena, CA 91101, USA +29Departamento de Astronom´ıa, Universidad de Chile, Camino del Observatorio 1515, Las Condes, Santiago, Chile +30University of Toledo, 2801 W. Bancroft St., Mail Stop 111, Toledo, OH, 43606 +31European Southern Observatory, Karl-Schwarzschild Straße 2, D-85748 Garching bei M¨unchen, Germany +32Univ Lyon, Univ Lyon 1, ENS de Lyon, CNRS, Centre de Recherche Astrophysique de Lyon UMR5574, +F-69230 Saint-Genis-Laval, France +33International Centre for Radio Astronomy Research, University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, +Australia +34AURA for the European Space Agency (ESA), Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA +35Max-Planck-Institut f¨ur extraterrestrische Physik, Giessenbachstraße 1, D-85748 Garching, Germany +36Leibniz-Institut f¨ur Astrophysik Potsdam (AIP), An der Sternwarte 16, 14482 Potsdam, Germany + +ID \ No newline at end of file diff --git a/Z9AyT4oBgHgl3EQf9vq-/content/tmp_files/load_file.txt b/Z9AyT4oBgHgl3EQf9vq-/content/tmp_files/load_file.txt new file mode 100644 index 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,6 Yixian Cao ,7 M´elanie Chevance ,8, 9 Daniel A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Dale ,10 Oleg V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Egorov ,8, 11 Simon C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Glover ,12 Kathryn Grasha ,13 Jonathan D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Henshaw ,14, 15 Ralf S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Klessen ,12, 16 Eric Koch ,17 J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Diederik Kruijssen ,9 Adam K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Leroy ,18 Ryan A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Lessing ,1 Sharon E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Meidt ,19 Francesca Pinna ,20 Miguel Querejeta ,21 Erik Rosolowsky ,22 Karin M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Sandstrom ,23 Eva Schinnerer ,24 Rowan J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Smith ,25 Elizabeth J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Watkins ,8 Thomas G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Williams ,24 Gagandeep S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Anand ,26 Francesco Belfiore ,27 Guillermo A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Blanc ,28, 29 Rupali Chandar ,30 Enrico Congiu ,29 Eric Emsellem ,31, 32 Brent Groves ,33, 13 Kathryn Kreckel ,8 Kirsten L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Larson ,34 Daizhong Liu ,35 Ismael Pessa ,24, 36 and Bradley C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Whitmore 26 ABSTRACT PHANGS-JWST mid-infrared (MIR) imaging of nearby spiral galaxies has revealed ubiquitous fil- aments of dust emission in intricate detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' We present a pilot study to systematically map the dust filament network (DFN) at multiple scales between 25–400 pc in NGC 628.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' MIRI images at 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='7, 10, 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='3 and 21µm of NGC 628 are used to generate maps of the filaments in emission, while PHANGS-HST B-band imaging yields maps of dust attenuation features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' We quantify the correspondence between filaments traced by MIR thermal continuum / polycyclic aromatic hydrocarbon (PAH) emission and filaments detected via extinction / scattering of visible light;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' the fraction of MIR flux contained in the DFN;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' and the fraction of HII regions, young star clusters and associations within the DFN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' We examine the dependence of these quantities with the physical scale at which the DFN is extracted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' With our highest resolution DFN maps (25 pc filament width), we find that filaments in emission and attenuation are co-spatial in 40% of sight lines, often exhibiting detailed morphological agreement;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' that ∼30% of the MIR flux is associated with the DFN;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' and that 75–80% of HII regions and 60% of star clusters younger than 5 Myr are contained within the DFN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' However, the DFN at this scale is anti-correlated with looser associations of stars identified using PHANGS-HST near-UV imaging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' We discuss the impact of these findings for studies of star formation and the ISM, and the broad range of new investigations enabled with multi-scale maps of the DFN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Keywords: Interstellar medium (847), Interstellar filaments (842), Interstellar dust (846), Dust contin- uum emission (412), Extinction (505), Star formation (1569), Star forming regions (1565) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' INTRODUCTION Two overwhelming impressions from inspecting JWST images of nearby galaxies are the sheer number of resolved stars seen in the near-IR (NIR) andthe stun- ning degree of structured, filamentary mid-IR (MIR) emission originating from small dust grains and poly- cyclic aromatic hydrocarbons (PAHs) in the interstel- lar medium (ISM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' JWST provides the spatial resolu- Corresponding author: David A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Thilker dthilker@jhu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='edu tion necessary to cleanly decompose the observed MIR dust emission into filament features, discrete compact sources, and a diffuse component throughout the Local Volume (d ≲11 Mpc) and beyond, as could only pre- viously be done in the Local Group (Hinz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2004;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Barmby et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2006;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Verley et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2007, 2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' This is of astrophysical importance not only because dust plays a central role in enabling star formation, but also hides the youngest clusters and star-forming regions from view at short wavelengths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' In HST optical multi-color imaging of star-forming galaxies, dust lanes stand out as highly structured attenuation features (La Vigne et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2006;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='00881v1 [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='GA] 2 Jan 2023 ID2 Dong et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2016) occasionally punctuated by H ii re- gions and clusters that have pierced the veil of their dusty natal molecular cloud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' The observation of such abundant organized extra- galactic structure in dust emission and attenuation is tantalising because studies of the cold gas and dust in the Milky Way have revealed filaments (Jackson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2010) of length >100 pc that have even been dubbed the ‘bones’ of the Milky Way’s cold ISM (Goodman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Ragan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Zucker et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Soler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Indeed, much recent work in the Milky Way points towards a view of the cold, dusty star-forming medium that is filamentary and multi-scale (Hacar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Pineda et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Zucker et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2018), very different from the classical ‘spherical molec- ular cloud’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Filamentary structure even persists at sub- pc, cloud-substructure scales (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Andr´e et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2010, 2014) though, in the Local Volume extragalactic con- text, we are limited to studying larger filaments (akin to those of Syed et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' The shift to a filament- centered paradigm implies that criteria for stability and fragmentation change, becoming a mass per unit length threshold rather than a more traditional Jeans mass ar- gument.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' All this filamentary structure seeds star forma- tion and determines the rate and efficiency of collapse, and defines the medium that the stellar feedback is sub- sequently driven into, thereby determining how feedback drives the baryon cycle within galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' A revolution in our view of the dust structure in nearby galaxies is underway, having overcome the bar- rier of resolution with the combined capabilities of JWST and HST .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' This enhanced extragalactic perspec- tive is a critical advance we can now quantify entire filament networks on scales ranging from the size of in- dividual GMCs up to morphological features dominat- ing entire galaxies and reveal their intimate connection with respect to star formation, feedback, and dynami- cal mechanisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' This new era of dusty ISM cartogra- phy will leverage representative galaxy samples to pro- vide systematic answers to: how the prevalence and properties of these filamentary features may depend on galactic environment;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' whether they universally form the backbone of the cold ISM, through comparison to CO maps;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' and how the joint dust and molecular gas distri- bution is related to structures like spiral arms and bars, contrasted to high-resolution pc-scale UV+IR tracers of star formation activity from HST and JWST .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Crit- ically, the new observations can be directly compared to state-of-the-art galaxy simulations (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Smith et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2014, 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Duarte-Cabral et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Duarte-Cabral & Dobbs 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Tress et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Treß et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Jeffreson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' JWST resolution and depth are sufficient to re- cover filamentary dust emission features, at GMC- scales, analogous to those of the Milky Way in galax- ies out to the distance of the Virgo cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' This let- ter focuses on NGC 628 (also known as Messier 74, ‘The Phantom Galaxy’) an archetypal face-on SA(s)c galaxy Buta et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' NGC 628 is nearby (d = 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='84±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='03 Mpc;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Anand et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2021a,b), star-forming (SFR = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='8 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='45 M⊙yr−1), massive (M∗ = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='2 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='56 × 1010 M⊙) and viewed at low inclination (i ∼ 9◦ ± 12◦, Lang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' NGC 628 is part of a broader sample of 19 “main sequence” star-forming galaxies for which systematic, uniform surveys with HST (Lee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2022), ALMA (Leroy et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2021) VLT-MUSE (Emsellem et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2022) and now JWST (Lee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' in prep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=') have been carried out by the PHANGS (Physics at High Angular resolution in Nearby GalaxieS) collaboration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='1 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' DATA 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' PHANGS-JWST imaging NGC 628 is one of the initial targets observed for the PHANGS-JWST Cycle 1 Treasury project (GO 2107, PI J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Lee).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Our observations of NGC 628 target the central region (Rgal ≲ 5 kpc) of the star-forming disk, to overlap areas where HST , ALMA, and MUSE data have been obtained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='2 The dataset includes imaging with NIRCam (F200W, F300M, F335M and F360M) and MIRI (F770W, F1000W, F1130W and F2100W).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Photospheric emission from resolved stellar populations is major component in the four NIRCam bands (except- ing F335M which primarily probes the 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='3µm PAH fea- ture), whereas MIRI traces the ISM (both PAHs and hot, small dust grains).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Resolution varies from 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='066 to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='12′′(NIRCam) and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='25 to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='67′′(MIRI).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' For MIRI, this corresponds to 12–32 pc at the distance of NGC 628.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' A detailed description of the PHANGS-JWST observa- tions and data reduction is presented by Lee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' (in prep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=').' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Here, we focus on MIRI imaging, deferring anal- ysis of filamentary structure seen in the 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='3µm PAH feature to future work in anticipation of improved as- trometric alignment among the PHANGS-JWST NIR- Cam and MIRI imaging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Of particular importance to the analysis in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='2 is the sky background adopted for the MIRI data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' We use background-corrected images which have been tied to the sky level measured in wide- field Spitzer and WISE archival imaging, as described in 1 https://sites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='google.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='com/view/phangs/home 2 Footprint maps of the HST , ALMA, and MUSE observations are available at https://archive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='stsci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='edu/hlsp/phangs-hst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Science- ready PHANGS-HST images are also available for download.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 3 Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Left: Pre-processed B-band HST image, filtered to remove compact positive sources but retain small nega- tive/concave morphological features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Center: Filament masks for visible attenuation (blue) and MIR emission (red) extracted at scale of 25 pc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Areas of overlap appear magenta.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Right: JWST /MIRI F770W image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' North is up, East is left, and the field of view spans 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='3 kpc from top to bottom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' The figure only shows a portion of the area observed with JWST .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' The entire image may be seen in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 5 and A1–A4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' the Appendix of Leroy et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' (in prep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=').' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' The MIRI back- ground levels are currently uncertain by ±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='1 MJy sr−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' PHANGS-HST imaging The HST NUV-U-B-V-I (F275W, F336W, F435W, F555W, F814W) observations of the central NGC 628 disk we use were obtained by LEGUS (GO 13364, Calzetti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2015) using WFC3/UVIS for NUV and U, and by R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Chandar (GO 10402) using ACS/WFC for B, V and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' All data were reprocessed by PHANGS- HST.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Full details are given in (Lee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' The ACS/WFC B-band images we use to identify dust lanes in attenuation have resolution (∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='09′′, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='3 pc), approx- imately 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='5× finer than MIRI F770W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' MUSE H ii region catalog We use the nebular catalog of H ii regions derived from the integral field unit (IFU) spectroscopy of the PHANGS-MUSE survey Emsellem et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' For NGC 628, the ”convolved, optimized” resolution in PHANGS-MUSE DR 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='2 is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='92′′, corresponding to a spatial resolution of 44 pc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Santoro et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' (2022) and Groves et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' (subm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=') used PHANGS-MUSE data to create a catalog of H ii regions and provide fluxes cor- rected for Milky Way and internal extinction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Only star-forming regions classified using the BPT diagram (Baldwin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 1981) are retained in our analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' HST stellar association and cluster catalogs PHANGS-HST resolved stellar photometry has been used to identify and characterize stellar associations as summarized in (Lee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2022) and described in detail by Larson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' (subm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Stellar clusters in NGC 628 have been studied by Thilker et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' PHANGS-HST catalogs are publicly available3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' For both associations and clusters, fluxes for the five avail- able HST bands were measured (using upper-limits in non-detected photometric bands) and then age, mass and reddening were estimated4 via fitting of observed SEDs (Turner et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2021) to solar metallicity stellar population models using cigale (Boquien et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' We use the PHANGS-HST associations catalog based on local over-densities of NUV point-like detections at a scale of 32 pc for our analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' The stellar associations have ages ranging up to ∼102 Myr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' We use a subset 3 https://archive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='stsci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='edu/hlsp/phangs-cat 4 Degeneracy between age and reddening is apparent for a subset of objects, and could be more relevant in our dust filaments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 4 Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Blue markings represent sight lines with attenuation-only, magenta markings represent areas of over- lap of between attenuation and emission, and red markings account for sight lines with emission-only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Top: F770W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Bot- tom: F2100W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Results generated for cumulative masks are shown with points and sloping lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' We disregard scales > 200 pc (shown faded in the plot) because the filament masks become unreliable (in the case of attenuation) or re- dundant with smaller scale features (for emission).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' The first bar of the F770W plot (25 pc) presents the measurement for masks shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' selected to have age less than five Myr in order to limit the population to the most recent star formation activ- ity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Clusters for our analysis were also selected with the same upper limit on age.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' DUST FILAMENT ANALYSIS 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Filament extraction We identify dust filaments using FilFinder (Koch & Rosolowsky 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' This code applies an adaptive thresholding algorithm and graph-based medial skele- ton analysis to isolate and then characterize filaments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Thresholding is conducted over local neighborhoods, al- Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Top: For F770W, the fraction of pixels cov- ered by a dust filament mask (emission or absorption) or left unassigned to a dust filament.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Scales we elect to exclude from the filament network (see text) are shown faded in the plot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Bottom: Same, for F2100W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' lowing for the extraction of structure over a large dy- namic range both in intensity and spatial scale (the lat- ter when the code is run multiple times with different pa- rameter choices).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' The potential effect of bright sources interspersed in the web of filaments is mitigated by an arctan intensity transform before thresholding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' We use a slightly modified version of FilFinder in which the arctan transformed image is convolved to the filament extraction scale before each run.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' In the current analy- sis we only utilize the filament masks produced by the code, leaving FilFinder’s skeleton analysis capabilities for future work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' We apply FilFinder independently to the background-corrected image in each MIRI band and to a pre-processed version of the B-band HST image (in which attenuation features are most evident compared to NUV, U, V, and I).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Attenuation-only / Both / Emission-only F770W 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='0 2535 50 70 100 140 200 280 400 Filament extraction scale (pc)Attenuation-only / Both / Emission-only F2100W 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='0 25 35 50 70 100 140 200 280 400 Filament extraction scale (pc)F770W 100 No filament (%) 80 60 Any Filament,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' [ 40 20 0 25 35 50 70 100 140 200 280 400 Filament extraction scale (pc)F2100W 100 No filament (%) 80 60 Any Filament,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' [ 40 20 0 25 35 50 70 100 140 200 280 400 Filament extraction scale (pc)5 For pre-processing the HST image,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' multi-scale median filtering is used to suppress peak-like features over a range in scale,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' while retaining small scale dips (concave areas).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Our specific filtering method follows from Hov- ersten et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' At each pixel the output value is assigned to be that location’s minimum in a stack of cir- cular median filtered images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Filter kernel diameters are taken from a ladder of physical scales (starting at the resolution limit and proceeding up to 32 pc).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' The result is that confusion by bright stars and stellar clusters is greatly reduced, emphasizing the dust lane structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 1 (left) and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 6 (left) show the pre-processed im- age.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' FilFinder nominally operates by finding positive filamentary features above the background.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' before pass- ing the pre-processed B-band image to FilFinder, we invert the sense of the intensity (subtracting the image from a constant value equal to the maximum in the field of view) For both attenuation and emission, we use FilFinder to identify potential filaments with narrow dimension (width) starting at 25 pc then stepping by factors of √ 2 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='15 dex) up to 400 pc (25, 35, 50, 70, 100, 140, 200, 280, 400 pc).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' The minimum scale of 25 pc corresponds to approximately twice the PSF FWHM of MIRI F770W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' For F2100W analysis, we begin at the 35 pc scale due to the larger F2100W PSF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' FilFinder parameters are set as follows: size thresh = 6πw2, adapt thresh = 2w, glob thresh = 2σ above sky level, smooth size = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='5w, fill hole size = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='5w2, where w is the extraction scale (in pixels) and σ is the standard deviation noise level ex- pected in the arctan transformed, convolved images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' In addition to the filament masks generated for ex- traction at specific scales, we also produce masks repre- senting the union of filaments detected cumulatively at different scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' For these cumulative masks, we sum the individual masks (for scales less than or equal to the cur- rent scale) and then flatten the result, such that it has a value of one anywhere a constituent scale contributes filament coverage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' The cumulative summed mask before flattening is also retained, as it highlights the multi-scale nature of the filament network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Appendix A presents individual scale and cumulative multi-scale masks for F770W, F2100W, and HST B-band as a Figure Set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' The wide range of scales initially allowed for fila- ment extraction is exploratory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' In the second half of Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='1), we argue that all emission and attenuation fil- ament masks for scales > 200 pc not be used, although we do include them in plots allowing for the reader to make their own.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' DFN characterization For Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='1, we measure filament mask overlap cate- gorizing each pixel as belonging to one of four classes: (1) attenuation filament only, (2) emission filament only, (3) both attenuation and emission filaments, or (4) no filamentary features detected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Note that the sight line fractions we report in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='1 for classes (1)-(3) are nor- malized to the total count of pixels with any detected filamentary feature, rather than the total count of pixels in the image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' It is beyond the scope of the current study to quantify the dependence of pixel classes on the depth of the imaging – however, given the pervasive character of the detected filament network, we suggest that at least the F770W, F1000W, and F1130W observations are sen- sitive enough to make this a moot point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Our F2100W data is about 2× less sensitive in absolute terms of lim- iting surface brightness, σI [MJy sr−1], and also suffers from a similar loss in resolution compared to F770W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' These factors likely contribute to loss of some smaller scale filamentary structure in the F2100W imaging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='2 (flux fractions) requires local estimation of the diffuse emission to obtain background-subtracted filament flux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' the photutils (Bradley et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2022) background2D code, supplying filament masks to indi- cate which pixels the procedure should ignore.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' A mesh of bins (each having size two-thirds the filament extrac- tion scale) is defined, and the mode of unmasked pixels is determined in each bin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' These mesh modes are me- dian filtered with a 3×3 boxcar (ignoring bins with too many pixels masked as within a filament) and the result- ing values are interpolated across the image grid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' from the input image and non-filament pixels are set to zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Integrating this result gives the background subtracted flux of the filament structures, which is then divided by the total flux in the MIRI footprint to obtain flux fractions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' RESULTS Figure 1 illustrates the dust lanes seen as deficits of visible light (left) and dust emission filaments detected in MIR emission (right).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Plotted for a single extraction scale (25 pc), the central panel emphasizes the detailed coincidence between these two tracers of dust (blue = attenuation, red = emission) in the interstellar medium, with magenta indicating overlap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' It is clear that the dust filament network (DFN) occupies a large fraction of sight lines and contributes a significant fraction of the MIR luminosity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Knots of emission from star-forming re- gions are generally distributed throughout the filaments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' In this section, we quantify each of these statements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Here we show results only for F770W and F2100W, as the filament masks and measured quantities based on 6 F1000W and F1130W are consistent with F770W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Any notable differences are discussed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Contrasting views of the dust filament network We start by highlighting the consistency between fil- amentary attenuation (dust lane) features and web-like MIR dust emission to illustrate the potential of using HST -detected features as a high resolution proxy for the dense dusty ISM morphology (and perhaps even molec- ular gas5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2 shows the results of filament overlap analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' For the PAH-dominated bands (F770W, F1130W) and 10µm thermal emission traced by F1000W, in the top panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2, we find that the percentage of sight lines in common between visible attenuation and MIR emission filaments is nearly 40%, at 25 pc and declines smoothly with increasing scale (filament width).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' This decline is due to more area becoming traced by attenua- tion only for larger individual filament extraction scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' The percentage of emission-only filament sight lines de- clines a small amount from 25 pc to 200 pc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Overlap statistics generated on the basis of cumulative multi- scale masks show a different picture, in which the per- centage of attenuation plus emission sight lines grows with scale from just over 40% at 35 pc to 55% up to 200 pc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' This is a consequence of different extraction scale masks picking up varied portions of the overall web-like DFN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' We return to this point further in the current subsection (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 4 and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' In the bottom panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2, we show the overlap for F2100W emission filaments with the dust lanes from HST .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' At 21µm the percentage is 24% for 35 pc indi- vidual extraction scale, substantially less than for the three other bands, declining to ∼16% for 200 pc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' For all separate scales, attenuation-only sight lines amount to more than 65% and emission-only ≲10%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Given that the attenuation filament mask remains constant F770W and F2100W, this could suggest that either we are sen- sitivity limited for F2100W or the filamentary emis- sion detected in 21µm imaging is less consistently recov- ered into coherent structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' The latter interpretation is supported by mask inspection in the figures of Ap- pendix A, and by the fact that the morphology of the F2100W image is more dominated by compact sources (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' IR-bright star-forming regions, see Hassani et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' in prep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=') than F770W, F1000W, and F1130W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' This serves as a reminder that we are tracing warm (140 K) dust at 21µm, whereas the dust attenuation provides a more complete inventory with respect to dust over a 5 The association between the DFN structures and 12CO(2-1)- traced molecular gas will be investigated in a future study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' wide range of [cooler] temperatures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Nevertheless, the overlap with the 200 pc cumulative multi-scale mask is 40% (only ∼1/3 less than for F770W).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' In summary, the 40% level of pixel-by-pixel agreement of the attenuation and emission filament masks at 25 pc and the trend for the greatest agreement on the small- est scales that the correspondence may be even tighter if smaller physical scales are probed, such as in Local Group galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' We stress that, although 40% overlap may sound low, inspection of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 1 shows that the de- tailed morphology (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' extent, shape) of filaments that are detected in attenuation and dust emission is fre- quently rather well-matched.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' We also note that regions of the filament network only found as dust emission are expected due to line-of-sight effects: some filaments will be positioned on the ‘back’ side of the face-on galaxy disk, and could account for the majority of ‘emission- only’ areas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Some attenuation-only regions also lie in false-negatives for MIR dust emission on the scale of in- terest, or lie in relatively MIR-faint, intermediate surface brightness regions of the visible galaxy disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' False nega- tives occur when a MIRI filament structure has a width that is somewhat different than the visible attenuation feature, or when scale-matched emission in the region is biased against detection at the scale of interest (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' a filament centered between brighter neighboring emission features spaced by about the width of the FilFinder adaptive thresholding box).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Figure 3 shows the division of sight lines between those associated to a dust filament (here, either attenuation or emission) and those that do not lie in a filament for the particular extraction scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' The plots show very lit- tle change between bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' We find that approximately 50–55% of sight lines are attributed to dust filaments for scales 25–100 pc with no variation due to extrac- tion scale, then a mild increase at larger scales (to ∼60– 65% for 200 pc).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Cumulative multi-scale mask measure- ments of the dust filament sight line fraction (dots and lines in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 3) steadily rise across the 25–200 pc range, despite the constancy for individual extraction scales smaller than 140 pc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Our filament masks are detecting a morphologically diverse dusty ISM, Though beyond the scope of this paper, it will be important to investi- gate if the component is increasingly atomic-dominated compared to narrower filaments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Figure 4 illustrates the tendency for dust filament masks to capture different morphological features when extracted using varied scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' In particular, we show the JWST F770W image in the top panel and HST B-band in the bottom panel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Using red and blue lines, overplot- ted on each of the images is a contour boundary of the 25 pc mask (dashed thin line) and 200 pc mask (solid 7 Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Top: JWST F770W image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Dust emission filament mask boundaries are shown for: 25 pc dashed, thin red;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 200 pc, thick red;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' and cumulative 400 pc, dashed thin yellow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Bottom: B-band F435W HST image, with attenuation filament mask coverage of 25 pc dashed, thin blue;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 200 pc, thick blue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' The scale bar in each panel is 1 kpc in length 、8 Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' JWST F770W image of NGC 628, overplotted with the contours showing the coverage of multi-scale masks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' The maximum scale is as follows: green, 100 pc;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' yellow, 140 pc;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' red, 200 pc;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' cyan, 280 pc;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' magenta, 400 pc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' We adopt 200 pc as a preferred value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' The scale bar corresponds to 1 kpc thick line), with the variety of mask corresponding to the dust detection property of each image (emission on top, attenuation on bottom).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Many of the single ex- traction scale 25 pc dust filaments are very long, with l >1 kpc and have rather high aspect ratio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' However, there are also frequent cases of the 25 pc masks (dashed thin lines) only including localized substructure within larger coherent filaments left unjoined by small scale ex- traction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' This selective property of the filament identi- fication outcome can be seen in spiral arms (markedly less so in interarm regions) and in both emission and at- tenuation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Conversely, the 200 pc filament masks (solid thick lines) often entirely exclude areas with a significant population of narrow GMC-scale width filaments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' We note that the 200 pc attenuation filament mask recov- ers continuous spiral structure more effectively than the F770W emission mask of the same scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Additionally, Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 4 demonstrates that the recovered dust attenuation features can be quite modest in terms of apparent A(B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Inspection in the peripheral areas of the HST panel nev- ertheless suggests the majority of such filaments are real.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' On the JWST image, we also plot a contour representing the cumulative (up to 400 pc) emission filament mask (dashed thin yellow).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' The 25 pc and 200 pc filament structures alone do not include all portions of the DFN, especially in dust emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' The yellow contour shows how using a cumulative mask addresses this issue, link- ing many smaller scale components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Using cumulative masks with large upper scales can excessively broaden the extent of filaments, and hence we urge caution in the choice of the upper limit on multi-scale integration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 5 provides empirical justification for maximum scale on the basis of emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' The figure plots cumu- lative F770W mask boundaries for different maximum scales, starting at 100 pc (green), running through 140, 200, 280 pc (yellow, red, cyan), up to 400 pc (magenta).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' The top layer contour (100 pc, green) already struc- ture of the DFN, but several regions of seemingly con- tiguous filamentary emission remain disconnected either internally or to the network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' By looking at other col- ored contours emerging from under the green bound- ary, one can infer how adding progressively larger scales changes the network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' The 200 pc cumulative mask (red) appears to provide reliable recovery of all filamentary emission structures without undue peripheral excess, al- though 140 pc and 280 pc are probably also acceptable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' HST B-band filament extraction at 280 and 400 pc oc- casionally confuses interarm gaps as attenuation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Such large (> 200 pc) scales also push the limit of what can be considered a filament in the sense of forming via tur- bulent Jeans scale gravitational instabilities (see Meidt et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' in prep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 6 presents a zoomed in view of a region east- southeast of the galaxy center, showing the filtered B- band data in comparison to an unprocessed version of the same image and to F1000W data from JWST .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Con- tours of the 25 pc B-band and F1000W filaments are overplotted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' This figure visually emphasizes the 40% sight line overlap and morphological agreement at this scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 6 also demonstrates feasibility to probe even smaller scales in visible dust lanes across the en- tire PHANGS-HST sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Significant substructuring (down to the ∼ 5 pc WFC3/UVIS resolution limit in NGC 628) in attenuation of the features detected as dust emission filaments at 25 pc scales is apparent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' We fur- ther expect HST to detect additional small scale fila- ments beyond the limit of MIRI – several super nar- row attenuation filaments without corresponding larger scale intensity depression are apparent in other regions of NGC 628.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Finally, Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 6 demonstrates that with HST we will be able to reveal candidate features we nickname ‘dust motes’ (examples marked with yellow circles), essentially compact (≲ 10 pc), dark clouds we cannot cleanly identify solely with JWST due to confu- 9 Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Left: Subsection of our pre-processed B-band image, overlaid with contours corresponding to the filament masks generated at 25 pc resolution in emission, red, and absorption, blue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Center: Unprocessed B-band image Right: JWST F1000W image, also with the filament mask contours shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Yellow circles surround three example dust motes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' There are many more in the field shown, left unmarked.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Green circles surround three example candidate dusty stars, others are not marked.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Circles are 1′′ in diameter, equivalent to 48 pc at the distance of NGC 628 sion with point-like dusty extreme AGB stars (Thilker et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' in prep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=') lying outside the emission filament net- work (examples marked with green circles) in the short wavelength MIRI images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' These dust motes could be individual molecular clouds in relative isolation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Their size is comparable to the Taurus Molecular Cloud, al- though Taurus is star-forming whereas the motes may often be quiescent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' A better Milky Way might be the smallest scale clouds found in the 3D extinction maps of e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Leike et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Dust mote clouds are challeng- ing to confirm with MIRI, but appear in the HST B- band images before any pre-processing (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 6 center).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' PHANGS-JWST F335M 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='3µm PAH imaging (Sand- strom et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' in prep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Rodriguez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' in prep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=') and forthcoming PHANGS-HST Hα imaging (GO 17126, PI R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Chandar) may prove useful to further vet dust can- didates as a class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Fraction of flux in MIR filament network The relative amount of structured and unstructured (diffuse) dust in a galaxy is fundamental metric of ISM morphology and offers a basis for comparison with sim- ulations that aim to understand the impact of factors such as stellar feedback and dynamical influences (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Smith et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' As noted in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='3, this observable is also relevant to star formation rate (SFR) estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' We measure the fraction of flux contained within the ex- tracted filaments compared to the total flux in the im- age.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' As the filaments are brighter than their surround- ings, this requires that we establish a local background estimate at all locations in the image, which we do us- ing the procedure given in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Figure 7 presents our results concerning flux fraction as a function of filament extraction scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' We find that at the smallest independent extraction scales considered (25 pc for F770W, F1000W, F1130W;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 35 pc for F2100W), the background-subtracted filament flux fractions are nearly 30% except for F2100W at ≈ 20%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' The flux fraction is essentially constant versus extraction scale for F770W, F1000, and F1130W, but peaks at 35 pc and 200 pc for F2100W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' The F2100W flux fractions are always significantly less than all three shorter wavelength MIRI bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Given the present residual ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='1 MJy sr−1 uncertainty in the background level of our MIRI images (see Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='1 and Leroy et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' in prep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' ), we assess the impact this has on filament flux fractions, by offsetting the image intensities by the un- certainty in a positive and negative sense.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Dashes over- plotted on the bars of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 7 indicate the resulting per- turbed fractions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Cumulative multi-scale mask filament flux fraction re- sults are also shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 7, indicated by the solid lines and dots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' As expected, the fraction increases as progressively more individual masks are combined and the maximum allowed extraction scale is increased.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' For our choice of maximum scale (200 pc) the background- subtracted filament flux is in the range 55% to 60% of the total F770W, F1000W, and F1130W flux in the field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' At the same cumulative scale, the F2100W measurement is 43%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Scatter due to uncertainty in background level 10 Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Top: Filament flux fraction in F770W ex- pressed as percentage, with individual filament extraction scales plotted as pink bars, and cumulative multi-scale re- sults as solid lines and points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' The faded region is shown for completeness, although we adopt a maximum cumula- tive scale of 200 pc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Horizontal dashes on each bar indicate the one-sigma uncertainty of the flux fraction measurements, obtained by perturbing the sky level in accord with the post- pipeline calibration described by Leroy et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' (in prep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' ), Lee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' (in prep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=').' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Dotted lines show the one-sigma range due to uncertainty of cumulative flux fractions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Bottom: Same, but for F2100W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' is also checked for cumulative values, and shown with dotted lines on Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' The impact is notably larger than for individual scales, but is generally less than sys- tematic uncertainty due to our choice of maximum scale included in the DFN cumulative mask.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' We note that if diffuse emission is neglected, rather than subtracted away as in our analysis, the inte- grated flux from the filament network becomes 40-100% higher boosting the cumulative filament flux fractions to ∼80% for F770W, F1000W, and F1130W and 60% for F2100W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Linking the dust filament network to star formation activity The results of Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='2 confirm that more than half of the MIR flux from NGC 628 originates in the intri- cately structured filament network, with the only excep- tion being for F2100W (43%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' This outcome is what we anticipated based on previous work for nearby galaxies (Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Leroy et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Crocker et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Calzetti 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Boquien et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Kumari et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Belfiore et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' in prep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=').' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' It reinforces the necessity of correcting the integrated MIR luminosity of a galaxy for the presence of inherently diffuse emission heated by older stellar populations, when using MIR to measure current SFR (Lonsdale Persson & Helou 1987;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Boquien et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' One of the goals of PHANGS-JWST is to clarify systematics of this correction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' We can position- ally test the linkage of the DFN to age-dated markers of star formation events, checking whether all regions of the filament network can be attributed to heating by current star formation or if some filamentary structure is effectively quiescent and should be removed alongside diffuse emission when estimating SFR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Put differently, perhaps only filamentary structure up to a certain max- imum scale, or down to a limiting dust surface density, is directly linked to the youngest stellar populations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' We take a first step toward the goal above by cross- correlating the filament masks with the PHANGS- MUSE H ii regions, plus PHANGS-HST young (≤ 5 Myr) clusters and associations, described in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' With these populations, we measure unweighted inclu- sion fractions (number of objects contained within the filament mask divided by the total count in the image footprint) and also tracer-weighted inclusion fractions (summing weights corresponding to SFR rather than ob- ject counts).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' For weighting we use extinction corrected L(Hα), effectively unobscured SFR, for H ii region popu- lations;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' and M∗ / age ≈ effective SFR(5 Myr) for young clusters and associations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 8 plots the measured inclusion fractions for each of the test populations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' We begin by making general comments about Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 8 which are applicable to all pan- els.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' We find that the inclusion fractions (at individ- ual scales or cumulatively) are consistently maximized for H ii regions but decline slightly when using young clusters and dramatically using young associations, re- gardless of scale or band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' The inclusion fraction mea- sured at individual filament extraction scales for H ii regions and young clusters (≤ 5 Myr), decline from a maximum at 25 pc until reaching 70–100 pc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' For as- sociations, there is far weaker, if any, dependence on scale over the same range, but an apparent enhancement at 140–200 pc scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' The random inclusion fractions F770W 100 Filament flux fraction (as %) 80 60 40 20 0 25 35 5070 100 140 200 280 400 Filament extraction scale (pc)F2100W 100 Filament flux fraction (as %) 80 60 40 20 0 25 35 50 70 100 140 200 280 400 Filament extraction scale (pc)11 Figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Top: Filament inclusion fractions for various star formation event tracers (H ii regions, young clusters, young multi- scale associations) versus the dust emission filament extraction scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Bars indicate results for each individual extraction scale, whereas lines and points indicate the cumulative filament mask measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Inclusion fractions for randomly distributed points are shown with inset bars and dotted lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Bottom: SFR-weighted inclusion fractions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' for unweighted measurements (top panels) provide fur- ther insight.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' They indicate strong correlation between dust emission filaments and H ii regions / young clusters, moderate anti-correlation of associations with filaments at scales <100 pc, and increasingly strong correlation of associations with the DFN for extraction scales of 100, 140, and 200 pc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' For measurements made with cumulative masks, the inclusion fractions (unweighted and weighted) increase with scale as would be expected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' The slope of the cumulative curves in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 8 (top) is consistent with the scale dependence of the random- ized control, showing the influence of significant multi- scale mask covering fraction, but normalization is sig- nificantly higher (excess over random 20 ± 5 σ for H ii regions, 3–6σ for young clusters) except for associa- tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' For associations, the small scale signal of anti- correlation dominates until our cumulative measurement finally reaches random equivalence by 200 pc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' The SFR-weighted inclusion fractions Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 8 (bottom) are perhaps more physically relevant to the questions raised at the start of this Section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Remarkably, our measurements show about 75% of the SF traced by H ii regions is occurring within the 25 pc scale of the F770W filament network (bottom left), whereas the peak SFR-weighted inclusion fraction for F2100W is ∼45% (at 35 pc, bottom right).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' We find the single scale SFR-weighted inclusion fractions are highest overall for F1130W and F1000W at nearly 80% for 25 pc filament extraction (not shown).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Perhaps the most striking mea- surement linking the dust emission filaments to current star formation is the attainment of ∼ 95% SFR-weighted inclusion by our uppermost cumulative scale,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 200 pc,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' for Unweighted,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='F770w 100 Hll regions Clusters <5 Myr % 80 Associations <5 Myr Inclusion fraction (as 60 40 20 0 25 3550 70 100 140 200 280 400 Filament extraction scale (pc)Unweighted,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' F2100w 100 Hll regions Clusters <5 Myr % 80 Associations<5 Myr (as Inclusion fraction ( 60 40 20 0 25 3550 70 100 140 200 280 400 Filament extraction scale (pc)SFR-weiahted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' F77oW 100 SFR-weighted incl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' fraction (as %) Hll regions Clusters <5 Myr 80 Associations <5 Myr 60 40 20 0 25 35 5070 100 140 200 280 400 Filament extraction scale (pc)SFR-weighted, F2100w 100 SFR-weighted incl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' fraction (as %) Hll regions Clusters <5 Myr 80 Associations <5 Myr 60 40 20 0 25 35 50 70100140 200 280 400 Filament extraction scale (pc)12 each of F770W, F1000W and F1130W when using the multi-scale masks, and 72% for F2100W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' We anticipated seeing a reduction in inclusion frac- tion for stellar associations, since, although the associ- ations are young, they are star formation events that have evolved from clusters via disruption/dissolution or were initially formed unbound, and either way seem more likely to have already cleared their environment of dust.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' However, the anti-correlation observed at small scales is an unexpected demonstration that such feed- back actively helps to sculpt the dust into bubble/shell structures (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Watkins et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' in prep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Barnes et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' subm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Work is currently underway to obtain a catalog of PHANGS-ALMA GMCs associated with embed- ded (t ∼ 0 Myr) star formation, indicated by compact F2100W sources coincident with a GMC (Lessing et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' in prep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=').' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' When ready, we will compare our dust emis- sion filaments to that population.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' We emphasize that the F2100W source population does not drive the identi- fication of filaments at 21µm due to FilFinder’s trans- formation of the image intensity scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' SUMMARY AND FUTURE WORK This paper presents initial exploratory analysis of PHANGS-JWST+HST imaging for NGC 628 revealing its extensive dust filament network (DFN) as seen in both MIR emission and visible attenuation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Our pilot investigation offers insight into extragalactic ISM struc- ture at small scales rarely probed by other tracers, in- cluding atomic and molecular gas, with an emphasis on quantifying filaments and associated star formation ac- tivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Conclusions from our study are as follows: 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' At the smallest extraction scale currently consid- ered (25 pc filament width), the agreement of in- dependently constructed attenuation and emission filament masks is 40%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' More so, the detailed mor- phology of filaments that are detected in both ways is frequently rather well-matched with only minor deviations in shape or extent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' We find evidence for emission-only filaments (and portions of filaments) likely on the ‘back side’ of the galaxy disk, but also a less well-understood set of attenuation-only fila- ments that requires further characterization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' No single extraction scale (filament width) pro- vides a complete inventory of all filamentary dust emission structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Our masks are detecting a morphologically diverse dusty ISM, spanning from very compact filaments to ultimately constitut- ing spiral arm features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' We anticipate that the molecular fraction probably declines with increas- ing scale in this hierarchy, but require higher reso- lution observations of atomic gas in order to check this.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' HST reveals candidate features we nickname ‘dust motes’ which are comparatively isolated (lying outside the DFN) and appear as compact (≲ 10 pc), dark clouds essentially unrecoverable with JWST /MIRI alone due to confusion with dusty stellar point sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' They could trace largely qui- escent individual molecular clouds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Regardless of whether candidate ‘dust motes’ are ultimately ver- ified as a bona fide population, HST is capable of probing substructure in dust filaments at smaller scales than MIRI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Approximately one-third of the total MIR flux in F770W, F1000W, F1130W bands is contained in the 25 pc scale mask of the emission filament net- work, using diffuse background subtracted mea- surements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' The flux fraction determined for the 200 pc limited cumulative multi-scale filament mask is 55–60% in the same bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' The F2100W filament flux fractions are significantly less than the others, with a cumulative measurement of ∼ 45%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' This is in-line with Leroy et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' (in prep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=') who showed that F2100W correlates less well with CO than the other MIRI bands and that it is not as clean of a tracer of column density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Our filament inclusion fraction analysis shows that 75–80% of the current star formation traced by H ii regions is occurring within the 25 pc scale of the filament network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' The analogous measurement for young (<5 Myr) clusters is slightly more than 60%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Integrated over cumulative scales up to 200 pc, the H ii region fraction exceeds 95%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Similar analy- sis demonstrates moderate anti-correlation of as- sociations younger than 5 Myr with dust filaments at scales <100 pc then a reversal to increasingly strong association-filament correlation for extrac- tion scales of 100, 140, and 200 pc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Expansion and further development of our work to the remaining PHANGS-JWST galaxies will: (a) pro- vide the clarity of an external and diversified perspec- tive which is absent from Galactic studies,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' and which can allow quantification of trends,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' (b) enable compari- son to increasingly detailed simulations,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' which can iso- late the effects of different ISM structuring mechanisms,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' (c) constrain the dependence of opacity on dust grain properties,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' and eventually (d) firmly quantify the di- vision of MIR emission between currently star-forming 13 and evolved stellar populations (related to the work of Belfiore et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' in prep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' ), with complete accounting of unobscured and embedded star formation (Rodriguez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' in prep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Hassani et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' in prep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=').' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' The union of JWST and HST dust tracing also motivates targeting for focused high-resolution ALMA follow-up mapping of dense gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' We further emphasize that ngVLA and/or SKA is required to obtain sensitive H i imaging at the substantially better than 6′′ resolution that is needed to constrain ISM phase changes within the filamentary structures we study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' We plan the following practical improvements to our work in the near term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Attenuation (dust lane) fea- tures will be identified on the basis of the complete multi-wavelength PHANGS-HST dataset and at sub- MIRI-resolution scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' We will study the integrated SED of the filament network versus scale, and use Fil- Finder capabilities to generate catalogs of filament sub- structures with measured properties (such as length, as- pect ratio, curvature, flux, mass per unit length) plus molecular-cloud-linked quantities (velocity gradient, CO velocity dispersion, virial parameter) when a GMC is found to be co-spatial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Such cataloged properties will be ripe for comparison to equivalent quantities measured from simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' We will assess whether or not embed- ded star-forming regions tend to be located at the in- tersection of filament spines, as they do in simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' of dust emission and attenuation filament network sub- structures versus physical condition metrics (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Sun et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2022) of the local (∼kpc-scale) environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' ACKNOWLEDGEMENTS This work was carried out as part of the PHANGS collaboration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Based on observations made with the NASA/ESA/CSA JWST and Hubble Space Telescopes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' The data were obtained from the Mikulski Archive for Space Telescopes at the Space Telescope Science Insti- tute, which is operated by the Association of Univer- sities for Research in Astronomy, Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', under NASA contract NAS 5-03127 for JWST and NASA contract NAS 5-26555 for HST.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' The JWST observations are associated with program 2107, and those from HST with program 15454 Based on observations collected at the European Southern Observatory under ESO pro- grammes 094.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='C-0623 (PI: Kreckel), 095.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='C-0473, 098.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='C- 0484 (PI: Blanc), 1100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='B-0651 (PHANGS-MUSE;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' PI: Schinnerer), as well as 094.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='B-0321 (MAGNUM;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' PI: Marconi), 099.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='B-0242, 0100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='B-0116, 098.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='B-0551 (MAD;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' PI: Carollo) and 097.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='B-0640 (TIMER;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' PI: Gadotti).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' We acknowledge the usage of the SAO/NASA Astro- physics Data System6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' acknowledges fund- ing support from STScI via JWST-GO-02107.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='002-A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' acknowledges support from the Smithsonian In- stitution as a Submillimeter Array (SMA) Fellow and the Natural Sciences and Engineering Research Coun- cil of Canada.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' gratefully acknowledges fund- ing from the European Research Council (ERC) under the European Union’s Horizon 2020 research and inno- vation programme via the ERC Starting Grant MUS- TANG (grant agreement number 714907).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' COOL Re- search DAO is a Decentralized Autonomous Organiza- tion supporting research in astrophysics aimed at un- covering our cosmic origins.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' acknowledges the funding provided by the Deutsche Forschungsgemein- schaft (DFG, German Research Foundation) – Project- ID 138713538 – SFB 881 (“The Milky Way System”, subproject P1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' gratefully acknowledges funding from the DFG through an Emmy Noether Research Group (grant number CH2137/1-1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' acknowl- edges support from FONDECYT regular grant 1211000 and by the ANID BASAL project FB210003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' acknowledge funding from the European Re- search Council (ERC) under the European Union’s Hori- zon 2020 research and innovation programme (grant agreement No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 694343).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' acknowledges the sup- port of the Natural Sciences and Engineering Re- search Council of Canada (NSERC), funding reference number RGPIN-2022-03499.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' would like to ac- knowledge funding from the European Research Coun- cil (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='726384/Empire) K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' is supported by the Australian Research Council through the Discovery Early Career Researcher Award (DECRA) Fellowship DE220100766 funded by the Australian Government.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' is sup- ported by the Australian Research Council Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), through project number CE170100013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' acknowledges financial support from the Euro- pean Research Council via the ERC Synergy Grant “ECOGAL” (project ID 855130), from the Deutsche Forschungsgemeinschaft (DFG) via the Collaborative Research Center “The Milky Way System” (SFB 881 – funding ID 138713538 – subprojects A1, B1, B2 and B8) and from the Heidelberg Cluster of Excellence (EXC 2181 - 390900948) “STRUCTURES”, funded by the German Excellence Strategy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' also thanks the German Ministry for Economic Affairs and Climate Ac- tion for funding in the project “MAINN” (funding ID 6 http://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='adsabs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='harvard.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='edu 14 50OO2206).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' acknowledges the support from ANID Basal project FB210003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' acknowledges support from the Spanish grant PID2019-106027GA- C44, funded by MCIN/AEI/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='13039/501100011033.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' acknowledges support from ANID Basal projects ACE210002 and FB210003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' is supported by fund- ing from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innova- tion programme (grant agreement no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 101018897 Cos- micExplorer).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' and O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' gratefully acknowledge funding from DFG in the form of an Emmy Noether Re- search Group (grant number KR4598/2-1, PI Kreckel).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Facilities: HST , JWST , VLT:Yepun Software: astropy (Astropy Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2013, 2018), numpy (Harris et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2020), mat- plotlib (Hunter 2007) and FilFinder (v1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Koch & Rosolowsky 2015) APPENDIX A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' DUST FILAMENT MASKS VERSUS BAND AND EXTRACTION SCALE In to permit examination of the extracted dust filaments with respect to the JWST and HST data, we present the filament masks as a Figure Set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' They are displayed first for F770W, then F2100W, and lastly HST B-band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' We show the filaments as transparent colored areas on the associated JWST or HST image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' For each band, we present all of the individual scale filament masks in order of increasing extraction scale, followed by the cumulative multi-scale masks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Set 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Dust filament masks REFERENCES Anand, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Rizzi, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Tully, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2021a, AJ, 162, 80, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='3847/1538-3881/ac0440 Anand, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Lee, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Van Dyk, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2021b, MNRAS, 501, 3621, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='1093/mnras/staa3668 Andr´e, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Di Francesco, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Ward-Thompson, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2014, in Protostars and Planets VI, ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Beuther, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Klessen, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Dullemond, & T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Henning, 27, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='2458/azu uapress 9780816531240-ch002 Andr´e, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Men’shchikov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Bontemps, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2010, A&A, 518, L102, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='1051/0004-6361/201014666 Astropy Collaboration, Robitaille, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Tollerud, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2013, A&A, 558, A33, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='1051/0004-6361/201322068 Astropy Collaboration, Price-Whelan, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Sip˝ocz, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2018, AJ, 156, 123, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='3847/1538-3881/aabc4f Baldwin, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Phillips, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', & Terlevich, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 1981, PASP, 93, 5, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='1086/130766 Barmby, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Ashby, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Bianchi, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2006, ApJL, 650, L45, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='1086/508626 Barnes, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Watkins, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' subm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', ApJL Belfiore, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' in prep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', A&A Boquien, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Burgarella, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Roehlly, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2019, A&A, 622, A103, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='1051/0004-6361/201834156 Boquien, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Kennicutt, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Calzetti, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2016, A&A, 591, A6, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='1051/0004-6361/201527759 Bradley, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Sip˝ocz, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Robitaille, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2022, astropy/photutils: 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='0, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='0, Zenodo, Zenodo, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='5281/zenodo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='6825092 Buta, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Sheth, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Athanassoula, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2015, ApJS, 217, 32, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='1088/0067-0049/217/2/32 Calzetti, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2013, in Secular Evolution of Galaxies, ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Falc´on-Barroso & J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Knapen, 419 Calzetti, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Lee, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Sabbi, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2015, AJ, 149, 51, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='1088/0004-6256/149/2/51 Crocker, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Calzetti, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Thilker, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2013, ApJ, 762, 79, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='1088/0004-637X/762/2/79 Dong, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Li, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Wang, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2016, MNRAS, 459, 2262, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='1093/mnras/stw778 Duarte-Cabral, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Acreman, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Dobbs, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2015, MNRAS, 447, 2144, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='1093/mnras/stu2586 Duarte-Cabral, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', & Dobbs, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2017, MNRAS, 470, 4261, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='1093/mnras/stx1524 Emsellem, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Schinnerer, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Santoro, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2022, A&A, 659, A191, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='1051/0004-6361/202141727 Goodman, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Alves, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Beaumont, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2014, ApJ, 797, 53, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='1088/0004-637X/797/1/53 Groves, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' subm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', MNRAS Hacar, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Clark, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Heitsch, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2022, arXiv e-prints, arXiv:2203.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='09562.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' https://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='org/abs/2203.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='09562 Harris, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Millman, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', van der Walt, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2020, Nature, 585, 357, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='1038/s41586-020-2649-2 Hassani, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' in prep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', ApJL Hinz, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Rieke, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Gordon, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2004, ApJS, 154, 259, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='1086/422558 Hoversten, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Gronwall, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Vanden Berk, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2011, AJ, 141, 205, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='1088/0004-6256/141/6/205 15 Figure A1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' JWST F770W image with extracted emission filaments (25 pc scale) shown as transparent colored areas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' The image is oriented with North up and East left.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' The complete figure set (44 images) is available in the online journal Hunter, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2007, Computing in Science & Engineering, 9, 90, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='1109/MCSE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='55 Jackson, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Finn, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Chambers, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Rathborne, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', & Simon, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2010, ApJL, 719, L185, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='1088/2041-8205/719/2/L185 Jeffreson, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Kruijssen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Keller, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Chevance, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', & Glover, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2020, MNRAS, 498, 385, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='1093/mnras/staa2127 Koch, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', & Rosolowsky, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2015, MNRAS, 452, 3435, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='1093/mnras/stv1521 Kumari, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Irwin, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', & James, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2020, A&A, 634, A24, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='1051/0004-6361/201732467 La Vigne, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Vogel, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', & Ostriker, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2006, ApJ, 650, 818, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='1086/506589 Lang, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Meidt, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Rosolowsky, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2020, ApJ, 897, 122, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content="3847/1538-4357/ab9953 F770W 25pc 15°49' 48' Declination (ICRS) 47' 46° 45° 1h36m48s 45s 42s 39s 36s Right Ascension (iCRS)16 Figure A2." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' JWST F770W image with extracted emission filaments (cumulative up to 200 pc scale) shown as transparent colored areas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' The image is oriented with North up and East left.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' The complete figure set (44 images) is available in the online journal Larson, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' subm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', MNRAS Lee, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' in prep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', ApJL Lee, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Whitmore, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Thilker, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2022, ApJS, 258, 10, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='3847/1538-4365/ac1fe5 Leike, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Glatzle, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', & Enßlin, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2020, A&A, 639, A138, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='1051/0004-6361/202038169 Leroy, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' in prep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', ApJL Leroy, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Bigiel, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', de Blok, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2012, AJ, 144, 3, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='1088/0004-6256/144/1/3 Leroy, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Hughes, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Liu, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2021, ApJS, 255, 19, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='3847/1538-4365/abec80 Lessing, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Thilker, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' in prep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', MNRAS Liu, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Koda, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Calzetti, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Fukuhara, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', & Momose, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2011, ApJ, 735, 63, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content="1088/0004-637X/735/1/63 F770W up to 200pc 15°49' 48' Declination (ICRS) 47' 46° 45° 1h36m48s 45s 42s 39s 36s Right Ascension (iCRS)17 Figure A3." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' JWST F2100W image with extracted emission filaments (35 pc scale) shown as transparent colored areas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' The image is oriented with North up and East left.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' The complete figure set (44 images) is available in the online journal Lonsdale Persson, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', & Helou, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 1987, ApJ, 314, 513, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='1086/165082 Meidt, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' in prep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', ApJL Pineda, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Arzoumanian, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Andr´e, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2022, arXiv e-prints, arXiv:2205.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='03935.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' https://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='org/abs/2205.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='03935 Ragan, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Henning, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Tackenberg, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2014, A&A, 568, A73, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='1051/0004-6361/201423401 Rodriguez, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' in prep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', ApJL Sandstrom, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' in prep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', ApJL Santoro, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Kreckel, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Belfiore, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2022, A&A, 658, A188, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='1051/0004-6361/202141907 Smith, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Glover, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Clark, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Klessen, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', & Springel, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2014, MNRAS, 441, 1628, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content="1093/mnras/stu616 F2100W 35pc 15°49' 48' Declination (ICRS) 471 46° 45° 1h36m48s 45s 42s 39s 36s Right Ascension (iCRS)18 Figure A4." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' JWST F2100W image with extracted emission filaments (cumulative up to 200 pc scale) shown as transparent colored areas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' The image is oriented with North up and East left.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' The complete figure set (44 images) is available in the online journal Smith, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Treß, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Sormani, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2020, MNRAS, 492, 1594, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='1093/mnras/stz3328 Soler, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Beuther, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Syed, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2020, A&A, 642, A163, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='1051/0004-6361/202038882 Sun, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Leroy, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Rosolowsky, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2022, AJ, 164, 43, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='3847/1538-3881/ac74bd Syed, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Soler, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Beuther, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2022, A&A, 657, A1, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='1051/0004-6361/202141265 Thilker, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Whitmore, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Lee, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2022, MNRAS, 509, 4094, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='1093/mnras/stab3183 Thilker, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' in prep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', MNRAS Tress, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Sormani, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Glover, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2020, MNRAS, 499, 4455, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content="1093/mnras/staa3120 F2100W,up to 200pc 15°49' 48' Declination (ICRS) 47' 46° 45° 1h36m48s 45s 42s 39s 36s Right Ascension (iCRS)19 Figure A5." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' HST B-band (F435W) image with extracted attenuation filaments (25 pc scale) shown as transparent colored areas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' The image is oriented with North up and East left.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' The complete figure set (44 images) is available in the online journal Treß, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Sormani, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Smith, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2021, MNRAS, 505, 5438, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='1093/mnras/stab1683 Turner, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Dale, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Lee, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2021, MNRAS, 502, 1366, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='1093/mnras/stab055 Verley, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Corbelli, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Giovanardi, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', & Hunt, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2009, A&A, 493, 453, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='1051/0004-6361:200810566 Verley, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Hunt, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Corbelli, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', & Giovanardi, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2007, A&A, 476, 1161, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='1051/0004-6361:20078179 Watkins, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' in prep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', ApJL Zucker, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', Battersby, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=', & Goodman, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2015, ApJ, 815, 23, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content='1088/0004-637X/815/1/23 —.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' 2018, ApJ, 864, 153, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content="3847/1538-4357/aacc66 HST F435W 25pc 15°49' 48' Declination (ICRS) 47' 46° 45° 1h36m48s 45s 42s 39s 36s Right Ascension (iCRS)20 Figure A6." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' HST B-band (F435W) image with extracted attenuation filaments (cumulative up to 200 pc scale) shown as transparent colored areas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' The image is oriented with North up and East left.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=" The complete figure set (44 images) is available in the online journal HST F435W up to 200pc 15°49' 48' Declination (ICRS) 47' 46° 45° 1h36m48s 45s 42s 39s 36s Right Ascension (iCRS)All Authors and Affiliations David A." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/Z9AyT4oBgHgl3EQf9vq-/content/2301.00881v1.pdf'} +page_content=' Thilker ,1 Janice C.' metadata={'source': 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a/ZNAzT4oBgHgl3EQfm_0c/content/tmp_files/2301.01571v1.pdf.txt b/ZNAzT4oBgHgl3EQfm_0c/content/tmp_files/2301.01571v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..2f1a81f4c50ee2861d414131959250410a0d6140 --- /dev/null +++ b/ZNAzT4oBgHgl3EQfm_0c/content/tmp_files/2301.01571v1.pdf.txt @@ -0,0 +1,1158 @@ +arXiv:2301.01571v1 [cs.DM] 4 Jan 2023 +Reconstructing words using queries on subwords or factors +Gwena¨el Richomme∗, Matthieu Rosenfeld† +January 5, 2023 +Abstract +We study word reconstruction problems. Improving a previous result by P. Fleischmann, +M. Lejeune, F. Manea, D. Nowotka and M. Rigo, we prove that, for any unknown word +w of length n over an alphabet of cardinality k, w can be reconstructed from the number +of occurrences as subwords (or scattered factors) of O(k2� +n log2(n)) words. Two previous +upper bounds obtained by S. S. Skiena and G. Sundaram are also slightly improved: one +when considering information on the existence of subwords instead of on the numbers of their +occurrences, and, the other when considering information on the existence of factors. +∗Universit´e Paul-Val´ery Montpellier 3, Universit´e de Montpellier, CNRS, Montpellier, France +†Universit´e de Montpellier, CNRS, Montpellier, France +1 + +1 +Introduction +A natural combinatorial question is to ask how much partial information on an object is needed +to reconstruct this object (see below and in our references for examples). +For example, in +[2, 3], P. Fleischmann, M. Lejeune, F. Manea, D. Nowotka and M. Rigo consider the problem +of reconstructing a word w from information on the number of occurrences as subwords of w of +some words. Let us recall that a word u is a subword of a word w (or a scattered subword of w) +if u and w can be decomposed in the form u = u1 · · · uℓ and w = v0u1v1 · · · uℓvℓ for some words +u1, . . . , uℓ, v0, . . . , vℓ. Such a double decomposition marks an occurrence of u as a subword of +w. The number of occurrences of u as a subword of w is sometimes denoted as the binomial +coefficient +�w +u +� +since this number coincides with the traditional coefficient +�|w| +|u| +� +when the words +u and w are written on a single letter (here, as usual in combinatorics on words, |w| denotes +the length of w), see for instance [8, chap. 6]. The problem addressed by Fleischmann et al. +is presented as a game in which the player has to guess an unknown word. In his task the +player asks questions in a certain form until he has enough information to uniquely determine +the word. More precisely, at each round, the player chooses a word u based on the previous +answers that he obtained and asks for the value of +�w +u +� +. The goal of the player is to minimize the +number of questions. Fleischmann et al. proved that there is a strategy to ensure that at most +min(|w|a, |w|b) + 1 ≤ ⌊|w| +2 ⌋ + 1 questions are needed when w is defined on the binary alphabet +{a, b} (for a letter α, |w|α = +�w +α +� +denotes the number of occurrences of α in w). For any word +w over the alphabet {1, . . . , k} they proved that the number of questions needed is bounded by +� +i∈{1,...,k} |w|i(k + 1 − i). Our main results (Theorem 2.1 and Corollary 2.6) prove that this +number of questions is at most +�k +2 +� � +7 +�� +|w| log2(|w|) +� ++ 4 +� +. For any fixed k, our upper bound +is asymptotically much stronger as the length of the word goes to infinity. For binary words in +particular, their upper bound is |w| +2 + 1 and ours is 7 +�� +|w| log2(|w|) +� ++ 4 . We also adapt this +strategy (Theorem 2.2) to provide an algorithm whose expected running time over a uniform +random binary word of length n is O(log2 n). +Let us recall that the previous game is related to another problem that seems to have been +first introduced by L. O. Kalashnik [5]: What is the smallest ℓ such that we can reconstruct +w from the values +�w +u +� +for all words u of length ℓ? As far as we know, the best upper bound, +⌊16 +7 +� +|w|⌋ + 5, for this problem was obtained by I. Krasikov and Y. Roditty in 1997 [6] using a +link with the Prouhet-Tarry-Escott problem about Diophantine analysis. Also the best known +lower bound, 3(√ +2/3−o(1)) log1/2 +3 +(|w|)), is due to [1]. Our result does not improve this upper bound +since, in the binary case, at least one query concerns a word u of length at least min(|w|0, |w|1) +which is around |w|/2 for many words w. +In a variant of the previous problem queries in the form “what is the value of +�w +u +� +?” is +replaced with queries in the form “Is +�w +u +� +≥ 1?” or equivalently “Is u a subword of w?”. More +precisely the problem is to determine the least value ℓ such that the set of subwords of length ℓ +determines uniquely a word w. This problem arose in various areas. In [8, Chap 6], it is proved +that any word w of length n over an alphabet A is uniquely determined by its set of subwords +in the form a∗b∗ of length at most ⌈|w|a + |w|b + 1/2⌉ with a and b distinct letters of A. The +problem is also studied in [7]. +In [9, 10], in the context of DNA sequencing of hybridization, S. S. Skiena and G. Sundaram +consider the problem of minimizing the number of queries in the form “Is u a subword of w?”. +They prove that a word w of length n over an alphabet A of cardinality k can be reconstructed +using O(n log2(k) + k log2(n)) such queries. +More precisely Theorem 15 in [10] states that +1.59n log2(k) + 2k log2(n) + 5k queries are sufficient to reconstruct w. Using a basic information +theory approach S. S. Skiena and G. Sundaram also provide the lower bound n log2 k for the +number of queries. In Section 3, we slightly improve S. S. Skiena and G. Sundaram’s strategy +and we provide a new upper bound, reducing the gap with the lower bound. More precisely, +2 + +we state that at most n log2(k) + k(2 + ⌊log2(n + 1)⌋) queries are sufficient to reconstruct w, +reducing the gap between the bounds from 0.59n log2(k) + O(k log2(n)) down to O(k log2(n)). +In Section 4, we consider factors instead of subwords (a word u is a factor of a word w if +there exist words p and s such that w = pus) and the corresponding problem of minimizing +the number of queries in the form “Is u a factor of w?” needed to reconstruct an unknown +word w. In [9, 10], S. S. Skiena and G. Sundaram prove that, for an unknown word w over an +alphabet A of cardinality k, if the length n of w is known then w can be reconstructed using +a number of queries which is in (k − 1)n + 2 log2(n) + O(k). Actually their proof leads to the +upper bound (k − 1)n + log2(n) + O(k), which is n + log2(n) + O(1) in the binary case. This +more accurate upper bound was already mentioned in the binary case in [10]. A simple double +counting argument (there are kn words of length n and each question has two possible outcomes) +leads to the lower bound n log2 k. We improve their strategy and reduce the upper bound to +(k − 1)(n + 2) + +� +log2(n) +2 +� ++ 3. In the binary case, this reduces the gap between the lower and +the upper bound from log2(n) + O(1) down to +� +log2(n) +2 +� ++ 5. +Queries in the form “What is the number of occurrences of a word u as a factor of w” +have also been considered by S.S. Skiena et G. Subraman [10]. Their lower bound nk/4 − o(n) +on the number of queries needed is, up to our knowledge, the best known. One can deduce +whether a word u occurs as a factor in a word w from the number of occurrences of u in w. +This observation allows them to obtain the same upper bounds for this fourth problem than for +the previous problem. Similarly, our bound applies. Hence, we also slightly improve the upper +bound in this case, but this improvement is negligible compared to the size of the gap between +the lower bound and the upper bound. +Basic definitions and notations have already been recalled (following [8]). Let us observe +that #S denotes the cardinality of a set S. Moreover, given a word w over an alphabet A, we +will simply use n to denote the length |w| of w and k to denote the cardinality #A of A. +2 +How-many-subwords queries +In this section, we focus on queries in the form “How many occurrences of u as a subword does +w contains?” or equivalently “What is the value of +�w +u +� +?”. We call such a query a #-subword +query. Our main result regarding this kind of query is the following. Of course, as it will be +the case for other queries in the next sections, we assume that such a query can be answered +without knowing w. +Theorem 2.1. The number of #-subword queries needed to reconstruct a word of length n over +{0, 1} is at most 7 +�√n log n +� ++ 4 whether n is known or not. +A word w that contains m occurrences of 1, can always be written as w = 0s010s11 . . . 10sm +where the si are nonnegative integers. Since m = +�w +1 +� +, it only requires one query to find m. Our +goal is to find the values of all the si. Our strategy relies on the fact that if we know which of +the si are “large” and if we know their values then we can determine multiple others si with a +single query (this is shown in Lemma 2.4). On the other hand since we cannot have too many +“large” si we have an efficient strategy to find all these si (see Lemma 2.5). Using these two +facts together and optimizing the meaning of “large” we get the desired result. +Actually, in a uniform random word we do not expect to have any si larger than O(log n) +and this leads to a more efficient average case algorithm. +Theorem 2.2. There is a deterministic strategy that, given any integer n, reconstructs in av- +erage in O(log2(n)) queries any word w taken uniformly at random among all binary words of +length n. +The next lemma allows to prove Lemma 2.4. +3 + +Lemma 2.3. Let r, ℓ, s1, . . . , sr be non-negative integers such that 1 ≤ r ≤ ℓ + 1 and for all +j ∈ {1, . . . , r}, sj < +ℓ+1 +r . The values of s1, . . . , sr are uniquely determined by the values of +�0sr 10sr−11···0s210s11ℓ +01ℓ +� +, r and ℓ. +Proof. Let us first express the number of occurrences of 01ℓ as subword in 0sr10sr−11 · · · 0s11ℓ. +By considering separately the different possible positions of the 0 in the occurrence we obtain +�0sr10sr−11 · · · 0s210s11ℓ +01ℓ +� += +r +� +j=1 +sj +�ℓ + j − 1 +ℓ +� += +r +� +j=1 +sj +�ℓ + j − 1 +j − 1 +� +. +(1) +Let β = maxj sj. We first show that for all t ∈ {1, . . . , r}, +t +� +j=1 +sj +�ℓ + j − 1 +j − 1 +� +≤ β +�ℓ + t +t − 1 +� +. +(2) +We proceed by induction on t. It is easily verified for t = 1. Now if (2) holds for t, then +t+1 +� +j=1 +sj +�ℓ + j − 1 +j − 1 +� += +t +� +j=1 +sj +�ℓ + j − 1 +j − 1 +� ++ st+1 +�ℓ + t +t +� +≤ β +�ℓ + t +t − 1 +� ++ st+1 +�ℓ + t +t +� +≤ β +��ℓ + t +t − 1 +� ++ +�ℓ + t +t +�� += β +�ℓ + t + 1 +t +� +which concludes the inductive proof of (2). +Moreover, for all t ∈ {1, . . . , r}, β +�ℓ+t +t−1 +� +< ℓ+1 +r +�ℓ+t +t−1 +� +≤ ℓ+1 +t +�ℓ+t +t−1 +� += +�ℓ+t +t +� +. Together with (2), it +implies that for all t ∈ {1, . . . , r}, +0 ≤ +t +� +j=1 +sj +�ℓ + j − 1 +j − 1 +� +< +�ℓ + t +t +� +. +(3) +Observe that, for all t ∈ {1, . . . , r − 1}, +st+1 = +�t+1 +j=1 sj +�ℓ+j−1 +j−1 +� +− �t +j=1 sj +�ℓ+j−1 +j−1 +� +�ℓ+t +t +� +. +But st+1 is an integer and by equation(3) the right part of the fraction in the left-hand-side is +in [0, 1[ we deduce +st+1 = +��t+1 +j=1 sj +�ℓ+j−1 +j−1 +� +�ℓ+t +t +� +� +. +(4) +By Equations (1) and (4), we can deduce the value of sr from r, l and �r +j=1 sj +�ℓ+j−1 +j−1 +� +which is it- +self deduced from +�0sr 10sr−11···0s210s11ℓ +01ℓ +� +. From the value of sr, we can now deduce �r−1 +j=1 sj +�ℓ+j−1 +j−1 +� +and thus sr−1 by (4). Thus, by an “inverse induction” from r − 1 to 1, we deduce the values of +all the sj. +Lemma 2.3 allows us to determine the length of multiple consecutive 0-blocks with only one +query under some strong hypothesis, but we can relax these hypotheses as follows. The idea is +that if we have some large si and a prefix, it is enough to know the value of these si and of the +prefix in order to remove their contribution before applying the previous lemma. +Lemma 2.4. Let p and v be words, r and s1, . . . , sr be nonnegative integers such that 1 ≤ r ≤ +|v|1 + 2 and let w = p0sr10sr−1 . . . 10s11v. Suppose that p, |v|1 and r are known and that for all +j, either sj is known or sj < |v|1+2 +r +, then the value of +� +w +011+|v|1 +� +uniquely determines the values +of all the unknown sj for j ∈ {1, . . . , r}. +4 + +Proof. For all j ∈ {1, . . . , r}, let s′ +j be such that if sj < |v|1+2 +r +, then s′ +j = sj and s′ +j = 0 otherwise. +Then sj − s′ +j is known for all j (it is sj if sj is known and 0 otherwise) and for all j, s′ +j < |v|1+2 +r +. +Now, by considering the possible positions of the 0 in the occurrences of 011+|v|1, we get +� +w +011+|v|1 +� += +�p1r+|v|1 +011+|v|1 +� ++ +�0sr10sr−1 . . . 10s111+|v|1 +011+|v|1 +� += +�p1r+|v|1 +011+|v|1 +� ++ +r +� +j=1 +sj +�j + |v|1 +1 + |v|1 +� += +�p1r+|v|1 +011+|v|1 +� ++ +r +� +j=1 +(sj − s′ +j) +�j + |v|1 +1 + |v|1 +� ++ +r +� +j=1 +s′ +j +�j + |v|1 +1 + |v|1 +� += +�p1r+|v|1 +011+|v|1 +� ++ +r +� +j=1 +(sj − s′ +j) +�j + |v|1 +1 + |v|1 +� ++ +�0s′ +r10s′ +r−1 . . . 10s′ +111+|v|1 +011+|v|1 +� +. +It implies that, +�0s′ +r10s′ +r−1 . . . 10s′ +111+|v|1 +011+|v|1 +� += +� +w +011+|v|1 +� +− +�p1r+|v|1 +011+|v|1 +� +− +r +� +j=1 +(sj − s′ +j) +�j + |v|1 +1 + |v|1 +� +. +By assumption, +� +w +011+|v|1 +� +, p, r, |v|1 and for all j, (sj − s′ +j) are known. Hence, the quantity +�0s′r 10s′ +r−1...10s′ +111+|v|1 +011+|v|1 +� +is uniquely determined. For all j, s′ +j < |v|1+2 +r +and we deduce from Lemma +2.3 that the values of all the s′ +j are uniquely determined which concludes our proof. +For any word w over {0, 1} decomposed as w = 0s010s11 · · · 0st−110st, we call i the index of +the 0-block 0si. If we want to use the previous lemma to reconstruct a word, we first need to +determine the indices of all the 0-blocks that are longer than some predetermined length. +Lemma 2.5. Let w ∈ {0, 1}∗ and m be an integer. Let I be the set of indices of 0-blocks of w +of length at least m. Suppose that we know |w| and |w|0 (and so also |w|1 = |w| − |w|0), then +the number of #-subword queries needed to determine I is at most +2|w|0⌈log2(|w|1 + 1)⌉ +m +. +Proof. We use Algorithm 1 to determine I calling it with ℓ = 0 and u = |w|1. +Note that +|w|1 = |w| − |w|0 is known. +Algorithm 1 An algorithm that prints the indices i ∈ {ℓ, . . . , u} of the 0-blocks of length at +least m that occur in w +procedure Recblocks(w, m, ℓ, u) +if +� +w +1ℓ0m1|w|1−u +� +≥ 1 then +if u = ℓ then +Print ℓ +else +Recblocks(w, m, ℓ, ⌊ℓ+u +2 ⌋) +Recblocks(w, m, ⌊ℓ+u +2 ⌋ + 1, u) +The condition of the main “if” verifies that the lengths of the 0-blocks whose indices are in +{ℓ, . . . , u} sum to at least m. If it doesn’t then we know that none of these blocks can have +length at least m so we do not need to call the function recursively on any of them. From this, +verifying the correctness of the algorithm is rather straightforward. +5 + +Let us now bound the total number of queries. For this, we consider the tree of recursive calls +to Recblocks defined as follows: the root of the tree is the initial call with ℓ = 0 and u = |w|1; +a call a is the child of another call b if the call a was made in b. The depth of a call is its +distance to the root. The weight of a call is the quantity u + 1 − ℓ. For any call of weight x, +the weights of its children are ⌈x/2⌉ or ⌊x/2⌋ (and the sum of the weights of the two children +is x). Let f be the function such that f : x → ⌈x +2⌉. The root has weight |w|1 + 1 and f is a +non-decreasing function, so any call of depth d has weight at most f d(|w|1 + 1). For any integer +x, f(x) ≤ x+1 +2 , and, in particular, for all d ≥ 1, f d(|w|1 + 1) ≤ fd−1(|w|1+1)+1 +2 +. By induction on +d, f d(|w|1 + 1) < |w|1+1 +2d ++ 1. Any call of depth ⌈log2(|w|1 + 1)⌉ has weight at most 1 (the weight +is an integer smaller than 2) and is a leaf of the tree. Hence, the depth of any call is at most +⌈log2(|w|1 + 1)⌉. +Moreover, one easily verifies by induction on the depth that for any two different calls c and +c′ at the same depth the corresponding intervals [ℓ, u] and [ℓ′, u′] are disjoint. We say that a +call with the values ℓ and u owns the occurrences of 0 that belongs to all the blocks of indices +between ℓ and u. Then by the previous remark, the set of occurrences of 0 owned by two calls +at the same depth are disjoint. Since the condition of the first “if” is true if the call owns at +least m occurrences of 0, we deduce that there are at most |w|0 +m +such calls on any given depth. +Since each such call has two children, we deduce that the number of calls at any depth is at +most 2|w|0 +m . Hence the total number of calls, is at most 2|w|0⌈log2(|w|1+1)⌉ +m +. Since we ask one query +by call this concludes the proof. +We are now ready to show our main result. We will first use the algorithm from Lemma 2.5 +to find all the blocks that are of length +�√n log n +� +and then we use Lemma 2.4 to determine all +the other blocks. +Proof of Theorem 2.1. +Phase 1. Let w be the unknown word. It costs two queries to get |w|0 = +�w +0 +� +and |w|1 = +�w +1 +� +. +Then n = |w| = |w|0 + |w|1 is known. Suppose without loss of generality that +�w +0 +� +≥ n/2 ≥ +�w +1 +� +(otherwise simply exchange the role of 0 and 1 in the following). +Phase 2. Let m = +�√n log n +� +. We use the algorithm from Lemma 2.5 to locate all the +0-blocks of length at least m. There are at most +n +m such blocks and we can use one query +for each of them to determine their respective length: Indeed if the block is at index i with +i ∈ {0, . . . , |w|1}, its length is +� +w +1i01|w|1−i +� +. Thus locating 0-blocks of length at least m together +with their lengths require at most 2|w|0⌈log(|w|1+1)⌉ +m ++ n +m queries. This number of queries is less +than 3n log n +m +≤ 3√n log n. +Phase 3. We now need to determine the lengths of 0-blocks of length at most m. We first +determine the 0-blocks occurring before the +� +|w|1 +2 +� +last occurrences of 1. Secondly, we determine +the 0-blocks occurring after the +� +|w|1 +2 +� +first occurrences of 1. After this, the lengths of all the +0-blocks are known and we know w. We describe only how to determine the first half of the +blocks, since reconstructing the second half of the blocks can be done symmetrically. +There are +� +|w|1 +2 +� ++ 1 0-blocks before the +� +|w|1 +2 +� +last occurrences of 1. We determine the +unknown blocks among them in at most m steps from left to right considering, at each step, at +most r = +� +|w|1 +2m +� +blocks. Since mr ≥ |w|1 +2 +− m, we might miss up to m + 1 blocks after this, that +we can recover one by one for up to m + 1 extra queries. At one step w = p0sr10sr−1 · · · 10s11v +with p an already known prefix of w (initially p is the empty word) and |v|1 ≥ +� +|w|1 +2 +� +. For each +i ∈ {1, . . . , r}, if si is unknown then si < m = +|w|1/2 +|w|1/(2m) < |v|1+2 +r +. By Lemma 2.4, only one query +is needed to know the r blocks. Hence, we determine the 0-blocks occurring before the +� +|w|1 +2 +� +last occurrences of 1 in at most 2m + 1 = 1 + 2 +�√n log n +� +queries (and similarly to know the +6 + +0-blocks occurring after the +� +|w|1 +2 +� +last occurrences of 1). +In total, our strategy uses 2 + 3 +�√n log n +� ++ 2(1 + 2 +�√n log n +� +) = 7 +�√n log n +� ++ 4. +For any alphabets A and B ⊆ A and any word u over A, the projection of u onto B is the +word obtained by removing from u any letter that does not belong to B. We denote it πB(u). For +instance, π{0,1}(0120201) = 01001. Over an alphabet of cardinality k if we know the projections +over all the binary sub-alphabets, we can uniquely determine the whole word [8, Lemma 6.2.19]. +So Theorem 2.1 has the following corollary. +Corollary 2.6. The number of #-subword queries needed to reconstruct a word of length n over +an alphabet of cardinality k is at most +�k +2 +� +(7 +�√n log n +� ++ 4) . +In Theorem 2.1 and Corollary 2.6, we did not try to optimize the multiplicative constant, +because we believe that the √n log n bound is not “sharp up to a multiplicative constant”. As +suggested by Theorem 2.2, the number of required queries in Theorem 1 and Corollary 6 might +be in O(log n). +As we will see in Lemma 2.7, the probability that there is a 0-block of length more than +⌈2 log2(n)⌉ is small. +Lemma 2.7. Let w be a word taken uniformly at random among all binary words of length n. +The probability that w contains the factor 0⌈2 log2(n)⌉ is at most 1/n. +Proof. Let m = ⌈2 log2(n)⌉. +Let w1, . . . , wn ∈ {0, 1} be such that w = w1 · · · wn. +For all +i ∈ {1, . . . , n − m + 1}, let Ei be the event that wiwi+1 . . . wi+m−1 = 0m. +Then for all i, +P(Ei) = 2−m ≤ 1/n2. By union bound, +P(0m is a factor of w) = P(∪n−m+1 +i=1 +Ei) ≤ +n−m+1 +� +i=1 +P(Ei) ≤ 1 +n +as desired. +Proof of Theorem 2.2. First, we determine the number of 0 and 1 in w in 2 queries. Let m = +⌈2 log2(n)⌉. We first assume that there is no factor 0m in w. We can now apply Lemma 2.4 as +in Phase 3 of the proof of Theorem 2.1, but with m = ⌈2 log2(n)⌉. We now have a candidate +word w′ and we can ask one more question, +� w +w′ +� +, to verify if w = w′ (this might not be the case, +if our starting assumption was false). All of this take O(log2(n)) queries. +If we did not obtain the correct word, we know that our assumption was false and we +use Theorem 2.1 to find w in O( +� +n log2(n)) extra queries. +By Lemma 2.7, this happens +with probability at most 1/n, so the expected number of queries of this procedure is at most +O(log2(n)) + O( +� +n log2(n)/n) = O(log2(n)). +3 +Exists-subword queries +In this section, we focus on queries in the form “Is u a subword of w?” or equivalently “Is +�w +u +� +≥ 1?”. We call such a query an ∃-subword query. The reconstruction problem using ∃- +subword queries of a word w of unknown length n over an alphabet A of cardinality k was +solved by S. S. Skiena and G. Sundaram [9, 10] using 1.59n log2(k) + 2k log2(n) + 5k queries. +We improve the main coefficient of the bound, replacing 1.59 by 1 which is optimal (any such +algorithm requires at least n log2(k) queries in the worst case [9, 10]). +Theorem 3.1. The number of ∃-subword queries needed to reconstruct an unknown word w of +unknown length n over an alphabet A of cardinality k is at most +n⌈log2(k)⌉ + k (2 + ⌊log2(n + 1)⌋) . +7 + +Actually, our approach is similar to the method used in [9, 10]. +We act essentially by +dichotomy on the alphabet but when reconstructing words from their projections on a smaller +alphabet we improve the bound on the number of queries. Also on small alphabets we use a +linear decomposition instead of a binary decomposition in order to reduce the number of queries +needed to deduce the number of occurrences of some letters. +To prove Theorem 3.1 we use the next two lemmas. The first one considers the reconstruction +problem in the one letter alphabet case. The second one describes upper bounds on the number +of queries needed to reconstruct a word from projections on disjoint alphabets. +Lemma 3.2. Given an unknown nonempty word w of length n over an alphabet A and a letter +α ∈ A, the value |w|α can be determined using +• at most 2⌊1 + log2(|w|α + 1)⌋ ∃-subword queries if n is unknown and +• at most ⌈log2(n + 1)⌉ ∃-subword queries if n is known. +The proof of this Lemma is a simple binary search. The details can be found in Appendix A. +In the next Lemma we explain how to reconstruct a word w from its projections on two disjoint +complementary alphabets. Note that [10, Lemma 14], is almost the same result with a number +of queries 2.18|πB(w)| + |πC(w)| + 5 instead of |πB(w)| + |πC(w)| + 1. The main difference is that +instead of using a binary search we simply go greedily from left to right when combining the two +words. This lemma almost exclusively explains the improvement we obtain over [10, Theorem +2]. +Lemma 3.3. Let w be an unknown word of length n over an alphabet A. Let B and C be two +disjoint alphabets such that A = B ∪ C, then +1. if we know both projections πB(w) and πC(w), then the word w can be reconstructed using +at most n − 1 ∃-subword queries, +2. if we know the word πB(w) and #C = 1, then the word w can be reconstructed using at +most n + 1 ∃-subword queries. +It may be observed that in item 1 of Lemma 3.3, the length of w can be determined without +asking any query since it is equal to |πB(w)| + |πC(w)|. This is not the case in item 2. In both +cases, the length is not directly used in the proof. +For any word x = x1 · · · xℓ ∈ {0, 1}ℓ and integers i, j ∈ {1, . . . , ℓ}, let x[i . . . j] = xixi+1 · · · xj +when i ≤ j. By extension, if i > j (and possibly i = |x| + 1 or j = 0), then x[i . . . j] is the empty +word. +Proof of Lemma 3.3. Assume first that u = πB(w) and v = πC(w) are known. The first letter +of w is either u1 or v1. More precisely, u1v is a subword of w if and only if u1 is the first letter +of w, otherwise v1 is the first letter of w. Thus in one question we can determine the first letter +of w, and the projections πB(w[2 . . . n]) and πC(w[2 . . . n]). We can repeat this process and after +each new query we obtain the next letter of w and the two projections of the rest of w over B +and C. +Hence Algorithm 2 allows to reconstruct w from u and v. In this algorithm i and j store +respectively the successive length of πB(w[1 . . . i + j]) and πC(w[1 . . . i + j]): at the beginning of +each while loop, we know p = w[1 . . . i + j]. +From the preliminary comments, it is straightforward that at the end of the algorithm p = w +and that the number of ∃-subword queries asked is at most n − 1. +From now on assume that we only know the word πB(w) and the fact that C = {a} for some +letter a. We use a strategy similar to the previous case, that is, we try to insert occurrences of +the letter a between the letters of πB(w) in a greedy way. Once the places of all letters of πB(w) +are known, one has to determine the remaining occurrences of a at the end of w. This leads to +8 + +Algorithm 2 An algorithm that returns an unknown word w over B ∪ C with B ∩ C = ∅ from +u = πB(w) and v = πC(w) +p ← ε ; i ← 0 ; j ← 0 +while i < |u| and j < |v| do +if pui+1v[j + 1..|v|] is a subword of w then +p ← pui+1 ; i ← i + 1 +else +p ← pvj+1 ; j ← j + 1 +p ← pu[i + 1..|u|]v[j + 1..|v|] +return p +the variant Algorithm 3 for which the number of ∃-subword queries asked is exactly n+1: there +is one query by letter of πB(w) and πC(w) and one additional query needed to determine when +there is no more letter in πC(w). +Algorithm 3 An algorithm that returns an unknown word w over B ∪ {a} with a ̸∈ B from +u = πB(w) +p ← ε ; i ← 0 +while i < |u| do +if pau[i + 1..|u|] is a subword of w then +p ← pa +else +p ← pui+1 ; i ← i + 1 +while pa is a subword of w do +p ← pa +return p +The proof of the next result explains the strategy to solve the reconstruction problem using +∃-subword queries. The length of w may be unknown. +Proposition 3.4. Let w be an unknown word over an alphabet of cardinality k. For any B ⊆ A +with #B ≥ 2, the number of ∃-subword queries needed to reconstruct the word πB(w) is at most +⌈log2(#B)⌉|πB(w)| + #B +� +2 + max +α∈B ⌊log2(|w|α + 1)⌋ +� +. +Proof. We proceed by induction on the cardinality of B with the two base cases being #B = 2 +and #B = 3. +If B = {x, y} ⊆ A with x ̸= y, we can apply Lemma 3.2 to determine π{x}(w) = x|w|x in at +most 2⌊1 + log2(|w|x + 1)⌋ queries. Case 2 of Lemma 3.3 implies that we can then determine +π{x,y}(w) in at most |π{x,y}(w)| + 1 extra queries. The total number of queries is at most +|π{x,y}(w)| + 1 + 2⌊1 + log2(|w|x + 1)⌋ ≤ ⌈log2(#B)⌉|πB(w)| + #B +� +2 + max +α∈B ⌊log2(|w|α + 1)⌋ +� +as desired. +If B = {x, y, z} for some distinct letters x, y, z ∈ A, we use the strategy of the previous +paragraph to determine π{x,y}(w) and we use case 2 of Lemma 3.3 once again to obtain π{x,y,z}(w) +in at most |π{x,y,z}(w)| + 1 extra queries. The total number of queries is then at most +|π{x,y}(w)|+|πB(w)|+2+2⌊1+log2(|w|x+1)⌋ ≤ ⌈log2(#B)⌉|πB(w)|+#B +� +2 + max +α∈B ⌊log2(|w|α + 1)⌋ +� +9 + +as desired. +We now have to deal with the induction. Assume #B ≥ 4. Let C, C′ ⊆ B be two disjoint +alphabets such that B = C ∪ C′, #C = ⌊#B +2 ⌋ and #C′ = ⌈#B +2 ⌉. The two last conditions imply +⌈log2 #C⌉ ≤ ⌈log2 #C′⌉ = ⌈log2 #B⌉ − 1 . +By induction hypothesis, the number of queries to determine πC(w) and πC′(w) is at most +⌈log2(#C)⌉|πC(w)| + #C +� +2 + max +α∈C ⌊log2(|w|α + 1)⌋ +� ++⌈log2(#C′)⌉|πC′(w)| + #C′ +� +2 + max +α∈C′⌊log2(|w|α + 1)⌋ +� +≤ (⌈log2(#B)⌉ − 1)(|πC(w)| + |πC′(w)|) + (#C′ + #C) +� +2 + max +α∈C′∪C⌊log2(|w|α + 1)⌋ +� +≤ (⌈log2(#B)⌉ − 1)(|πB(w)|) + #B +� +2 + max +α∈B ⌊log2(|w|α + 1)⌋ +� +. +By case 1 of Lemma 3.3, we only need |πB(w)| extra queries to determine πB(w). In total, we +used at most ⌈log2(#B)⌉(|πB(w)|) + #B +� +2 + max +α∈B ⌊log2(|w|α + 1)⌋ +� +queries as required. +Proof of Theorem 3.1. Theorem 3.1 is an immediate consequence of Proposition 3.4 taking B = +A and using max +α∈B ⌊log2(|w|α + 1)⌋ ≤ ⌊log2(|w| + 1)⌋ +4 +Exists-factor queries +In this section, we focus on queries in the form “Is u a factor of w?”. Our aim is to prove +Theorem 16. As for the result from [10] that we improve here, we assume in this section that +the length of the word to determine is known. +A factor u is said right-extendable in a word w if there exists a letter a such that ua is also +a factor of w. The word ua is a right extension of u. A non-right-extendable factor u of w is a +suffix of w but the converse does not hold. For instance the word u = a is a suffix of the word +w = aa but it is right-extendable. Actually it can be straightforwardly checked that a factor u +is not right-extendable in w if and only if u is a suffix of w which has only one occurrence as a +factor of w. The notions of left-extendability and left extensions are defined similarly. +The global strategy to reconstruct an unknown word w using queries on factors is to apply +the following three steps. First we find a long block of a fixed letter α (proof of Lemma 4.4). +Second we determine a non-right-extendable factor of w having this long block of α as a prefix. +Two different approaches are developed in the proof of Lemmas 4.2 and 4.3. Depending on the +length of the previously found long block of α, one or the other of the two approaches reveals +to be more efficient. +Finally we determine w from the previous non-right-extendable factor +(Lemma 4.1). Let us first explain this last step. +Lemma 4.1. Let w be an unknown word of known length n over an alphabet of cardinality +k. If we know a non-right-extendable factor s of w then we can reconstruct w with at most +(k − 1)(n − |s|) ∃-factor queries. +Proof. Assume that |s| < n. Then s is a proper suffix of w. Fix a letter α. We can ask “is βs +a factor of w?” for each letter β different from α. If the answer is positive for some β then we +know that βs is a non-right-extendable factor of w and if the answer is negative for all β then +we know that αs is a non-right-extendable factor of w. We then repeat the same process until +we reach a word of length n (this word necessarily is w). It costs us at most k − 1 queries by +letter that we have to determine, that is, (k − 1)(n − |s|) queries. +10 + +We now explain how to efficiently find a non-right-extendable factor of w. For this a letter +α is fixed and we assume that we know the greatest t such that αt occurs as a factor in w. And +we will present two different strategies that we will use for different values of t in the proof of +Theorem 4.5. The first strategy will be used when t is not too large. It is described in the proof +of the following result. +Lemma 4.2. Let w be an unknown word of known length n over an alphabet A of cardinality +k. Let α ∈ A. If we know the largest integer t such that αt is a factor of w, then a non-right- +extendable factor s of w can be determined with at most (k − 1)(|s| + 2) ∃-factor queries. +Proof. Let σ be a variable that aims to contain the searched non-right-extendable factor of w. +We initialize σ with the word αt. We search for successive right extensions of σ asking the query +“is σβ a factor of w?” for each letter β ̸= α. If the answer is “yes” for some β ̸= α then we +know that σβ is a factor of w and we set σβ to be the new value of σ. +If the answer is “no” for all β ̸= α, then either σα is a factor of w or σ is non-right-extendable. +If σ does not end with the suffix αt, we set σα to be the new value of σ. It is possible that σ is +no longer a factor of w (and so σ is not a non-right-extendable factor of w), in particular, when +the previous value of σ already was the searched non-right-extendable factor of w. But if later, +while trying to add a letter β ̸= α, we get “yes” as an answer we deduce that we were right for +every previous assumption. If we obtain the answer “no” t + 1 consecutive times then we have +added t+1 occurrences of α at the end of σ. This implies that we were wrong since by definition +of t, αt+1 is not a factor of w. At this point σ = vαt+1 for some word v that ends with a letter +different from α and there exists r ≤ t such that vαr is a suffix of w and both vαr+1 and all +words vαrβ with β ̸= α are not factors of w: vαr is the searched non-right-extendable factor of +w. We can determine r by asking “is vαr+1 a factor of w?” from r = 0 and until a negative +answer. +Let us now provide an upper-bound for the number of queries. Let vαt+1 be the value of σ +obtained after t+1 consecutive negative queries and let r+1 be the number of additional queries +asked to determine the final value s of σ. Observe that v was determined using (k − 1)(|v| − t) +queries. Then we use (k−1)(t+1) queries to get vαt+1 and finally we use r+1 queries to determine +the final value. The total amount of queries is thus bounded by (k−1)((|v|−t)+(t+1)+(r+1)). +Since |s| = |v| + r, this number of queries is bounded by (k − 1)(|s| + 2). +Let us illustrate in an example the strategy used in the proof of Lemma 4.2. Assume that +the word to reconstruct is w = 00011100111011 and that we use α = 1. We have t = 3 and +initially σ = 111. +The answer to the two first queries are positive and we get σ = 11100. +Then the answers to the next three queries are negative and we assume that σ = 11100111 is +a prefix of the expected result. This is confirmed by the next query that sets v = 111001110. +The next four negative queries on v0, v10, v110 and v1110 imply that the non-right-extendable +factor is v, v1, v11, or v111. After three additional queries, we know that 11100111011 is a +non-right-extendable factor (hence a suffix) of w. +If t is large (essentially if t ≥ ⌈4√n ⌉; see the proof of Theorem 4.5), then a better strategy +is to verify slightly more often that our assumptions are correct when building the non-right- +extendable factor. Doing so leads to the alternative strategy provided in the proof of the next +result. +Lemma 4.3. Let w be an unknown word of known length n over an alphabet A of cardinality +k. Let α ∈ A be a letter with at least one occurrence in w. Assume that we know n and the +largest positive integer t such that αt is a factor of w. A non-right-extendable factor s of w can +be determined using at most (k − 1)(|s| − t) + k ⌈√n ⌉ + 1 ∃-factor queries. +Proof. The strategy is almost identical to the previous one. We initialize σ with the word αt +and we try to extend it by asking whether σβ for some β ̸= α is a factor of w and we proceed +as previously. +11 + +If we obtain the answer “no” r consecutive times then we added r occurrences of α at the +end of s. In this case, every ⌈√n ⌉ new consecutive occurrences of α, we verify if our current +value of σ is a factor of w. If this holds we keep going. Otherwise letting v be the word such +that σ = vα⌈ +√n⌉, vα⌈ +√n⌉ is not a factor of w. We need to find the largest r such that vαr is a +factor of w. This can be done by setting σ = v and asking the query “is σαi a factor of w ?”, +where i starts at 1 and increases until we receive the answer “no”. +Let us now count the number of queries. +In the first phase, until reaching vα⌈ +√n⌉, the +length of σ increases from t to |vα⌈ +√n⌉|. Each new letter requires at most k − 1 queries, but +each ⌈√n ⌉ query a verification query is done. So the number of queries in this first phase is at +most (remember t ≥ 1) +(k − 1)(|vα⌈ +√n⌉| − t) + +� +|vα⌈ +√n⌉| − t +⌈√n⌉ +� +≤ (k − 1)(|vα⌈ +√n⌉| − t) + 1 + +�|w| − 1 +⌈√n⌉ +� +which is upper-bounded by (k − 1)(|v| − t) + k⌈√n⌉ . +In the second phase there is one verification query and every other query increases the value +of i from 1 to r + 1. So there are at most 1 + r = 1 + |s| − |v| ≤ 1 + (k − 1)(|s| − |v|) other +queries in this second phase. Summing the queries of the first and second phase, we deduce that +at most (k − 1)(|s| − t) + k ⌈√n ⌉ + 1 queries are used. +Before using Lemma 4.2 or Lemma 4.3 we need to determine the greatest power of a letter +in a word w. This can be done using a binary search with queries in the form “Is at a factor of +w?” for 1 ≤ t ≤ n. A negative answer to the query “Is a1 a factor of w?” shows that the letter +a does not occur in w. The next result holds for arbitrary alphabets. Its proof specifies how the +binary search is done. +Lemma 4.4. Let w be an unknown word. Let a be a letter, x, y be two known integers and t +be the largest integer such that at is a factor of w. If we know that x ≤ t ≤ y then at most +⌈log2(y + 1 − x)⌉ ∃-factor queries are needed to determine the value of t. +Once again the idea of this Lemma is to use a binary search and the details of the proof can +be found in Appendix B. +Applying successively Lemma 4.4, then Lemma 4.2 or Lemma 4.3 and finally Lemma 4.1, +we get the next result. +Theorem 4.5. An unknown nonempty word w of known length n over an alphabet of cardinality +k ≥ 2 can be reconstructed in at most (k − 1)(n + 2) + ⌈log2 n +2 +⌉ + 3 ∃-factor queries. +Proof. We start with the query “is α⌈4√n ⌉ a factor of w?”. +If we obtain a positive answer, we use Lemma 4.4 (with x = ⌈4√n ⌉ and y = n (n ≥ 1)) to +compute the largest t such that αt is a factor of w in at most ⌈log2 n⌉ queries. Then we apply +Lemma 4.3 to find a non-right-extendable factor s in at most (k−1)(|s|−t)+k⌈√n ⌉+1 queries. +Since t ≥ ⌈4√n ⌉ ≥ 4⌈√n ⌉ − 3, +(k − 1)(|s| − t) + k⌈√n ⌉ + 1 ≤ (k − 1)(|s| + 3) − (3k − 4)⌈√n⌉ + 1 . +We finally apply Lemma 4.1 to find w in (k−1)(n−|s|) queries. In this case, including the initial +query, we need a total of at most (k − 1)(n + 3) + ⌈log2 n⌉ − (3k − 4)⌈√n ⌉ + 2 ≤ (k − 1)(n + 2) +queries (we use k ≥ 2 and n ≥ 1 for this inequality). +If we obtain a negative answer, we use Lemma 4.4 (with x = 0 and y = ⌈4√n ⌉ − 1) to +compute the largest t such that αt is a factor of w in at most ⌈log2(4√n)⌉ = ⌈log2 n +2 +⌉ + 2 queries. +Then we apply Lemma 4.2 to find a non-right-extendable factor s in (k − 1)(|s| + 2) queries and +we finally apply Lemma 4.1 to find w in (k − 1)(n − |s|) queries. In this case we need a total of +(k − 1)(n + 2) + ⌈log2 n +2 +⌉ + 3 queries including the initial query. +12 + +5 +Conclusion +We have studied three reconstruction problems and, for each of them, we have improved upper +bounds on the number of necessary queries. For reconstruction of a word w of length n over +an alphabet of cardinality k using ∃-subword queries, we have a lower bound n log2(k) and in +Section 3, we reduce the gap between the lower and the upper bound to an O(k log2(n)). An +open question is whether this gap can be further reduced to an O(k) number of queries or even +lower. +For the reconstruction using #-subword queries as considered in Section 2, up to our knowl- +edge, no lower bound is known. Our upper bound is much lower than the previous one, but +it could still be far from the truth. In particular, we showed that there exists a deterministic +algorithm that requires in average O(log n) queries to reconstruct a uniform random binary word +of length n, but this algorithm requires Θ(√n log n) queries in the worst case. This might be +possible to find a deterministic algorithm that requires O(log n) queries in the worst case. We +were not able to find a simple proof that this cannot be done in constant time only depending +on the size of the alphabet. +For the reconstruction using ∃-factor queries as considered in Section 4, a simple counting +argument yields the lower bound n log2(k) on the number of queries. S. S. Skiena and G. Sun- +daram provide in [10] a lower bound in kn/4 − o(n) queries which is better for large alphabets. +In the binary case, we were able to improve the gap between the lower and the upper bound, +reducing it to +� +log2(n) +2 +� ++ 5. In the general case, even if our result improves the gap between the +lower and upper bounds, this gap is still important. As already mentioned in the introduction, +the lower bound kn/4−o(n) given by S. S. Skiena and G. Sundaram is also valid if one considers +queries in the form “What is the number of occurrences of u as a factor of w?”. In some sense, +considering the numbers of occurrences of factors does not bring a significant amount of extra- +information for reconstruction comparatively to information on the existence of factors. This +contrasts with the subword case where the number of occurrences gives much more information +than the existence of occurrences. +To end, let us mention the existence, in the binary case, of a deterministic algorithm that +requires, in average, n + O(1) ∃-factor queries over a uniform random word [4] which is optimal +up to an additive constant. The main idea of this algorithm is similar to the approach used in +Section 4, but the length t of the longest block of 0 is determined faster. Indeed, for a binary +word of length n taken uniformly at random, the average value of |t − log2(n)| is in O(1). The +existence of a deterministic algorithm using an n + O(1) number of ∃-factor queries in the worst +case is open. +Acknowledgment +Authors thank Victor Poupet for useful discussions. Many thanks also for the referees for their +accurate reading and their valuable suggestions. +References +[1] M. Dudik and L.J. Schulman. Reconstruction from subsequences. J. Combin. Theory Ser. +A, 103:337–348, 2003. +[2] P. Fleischmann, M. Lejeune, F. Manea, D. Nowotka, and M. Rigo. Reconstructing words +from right-bounded-block words. In N. Jonoska and D. Savchuk, editors, Developments in +Language Theory - 24th International Conference, DLT 2020, Tampa, FL, USA, May 11- +15, 2020, Proceedings, volume 12086 of Lecture Notes in Computer Science, pages 96–109. +Springer, 2020. +13 + +[3] P. Fleischmann, M. Lejeune, F. Manea, D. Nowotka, and M. Rigo. Reconstructing words +from right-bounded-block words. Internat. J. Found. Comput. Sci., 32(6):619–640, 2021. +[4] Kazuo Iwama, Junichi Teruyama, and Shuntaro Tsuyama. Reconstructing Strings from +Substrings: Optimal Randomized and Average-Case Algorithms. arXiv e-prints, 2018. +[5] L.O. Kalashnik. The reconstruction of a word from fragments. In Numerical Mathematics +and Computer Technology, Preprint IV, pages 56–57. Akad. Nauk. Ukrain. SSR Inst. Mat., +1973. +[6] I. Krasikov and Y. Roditty. On a reconstruction problem for sequences. J. Combin. Theory +Ser. A, 77:344–348, 1997. +[7] V. I. Levenshtein. Efficient reconstruction of sequences from their subsequences or super- +sequences. In J. Combin. Theory Ser. A, volume 93, pages 310–332, 2001. +[8] M. Lothaire. Combinatorics on Words, volume 17 of Encyclopedia of Mathematics and its +Applications. Addison-Wesley, 1983. Reprinted in the Cambridge Mathematical Library, +Cambridge University Press, UK, 1997. +[9] S. Skiena and G. Sundaram. Reconstructing strings from substrings (extended abstract). +In F. Dehne, J.-R. Sack, N. Santoro, and S. Whitesides, editors, Proceedings of the third +workshop an Algorithms and Data Structures (WADS ’93), Montr´eal, Canada, August 11- +13, number 709 in Lecture Notes in Comput. Sci., pages 565–576. Springer-Verlag, Berlin, +1993. +[10] S.S. Skiena and G. Sundaram. Reconstructing strings from substrings. J. Comput. Bio., +2(2):333–353, 1995. +14 + +A +Proof of Lemma 3.2 +Proof of Lemma 3.2. Assume first that n is unknown. We start by finding M the smallest power +of 2 larger than |w|α. This can be done asking whether αi is a subword of w starting from i = 1 +and doubling i while the answer is positive. The upper bound is reached by M = i when the +answer is negative. +If M = 1, then |w|α = 0 and exactly one query was asked (and 1 ≤ 2⌊1 + log2(|w|α + 1)⌋ +as desired). Otherwise, M = 2⌊log2 |w|α⌋+1 is found in ⌊log2 |w|α⌋ + 2 queries. In this case we +know, M/2 ≤ |w|α < M, and we can find the value of |w|α by binary search. The interval +{M/2, . . . , M − 1} contains 2⌊log2 |w|α⌋ values, hence the binary search requires ⌊log2 |w|α⌋ ∃- +subword queries. In the whole process |w|α can be found using 2⌊1+log2 |w|α⌋ ≤ 2⌊1+log2(|w|α+ +1)⌋ ∃-subword queries as desired. +When n is known, n is an upper bound on |w|α and the binary search can be done in the +interval [0, n]. Hence |w|α can be determined using at most ⌈log2(n+1)⌉ ∃-subword queries. +B +Proof of Lemma 4.4 +Proof of Lemma 4.4. We proceed by induction on the value y + 1 − x. If x = y then we know +the value of t and no more queries are needed as expected. If y > x, then we ask the query “is +a⌈(x+y)/2⌉ a factor of w?”. +We deduce x′ ≤ t ≤ y′ where, if the answer is “yes”, x′ = ⌈(x + y)/2⌉ and y′ = y and, if the +answer is “no”, x′ = x and y′ = ⌈(x + y)/2⌉ − 1. In the two cases, +y′ − x′ + 1 ≤ 1 + ⌊(y − x)/2⌋ . +(5) +The map f : z �→ ⌊z−1 +2 ⌋ + 1 is non-decreasing over the non-negative reals and for all integers +n, f(2n) = 2n−1, thus for all z ≤ 2n, we have f(z) ≤ 2n−1. +Since (5) can be rewritten, +y′−x′+1 ≤ f(y+1−x), we deduce that for all integers n, if y+1−x ≤ 2n then y′+1−x′ ≤ 2n−1. +In particular, choosing n = ⌈log2(y + 1 − x)⌉ yields, y′ + 1 − x′ ≤ 2⌈log2(y+1−x)⌉−1, hence +⌈log2(y′ + 1 − x′)⌉ ≤ ⌈log2(y + 1 − x)⌉ − 1 . +By induction hypothesis, it implies that we need at most ⌈log2(y + 1 − x)⌉ − 1 other queries +to determine the value of t. With the initial query, this is a total of at most ⌈log2(y + 1 − x)⌉ +queries as desired. +15 + diff --git a/ZNAzT4oBgHgl3EQfm_0c/content/tmp_files/load_file.txt b/ZNAzT4oBgHgl3EQfm_0c/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..e3bf56905a7358a32d90594e09fd6499f043e38f --- /dev/null +++ b/ZNAzT4oBgHgl3EQfm_0c/content/tmp_files/load_file.txt @@ -0,0 +1,752 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf,len=751 +page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='01571v1 [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='DM] 4 Jan 2023 Reconstructing words using queries on subwords or factors Gwena¨el Richomme∗, Matthieu Rosenfeld† January 5, 2023 Abstract We study word reconstruction problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Improving a previous result by P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Fleischmann, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Lejeune, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Manea, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Nowotka and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Rigo, we prove that, for any unknown word w of length n over an alphabet of cardinality k, w can be reconstructed from the number of occurrences as subwords (or scattered factors) of O(k2� n log2(n)) words.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Two previous upper bounds obtained by S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Skiena and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Sundaram are also slightly improved: one when considering information on the existence of subwords instead of on the numbers of their occurrences, and, the other when considering information on the existence of factors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' ∗Universit´e Paul-Val´ery Montpellier 3, Universit´e de Montpellier, CNRS, Montpellier, France †Universit´e de Montpellier, CNRS, Montpellier, France 1 1 Introduction A natural combinatorial question is to ask how much partial information on an object is needed to reconstruct this object (see below and in our references for examples).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' For example, in [2, 3], P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Fleischmann, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Lejeune, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Manea, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Nowotka and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Rigo consider the problem of reconstructing a word w from information on the number of occurrences as subwords of w of some words.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Let us recall that a word u is a subword of a word w (or a scattered subword of w) if u and w can be decomposed in the form u = u1 · · · uℓ and w = v0u1v1 · · · uℓvℓ for some words u1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' , uℓ, v0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' , vℓ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Such a double decomposition marks an occurrence of u as a subword of w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' The number of occurrences of u as a subword of w is sometimes denoted as the binomial coefficient �w u � since this number coincides with the traditional coefficient �|w| |u| � when the words u and w are written on a single letter (here, as usual in combinatorics on words, |w| denotes the length of w), see for instance [8, chap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' 6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' The problem addressed by Fleischmann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' is presented as a game in which the player has to guess an unknown word.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' In his task the player asks questions in a certain form until he has enough information to uniquely determine the word.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' More precisely, at each round, the player chooses a word u based on the previous answers that he obtained and asks for the value of �w u � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' The goal of the player is to minimize the number of questions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Fleischmann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' proved that there is a strategy to ensure that at most min(|w|a, |w|b) + 1 ≤ ⌊|w| 2 ⌋ + 1 questions are needed when w is defined on the binary alphabet {a, b} (for a letter α, |w|α = �w α � denotes the number of occurrences of α in w).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' For any word w over the alphabet {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' , k} they proved that the number of questions needed is bounded by � i∈{1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=',k} |w|i(k + 1 − i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Our main results (Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='1 and Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='6) prove that this number of questions is at most �k 2 � � 7 �� |w| log2(|w|) � + 4 � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' For any fixed k, our upper bound is asymptotically much stronger as the length of the word goes to infinity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' For binary words in particular, their upper bound is |w| 2 + 1 and ours is 7 �� |w| log2(|w|) � + 4 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' We also adapt this strategy (Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='2) to provide an algorithm whose expected running time over a uniform random binary word of length n is O(log2 n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Let us recall that the previous game is related to another problem that seems to have been first introduced by L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Kalashnik [5]: What is the smallest ℓ such that we can reconstruct w from the values �w u � for all words u of length ℓ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' As far as we know, the best upper bound, ⌊16 7 � |w|⌋ + 5, for this problem was obtained by I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Krasikov and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Roditty in 1997 [6] using a link with the Prouhet-Tarry-Escott problem about Diophantine analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Also the best known lower bound, 3(√ 2/3−o(1)) log1/2 3 (|w|)), is due to [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Our result does not improve this upper bound since, in the binary case, at least one query concerns a word u of length at least min(|w|0, |w|1) which is around |w|/2 for many words w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' In a variant of the previous problem queries in the form “what is the value of �w u � ?”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' is replaced with queries in the form “Is �w u � ≥ 1?”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' or equivalently “Is u a subword of w?”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' More precisely the problem is to determine the least value ℓ such that the set of subwords of length ℓ determines uniquely a word w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' This problem arose in various areas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' In [8, Chap 6], it is proved that any word w of length n over an alphabet A is uniquely determined by its set of subwords in the form a∗b∗ of length at most ⌈|w|a + |w|b + 1/2⌉ with a and b distinct letters of A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' The problem is also studied in [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' In [9, 10], in the context of DNA sequencing of hybridization, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Skiena and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Sundaram consider the problem of minimizing the number of queries in the form “Is u a subword of w?”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' They prove that a word w of length n over an alphabet A of cardinality k can be reconstructed using O(n log2(k) + k log2(n)) such queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' More precisely Theorem 15 in [10] states that 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='59n log2(k) + 2k log2(n) + 5k queries are sufficient to reconstruct w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Using a basic information theory approach S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Skiena and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Sundaram also provide the lower bound n log2 k for the number of queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' In Section 3, we slightly improve S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Skiena and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Sundaram’s strategy and we provide a new upper bound, reducing the gap with the lower bound.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' More precisely, 2 we state that at most n log2(k) + k(2 + ⌊log2(n + 1)⌋) queries are sufficient to reconstruct w, reducing the gap between the bounds from 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='59n log2(k) + O(k log2(n)) down to O(k log2(n)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' In Section 4, we consider factors instead of subwords (a word u is a factor of a word w if there exist words p and s such that w = pus) and the corresponding problem of minimizing the number of queries in the form “Is u a factor of w?”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' needed to reconstruct an unknown word w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' In [9, 10], S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Skiena and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Sundaram prove that, for an unknown word w over an alphabet A of cardinality k, if the length n of w is known then w can be reconstructed using a number of queries which is in (k − 1)n + 2 log2(n) + O(k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Actually their proof leads to the upper bound (k − 1)n + log2(n) + O(k), which is n + log2(n) + O(1) in the binary case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' This more accurate upper bound was already mentioned in the binary case in [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' A simple double counting argument (there are kn words of length n and each question has two possible outcomes) leads to the lower bound n log2 k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' We improve their strategy and reduce the upper bound to (k − 1)(n + 2) + � log2(n) 2 � + 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' In the binary case, this reduces the gap between the lower and the upper bound from log2(n) + O(1) down to � log2(n) 2 � + 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Queries in the form “What is the number of occurrences of a word u as a factor of w” have also been considered by S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Skiena et G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Subraman [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Their lower bound nk/4 − o(n) on the number of queries needed is, up to our knowledge, the best known.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' One can deduce whether a word u occurs as a factor in a word w from the number of occurrences of u in w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' This observation allows them to obtain the same upper bounds for this fourth problem than for the previous problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Similarly, our bound applies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Hence, we also slightly improve the upper bound in this case, but this improvement is negligible compared to the size of the gap between the lower bound and the upper bound.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Basic definitions and notations have already been recalled (following [8]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Let us observe that #S denotes the cardinality of a set S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Moreover, given a word w over an alphabet A, we will simply use n to denote the length |w| of w and k to denote the cardinality #A of A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' 2 How-many-subwords queries In this section, we focus on queries in the form “How many occurrences of u as a subword does w contains?”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' or equivalently “What is the value of �w u � ?”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' We call such a query a #-subword query.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Our main result regarding this kind of query is the following.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Of course, as it will be the case for other queries in the next sections, we assume that such a query can be answered without knowing w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' The number of #-subword queries needed to reconstruct a word of length n over {0, 1} is at most 7 �√n log n � + 4 whether n is known or not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' A word w that contains m occurrences of 1, can always be written as w = 0s010s11 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' 10sm where the si are nonnegative integers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Since m = �w 1 � , it only requires one query to find m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Our goal is to find the values of all the si.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Our strategy relies on the fact that if we know which of the si are “large” and if we know their values then we can determine multiple others si with a single query (this is shown in Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' On the other hand since we cannot have too many “large” si we have an efficient strategy to find all these si (see Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Using these two facts together and optimizing the meaning of “large” we get the desired result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Actually, in a uniform random word we do not expect to have any si larger than O(log n) and this leads to a more efficient average case algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' There is a deterministic strategy that, given any integer n, reconstructs in av- erage in O(log2(n)) queries any word w taken uniformly at random among all binary words of length n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' The next lemma allows to prove Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' 3 Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Let r, ℓ, s1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' , sr be non-negative integers such that 1 ≤ r ≤ ℓ + 1 and for all j ∈ {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' , r}, sj < ℓ+1 r .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' The values of s1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' , sr are uniquely determined by the values of �0sr 10sr−11···0s210s11ℓ 01ℓ � , r and ℓ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Let us first express the number of occurrences of 01ℓ as subword in 0sr10sr−11 · · · 0s11ℓ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' By considering separately the different possible positions of the 0 in the occurrence we obtain �0sr10sr−11 · · · 0s210s11ℓ 01ℓ � = r � j=1 sj �ℓ + j − 1 ℓ � = r � j=1 sj �ℓ + j − 1 j − 1 � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' (1) Let β = maxj sj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' We first show that for all t ∈ {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' , r}, t � j=1 sj �ℓ + j − 1 j − 1 � ≤ β �ℓ + t t − 1 � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' (2) We proceed by induction on t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' It is easily verified for t = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Now if (2) holds for t, then t+1 � j=1 sj �ℓ + j − 1 j − 1 � = t � j=1 sj �ℓ + j − 1 j − 1 � + st+1 �ℓ + t t � ≤ β �ℓ + t t − 1 � + st+1 �ℓ + t t � ≤ β ��ℓ + t t − 1 � + �ℓ + t t �� = β �ℓ + t + 1 t � which concludes the inductive proof of (2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Moreover, for all t ∈ {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' , r}, β �ℓ+t t−1 � < ℓ+1 r �ℓ+t t−1 � ≤ ℓ+1 t �ℓ+t t−1 � = �ℓ+t t � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Together with (2), it implies that for all t ∈ {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' , r}, 0 ≤ t � j=1 sj �ℓ + j − 1 j − 1 � < �ℓ + t t � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' (3) Observe that, for all t ∈ {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' , r − 1}, st+1 = �t+1 j=1 sj �ℓ+j−1 j−1 � − �t j=1 sj �ℓ+j−1 j−1 � �ℓ+t t � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' But st+1 is an integer and by equation(3) the right part of the fraction in the left-hand-side is in [0, 1[ we deduce st+1 = ��t+1 j=1 sj �ℓ+j−1 j−1 � �ℓ+t t � � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' (4) By Equations (1) and (4), we can deduce the value of sr from r, l and �r j=1 sj �ℓ+j−1 j−1 � which is it- self deduced from �0sr 10sr−11···0s210s11ℓ 01ℓ � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' From the value of sr, we can now deduce �r−1 j=1 sj �ℓ+j−1 j−1 � and thus sr−1 by (4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Thus, by an “inverse induction” from r − 1 to 1, we deduce the values of all the sj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='3 allows us to determine the length of multiple consecutive 0-blocks with only one query under some strong hypothesis, but we can relax these hypotheses as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' The idea is that if we have some large si and a prefix, it is enough to know the value of these si and of the prefix in order to remove their contribution before applying the previous lemma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Let p and v be words, r and s1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' , sr be nonnegative integers such that 1 ≤ r ≤ |v|1 + 2 and let w = p0sr10sr−1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' 10s11v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Suppose that p, |v|1 and r are known and that for all j, either sj is known or sj < |v|1+2 r , then the value of � w 011+|v|1 � uniquely determines the values of all the unknown sj for j ∈ {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' , r}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' 4 Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' For all j ∈ {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' , r}, let s′ j be such that if sj < |v|1+2 r , then s′ j = sj and s′ j = 0 otherwise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Then sj − s′ j is known for all j (it is sj if sj is known and 0 otherwise) and for all j, s′ j < |v|1+2 r .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Now, by considering the possible positions of the 0 in the occurrences of 011+|v|1, we get � w 011+|v|1 � = �p1r+|v|1 011+|v|1 � + �0sr10sr−1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' 10s111+|v|1 011+|v|1 � = �p1r+|v|1 011+|v|1 � + r � j=1 sj �j + |v|1 1 + |v|1 � = �p1r+|v|1 011+|v|1 � + r � j=1 (sj − s′ j) �j + |v|1 1 + |v|1 � + r � j=1 s′ j �j + |v|1 1 + |v|1 � = �p1r+|v|1 011+|v|1 � + r � j=1 (sj − s′ j) �j + |v|1 1 + |v|1 � + �0s′ r10s′ r−1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' 10s′ 111+|v|1 011+|v|1 � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' It implies that, �0s′ r10s′ r−1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' 10s′ 111+|v|1 011+|v|1 � = � w 011+|v|1 � − �p1r+|v|1 011+|v|1 � − r � j=1 (sj − s′ j) �j + |v|1 1 + |v|1 � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' By assumption, � w 011+|v|1 � , p, r, |v|1 and for all j, (sj − s′ j) are known.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Hence, the quantity �0s′r 10s′ r−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='10s′ 111+|v|1 011+|v|1 � is uniquely determined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' For all j, s′ j < |v|1+2 r and we deduce from Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='3 that the values of all the s′ j are uniquely determined which concludes our proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' For any word w over {0, 1} decomposed as w = 0s010s11 · · · 0st−110st, we call i the index of the 0-block 0si.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' If we want to use the previous lemma to reconstruct a word, we first need to determine the indices of all the 0-blocks that are longer than some predetermined length.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Let w ∈ {0, 1}∗ and m be an integer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Let I be the set of indices of 0-blocks of w of length at least m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Suppose that we know |w| and |w|0 (and so also |w|1 = |w| − |w|0), then the number of #-subword queries needed to determine I is at most 2|w|0⌈log2(|w|1 + 1)⌉ m .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' We use Algorithm 1 to determine I calling it with ℓ = 0 and u = |w|1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Note that |w|1 = |w| − |w|0 is known.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Algorithm 1 An algorithm that prints the indices i ∈ {ℓ, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' , u} of the 0-blocks of length at least m that occur in w procedure Recblocks(w, m, ℓ, u) if � w 1ℓ0m1|w|1−u � ≥ 1 then if u = ℓ then Print ℓ else Recblocks(w, m, ℓ, ⌊ℓ+u 2 ⌋) Recblocks(w, m, ⌊ℓ+u 2 ⌋ + 1, u) The condition of the main “if” verifies that the lengths of the 0-blocks whose indices are in {ℓ, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' , u} sum to at least m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' If it doesn’t then we know that none of these blocks can have length at least m so we do not need to call the function recursively on any of them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' From this, verifying the correctness of the algorithm is rather straightforward.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' 5 Let us now bound the total number of queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' For this, we consider the tree of recursive calls to Recblocks defined as follows: the root of the tree is the initial call with ℓ = 0 and u = |w|1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' a call a is the child of another call b if the call a was made in b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' The depth of a call is its distance to the root.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' The weight of a call is the quantity u + 1 − ℓ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' For any call of weight x, the weights of its children are ⌈x/2⌉ or ⌊x/2⌋ (and the sum of the weights of the two children is x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Let f be the function such that f : x → ⌈x 2⌉.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' The root has weight |w|1 + 1 and f is a non-decreasing function, so any call of depth d has weight at most f d(|w|1 + 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' For any integer x, f(x) ≤ x+1 2 , and, in particular, for all d ≥ 1, f d(|w|1 + 1) ≤ fd−1(|w|1+1)+1 2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' By induction on d, f d(|w|1 + 1) < |w|1+1 2d + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Any call of depth ⌈log2(|w|1 + 1)⌉ has weight at most 1 (the weight is an integer smaller than 2) and is a leaf of the tree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Hence, the depth of any call is at most ⌈log2(|w|1 + 1)⌉.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Moreover, one easily verifies by induction on the depth that for any two different calls c and c′ at the same depth the corresponding intervals [ℓ, u] and [ℓ′, u′] are disjoint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' We say that a call with the values ℓ and u owns the occurrences of 0 that belongs to all the blocks of indices between ℓ and u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Then by the previous remark, the set of occurrences of 0 owned by two calls at the same depth are disjoint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Since the condition of the first “if” is true if the call owns at least m occurrences of 0, we deduce that there are at most |w|0 m such calls on any given depth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Since each such call has two children, we deduce that the number of calls at any depth is at most 2|w|0 m .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Hence the total number of calls, is at most 2|w|0⌈log2(|w|1+1)⌉ m .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Since we ask one query by call this concludes the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' We are now ready to show our main result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' We will first use the algorithm from Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='5 to find all the blocks that are of length �√n log n � and then we use Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='4 to determine all the other blocks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Proof of Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Phase 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Let w be the unknown word.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' It costs two queries to get |w|0 = �w 0 � and |w|1 = �w 1 � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Then n = |w| = |w|0 + |w|1 is known.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Suppose without loss of generality that �w 0 � ≥ n/2 ≥ �w 1 � (otherwise simply exchange the role of 0 and 1 in the following).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Phase 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Let m = �√n log n � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' We use the algorithm from Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='5 to locate all the 0-blocks of length at least m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' There are at most n m such blocks and we can use one query for each of them to determine their respective length: Indeed if the block is at index i with i ∈ {0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' , |w|1}, its length is � w 1i01|w|1−i � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Thus locating 0-blocks of length at least m together with their lengths require at most 2|w|0⌈log(|w|1+1)⌉ m + n m queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' This number of queries is less than 3n log n m ≤ 3√n log n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Phase 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' We now need to determine the lengths of 0-blocks of length at most m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' We first determine the 0-blocks occurring before the � |w|1 2 � last occurrences of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Secondly, we determine the 0-blocks occurring after the � |w|1 2 � first occurrences of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' After this, the lengths of all the 0-blocks are known and we know w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' We describe only how to determine the first half of the blocks, since reconstructing the second half of the blocks can be done symmetrically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' There are � |w|1 2 � + 1 0-blocks before the � |w|1 2 � last occurrences of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' We determine the unknown blocks among them in at most m steps from left to right considering, at each step, at most r = � |w|1 2m � blocks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Since mr ≥ |w|1 2 − m, we might miss up to m + 1 blocks after this, that we can recover one by one for up to m + 1 extra queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' At one step w = p0sr10sr−1 · · · 10s11v with p an already known prefix of w (initially p is the empty word) and |v|1 ≥ � |w|1 2 � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' For each i ∈ {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' , r}, if si is unknown then si < m = |w|1/2 |w|1/(2m) < |v|1+2 r .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' By Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='4, only one query is needed to know the r blocks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Hence, we determine the 0-blocks occurring before the � |w|1 2 � last occurrences of 1 in at most 2m + 1 = 1 + 2 �√n log n � queries (and similarly to know the 6 0-blocks occurring after the � |w|1 2 � last occurrences of 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' In total, our strategy uses 2 + 3 �√n log n � + 2(1 + 2 �√n log n � ) = 7 �√n log n � + 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' For any alphabets A and B ⊆ A and any word u over A, the projection of u onto B is the word obtained by removing from u any letter that does not belong to B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' We denote it πB(u).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' For instance, π{0,1}(0120201) = 01001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Over an alphabet of cardinality k if we know the projections over all the binary sub-alphabets, we can uniquely determine the whole word [8, Lemma 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' So Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='1 has the following corollary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' The number of #-subword queries needed to reconstruct a word of length n over an alphabet of cardinality k is at most �k 2 � (7 �√n log n � + 4) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' In Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='1 and Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='6, we did not try to optimize the multiplicative constant, because we believe that the √n log n bound is not “sharp up to a multiplicative constant”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' As suggested by Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='2, the number of required queries in Theorem 1 and Corollary 6 might be in O(log n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' As we will see in Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='7, the probability that there is a 0-block of length more than ⌈2 log2(n)⌉ is small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Let w be a word taken uniformly at random among all binary words of length n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' The probability that w contains the factor 0⌈2 log2(n)⌉ is at most 1/n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Let m = ⌈2 log2(n)⌉.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Let w1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' , wn ∈ {0, 1} be such that w = w1 · · · wn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' For all i ∈ {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' , n − m + 1}, let Ei be the event that wiwi+1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' wi+m−1 = 0m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Then for all i, P(Ei) = 2−m ≤ 1/n2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' By union bound, P(0m is a factor of w) = P(∪n−m+1 i=1 Ei) ≤ n−m+1 � i=1 P(Ei) ≤ 1 n as desired.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Proof of Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' First, we determine the number of 0 and 1 in w in 2 queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Let m = ⌈2 log2(n)⌉.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' We first assume that there is no factor 0m in w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' We can now apply Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='4 as in Phase 3 of the proof of Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='1, but with m = ⌈2 log2(n)⌉.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' We now have a candidate word w′ and we can ask one more question, � w w′ � , to verify if w = w′ (this might not be the case, if our starting assumption was false).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' All of this take O(log2(n)) queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' If we did not obtain the correct word, we know that our assumption was false and we use Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='1 to find w in O( � n log2(n)) extra queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' By Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='7, this happens with probability at most 1/n, so the expected number of queries of this procedure is at most O(log2(n)) + O( � n log2(n)/n) = O(log2(n)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' 3 Exists-subword queries In this section, we focus on queries in the form “Is u a subword of w?”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' or equivalently “Is �w u � ≥ 1?”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' We call such a query an ∃-subword query.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' The reconstruction problem using ∃- subword queries of a word w of unknown length n over an alphabet A of cardinality k was solved by S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Skiena and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Sundaram [9, 10] using 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='59n log2(k) + 2k log2(n) + 5k queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' We improve the main coefficient of the bound, replacing 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='59 by 1 which is optimal (any such algorithm requires at least n log2(k) queries in the worst case [9, 10]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' The number of ∃-subword queries needed to reconstruct an unknown word w of unknown length n over an alphabet A of cardinality k is at most n⌈log2(k)⌉ + k (2 + ⌊log2(n + 1)⌋) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' 7 Actually, our approach is similar to the method used in [9, 10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' We act essentially by dichotomy on the alphabet but when reconstructing words from their projections on a smaller alphabet we improve the bound on the number of queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Also on small alphabets we use a linear decomposition instead of a binary decomposition in order to reduce the number of queries needed to deduce the number of occurrences of some letters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' To prove Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='1 we use the next two lemmas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' The first one considers the reconstruction problem in the one letter alphabet case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' The second one describes upper bounds on the number of queries needed to reconstruct a word from projections on disjoint alphabets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Given an unknown nonempty word w of length n over an alphabet A and a letter α ∈ A, the value |w|α can be determined using at most 2⌊1 + log2(|w|α + 1)⌋ ∃-subword queries if n is unknown and at most ⌈log2(n + 1)⌉ ∃-subword queries if n is known.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' The proof of this Lemma is a simple binary search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' The details can be found in Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' In the next Lemma we explain how to reconstruct a word w from its projections on two disjoint complementary alphabets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Note that [10, Lemma 14], is almost the same result with a number of queries 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='18|πB(w)| + |πC(w)| + 5 instead of |πB(w)| + |πC(w)| + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' The main difference is that instead of using a binary search we simply go greedily from left to right when combining the two words.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' This lemma almost exclusively explains the improvement we obtain over [10, Theorem 2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Let w be an unknown word of length n over an alphabet A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Let B and C be two disjoint alphabets such that A = B ∪ C, then 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' if we know both projections πB(w) and πC(w), then the word w can be reconstructed using at most n − 1 ∃-subword queries, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' if we know the word πB(w) and #C = 1, then the word w can be reconstructed using at most n + 1 ∃-subword queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' It may be observed that in item 1 of Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='3, the length of w can be determined without asking any query since it is equal to |πB(w)| + |πC(w)|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' This is not the case in item 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' In both cases, the length is not directly used in the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' For any word x = x1 · · · xℓ ∈ {0, 1}ℓ and integers i, j ∈ {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' , ℓ}, let x[i .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' j] = xixi+1 · · · xj when i ≤ j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' By extension, if i > j (and possibly i = |x| + 1 or j = 0), then x[i .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' j] is the empty word.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Proof of Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Assume first that u = πB(w) and v = πC(w) are known.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' The first letter of w is either u1 or v1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' More precisely, u1v is a subword of w if and only if u1 is the first letter of w, otherwise v1 is the first letter of w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Thus in one question we can determine the first letter of w, and the projections πB(w[2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' n]) and πC(w[2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' n]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' We can repeat this process and after each new query we obtain the next letter of w and the two projections of the rest of w over B and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Hence Algorithm 2 allows to reconstruct w from u and v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' In this algorithm i and j store respectively the successive length of πB(w[1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' i + j]) and πC(w[1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' i + j]): at the beginning of each while loop, we know p = w[1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' i + j].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' From the preliminary comments, it is straightforward that at the end of the algorithm p = w and that the number of ∃-subword queries asked is at most n − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' From now on assume that we only know the word πB(w) and the fact that C = {a} for some letter a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' We use a strategy similar to the previous case, that is, we try to insert occurrences of the letter a between the letters of πB(w) in a greedy way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Once the places of all letters of πB(w) are known, one has to determine the remaining occurrences of a at the end of w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' This leads to 8 Algorithm 2 An algorithm that returns an unknown word w over B ∪ C with B ∩ C = ∅ from u = πB(w) and v = πC(w) p ← ε ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' i ← 0 ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' j ← 0 while i < |u| and j < |v| do if pui+1v[j + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='.|v|] is a subword of w then p ← pui+1 ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' i ← i + 1 else p ← pvj+1 ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' j ← j + 1 p ← pu[i + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='.|u|]v[j + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='.|v|] return p the variant Algorithm 3 for which the number of ∃-subword queries asked is exactly n+1: there is one query by letter of πB(w) and πC(w) and one additional query needed to determine when there is no more letter in πC(w).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Algorithm 3 An algorithm that returns an unknown word w over B ∪ {a} with a ̸∈ B from u = πB(w) p ← ε ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' i ← 0 while i < |u| do if pau[i + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='.|u|] is a subword of w then p ← pa else p ← pui+1 ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' i ← i + 1 while pa is a subword of w do p ← pa return p The proof of the next result explains the strategy to solve the reconstruction problem using ∃-subword queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' The length of w may be unknown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Let w be an unknown word over an alphabet of cardinality k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' For any B ⊆ A with #B ≥ 2, the number of ∃-subword queries needed to reconstruct the word πB(w) is at most ⌈log2(#B)⌉|πB(w)| + #B � 2 + max α∈B ⌊log2(|w|α + 1)⌋ � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' We proceed by induction on the cardinality of B with the two base cases being #B = 2 and #B = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' If B = {x, y} ⊆ A with x ̸= y, we can apply Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='2 to determine π{x}(w) = x|w|x in at most 2⌊1 + log2(|w|x + 1)⌋ queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Case 2 of Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='3 implies that we can then determine π{x,y}(w) in at most |π{x,y}(w)| + 1 extra queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' The total number of queries is at most |π{x,y}(w)| + 1 + 2⌊1 + log2(|w|x + 1)⌋ ≤ ⌈log2(#B)⌉|πB(w)| + #B � 2 + max α∈B ⌊log2(|w|α + 1)⌋ � as desired.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' If B = {x, y, z} for some distinct letters x, y, z ∈ A, we use the strategy of the previous paragraph to determine π{x,y}(w) and we use case 2 of Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='3 once again to obtain π{x,y,z}(w) in at most |π{x,y,z}(w)| + 1 extra queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' The total number of queries is then at most |π{x,y}(w)|+|πB(w)|+2+2⌊1+log2(|w|x+1)⌋ ≤ ⌈log2(#B)⌉|πB(w)|+#B � 2 + max α∈B ⌊log2(|w|α + 1)⌋ � 9 as desired.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' We now have to deal with the induction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Assume #B ≥ 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Let C, C′ ⊆ B be two disjoint alphabets such that B = C ∪ C′, #C = ⌊#B 2 ⌋ and #C′ = ⌈#B 2 ⌉.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' The two last conditions imply ⌈log2 #C⌉ ≤ ⌈log2 #C′⌉ = ⌈log2 #B⌉ − 1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' By induction hypothesis, the number of queries to determine πC(w) and πC′(w) is at most ⌈log2(#C)⌉|πC(w)| + #C � 2 + max α∈C ⌊log2(|w|α + 1)⌋ � +⌈log2(#C′)⌉|πC′(w)| + #C′ � 2 + max α∈C′⌊log2(|w|α + 1)⌋ � ≤ (⌈log2(#B)⌉ − 1)(|πC(w)| + |πC′(w)|) + (#C′ + #C) � 2 + max α∈C′∪C⌊log2(|w|α + 1)⌋ � ≤ (⌈log2(#B)⌉ − 1)(|πB(w)|) + #B � 2 + max α∈B ⌊log2(|w|α + 1)⌋ � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' By case 1 of Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='3, we only need |πB(w)| extra queries to determine πB(w).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' In total, we used at most ⌈log2(#B)⌉(|πB(w)|) + #B � 2 + max α∈B ⌊log2(|w|α + 1)⌋ � queries as required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Proof of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='1 is an immediate consequence of Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='4 taking B = A and using max α∈B ⌊log2(|w|α + 1)⌋ ≤ ⌊log2(|w| + 1)⌋ 4 Exists-factor queries In this section, we focus on queries in the form “Is u a factor of w?”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Our aim is to prove Theorem 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' As for the result from [10] that we improve here, we assume in this section that the length of the word to determine is known.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' A factor u is said right-extendable in a word w if there exists a letter a such that ua is also a factor of w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' The word ua is a right extension of u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' A non-right-extendable factor u of w is a suffix of w but the converse does not hold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' For instance the word u = a is a suffix of the word w = aa but it is right-extendable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Actually it can be straightforwardly checked that a factor u is not right-extendable in w if and only if u is a suffix of w which has only one occurrence as a factor of w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' The notions of left-extendability and left extensions are defined similarly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' The global strategy to reconstruct an unknown word w using queries on factors is to apply the following three steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' First we find a long block of a fixed letter α (proof of Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Second we determine a non-right-extendable factor of w having this long block of α as a prefix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Two different approaches are developed in the proof of Lemmas 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='2 and 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Depending on the length of the previously found long block of α, one or the other of the two approaches reveals to be more efficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Finally we determine w from the previous non-right-extendable factor (Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Let us first explain this last step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Let w be an unknown word of known length n over an alphabet of cardinality k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' If we know a non-right-extendable factor s of w then we can reconstruct w with at most (k − 1)(n − |s|) ∃-factor queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Assume that |s| < n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Then s is a proper suffix of w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Fix a letter α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' We can ask “is βs a factor of w?”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' for each letter β different from α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' If the answer is positive for some β then we know that βs is a non-right-extendable factor of w and if the answer is negative for all β then we know that αs is a non-right-extendable factor of w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' We then repeat the same process until we reach a word of length n (this word necessarily is w).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' It costs us at most k − 1 queries by letter that we have to determine, that is, (k − 1)(n − |s|) queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' 10 We now explain how to efficiently find a non-right-extendable factor of w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' For this a letter α is fixed and we assume that we know the greatest t such that αt occurs as a factor in w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' And we will present two different strategies that we will use for different values of t in the proof of Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' The first strategy will be used when t is not too large.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' It is described in the proof of the following result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Let w be an unknown word of known length n over an alphabet A of cardinality k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Let α ∈ A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' If we know the largest integer t such that αt is a factor of w, then a non-right- extendable factor s of w can be determined with at most (k − 1)(|s| + 2) ∃-factor queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Let σ be a variable that aims to contain the searched non-right-extendable factor of w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' We initialize σ with the word αt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' We search for successive right extensions of σ asking the query “is σβ a factor of w?”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' for each letter β ̸= α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' If the answer is “yes” for some β ̸= α then we know that σβ is a factor of w and we set σβ to be the new value of σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' If the answer is “no” for all β ̸= α, then either σα is a factor of w or σ is non-right-extendable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' If σ does not end with the suffix αt, we set σα to be the new value of σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' It is possible that σ is no longer a factor of w (and so σ is not a non-right-extendable factor of w), in particular, when the previous value of σ already was the searched non-right-extendable factor of w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' But if later, while trying to add a letter β ̸= α, we get “yes” as an answer we deduce that we were right for every previous assumption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' If we obtain the answer “no” t + 1 consecutive times then we have added t+1 occurrences of α at the end of σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' This implies that we were wrong since by definition of t, αt+1 is not a factor of w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' At this point σ = vαt+1 for some word v that ends with a letter different from α and there exists r ≤ t such that vαr is a suffix of w and both vαr+1 and all words vαrβ with β ̸= α are not factors of w: vαr is the searched non-right-extendable factor of w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' We can determine r by asking “is vαr+1 a factor of w?”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' from r = 0 and until a negative answer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Let us now provide an upper-bound for the number of queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Let vαt+1 be the value of σ obtained after t+1 consecutive negative queries and let r+1 be the number of additional queries asked to determine the final value s of σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Observe that v was determined using (k − 1)(|v| − t) queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Then we use (k−1)(t+1) queries to get vαt+1 and finally we use r+1 queries to determine the final value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' The total amount of queries is thus bounded by (k−1)((|v|−t)+(t+1)+(r+1)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Since |s| = |v| + r, this number of queries is bounded by (k − 1)(|s| + 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Let us illustrate in an example the strategy used in the proof of Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Assume that the word to reconstruct is w = 00011100111011 and that we use α = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' We have t = 3 and initially σ = 111.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' The answer to the two first queries are positive and we get σ = 11100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Then the answers to the next three queries are negative and we assume that σ = 11100111 is a prefix of the expected result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' This is confirmed by the next query that sets v = 111001110.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' The next four negative queries on v0, v10, v110 and v1110 imply that the non-right-extendable factor is v, v1, v11, or v111.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' After three additional queries, we know that 11100111011 is a non-right-extendable factor (hence a suffix) of w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' If t is large (essentially if t ≥ ⌈4√n ⌉;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' see the proof of Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='5), then a better strategy is to verify slightly more often that our assumptions are correct when building the non-right- extendable factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Doing so leads to the alternative strategy provided in the proof of the next result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Let w be an unknown word of known length n over an alphabet A of cardinality k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Let α ∈ A be a letter with at least one occurrence in w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Assume that we know n and the largest positive integer t such that αt is a factor of w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' A non-right-extendable factor s of w can be determined using at most (k − 1)(|s| − t) + k ⌈√n ⌉ + 1 ∃-factor queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' The strategy is almost identical to the previous one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' We initialize σ with the word αt and we try to extend it by asking whether σβ for some β ̸= α is a factor of w and we proceed as previously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' 11 If we obtain the answer “no” r consecutive times then we added r occurrences of α at the end of s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' In this case, every ⌈√n ⌉ new consecutive occurrences of α, we verify if our current value of σ is a factor of w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' If this holds we keep going.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Otherwise letting v be the word such that σ = vα⌈ √n⌉, vα⌈ √n⌉ is not a factor of w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' We need to find the largest r such that vαr is a factor of w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' This can be done by setting σ = v and asking the query “is σαi a factor of w ?”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=', where i starts at 1 and increases until we receive the answer “no”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Let us now count the number of queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' In the first phase, until reaching vα⌈ √n⌉, the length of σ increases from t to |vα⌈ √n⌉|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Each new letter requires at most k − 1 queries, but each ⌈√n ⌉ query a verification query is done.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' So the number of queries in this first phase is at most (remember t ≥ 1) (k − 1)(|vα⌈ √n⌉| − t) + � |vα⌈ √n⌉| − t ⌈√n⌉ � ≤ (k − 1)(|vα⌈ √n⌉| − t) + 1 + �|w| − 1 ⌈√n⌉ � which is upper-bounded by (k − 1)(|v| − t) + k⌈√n⌉ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' In the second phase there is one verification query and every other query increases the value of i from 1 to r + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' So there are at most 1 + r = 1 + |s| − |v| ≤ 1 + (k − 1)(|s| − |v|) other queries in this second phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Summing the queries of the first and second phase, we deduce that at most (k − 1)(|s| − t) + k ⌈√n ⌉ + 1 queries are used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Before using Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='2 or Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='3 we need to determine the greatest power of a letter in a word w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' This can be done using a binary search with queries in the form “Is at a factor of w?”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' for 1 ≤ t ≤ n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' A negative answer to the query “Is a1 a factor of w?”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' shows that the letter a does not occur in w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' The next result holds for arbitrary alphabets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Its proof specifies how the binary search is done.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Let w be an unknown word.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Let a be a letter, x, y be two known integers and t be the largest integer such that at is a factor of w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' If we know that x ≤ t ≤ y then at most ⌈log2(y + 1 − x)⌉ ∃-factor queries are needed to determine the value of t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Once again the idea of this Lemma is to use a binary search and the details of the proof can be found in Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Applying successively Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='4, then Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='2 or Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='3 and finally Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='1, we get the next result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' An unknown nonempty word w of known length n over an alphabet of cardinality k ≥ 2 can be reconstructed in at most (k − 1)(n + 2) + ⌈log2 n 2 ⌉ + 3 ∃-factor queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' We start with the query “is α⌈4√n ⌉ a factor of w?”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' If we obtain a positive answer, we use Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='4 (with x = ⌈4√n ⌉ and y = n (n ≥ 1)) to compute the largest t such that αt is a factor of w in at most ⌈log2 n⌉ queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Then we apply Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='3 to find a non-right-extendable factor s in at most (k−1)(|s|−t)+k⌈√n ⌉+1 queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Since t ≥ ⌈4√n ⌉ ≥ 4⌈√n ⌉ − 3, (k − 1)(|s| − t) + k⌈√n ⌉ + 1 ≤ (k − 1)(|s| + 3) − (3k − 4)⌈√n⌉ + 1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' We finally apply Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='1 to find w in (k−1)(n−|s|) queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' In this case, including the initial query, we need a total of at most (k − 1)(n + 3) + ⌈log2 n⌉ − (3k − 4)⌈√n ⌉ + 2 ≤ (k − 1)(n + 2) queries (we use k ≥ 2 and n ≥ 1 for this inequality).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' If we obtain a negative answer, we use Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='4 (with x = 0 and y = ⌈4√n ⌉ − 1) to compute the largest t such that αt is a factor of w in at most ⌈log2(4√n)⌉ = ⌈log2 n 2 ⌉ + 2 queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Then we apply Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='2 to find a non-right-extendable factor s in (k − 1)(|s| + 2) queries and we finally apply Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='1 to find w in (k − 1)(n − |s|) queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' In this case we need a total of (k − 1)(n + 2) + ⌈log2 n 2 ⌉ + 3 queries including the initial query.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' 12 5 Conclusion We have studied three reconstruction problems and, for each of them, we have improved upper bounds on the number of necessary queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' For reconstruction of a word w of length n over an alphabet of cardinality k using ∃-subword queries, we have a lower bound n log2(k) and in Section 3, we reduce the gap between the lower and the upper bound to an O(k log2(n)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' An open question is whether this gap can be further reduced to an O(k) number of queries or even lower.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' For the reconstruction using #-subword queries as considered in Section 2, up to our knowl- edge, no lower bound is known.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Our upper bound is much lower than the previous one, but it could still be far from the truth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' In particular, we showed that there exists a deterministic algorithm that requires in average O(log n) queries to reconstruct a uniform random binary word of length n, but this algorithm requires Θ(√n log n) queries in the worst case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' This might be possible to find a deterministic algorithm that requires O(log n) queries in the worst case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' We were not able to find a simple proof that this cannot be done in constant time only depending on the size of the alphabet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' For the reconstruction using ∃-factor queries as considered in Section 4, a simple counting argument yields the lower bound n log2(k) on the number of queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Skiena and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Sun- daram provide in [10] a lower bound in kn/4 − o(n) queries which is better for large alphabets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' In the binary case, we were able to improve the gap between the lower and the upper bound, reducing it to � log2(n) 2 � + 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' In the general case, even if our result improves the gap between the lower and upper bounds, this gap is still important.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' As already mentioned in the introduction, the lower bound kn/4−o(n) given by S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Skiena and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Sundaram is also valid if one considers queries in the form “What is the number of occurrences of u as a factor of w?”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' In some sense, considering the numbers of occurrences of factors does not bring a significant amount of extra- information for reconstruction comparatively to information on the existence of factors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' This contrasts with the subword case where the number of occurrences gives much more information than the existence of occurrences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' To end, let us mention the existence, in the binary case, of a deterministic algorithm that requires, in average, n + O(1) ∃-factor queries over a uniform random word [4] which is optimal up to an additive constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' The main idea of this algorithm is similar to the approach used in Section 4, but the length t of the longest block of 0 is determined faster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Indeed, for a binary word of length n taken uniformly at random, the average value of |t − log2(n)| is in O(1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' The existence of a deterministic algorithm using an n + O(1) number of ∃-factor queries in the worst case is open.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Acknowledgment Authors thank Victor Poupet for useful discussions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Many thanks also for the referees for their accurate reading and their valuable suggestions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' References [1] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Dudik and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Schulman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Reconstruction from subsequences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Combin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Theory Ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' A, 103:337–348, 2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' [2] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Fleischmann, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Lejeune, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Manea, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Nowotka, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Rigo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Reconstructing words from right-bounded-block words.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' In N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Jonoska and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Savchuk, editors, Developments in Language Theory - 24th International Conference, DLT 2020, Tampa, FL, USA, May 11- 15, 2020, Proceedings, volume 12086 of Lecture Notes in Computer Science, pages 96–109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Springer, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' 13 [3] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Fleischmann, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Lejeune, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Manea, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Nowotka, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Rigo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Reconstructing words from right-bounded-block words.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Internat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Found.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=', 32(6):619–640, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' [4] Kazuo Iwama, Junichi Teruyama, and Shuntaro Tsuyama.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Reconstructing Strings from Substrings: Optimal Randomized and Average-Case Algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' arXiv e-prints, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' [5] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Kalashnik.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' The reconstruction of a word from fragments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' In Numerical Mathematics and Computer Technology, Preprint IV, pages 56–57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Akad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Nauk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Ukrain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' SSR Inst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Mat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=', 1973.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' [6] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Krasikov and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Roditty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' On a reconstruction problem for sequences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Combin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Theory Ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' A, 77:344–348, 1997.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' [7] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Levenshtein.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Efficient reconstruction of sequences from their subsequences or super- sequences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' In J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Combin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Theory Ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' A, volume 93, pages 310–332, 2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' [8] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Lothaire.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Combinatorics on Words, volume 17 of Encyclopedia of Mathematics and its Applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Addison-Wesley, 1983.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Reprinted in the Cambridge Mathematical Library, Cambridge University Press, UK, 1997.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' [9] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Skiena and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Sundaram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Reconstructing strings from substrings (extended abstract).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' In F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Dehne, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='-R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Sack, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Santoro, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Whitesides, editors, Proceedings of the third workshop an Algorithms and Data Structures (WADS ’93), Montr´eal, Canada, August 11- 13, number 709 in Lecture Notes in Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=', pages 565–576.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Springer-Verlag, Berlin, 1993.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' [10] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Skiena and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Sundaram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Reconstructing strings from substrings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Bio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=', 2(2):333–353, 1995.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' 14 A Proof of Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='2 Proof of Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Assume first that n is unknown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' We start by finding M the smallest power of 2 larger than |w|α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' This can be done asking whether αi is a subword of w starting from i = 1 and doubling i while the answer is positive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' The upper bound is reached by M = i when the answer is negative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' If M = 1, then |w|α = 0 and exactly one query was asked (and 1 ≤ 2⌊1 + log2(|w|α + 1)⌋ as desired).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Otherwise, M = 2⌊log2 |w|α⌋+1 is found in ⌊log2 |w|α⌋ + 2 queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' In this case we know, M/2 ≤ |w|α < M, and we can find the value of |w|α by binary search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' The interval {M/2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' , M − 1} contains 2⌊log2 |w|α⌋ values, hence the binary search requires ⌊log2 |w|α⌋ ∃- subword queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' In the whole process |w|α can be found using 2⌊1+log2 |w|α⌋ ≤ 2⌊1+log2(|w|α+ 1)⌋ ∃-subword queries as desired.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' When n is known, n is an upper bound on |w|α and the binary search can be done in the interval [0, n].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Hence |w|α can be determined using at most ⌈log2(n+1)⌉ ∃-subword queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' B Proof of Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='4 Proof of Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' We proceed by induction on the value y + 1 − x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' If x = y then we know the value of t and no more queries are needed as expected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' If y > x, then we ask the query “is a⌈(x+y)/2⌉ a factor of w?”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content='.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' We deduce x′ ≤ t ≤ y′ where, if the answer is “yes”, x′ = ⌈(x + y)/2⌉ and y′ = y and, if the answer is “no”, x′ = x and y′ = ⌈(x + y)/2⌉ − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' In the two cases, y′ − x′ + 1 ≤ 1 + ⌊(y − x)/2⌋ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' (5) The map f : z �→ ⌊z−1 2 ⌋ + 1 is non-decreasing over the non-negative reals and for all integers n, f(2n) = 2n−1, thus for all z ≤ 2n, we have f(z) ≤ 2n−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' Since (5) can be rewritten, y′−x′+1 ≤ f(y+1−x), we deduce that for all integers n, if y+1−x ≤ 2n then y′+1−x′ ≤ 2n−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' In particular, choosing n = ⌈log2(y + 1 − x)⌉ yields, y′ + 1 − x′ ≤ 2⌈log2(y+1−x)⌉−1, hence ⌈log2(y′ + 1 − x′)⌉ ≤ ⌈log2(y + 1 − x)⌉ − 1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' By induction hypothesis, it implies that we need at most ⌈log2(y + 1 − x)⌉ − 1 other queries to determine the value of t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' With the initial query, this is a total of at most ⌈log2(y + 1 − x)⌉ queries as desired.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} +page_content=' 15' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZNAzT4oBgHgl3EQfm_0c/content/2301.01571v1.pdf'} diff --git a/ZdE5T4oBgHgl3EQfDQ4I/content/2301.05403v1.pdf b/ZdE5T4oBgHgl3EQfDQ4I/content/2301.05403v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..f4d36e02a6c4cb6535df335f2c5b09cdad29001a --- /dev/null +++ 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100644 index 0000000000000000000000000000000000000000..6dc0f23837a4e43414fb5821bd63e8904ba84477 --- /dev/null +++ b/_9E4T4oBgHgl3EQf4w0P/content/tmp_files/2301.05315v1.pdf.txt @@ -0,0 +1,1838 @@ +1 +GH-Feat: Learning Versatile Generative +Hierarchical Features from GANs +Yinghao Xu, Yujun Shen, Jiapeng Zhu, Ceyuan Yang, and Bolei Zhou, Member, IEEE +Abstract—Recent years witness the tremendous success of generative adversarial networks (GANs) in synthesizing photo-realistic +images. GAN generator learns to compose realistic images and reproduce the real data distribution. Through that, a hierarchical visual +feature with multi-level semantics spontaneously emerges. In this work we investigate that such a generative feature learned from +image synthesis exhibits great potentials in solving a wide range of computer vision tasks, including both generative ones and more +importantly discriminative ones. We first train an encoder by considering the pre-trained StyleGAN generator as a learned loss +function. The visual features produced by our encoder, termed as Generative Hierarchical Features (GH-Feat), highly align with the +layer-wise GAN representations, and hence describe the input image adequately from the reconstruction perspective. Extensive +experiments support the versatile transferability of GH-Feat across a range of applications, such as image editing, image processing, +image harmonization, face verification, landmark detection, layout prediction, image retrieval, etc. We further show that, through a +proper spatial expansion, our developed GH-Feat can also facilitate fine-grained semantic segmentation using only a few annotations. +Both qualitative and quantitative results demonstrate the appealing performance of GH-Feat. Code and models are available at +https://genforce.github.io/ghfeat/. +Index Terms—Generative adversarial network, generative representation, feature learning, image editing. +! +1 +INTRODUCTION +R +EPRESENTATION learning plays an essential role in the +rise of deep learning. The learned representations are +able to express the variation factors of the complex visual +world. Accordingly, the performance of a deep learning +algorithm largely depends on the features extracted from +the input data. As pointed out by Bengio et al. [1], a good +representation is expected to have the following properties. +First, it should capture multiple configurations of the input. +Second, it should organize the explanatory factors of the +input data as a hierarchy, where more abstract concepts are +at a higher level. Third, it should have strong transferability, +not only from datasets to datasets but also from tasks to +tasks. +Deep neural networks supervisedly trained for image +classification on large-scale datasets (e.g., ImageNet [2] and +Places [3]) have resulted in expressive and discriminative +visual features [4]. However, the developed features are +heavily dependent on the training objective. For example, +the deep features learned for the object recognition task may +give more attention to the shapes and parts of the objects +while remain invariant to rotation [5], [6], and the deep +features from a scene classification model may focus more +on detecting the categorical objects (e.g., bed for bedroom +and sofa for living room) [7]. Thus the discriminative +features learned from solving high-level image classification +tasks might not be necessarily good for other mid-level and +low-level tasks, limiting their transferability [8], [9]. Besides, +• +Y. Xu and C. Yang are with the Department of Information Engineering, +the Chinese University of Hong Kong, Hong Kong SAR. +• +Y. Shen is with Ant Research, China. +• +J. Zhu is with the School of Computer Science and Engineering, the Hong +Kong University of Science and Technology, Hong Kong SAR. +• +B. Zhou is with Computer Science Department, University of California, +Los Angeles, USA. +it remains unknown how the discriminative features can be +used in generative applications like image editing. +In contrast to discriminative models, generative models +such as generative adversarial networks (GANs) [10] offer +an alternative way for representation learning. A GAN is +typically formulated to match the synthetic data distribution +to the observed data distribution. Through adversarial +training, the generator in GAN is required to capture the +multi-level variation factors underlying the input data to +the most extent, otherwise, the discrepancy between the +real and synthesized data would be spotted by the discrim- +inator. Recent studies have confirmed that the StyleGAN +family [11], [12] spontaneously encodes rich semantics in +a hierarchical manner [13], [14]. But the transferability +of the per-layer representation learned by GANs is not +fully verified in the literature. Some attempts have been +made to apply the generative representations (i.e., the +representations emerging from solving generative tasks) to +the high-level image classification task [15], [16], [17], yet +leaving mid-level and low-level tasks less explored. +In this work, we make a thorough investigation into +the utility of GAN representations and demonstrate their +wide applications to downstream tasks, including both +generative ones and more importantly discriminative ones. +To appropriately obtain the GAN-derived features from +a given image, we train a hierarchical encoder using the +pre-trained StyleGAN generator as a learned loss function. +Through that way, our encoder works together with the +generator to reconstruct the image, implicitly required to +extract the variation factors that describe the input. We call +the output visual features as Generative Hierarchical Features +(GH-Feat). We also observe in the encoder training that, only +exploiting the supervision at the image level (i.e., the per- +pixel reconstruction loss) may cause the overfitting of pixel +arXiv:2301.05315v1 [cs.CV] 12 Jan 2023 + +2 +values, severely limiting the transferability of the extracted +representations. To mitigate such a negative effect, we intro- +duce a training regularizer from the statistical perspective. It +alleviates the problem of distribution mismatching between +the learned GH-Feat and the native GAN representations. +After the encoder is well prepared, we evaluate the +resulting GH-Feat on a broad range of downstream appli- +cations. On one hand, we verify that the representations +learned by GANs naturally support various generative +tasks. Concretely, to edit or process target images, we can +simply modulate their corresponding features, and reuse +the generator (i.e., the same as the one used in encoder +training) as a renderer to decode features back to images. +The extensive experiments show that our approach achieves +global and local image manipulation, transferring styles +between two images, image colorization, image inpainting, +image super-resolution, etc. Besides, our GH-Feat also +allows fusing objects from an image into another as the +application of image harmonization. On the other hand, +we are interested in the discriminative capability of the +generative features.For this purpose, we treat the features +extracted by our encoder as the base representations, on top +of which we learn different linear task heads for a range of +high-level and middle-level tasks. Experiments on multiple +datasets validate the effectiveness of GH-Feat on large- +scale image classification, face verification, facial landmark +detection, room layout prediction, transferring learning, +image retrieval, etc. Furthermore, to enable dense prediction +tasks, we manage to expand GH-Feat along spatial dimen- +sions with an adequate modification of our encoder. The +improved spatial-aware visual features suggest compelling +performance on fine-grained semantic segmentation using +only a few annotations. +The preliminary result of this work is published at [18] +as oral presentation. We include the following new contents +as the extension to the conference paper. (1) We find the +limitation of only using image-level supervision for encoder +training, and provide an effective solution by introducing a +distribution-level regularizer. Analyses and improvements +are illustrated in Sec. 4.2.2. (2) We include two more image +editing tasks, i.e. style transfer (Sec. 4.3.4) and semantic +manipulation (Sec. 4.3.5), to validate that our GH-Feat +can describe images moderately, aligning with human +perception. (3) We confirm in Sec. 4.3.6 that GH-Feat also +facilitates conventional image processing tasks, including +image colorization, image inpainting, and image super- +resolution. (4) We include image retrieval as an addition +discriminative task to verify the hierarchical property of +GH-Feat, whose details are explained in Sec. 4.4.5. (5) We +propose a spatial expansion to our GH-Feat via learning +a spatial-aware encoder, and show the great potential of +the improved representations in data-efficient fine-grained +semantic segmentation in Sec. 4.5. +2 +RELATED WORK +Visual Features. Visual Feature plays a fundamental role +in the computer vision field. Traditional methods used +manually designed features [19], [20], [21] for pattern +matching and object detection. These features are signif- +icantly improved by deep models [22], [23], [24], which +automatically learn the feature extraction from large-scale +datasets. However, the features supervisedly learned for a +particular task could be biased to the training task and hence +become difficult to transfer to other tasks, especially when +the target task is too far away from the base task [8], [9]. +Unsupervised representation learning is widely explored +to learn a more general and transferable feature [25], [26], +[27], [28], [29], [30], [31], [32], [33], [34]. However, most of +existing unsupervised feature learning methods focus on +evaluating their features on the tasks of image recognition, +yet seldom evaluate them on other mid-level or low-level +tasks, let alone generative tasks. Shocher et al. [35] discover +the potential of discriminative features in image generation, +but the transferability of such features are not fully verified. +Generative Adversarial Networks. GANs [10] are able to +produce photo-realistic images via learning the underly- +ing data distribution. The recent advance of GANs [36], +[37], [38] has significantly improved the synthesis quality. +StyleGAN [11] proposes a style-based generator with multi- +level style codes and achieves the start-of-the-art generation +performance. However, little work explores the represen- +tation learned by GANs as well as how to apply such +representation for other applications. Some recent work +interprets the semantics encoded in the internal represen- +tation of GANs and applies them for image editing [13], +[14], [39], [40], [41], [42]. But it remains much less explored +whether the learned GAN representations are transferable +to discriminative tasks. +Adversarial Representation Learning. The main reason +of hindering GANs from being applied to discriminative +tasks comes from the lack of inference ability. To fill this +gap, prior work introduces an additional encoder to the +GAN structure [15], [16]. Donahue and Simonyan [17] and +Pidhorskyi et al. [43] extend this idea to the state-of-the- +art BigGAN [38] and StyleGAN [11] models respectively. +In this paper, we also study the representation learning +using GANs, with following improvements compared to +existing methods. First, we propose to treat the well-trained +StyleGAN generator as a learned loss function. Second, +instead of mapping the images to the initial GAN latent +space, like most algorithms [15], [16], [17], [43] have done, +we design a novel encoder to produce hierarchical features +that well align with the layer-wise representation learned +by StyleGAN. Third, besides the image classification task +that is mainly targeted at by prior work [15], [16], [17], [43], +we validate the transferability of our proposed GH-Feat on a +range of generative and discriminative tasks, demonstrating +its generalization ability. +3 +METHODOLOGY +This section introduces the encoder used to extract hierar- +chical visual features from the input images. This encoder +is trained in an unsupervised manner using a well-prepared +StyleGAN generator. Sec. 3.1 describes how we abstract the +multi-level representation from StyleGAN. Sec. 3.2 presents +the structure of the novel hierarchical encoder. Sec. 3.4 +describes the idea of using pre-trained StyleGAN generator +as a learned loss function for representation learning. +Sec. 3.3 introduces the training regularizer to prevent the +encoder from overfitting pixel values. + +3 +AdaIN +Encoder +GH-Feat +Generator +𝐟! +𝐟" +AdaIN +AdaIN +AdaIN +Discriminative Task +Generative Task +(3). Layout estimation +(2). Segmentation +(1). Classification +(1). Semantic editing +(2). Style transfer +Dog +(3). Image harmonization +Fig. 1. Framework of the GH-Feat. This feature hierarchy highly aligns with the layer-wise representation (i.e., style codes of per-layer AdaIN) +learned by the StyleGAN generator. Parameters in blue blocks are learnable while others are frozen. +TABLE 1 +Encoder structure, which is based on ResNet-50 [24]. Fully-connected (FC) layers are employed to map the feature maps produced by the +Spatial Alignment Module (SAM) to our proposed Generative Hierarchical Features (GH-Feat). GH-Feat exactly align with the multi-scale style +codes used in StyleGAN [11]. The numbers in brackets indicate the dimension of features at each level. +Stage +Encoder Pathway +Output Size +SAM & Pool +FC Dimension +GH-Feat +Style Code in StyleGAN +input +− +3 × 2562 +conv1 +7×7, 64 +64 × 1282 +stride 2, 2 +pool1 +3×3, max +64 × 642 +stride 2, 2 +res2 +� +1×1, 64 +3×3, 64 +1×1, 256 +� +×3 +256 × 642 +res3 +� 1×1, 128 +3×3, 128 +1×1, 512 +� +×4 +512 × 322 +512 × 42 +8192×1792 +Level 1-2 +Layer 14-13 (128d × 2) +Level 3-4 +Layer 12-11 (256d × 2) +Level 5-6 +Layer 10-9 (512d × 2) +res4 +� +1×1, 256 +3×3, 256 +1×1, 1024 +� +×6 +1024 × 162 +512 × 42 +8192×4096 +Level 7-8 +Layer 8-7 (1024d × 2) +Level 9-10 +Layer 6-5 (1024d × 2) +res5 +� +1×1, 512 +3×3, 512 +1×1, 2048 +� +×3 +2048 × 82 +512 × 42 +8192×4096 +Level 11-12 +Layer 4-3 (1024d × 2) +Level 13-14 +Layer 2-1 (1024d × 2) +3.1 +Layer-wise Representation from StyleGAN +The generator G(·) of GANs typically takes a latent code +z +∈ +Z as the input and is trained to synthesize a +photo-realistic image x = G(z). The recent state-of-the-art +StyleGAN [11] proposes to first map z to a disentangled +space W with w = f(z). Here, f(·) denotes the mapping +implemented by multi-layer perceptron (MLP). The w code +is then projected to layer-wise style codes {y(ℓ)}L +ℓ=1 ≜ +{(y(ℓ) +s , y(ℓ) +b )}L +ℓ=1 with affine transformations, where L is the +number of convolutional layers. y(ℓ) +s +and y(ℓ) +b +correspond to +the channel-wise scale and weight parameters in Adaptive +Instance Normalization (AdaIN) [44]. The space constructed +by these layer-wise style parameters is named as Y space. +These style codes are used to modulate the output feature +maps of each convolutional layer with +AdaIN(x(ℓ) +i , y(ℓ)) = y(ℓ) +s,i +x(ℓ) +i +− µ(x(ℓ) +i ) +σ(x(ℓ) +i ) ++ y(ℓ) +b,i , +(1) +MLP +FC7 +AdaIN +FC1 +AdaIN +FC14 +AdaIN +ys,1 +yb,1 +ys,7 +yb,7 +ys,14 +yb,14 +Fig. 2. Multiple latent spaces of StyleGAN. FC refers to the affine layer +between W space and Y space. +where x(ℓ) +i +indicates the i-th channel of the output feature +map from the ℓ-th layer. µ(·) and σ(·) denote the mean and +variance respectively. Fig. 2 illustrates the Z, W and Y space +of StyleGAN. +Here, we treat the layer-wise style codes of Y space, +{y(ℓ)}L +ℓ=1, as the generative visual features that we would +like to extract from the input image. There are two + +YiEZ2W4 +major advantages. First, the synthesized image can be +completely determined by these style codes without any +other variations, making them suitable to express the +information contained in the input data from the generative +perspective. Second, these style codes are organized as a +hierarchy where codes at different layers correspond to +semantics at different levels [11], [14]. To the best of our +knowledge, this is the first work that adopts the style +codes for the per-layer AdaIN module as the learned +representations of StyleGAN. Wu et al. [45] also shows Y +space can be leveraged for disentangled control of image +editing, while our work explores the potential of generative +representations in facilitating both generative and more +importantly discriminative downstream tasks. +3.2 +Hierarchical Encoder +Based on the layer-wise representation described in Sec. 3.1, +we propose a novel encoder E(·) with a hierarchical +structure to extract multi-level visual features from a given +image. As shown in Fig. 1, the encoder is designed to +best align with the StyleGAN generator. In particular, the +Generative Hierarchical Features (GH-Feat) produced by the +encoder, {f (ℓ)}L +ℓ=1 ≜ {(f (ℓ) +s , f (ℓ) +b )}L +ℓ=1, are fed into the per- +layer AdaIN module of the generator by replacing the style +code y(L−ℓ+1) in Eq. (1). +We adopt ResNet [24] architecture as the encoder +backbone and add an extra residual block to get an +additional feature map with lower resolution.In fact, there +are totally six stages in our encoder, where the first one is a +convolutional layer (followed by a pooling layer) and each +of the others consists of several residual blocks. Besides, +we introduce a feature pyramid network [46] to learn the +features from multiple levels. The output feature maps from +the last three stages, {R4, R5, R6}, are used to produce GH- +Feat. Taking a 14-layer StyleGAN generator as an instance, +R4 aligns with layer 9-14, R5 with 5-8, while R6 with 1-4. +Here, to bridge the feature map with each style code, we first +downsample it to 4×4 resolution and then map it to a vector +of the target dimension using a fully-connect (FC) layer. +In addition, we introduce a lightweight Spatial Alignment +Module (SAM) [47], [48] into the encoder structure to better +capture the spatial information from the input image. SAM +works in a simple yet efficient way: +Ri = Widown(Ri) + W6R6 +i ∈ {4, 5}, +where W4, W5, and W6 (all are implemented with an 1 × 1 +convolutional layer) are used to project the feature maps R4, +R5, and R6 to have the same number of feature channels +respectively. R4 and R5 are downsampled to the same +resolution of R6 before fusion. +Encoder Structure. Tab. 1 provides the detailed archi- +tecture of our hierarchical encoder by taking a 14-layer +StyleGAN [11] generator as an instance. Recall that the +design of GH-Feat treats the layer-wise style codes used +in the StyleGAN model (i.e., the code fed into the AdaIN +module [44]) as generative features. Accordingly, GH-Feat +consists of 14 levels that exactly align with the multi-scale +style codes yet in a reverse order, as shown in the last two +columns of Tab. 1. +3.3 +Statistical Training Regularizer +As discussed in Sec. 3.1, our approach aims at learning the +style representations encoded in y, which are transformed +from the w code using pre-layer linear projection. Y space +is less constrained than W space and hence may suffer from +the problem of overfitting pixel values, which further leads +to poor transferability of the learned features. To solve such +a problem, we infer {y(ℓ) +avg}L +ℓ=1 from the averaged latent code +(i.e., a statistics from the training stage), wavg, and propose +to only learn the residual code at each layer. Thus, we have +E(x) = {∆y(ℓ)}L +ℓ=1, which induces the final features as +{y(ℓ) +avg + ∆y(ℓ)}L +ℓ=1. We then penalize the l2 norm of each +residual code to prevent it from shifting too far from the +native distribution, resulting in a training regularizer +Lreg = +L +� +ℓ=1 +∥∆y(ℓ)∥2 +2. +(2) +e4e [49] also regularizes the inversion space when +training the encoder yet from a different aspect against +GH-Feat. In particular, the regularization in e4e [49] targets +minimizing the latent code variation across layers (i.e., +they expect the inverted codes regarding different layers +to be close to each other) to reconstruct the input image +from coarse to fine. Differently, the regularization in our +work bonds the latent code close to the distribution center +(i.e., the statistical average) to prevent the model from +overfitting pixel values. In this way, our approach could +better represent an image from the semantic level, further +facilitating downstream tasks. +3.4 +StyleGAN Generator as Learned Loss +We consider the pre-trained StyleGAN generator as a leaned +loss function. Specifically, we employ a StyleGAN generator +to supervise the encoder training with the objective of +image reconstruction. We also introduce a discriminator +to compete with the encoder, following the formulation +of GANs [10], to ensure the reconstruction quality. To +summarize, the encoder E(·) and the discriminator D(·) are +jointly trained with +min +ΘE LE = ||x − G(E(x))||2 − λ1Ex[D(G(E(x)))] ++ λ2||F(x) − F(G(E(x)))||2 + λ3Lreg, +(3) +min +ΘD LD = Ex[D(G(E(x)))] − Ex[D(x)] ++ λ4Ex[||∇xD(x)||2 +2], +(4) +where || · ||2 denotes the l2 norm and λ1, λ2, λ3, λ4 are loss +weights to balance different loss terms. The last term in +Eq. (3) represents the perceptual loss [50] and F(·) denotes +the conv4 3 output from a pre-trained VGG [23] model. +4 +EXPERIMENTS +We evaluate Generative Hierarchical Features (GH-Feat) +on a wide range of downstream applications. Sec. 4.1 +introduces the experimental settings, such as implemen- +tation details, datasets, and tasks. Sec. 4.2 presents the +analysis of our approach including ablation study and +the importance of the regularizer. Sec. 4.3 and Sec. 4.4 +evaluate the applicability of GH-Feat on generative and + +5 +discriminative tasks respectively. Sec. 4.5 shows the results +of the introduced spatial expansion. +4.1 +Experimental Settings +Implementation Details. The loss weights are set as λ1 = +0.1, λ2 = 5e−5, λ3 = 5e−4 and λ4 = 5. We use Adam [51] +optimizer, with β1 = 0 and β2 = 0.99, to train both the +encoder and the discriminator. The learning rate is initially +set as 1e−4 and exponentially decayed with the factor of 0.8. +Datasets and Models. We conduct experiments on four +StyleGAN [11] models, pre-trained on MNIST [52], FF- +HQ [11], LSUN bedrooms [53], and ImageNet [2] respec- +tively. The MNIST model is with 32 × 32 resolution and the +remaining models are with 256 × 256 resolution. +Generative Tasks. (1) Image editing. It focuses on manip- +ulating the image content or style, e.g., global editing, +local editing. (2) Image harmonization. This task harmonizes +a discontinuous image to produce a realistic output. (3) +Style transfer. This task focuses on transferring the style +of the reference image to the source image. (4) Semantic +manipulation. It targets at modifying the semantic meaning +of an object while preserving other characteristics. (5) Image +colorization. It focuses on colorizing the grayscale image. (6) +Image inpainting. This task reconstructs missing regions in +an image. (7) Image super-resolution. It aims at improving the +resolution of the image. +Discriminative Tasks. (1) MNIST digit recognition. It is a +long-standing image classification task. We report the Top-1 +accuracy on the test set following [52]. (2) Face verification. It +aims at distinguishing whether the given pair of faces come +from the same identity. We validate on the LFW dataset [54] +following the standard protocol [54]. (3) ImageNet classifi- +cation. This is a large-scale image classification dataset [2], +consisting of over 1M training samples across 1,000 classes +and 50K validation samples. We use Top-1 accuracy as +the evaluation metric following existing work [15], [17]. +(4) Pose estimation. This task targets at estimating the yaw +pose of the input face. 70K real faces on FF-HQ [11] are +split into 60K training samples and 10K test samples. +The ℓ1 regression error is used as the evaluation metric. +(5) Landmark detection. This task learns a set of semantic +points with visual meaning. We use FF-HQ [11] dataset and +follow the standard MSE metric [55] to report performances +in inter-ocular distance (IOD). (6) Layout prediction. We +extract the corner points of the layout line and convert the +task to a landmark regression task. The annotations of the +collected 90K bedroom images (70K for training and 20K +for validation) are obtained with [56]. Following [57], we +report the corner distance as the metric. (7) Face luminance +regression. It focuses on regressing the luminance of face +images. We use it as a low-level task on the FF-HQ [11] +dataset. (8) Image retrieval. It aims at retrieving the images +with specific attributes. (9) Data-efficient image segmentation. +This task focuses on predicting the class of each spatial pixel +with limited annotated data. +4.2 +Analysis on GH-Feat +4.2.1 +Ablation Study +We make ablation studies on the training of encoder from +two perspectives. (1) We choose the layer-wise style codes +TABLE 2 +Ablation studies on the feature space and the SAM module. +Space +SAM +Reg +MSE↓ +SSIM↑ +FID↓ +W + +0.0601 +0.540 +22.24 +Y +0.0502 +0.550 +19.06 +Y + +0.0464 +0.558 +18.48 +Y + + +0.0494 +0.551 +16.84 +Input +Training G & E +together +Ours +Fig. 3. Qualitative comparison on image reconstruction between training +the generator from scratch together with the encoder, and our GH-Feat +that treats the well-learned StyleGAN generator as a loss function. +y over the w codes as the representation from StyleGAN. +(2) We introduce Spatial Alignment Module (SAM) into the +encoder to better handle the spatial information. (3) We +involve a regularizer in the training of encoder. +Since the encoder is trained with the objective of image +reconstruction, we use mean square error (MSE), SSIM [58], +and FID [59] to evaluate the encoder performance. Tab. 2 +shows the results where we can tell that our encoder +benefits from the effective SAM module and that choosing +an adequate representation space (i.e., the comparison +between the first row and the last row) results in a better +reconstruction. Introducing the regularizer alleviates the +pixel value overfitting and improves the reconstruction +quality at the distribution level. More discussion on the +differences between W space and Y space can be found in +Sec. 4.4.1. +Random Generator. Recall that, during the training of the +encoder, we propose to treat the well-trained StyleGAN +generator as a learned loss function. In this part, we +explore what will happen if we train the generator from +scratch together with the encoder. Fig. 3 and Tab. 3 show +the qualitative and quantitative results respectively, which +demonstrate the strong performance of GH-Feat. It suggests +that besides higher efficiency, reusing the knowledge from a +well-trained generator can also bring better performance. +4.2.2 +Importance of Regularizer +Although GH-Feat has achieved good results in image +reconstruction, it cannot perform very well on image +editing. Compared with the W space that previous attempts +adopt as the inversion space, the Y space used by GH- +Feat ignores the linear transformation between w code and +y code, resulting in its flexibility. Hence, it is easier to +overfit a given image through a simple combination of +generative features. This leads to a mismatch between the + +6 +Real Image +w/o 𝐿!"# +w/ 𝐿!"# +Sampled Image +Fig. 4. Qualitative comparison on the style mixing task between using training regularizer or not. The first row are the sampled images. The second +row shows the results mixed with the codes predicted by our encoder. The third row presents the mixing results with original latent code. +Input +ALAE +e4e +pSp +GH-Feat +GH-Feat-S +Fig. 5. Qualitative comparison on reconstructing real images. GH-Feat-S denotes the spatial GH-Feat. Our GH-Feat and GH-Feat-S, which are +built on StyleGAN, could get comparable and better performance as pSp [60] and e4e [49], which employ a more powerful StyleGAN2 generator. +TABLE 3 +Quantitative comparison on image reconstruction between training the +generator from scratch together with the encoder, and our GH-Feat that +treats the well-learned StyleGAN generator as a loss function. +GH-Feat-R denotes GH-Feat trained with regularizer. +MSE↓ +SSIM↑ +FID↓ +Training G(·) from Scratch +0.429 +0.301 +46.20 +GH-Feat (Ours) +0.0464 +0.558 +18.48 +GH-Feat-R +0.0494 +0.551 +16.84 +TABLE 4 +Cosine similarity of the encoder output and the native latent code. +w/o Lreg +w/ Lreg +FED +0.444 +0.879 +learned visual features and the latent space distribution of +the generator. +We choose the task of global editing as a benchmark +to explore the mismatch problem. Specifically, we extract +the generative features of the real image first and then +randomly replace them with the randomly sampled features +in the latent space at layers 0-4 to achieve global editing. +The results are shown in the 2nd row of Fig. 4. Besides, +we also extract the visual feature of the sampled images +and do the same operation to achieve the editing result +in the third line of Fig. 4. Obviously, the mixed results +by the two sets of features both extracted by the encoder +are better, suggesting the domain shift between the visual +features and the latent space of the generator. Based on this, +we apply the constraints proposed in Sec. 3 to the encoder +training. The right part of Fig. 4 shows the editing results +with the Lreg. The global editing results with sampled +and extracted features are very similar, and both are much +better than the result without Lreg. It demonstrates that the +generative features learned with Lreg are more in line with +its distribution of latent space. +To quantitatively measure the similarity between two +domains, we use cosine distance between generative feature + +7 +and native code. Specifically, we sample 10k fake images +and extract the corresponding GH-Feat by our encoder, and +then cosine similarity is calculated for the two distributions. +As shown in Tab. 4, minimizing the variation of the +generative features can improve the similarity from 0.444 +to 0.879, suggesting the effectiveness of this regularization. +4.3 +Evaluation on Generative Tasks +Thanks to using the StyleGAN as a learned loss function, +a huge advantage of GH-Feat over existing unsupervised +feature learning approaches [29], [30], [31], [32], [34], +which mainly focus on the image classification task, is its +generative capability. In this section, we conduct a number +of generative experiments to verify this point. +4.3.1 +Image Reconstruction +Image reconstruction is an important evaluation on whether +the learned features can best represent the input image. +MSE and SSIM [58] are used as quantitative metrics to +evaluate the reconstruction performance. Tab. 5 and Fig. 5 +show the quantitative and qualitative comparison between +our GH-Feat and other GAN inversion methods on FF- +HQ faces [11] and LSUN bedrooms [53]. The very recent +work ALAE [43] also employs StyleGAN for representation +learning. We have following differences from ALAE: (1) We +use the Y space instead of the W space of StyleGAN as the +representation space. (2) We learn hierarchical features that +highly align with the per-layer style codes in StyleGAN. (3) +Our encoder can be efficiently trained with a well-learned +generator by treating StyleGAN as a loss function. We can +tell that GH-Feat better reconstructs the input by preserving +more information, resulting a more expressiveness represen- +tation. +Besides pSp [60], e4e [49] and Restyle [62], we include +the results of PTI [61] as well as the improved version of our +GH-Feat (i.e., spatial expansion introduced in Sec. 4.5). We +also include the inference time to help evaluate the model +efficiency. We have three observations from the table below. +(1) Our GH-Feat, which is built on StyleGAN, could get +comparable performance as pSp [60] and e4e [49], which +employ a more powerful StyleGAN2 generator. We surmise +that such an advantage originates from the replacement +from W space to Y space. (2) Restyle [62] (which requires +iterative refinement) and PTI [61] (which requires tuning of +the weights of the generator) provide good reconstruction +results but suffer from slow inference speed. (3) Our +improved version, i.e., Spatial GH-Feat, substantially im- +proves the inversion quality without sacrificing the model +efficiency, and achieves the best performance among all +encoder-based methods without generator tuning. +4.3.2 +Image Editing +In this part, we evaluate GH-Feat on a number of image +editing tasks. Different from the features learned from dis- +criminative tasks [24], [31], our GH-Feat naturally supports +sampling and enables creating new data. +Style Mixing. To achieve style mixing, we use the encoder to +extract visual features from both the content image and the +style image and swap these two features at some particular +level. The swapped features are then visualized by the +generator, as shown in Fig. 6. We can observe the compelling +hierarchical property of the learned GH-Feat. For example, +by exchanging low-level features, only the image color +tone and the skin color are changed. Meanwhile, mid-level +features controls the expression, age, or even hair styles. +Finally, high-level features correspond to the face shape and +pose information (last two columns). +Global Editing. The style mixing results have suggested +the potential of GH-Feat in multi-level image stylization. +Sometime, however, we may not have a target style image +to use as the reference. Thanks to the design of the +latent space in GANs [10], the generative representation +naturally supports sampling, resulting in a strong creativity. +In other words, based on GH-Feat, we can arbitrarily sample +meaningful visual features and use them for image editing. +Fig. 7 presents some high-fidelity editing results at multiple +levels. This benefits from the matching between the learned +GH-Feat and the internal representation of StyleGAN. +Local Editing. Besides global editing, our GH-Feat also +facilitates editing the target image locally by deeply coop- +erating with the generator. In particular, instead of directly +swapping features, we can exchange a certain region of the +spatial feature map at some certain level. In this way, only +a local patch in the output image will be modified while +other parts remain untouched. As shown in Fig. 8, we can +successfully manipulate the input face with different eyes, +noses, and mouths. +4.3.3 +Image Harmonization +Our hierarchical encoder is robust such that it can extract +reasonable visual features even from discontinuous image +content. We copy the patches from other images onto +the original image and feed the stitched image into our +proposed encoder for feature extraction. The extracted +features are then visualized via the pre-trained generator, as +in Fig. 9. On the bedroom, we can see that the copied bed, +window and ceiling light well blend into the “background”. +We also surprisingly find that when copying a window +into the source image, the view from the original window +and that from the new window highly align with each +other (e.g., vegetation or ocean). On face image, besides eye, +nose and mouth, GH-Feat also blends the glasses with the +background very well, benefiting from the robust generative +visual features. +4.3.4 +Style Transfer +Our GH-Feat can not only edit the image attributes by +replacing the randomly sampling feature at a particular +level but also can facilitate the editing with the given +conditional input. Here, we take style transfer as an +example, aiming to transfer the style of the given image to +the source image. We first extract the generative features +of the content image Ic and style image Is, and then +style-mixing is performed by replacing the visual features +of Ic with the corresponding ones of Is at the layer 8- +16. We leverage the disentanglement of the generative +features across different layers to perform style transfer. As +shown in Fig. 10, our encoder can successfully transfer the +style of the given image to the source images, suggesting +the effectiveness of the generative features. It is worth +noting that although the texture of the given style images + +8 +TABLE 5 +Quantitative comparison on reconstructing images from FF-HQ faces [11] and LSUN bedrooms [53]. GH-Feat-S denotes the spatial GH-Feat. +bold ones rank the best among the methods w/o generator tuning and underlined ones are the second. +Face +Bedroom +Method +MSE↓ +SSIM↑ +TIME↓ +MSE↓ +SSIM↑ +w/ generator tuning +PTI [61] +0.009 +0.74 +58.02 +- +- +w/o generator tuning +ALAE [43] +0.182 +0.40 +0.023 +0.275 +0.32 +pSp [60] +0.034 +0.56 +0.063 +- +- +e4e [49] +0.052 +0.50 +0.063 +- +- +Restyle [62] +0.030 +0.66 +0.304 +- +- +GH-Feat +0.046 +0.56 +0.035 +0.068 +0.52 +GH-Feat-S +0.029 +0.67 +0.038 +0.057 +0.581 +Content Image +Level 0-1 +Level 2-3 +Level 4-5 +Level 6-7 +Level 8-9 +Level 10-11 +Level 12-13 +Fig. 6. Style mixing results by exchanging the GH-Feat extracted from the content image and the style image (first row) at different levels. Higher +level corresponds to the high-level semantics like the face shape and pose information. +Level 0-1 +Level 2-5 +Level 6-11 +Level 12-13 +Fig. 7. Global image editing achieved by GH-Feat. On the left is the input image, while the others are generated by randomly sampling the visual +feature at some particular level. +Input +Eyes +Nose +Mouth +Fig. 8. Local image editing achieved by GH-Feat. On the left is the input image, while the others are generated by randomly sampling the visual +feature and replacing the spatial feature map (for different regions) at some particular level. Zoom in for details. +rarely appears in the training dataset, our encoder can still +reconstruct it and extract reasonable visual features with +good disentangle properties. It also supports the robustness +and generalization of the visual features extracted by our +hierarchical encoder. +4.3.5 +Semantic Manipulation +Here we explore the semantic editability of the generative +features. We utilize off-the-shelf semantic directions from +InterFaceGAN +[13] to edit the inversion results. Fig. 11 +presents the results of the manipulated faces. Obviously, the +learned generative features can preserve most other details +when manipulating a particular facial attribute. These +editing results demonstrate that generative features can not +only reconstruct the given image in high quality, but also +facilitate it with good semantic manipulation properties. +4.3.6 +Image Processing +In this section, we demonstrate that our method facilitates +various image processing tasks such as image colorization, +image inpainting, and image super-resolution by utilizing +the prior knowledge learned by GANs. Generally, these +tasks can be formulated as follows: +s∗ = arg min +s∈S L(G(s), x). +(5) + +9 +Eye +Nose +Mouth +Bed +Window +Ceiling Light +Fig. 9. Image harmonization on bedroom and face with GH-Feat. The top left corner of the first and third rows are the original images. Pasting +a target image patch onto the original image then feeding it as the input (first and third row), our hierarchical encoder is able to smooth the image +content and produce a photo-realistic image (second and fourth row). +Source Image +Transferring Results +Style Image +Fig. 10. Style transfer results with GH-Feat. GH-Feat can extract and then transfer the style of the reference image to the given image. +where s is the style code initialized by our encoder, L is +the l2 loss function, and x is the reference image (e.g., gray- +scale image for image colorization, corrupted image for the +inpainting, and low-resolution image for super-resolution). +Image colorization tries to restore the original color of a +gray-scale image. The results from our method are listed +in Fig. 12a. Image inpainting aims at filling the missing +pixels of the input images. As shown in Fig. 12b, when some +pixels value of the input image is missing, our method still +successfully recovers them. The last one is super-resolution, +which manages to generate a high-resolution image of the +low-resolution one. Fig. 12c shows the super-resolution +result scale 16 times using our method. +4.4 +Evaluation on Discriminative Tasks +In this part, we verify that even the proposed GH-Feat +is learned from generative models, it can be applicable +to a wide range of discriminative tasks with competitive +performances. Here, we do not fine-tune the encoder for +any certain task. In particular, we choose multi-level down- +stream applications, including image classification, face +verification, pose estimation, layout prediction, landmark +detection, and luminance regression. For each task, we use +our encoder to extract visual features from both the training +and the test set. A linear regression model (i.e., a fully- +connected layer) is learned on the training set with ground- +truth and then evaluated on the test set. Besides, we include +image retrieval as an addition discriminative task to verify +the hierarchical property of GH-Feat, whose details are +explained in Sec. 4.4.5. +4.4.1 +Discriminative and Hierarchical Property +Recall that GH-Feat is a multi-scale representation learned +by using StyleGAN as a loss function. As a results, it +consists of features from multiple levels, each of which +correspond to a certain layer in the StyleGAN generator. +Here, we would to explore how this feature hierarchy is +organized as well as how they can facilitate multi-level + +10 +Input +Inversion +Semantic ++ +Female +Glasses +Fig. 11. Semantic Manipulation results with GH-Feat. We utilize the off-the-shelf semantic directions from InterFaceGAN [13] to edit the gender +and glasses of the given images. +(a) Colorization +(b) Inpainting +(c) Super-resolution +Fig. 12. Image processing with GH-Feat. GH-Feat facilitates many image processing applications using the hierarchical encoder. +Fig. 13. Performances on different discriminative tasks using GH-Feat. Left three columns enclose the comparisons between using different spaces +of StyleGAN as the representation space, where Y space (in red color) shows stronger discriminative and hierarchical property than W space (in +blue color). This is discussed in Sec. 4.4.1. The last column compares the two different strategies used in the face verification task, which is +explained in Sec. 4.4.2. +discriminative tasks, including face pose estimation, indoor +scene layout prediction, and luminance1 regression from +face images. In particular, we evaluate GH-Feat on each +task level by level. As a comparison, we also train encoders +by treating the w code, instead of the style code y, as the +representation. From Fig. 13, we have three observations: +(1) GH-Feat is discriminative. (2) Features at lower level are +more suitable for low-level tasks (e.g., luminance regression) +and those at higher level better aid high-level tasks (e.g., +pose estimation). (3) Y space demonstrates a more obvious +hierarchical property than W space. The comparison on +hierarchical property between using regularizer or not is +included at Supplementay Material. +4.4.2 +Digit Recognition & Face Verification +Image classification is widely used to evaluate the perfor- +mance of learned representations [17], [29], [30], [31], [32]. +In this section, we first compare our proposed GH-Feat with +1. We convert images from RGB space to YUV space and use the +mean value from Y space as the luminance. +other alternatives on a toy dataset, i.e., MNIST [52]. Then, we +use a more challenging task, i.e., face verification, to evaluate +the discriminative property of GH-Feat. +MNIST Digit Recognition. We first show a toy example +on MNIST following prior work [15], [43]. We make a +little modification to ResNet-18 like [63] which is widely +used in literatures to handle samples from MNIST [52] in +lower resolution. The Top-1 accuracy is reported in Tab. 6a. +Our GH-Feat outperforms ALAE [43] and BiGAN [15] +with 1.45% and 1.92%, suggesting a stronger discriminative +power. Here, ResNet-18 [24] is employed as the backbone +structure for both MoCo [31] and GH-Feat. +LFW Face Verification. We directly use the proposed +encoder, which is trained on FF-HQ [11], to extract GH- +Feat from face images in LFW [54] and tries three different +strategies on exploiting GH-Feat for face verification: (1) +using a single level feature; (2) grouping multi-level features +(starting from the highest level) together; (3) voting by +choosing the largest face similarity across all levels. Fig. 13 +(last column) shows the results from the first two strategies. + +0.08 +0.04 +W +2 +4 +6 +8 +10 +12 +Level Indexandmark +DetectionMSE (IOD)0.076 +W +0.06 +2 +4 +6 +8 +10 +12 +14 +LevelIndexLayout PredictionCorner Distance26 +y +W +22 +2 +4 +6 +8 +10 +12 +14 +Level IndexLuminance RegressionRegression Error0.7 +Layer-wise +Grouping +0.5 +2 +4 +6 +8 +10 +12 +14 +Level IndexFace VerificationAccuracyLevelIndex11 +Fig. 14. Image reconstruction results on LFW [54]. For each pair of images, left is the low-resolution input while right is reconstructed by GH-Feat. +All samples are with the same identity. +Ours +Input +BigBiGAN +Fig. 15. Qualitative comparison between BigBiGAN [17] and GH-Feat on reconstructing images from ImageNet [2]. +TABLE 6 +Quantitative comparison between our proposed GH-Feat and other +alternatives on MNIST [52] and LFW [54]. GH-Feat-R denotes GH-Feat +trained with regularizer. +(a) Digit recognition on MNIST. +Methods +Acc. +AE(ℓ1) [64] +97.43 +AE(ℓ2) [64] +97.37 +BiGAN [15] +97.14 +ALAE [43] +97.61 +MoCo-R18 [31] +95.89 +GH-Feat (Ours) +99.06 +GH-Feat-R +98.78 +(b) Face verification on LFW. +Methods +Acc. +VAE [65] +49.3 +MoCo-R50 [31] +48.9 +ALAE [43] +55.7 +GH-Feat (Grouping) +60.1 +GH-Feat (Layer-wise) +67.5 +GH-Feat (Voting) +69.7 +GH-Feat-R (Voting) +69.1 +Obviously, GH-Feat from the 5-th to the 9-th levels best +preserve the identity information. Tab. 6b compares GH- +Feat with other unsupervised feature learning methods, +including VAE [65], MoCo [31], and ALAE [43]. All these +competitors are also trained on FF-HQ dataset [11] with +optimally chosen hyper-parameters. ResNet-50 [24] is em- +ployed as the backbone for MoCo and GH-Feat. Our method +with voting strategy achieves 69.7% accuracy, surpassing +other competitors by a large margin. We also visualize some +reconstructed LFW faces in Fig. 14, where our GH-Feat +well handles the domain gap (e.g., image resolution) and +preserves the identity information. +4.4.3 +Large-Scale Image Classification +We further evaluate GH-Feat on the high-level image +classification task using ImageNet [2]. Before the training +of encoder, we first train a StyleGAN model, with 256 × 256 +resolution, on the ImageNet training collection. After that, +we learn the hierarchical encoder by using the pre-trained +generator as the supervision. No labels are involved in +the above training process.2 For the image classification +problem, we train a linear model on top of the features +extracted from the training set with the softmax loss. +Then, this linear model is evaluated on the validation set.3 +Tab. 7 shows the comparison between GH-Feat and other +unsupervised representation learning approaches [15], [17], +[31], [32], [67], [68], where we beat most of the competitors. +The state-of-the-art MoCo [31] gives the most compelling +performance. But different from the representations learned +with contrastive learning, GH-Feat has huge advantages +in generative tasks, as already discussed in Sec. 4.3. +Among adversarial representation learning approaches, +BigBiGAN [17] achieves the best performance, benefiting +from the incredible large-scale training. However, GH- +Feat presents a stronger ability for image reconstruction. +BigBiGAN is learned by discriminating the data-latent joint +distribution, while our GH-Feat targets image reconstruc- +tion by treating a well-trained GAN generator as a learned +loss function. Consequently, as shown in Fig. 15, BigBiGAN +can only recover the input images from the category level, +instead, our approach can recover the inputs with much +more details. The reconstruction error in Tab. 8 conveys the +same conclusion. This is also the reason why GH-Feat could +facilitate various low-level and middle-level discriminative +tasks beyond image classification. More details about Ima- +geNet training can be found in Supplementary Material. +4.4.4 +Transfer Learning +In this part, we explore how GH-Feat can be transferred +from one dataset to another. +2. Our encoder can be trained very efficiently, usually 3× faster than +the GAN training. +3. During testing, we adopt the fully convolutional form as in [66] +and average the scores at multiple scales. + +MGT589P12 +FF-HQ +CelebA +Fig. 16. Landmark detection results. GH-Feat is trained on FF-HQ [11] dataset but can successfully handle the hard cases (large pose and low +image quality) in MAFL dataset [55], a subset of CelebA [74]. +Bedroom +Kitchen +Fig. 17. Layout prediction results using feature learned by MoCo [31] (top row) and our GH-Feat (bottom row). Both methods are trained on LSUN +bedrooms [53] and then transferred to LSUN kitchens. +TABLE 7 +Quantitative comparison on the ImageNet [2] classification task. +Method +Architecture +Top-1 Acc. +Motion Seg (MS) [69], [70] +ResNet-101 +27.6 +Exemplar (Ex) [70], [71] +ResNet-101 +31.5 +Relative Po (RP) [70], [72] +ResNet-101 +36.2 +Colorization (Col) [70], [73] +ResNet-101 +39.6 +Contrastive Learning +InstDisc [67] +ResNet-50 +42.5 +CPC [32] +ResNet-101 +48.7 +MoCo [31] +ResNet-50 +60.6 +Generative Modeling +BiGAN [15] +AlexNet +31.0 +SS-GAN [68] +ResNet-19 +38.3 +BigBiGAN [17] +ResNet-50 +55.4 +GH-Feat (Ours) +ResNet-50 +51.1 +TABLE 8 +Qualitative comparison between BigBiGAN [17] and GH-Feat on +reconstructing images from ImageNet [2]. +MSE↓ +SSIM↑ +FID↓ +BigBiGAN [17] +0.363 +0.236 +33.42 +GH-Feat (Ours) +0.078 +0.431 +22.70 +Landmark Detection. We train a linear regression model +using GH-Feat on FF-HQ [11] and test it on MAFL [55], +which is a subset of CelebA [74]. This two datasets have a +large domain gap, e.g., faces in MAFL have larger poses yet +lower image quality. As shown in Fig. 16, GH-Feat shows a +strong transferability across these two datasets. We compare +our approach with some supervised and unsupervised +alternatives [31], [55], [75], [76]. CLIP [77] trained with +400,000,000 image-text paired samples is also included to +serve as a strong baseline to compare with GH-Feat. +For +a fair comparison, we try the multi-scale representations +from MoCo [31] and CLIP [77] (i.e., Res2, Res3, Res4, and +Res5 feature maps) and report the best results. Tab. 9 +demonstrates the strong generalization ability of GH-Feat. +TABLE 9 +Landmark detection results on MAFL [55]. GH-Feat-R denotes +GH-Feat trained with regularizer. +Method +Supervision +MSE↓ +TCDCN [55] + +7.95 +MTCNN [75] + +5.39 +Cond. ImGen [76] +4.95 +ALAE [43]. +10.13 +MoCo-R50 [31] +9.07 +CLIP-R50 +4.98 +GH-Feat (Ours) +5.12 +GH-Feat-R +4.92 +In particular, it achieves on-par or better performance than +the methods that are particular designed for this task [55], +[75], [76]. Also, it outperforms MoCo [31] on this mid-level +discriminative task. As the Tab. 9 below suggests, GH- +Feat achieves comparable performance as CLIP-R50 with +significantly better data efficiency. Such a comparison is +not 100% eye-to-eye because our approach is particularly +trained on human faces while CLIP could cover a much +larger data domain. But it still demonstrates, to some extent, +that adequately leveraging the pre-trained GAN generator +as a learned loss function yields a discriminative and +transferable visual representation. +Layout +Prediction. We train the layout predictor on +LSUN [53] bedrooms and test it on kitchens to validate how +GH-Feat can be transferred from one scene category to an- +other. Feature learned by MoCo [31] on the bedroom dataset +is used for comparison. We can tell from Fig. 17 that GH-Feat +shows better predictions than MoCo, especially on the target +set (i.e., kitchens), suggesting a stronger transferability. Like +landmark detection, we also conduct experiments with the +4-level representations from MoCo [31] and select the best. +4.4.5 +Image Retrieval +In this section, we verify the hierarchical property of the +proposed GH-Feat with image retrieval. Concretely, given a + +13 +Query +Top-1 +Top-2 +Top-3 +Top-4 +High-Level +Middle-Level +Low-Level +Fig. 18. Retrieval results on LSUN bedroom [53]. +query image, we use encoder to extract its GH-Feat. Then, +we use different levels of GH-Feat to perform retrieval from +10K real images. Note that GH-Feat from these 10K images +are prepared in advance and ℓ1 distance is used as the metric +for retrieval. Fig. 18 shows the retrieval results on LSUN +bedroom [53]. We can tell that when we use higher level +(first row) features for retrieval, all retrieved results are with +the same layout as the query image, but they may have +different lighting conditions. Meanwhile, when using lower +level (bottom row) features for retrieval, the retrieved results +are with similar lighting condition as the query image. +4.5 +Spatial Expansion +4.5.1 +Spatial GH-Feat +Spatial-Aware Style Codes. Even though the layer-wise +style codes can describe the global semantics of synthesized +images, the fine-grained semantics cannot be expressed +precisely because the style codes are too coarse to maintain +spatial semantics. To facilitate the style codes with semantic +segmentation, we equip the layer-wise style codes with +spatial dimension. It is noteworthy that the introduced +spatial dimension make the layer-wise representation more +flexible for various of vision tasks. +Spatial-Aware Encoder. For the vision tasks requiring the +spatial-aware representation of the input image, a spatial- +aware encoder is also needed to produce the spatial-aware +style codes. We inherit the backbone and FPN to fuse the +semantics encoded at different level. The last three stages +feature maps {R4, R5, R6}, are used to produce spatial- +aware GH-Feat. We also use the same instantiation for the +layer equipment. But differently, we use an 1×1 convolution +layer to embed the feature maps {R4, R5, R6} and an +upsampler to match the spatial size of the corresponding +convolution feature map. It can be formulated as: +GHj = up(WjRa[j], hCj/hRa[j]) +j ∈ {1, N}, +where GHj is the learned spatial-aware representation, +Cj is the convolutional feature map, a[j] denotes the +corresponding index of the output feature map from FPN, +and hCj, hRa[j] denotes the spatial dimension of feature map +Cj and Ra[j]. +Ablation. +The +proposed +spatial +generative +feature +is +adopted to provide spatial information, and thus it is critical +to the quality of the reconstructed image. As shown in +Tab. 10, the spatial generative feature can improve the +TABLE 10 +Quantitative comparison on image reconstruction between GH-Feat +and spatial GH-Feat. GH-Feat-R denotes GH-Feat trained with +regularizer. +Face +Bedroom +Method +MSE↓ +SSIM↑ +MSE↓ +SSIM↑ +GH-Feat +0.046 +0.56 +0.068 +0.52 +GH-Feat-R +0.049 +0.55 +0.070 +0.50 +Spatial GH-Feat +0.029 +0.67 +0.057 +0.58 +reconstruction performance, and the qualitative results in +Fig. 21 present that the spatial GH-Feat is able to reconstruct +the background and the out-of-the-distribution objects i.e. +hands and hats well. It supports the effectiveness of the +spatial-aware generative features. +4.5.2 +Data-Efficient Semantic Segmentation +Compared with classification, image segmentation needs +more precise prediction along the spatial dimension. How- +ever, the generative features without spatial dimension +cannot facilitate this task because they cannot be aware +of the semantics for each pixel. To enable this task, we +use the spatial-aware encoder to obtain a set of generative +features with spatial dimension, and a segmentation head +i.e. the Style Interpreter in [78] is followed to obtain the +segmentation results. Because of the generalization of the +spatial visual features, we only need a few samples to +achieve a good segmentation head. In our experiment, we +used 20 annotated samples for the training. We visualize +predictions learned from our visual features in Fig. 19. +Obviously, the spatial-aware generative features provide +precise information for dense pixels, facilitating image +segmentation with a few annotations. +We include several extreme cases in Fig. 20 to verify the +robustness of the segmentation results achieved by GH-Feat. +Concretely, we include samples under extreme poses, as +well as samples containing out-of-distribution objects (i.e., +the objects without annotations during the training of the +segmentation branch). We have three observations: (1) Even +there are few samples under extreme poses during training, +our approach could still produce promising segmentation +results on such challenging cases at the inference stage. (2) +The model could well recognize the eyeglass frames yet +perform poorly on eyeglass lens. We guess this is caused by +the overlap between lens and eyes. (3) Hats (recognized as +hair), earrings and microphones (recognized as background) +could be regarded as failure cases, because our segmentation +branch is learned with simple annotations (e.g., eyes, nose, +cheek, etc.). A more competitive performance could be +expected given richer segmentation labels. +5 +CONCLUSION +In this work, we consider the well-trained GAN generator +as a learned loss function for learning multi-scale features. +Unlike previous work, we treat layer-wise style codes in +Y space as generative visual features rather than W space, +resulting in better hierarchical properties. A distribution- +level regularizer is introduced to overcome the limitation +of only using image-level supervision for encoder training. +The resulting Generative Hierarchical Features are shown + +14 +Real Image +Segmentation +Fig. 19. Data-efficient Image Segmentation with Spatial GH-Feat. We use the spatial-aware encoder to obtain a set of generative features with +spatial dimension and a segmentation head trained with limited annotated data to obtain segmentation results. +Real Image +Segmentation +Extreme Poses +Earrings +Microphones +Hats +Sunglasses +Fig. 20. Extreme cases of data-efficient image segmentation with Spatial GH-Feat. These extreme samples (i.e. extreme pose, hat, sunglasses, +earrings as well as microphones) show the robustness of the segmentation head only trained with fewer annotated samples. +Input +GH-Feat +Spatial GH-Feat +Fig. 21. Qualitative comparison between GH-Feat and spatial GH-Feat. +to be generalizable to a wide range of vision tasks. Since +GH-Feat only leverages the semantics learned in GANs, the +features may lack the good properties of the discriminative +model features. In the future, we hope to learn deep +representations by unifying discriminative and generative +models that can complement each other. +ACKNOWLEDGMENTS +This work is supported in part by the Early Career Scheme +(ECS) through the Research Grants Council (RGC) of Hong +Kong under Grant No.24206219, Grant No.14204521, CUHK +FoE RSFS Grant, and Centre for Perceptual and Interactive +Intelligence (CPII) Ltd under the Innovation and Technology +Fund. +REFERENCES +[1] +Y. Bengio, A. Courville, and P. Vincent, “Representation learning: +A review and new perspectives,” IEEE Trans. Pattern Anal. Mach. +Intell., 2013. 1 +[2] +J. Deng, W. Dong, R. Socher, L.-J. Li, K. Li, and L. Fei-Fei, +“Imagenet: A large-scale hierarchical image database,” in IEEE +Conf. Comput. Vis. Pattern Recog., 2009. 1, 5, 11, 12, 16 +[3] +B. Zhou, A. Lapedriza, A. Khosla, A. Oliva, and A. Torralba, +“Places: A 10 million image database for scene recognition,” IEEE +Trans. Pattern Anal. Mach. Intell., 2017. 1 +[4] +A. Sharif Razavian, H. Azizpour, J. Sullivan, and S. Carlsson, “Cnn +features off-the-shelf: an astounding baseline for recognition,” in +IEEE Conf. Comput. Vis. Pattern Recog. Worksh., 2014. 1 +[5] +D. Bau, B. Zhou, A. Khosla, A. Oliva, and A. Torralba, “Network +dissection: Quantifying interpretability of deep visual representa- +tions,” in IEEE Conf. Comput. Vis. Pattern Recog., 2017. 1 +[6] +D. Matthew and R. Fergus, “Visualizing and understanding +convolutional neural networks,” in IEEE Conf. Comput. Vis. +Pattern Recog., 2014. 1 +[7] +B. Zhou, A. Khosla, A. Lapedriza, A. Oliva, and A. Torralba, +“Object detectors emerge in deep scene cnns,” in Int. Conf. Learn. +Represent., 2015. 1 +[8] +J. Yosinski, J. Clune, Y. Bengio, and H. Lipson, “How transferable +are features in deep neural networks?” in Adv. Neural Inform. +Process. Syst., 2014. 1, 2 +[9] +N. Zhao, Z. Wu, R. W. Lau, and S. Lin, “What makes in- +stance discrimination good for transfer learning?” arXiv preprint +arXiv:2006.06606, 2020. 1, 2 +[10] I. Goodfellow, J. Pouget-Abadie, M. Mirza, B. Xu, D. Warde-Farley, +S. Ozair, A. Courville, and Y. Bengio, “Generative adversarial +nets,” in Adv. Neural Inform. Process. Syst., 2014. 1, 2, 4, 7 +[11] T. Karras, S. Laine, and T. Aila, “A style-based generator +architecture for generative adversarial networks,” in IEEE Conf. +Comput. Vis. Pattern Recog., 2019. 1, 2, 3, 4, 5, 7, 8, 10, 11, 12 +[12] T. Karras, S. Laine, M. Aittala, J. Hellsten, J. Lehtinen, and T. Aila, +“Analyzing and improving the image quality of stylegan,” in IEEE +Conf. Comput. Vis. Pattern Recog., 2020, pp. 8110–8119. 1 +[13] Y. Shen, C. Yang, X. Tang, and B. Zhou, “Interfacegan: Interpreting +the disentangled face representation learned by gans,” IEEE Trans. +Pattern Anal. Mach. Intell., 2020. 1, 2, 8, 10 + +OLU二8二B15 +[14] C. Yang, Y. Shen, and B. Zhou, “Semantic hierarchy emerges +in deep generative representations for scene synthesis,” Int. J. +Comput. Vis., 2020. 1, 2, 4 +[15] J. Donahue, P. Kr¨ahenb¨uhl, and T. Darrell, “Adversarial feature +learning,” in Int. Conf. Learn. Represent., 2017. 1, 2, 5, 10, 11, 12 +[16] V. Dumoulin, I. Belghazi, B. Poole, O. Mastropietro, A. Lamb, +M. Arjovsky, and A. Courville, “Adversarially learned inference,” +in Int. Conf. Learn. Represent., 2017. 1, 2 +[17] J. Donahue and K. Simonyan, “Large scale adversarial representa- +tion learning,” in Adv. Neural Inform. Process. Syst., 2019. 1, 2, 5, +10, 11, 12, 16 +[18] Y. Xu, Y. Shen, J. Zhu, C. Yang, and B. Zhou, “Generative +hierarchical features from synthesizing images,” in CVPR, 2021. +2 +[19] D. G. Lowe, “Distinctive image features from scale-invariant +keypoints,” Int. J. Comput. Vis., 2004. 2 +[20] H. Bay, T. Tuytelaars, and L. Van Gool, “Surf: Speeded up robust +features,” in Eur. Conf. Comput. Vis., 2006. 2 +[21] N. Dalal and B. Triggs, “Histograms of oriented gradients for +human detection,” in IEEE Conf. Comput. Vis. Pattern Recog., +2005. 2 +[22] A. Krizhevsky, I. Sutskever, and G. E. Hinton, “Imagenet classifi- +cation with deep convolutional neural networks,” in Adv. Neural +Inform. Process. Syst., 2012. 2 +[23] K. Simonyan and A. Zisserman, “Very deep convolutional net- +works for large-scale image recognition,” in Int. Conf. Learn. +Represent., 2015. 2, 4 +[24] K. He, X. Zhang, S. Ren, and J. Sun, “Deep residual learning for +image recognition,” in IEEE Conf. Comput. Vis. Pattern Recog., +2016. 2, 3, 4, 7, 10, 11, 16 +[25] C. Doersch and A. Zisserman, “Multi-task self-supervised visual +learning,” in Int. Conf. Comput. Vis., 2017. 2 +[26] R. Zhang, P. Isola, and A. A. Efros, “Split-brain autoencoders: +Unsupervised learning by cross-channel prediction,” in IEEE +Conf. Comput. Vis. Pattern Recog., 2017. 2 +[27] Z. Wu, Y. Xiong, S. X. Yu, and D. Lin, “Unsupervised feature +learning via non-parametric instance discrimination,” in IEEE +Conf. Comput. Vis. Pattern Recog., 2018. 2 +[28] S. Gidaris, P. Singh, and N. Komodakis, “Unsupervised represen- +tation learning by predicting image rotations,” in Int. Conf. Learn. +Represent., 2018. 2 +[29] R. D. Hjelm, A. Fedorov, S. Lavoie-Marchildon, K. Grewal, P. Bach- +man, A. Trischler, and Y. Bengio, “Learning deep representations +by mutual information estimation and maximization,” in Int. +Conf. Learn. Represent., 2019. 2, 7, 10 +[30] C. Zhuang, A. L. Zhai, and D. Yamins, “Local aggregation +for unsupervised learning of visual embeddings,” in Int. Conf. +Comput. Vis., 2019. 2, 7, 10 +[31] K. He, H. Fan, Y. Wu, S. Xie, and R. Girshick, “Momentum contrast +for unsupervised visual representation learning,” in IEEE Conf. +Comput. Vis. Pattern Recog., 2020. 2, 7, 10, 11, 12 +[32] A. v. d. Oord, Y. Li, and O. Vinyals, “Representation learning with +contrastive predictive coding,” arXiv preprint arXiv:1807.03748, +2018. 2, 7, 10, 11, 12 +[33] O. J. H´enaff, A. Srinivas, J. De Fauw, A. Razavi, C. Doersch, +S. Eslami, and A. v. d. Oord, “Data-efficient image recognition with +contrastive predictive coding,” arXiv preprint arXiv:1905.09272, +2019. 2 +[34] Y. Tian, D. Krishnan, and P. Isola, “Contrastive multiview coding,” +arXiv preprint arXiv:1906.05849, 2019. 2, 7 +[35] A. Shocher, Y. Gandelsman, I. Mosseri, M. Yarom, M. Irani, W. T. +Freeman, and T. Dekel, “Semantic pyramid for image generation,” +in IEEE Conf. Comput. Vis. Pattern Recog., 2020. 2 +[36] A. Radford, L. Metz, and S. Chintala, “Unsupervised represen- +tation learning with deep convolutional generative adversarial +networks,” in Int. Conf. Learn. Represent., 2016. 2 +[37] T. Karras, T. Aila, S. Laine, and J. Lehtinen, “Progressive growing +of gans for improved quality, stability, and variation,” in Int. Conf. +Learn. Represent., 2018. 2 +[38] A. Brock, J. Donahue, and K. Simonyan, “Large scale GAN +training for high fidelity natural image synthesis,” in Int. Conf. +Learn. Represent., 2019. 2 +[39] A. Jahanian, L. Chai, and P. Isola, “On the ”steerability” of +generative adversarial networks,” in Int. Conf. Learn. Represent., +2020. 2 +[40] D. Bau, J.-Y. Zhu, H. Strobelt, B. Zhou, J. B. Tenenbaum, W. T. +Freeman, and A. Torralba, “Gan dissection: Visualizing and +understanding generative adversarial networks,” in Int. Conf. +Learn. Represent., 2019. 2 +[41] J. Gu, Y. Shen, and B. Zhou, “Image processing using multi-code +gan prior,” in IEEE Conf. Comput. Vis. Pattern Recog., 2020. 2 +[42] J. Zhu, Y. Shen, D. Zhao, and B. Zhou, “In-domain gan inversion +for real image editing,” in Eur. Conf. Comput. Vis., 2020. 2 +[43] S. Pidhorskyi, D. Adjeroh, and G. Doretto, “Adversarial latent +autoencoders,” in IEEE Conf. Comput. Vis. Pattern Recog., 2020. +2, 7, 8, 10, 11, 12 +[44] X. Huang and S. Belongie, “Arbitrary style transfer in real-time +with adaptive instance normalization,” in Int. Conf. Comput. Vis., +2017. 3, 4 +[45] Z. Wu, D. Lischinski, and E. Shechtman, “Stylespace analysis: +Disentangled controls for stylegan image generation,” in CVPR, +2021. 4 +[46] T.-Y. Lin, P. Doll´ar, R. Girshick, K. He, B. Hariharan, and +S. Belongie, “Feature pyramid networks for object detection,” in +IEEE Conf. Comput. Vis. Pattern Recog., 2017. 4 +[47] C. Yang, Y. Xu, J. Shi, B. Dai, and B. Zhou, “Temporal pyramid +network for action recognition,” in IEEE Conf. Comput. Vis. +Pattern Recog., 2020. 4 +[48] S. Liu, L. Qi, H. Qin, J. Shi, and J. Jia, “Path aggregation network +for instance segmentation,” in IEEE Conf. Comput. Vis. Pattern +Recog., 2018. 4 +[49] O. Tov, Y. Alaluf, Y. Nitzan, O. Patashnik, and D. Cohen-Or, +“Designing an encoder for StyleGAN image manipulation,” ACM +Trans. Graph., 2021. 4, 6, 7, 8 +[50] J. Johnson, A. Alahi, and L. Fei-Fei, “Perceptual losses for real- +time style transfer and super-resolution,” in Eur. Conf. Comput. +Vis., 2016. 4 +[51] D. P. Kingma and J. Ba, “Adam: A method for stochastic +optimization,” in Int. Conf. Learn. Represent., 2015. 5 +[52] Y. LeCun, L. Bottou, Y. Bengio, and P. Haffner, “Gradient-based +learning applied to document recognition,” Proceedings of the +IEEE, 1998. 5, 10, 11 +[53] F. Yu, A. Seff, Y. Zhang, S. Song, T. Funkhouser, and J. Xiao, “Lsun: +Construction of a large-scale image dataset using deep learning +with humans in the loop,” arXiv preprint arXiv:1506.03365, 2015. +5, 7, 8, 12, 13 +[54] G. B. Huang, M. Ramesh, T. Berg, and E. Learned-Miller, “Labeled +faces in the wild: A database for studying face recognition in +unconstrained environments,” Technical Report 07-49, University +of Massachusetts, Amherst, Tech. Rep., 2007. 5, 10, 11 +[55] Z. Zhang, P. Luo, C. C. Loy, and X. Tang, “Facial landmark +detection by deep multi-task learning,” in Eur. Conf. Comput. Vis., +2014. 5, 12 +[56] W. Zhang, W. Zhang, and J. Gu, “Edge-semantic learning strategy +for layout estimation in indoor environment,” Transactions On +Cybernetics, 2019. 5 +[57] C. Zou, A. Colburn, Q. Shan, and D. Hoiem, “Layoutnet: +Reconstructing the 3d room layout from a single rgb image,” in +IEEE Conf. Comput. Vis. Pattern Recog., 2018. 5 +[58] Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image +quality assessment: from error visibility to structural similarity,” +IEEE Trans. Image Process., 2004. 5, 7 +[59] M. Heusel, H. Ramsauer, T. Unterthiner, B. Nessler, and S. Hochre- +iter, “Gans trained by a two time-scale update rule converge to +a local nash equilibrium,” in Adv. Neural Inform. Process. Syst., +2017. 5 +[60] E. Richardson, Y. Alaluf, O. Patashnik, Y. Nitzan, Y. Azar, +S. Shapiro, and D. Cohen-Or, “Encoding in style: a StyleGAN +encoder for image-to-image translation,” in IEEE Conf. Comput. +Vis. Pattern Recog., 2021. 6, 7, 8 +[61] D. Roich, R. Mokady, A. H. Bermano, and D. Cohen-Or, “Pivotal +tuning for latent-based editing of real images,” ACM Trans. +Graph., 2021. 7, 8 +[62] Y. Alaluf, O. Patashnik, and D. Cohen-Or, “ReStyle: A residual- +based StyleGAN encoder via iterative refinement,” in Int. Conf. +Comput. Vis., 2021. 7, 8 +[63] K. +Liu, +“Pyotrch +cifar10,” +https://github.com/kuangliu/ +pytorch-cifar.git, 2019. 10 +[64] G. E. Hinton and R. R. Salakhutdinov, “Reducing the dimension- +ality of data with neural networks,” Science, 2006. 11 +[65] D. P. Kingma and M. Welling, “Auto-encoding variational bayes,” +in Int. Conf. Learn. Represent., 2014. 11 +[66] C. Szegedy, W. Liu, Y. Jia, P. Sermanet, S. Reed, D. Anguelov, +D. Erhan, V. Vanhoucke, and A. Rabinovich, “Going deeper with + +16 +convolutions,” in IEEE Conf. Comput. Vis. Pattern Recog., 2015. +11 +[67] Z. Wu, Y. Xiong, S. X. Yu, and D. Lin, “Unsupervised feature +learning via non-parametric instance discrimination,” in IEEE +Conf. Comput. Vis. Pattern Recog., 2018. 11, 12 +[68] T. Chen, X. Zhai, M. Ritter, M. Lucic, and N. Houlsby, “Self- +supervised gans via auxiliary rotation loss,” in IEEE Conf. +Comput. Vis. Pattern Recog., 2019. 11, 12 +[69] D. Pathak, R. Girshick, P. Doll´ar, T. Darrell, and B. Hariharan, +“Learning features by watching objects move,” in IEEE Conf. +Comput. Vis. Pattern Recog., 2017. 12 +[70] C. Doersch and A. Zisserman, “Multi-task self-supervised visual +learning,” in Int. Conf. Comput. Vis., 2017. 12 +[71] A. Dosovitskiy, J. T. Springenberg, M. Riedmiller, and T. Brox, +“Discriminative unsupervised feature learning with convolutional +neural networks,” in Adv. Neural Inform. Process. Syst., 2014. 12 +[72] C. Doersch, A. Gupta, and A. A. Efros, “Unsupervised visual +representation learning by context prediction,” in Int. Conf. +Comput. Vis., 2015. 12 +[73] R. Zhang, P. Isola, and A. A. Efros, “Colorful image colorization,” +in Eur. Conf. Comput. Vis., 2016. 12 +[74] Z. Liu, P. Luo, X. Wang, and X. Tang, “Deep learning face attributes +in the wild,” in Int. Conf. Comput. Vis., 2015. 12 +[75] K. Zhang, Z. Zhang, Z. Li, and Y. Qiao, “Joint face detection +and alignment using multitask cascaded convolutional networks,” +IEEE Signal Processing Letters, 2016. 12 +[76] T. Jakab, A. Gupta, H. Bilen, and A. Vedaldi, “Unsupervised learn- +ing of object landmarks through conditional image generation,” in +Adv. Neural Inform. Process. Syst., 2018. 12 +[77] A. Radford, J. W. Kim, C. Hallacy, A. Ramesh, G. Goh, S. Agarwal, +G. Sastry, A. Askell, P. Mishkin, J. Clark et al., “Learning +transferable visual models from natural language supervision,” +in ICML, 2021. 12 +[78] Y. Zhang, H. Ling, J. Gao, K. Yin, J.-F. Lafleche, A. Barriuso, +A. Torralba, and S. Fidler, “Datasetgan: Efficient labeled data +factory with minimal human effort,” in CVPR, 2021. 13 +[79] T. Karras, S. Laine, and T. Aila, “Stylegan - official tensorflow +implementation,” https://github.com/NVlabs/stylegan, 2019. 16 +A1. HIERARCHICAL PROPERTY +We also re-evaluate the layer-wise representation on dif- +ferent discriminative tasks. As shown in Fig. 22, the +training regularizer improves the hierarchical property of +the original GH-Feat. Since the training regularizer prevents +the model from overfitting pixel values, the layer-wise +representation is closer to the distribution center and +achieve better hierarchical properties on the discriminative +tasks. +A2. EXPERIMENTS ON IMAGENET +Training Details. During the training of the StyleGAN +model on the ImageNet dataset [2], we resize all images +in the training set such that the short side of each image is +256, and then centrally crop them to 256 × 256 resolution. +All training settings follow the StyleGAN official implemen- +tation [79], including the progressive strategy, optimizer, +learning rate, etc. The generator and the discriminator are +alternatively optimized until the discriminator have seen +250M real images. After that, the generator is fixed and +treated as a well-learned loss function to guide the training +of the encoder. During the training of the hierarchical +encoder, images in the training collection are pre-processed +in the same way as mentioned above. After the encoder +is ready, we treat it as a feature extractor. We use the +output feature map at the “res5” stage, apply adaptively +average pooling to obtain 2×2 spatial feature and vectorize +it. A linear classifier, i.e., with one fully-connected layer, +takes these extracted features as the inputs to learn the +image classification task. SGD optimizer, together with +batch size 2048, is used. The learning rate is initially set +as 1 and decayed to 0.1 and 0.01 at the 60-th and the 80-th +epoch respectively. During the training of the final classifier, +ResNet-style data augmentation [24] is applied. +The FID score on ImageNet is 40.92. Fig 23 shows the +uncurated samples of the pretrained ImageNet samples. Al- +though the synthesized samples are not very realistic, they +can still help downstream tasks like ImageNet classification. +Discussion. We have already shown in the main submission +that GH-Feat achieves comparable accuracy to existing +alternatives. Especially, among all methods based on gener- +ative modeling, GH-Feat obtains second performance only +to BigBiGAN [17], which requires incredible large-scale +training. However, as discussed in the main submission, +our GH-Feat facilitates a wide rage of tasks besides image +classification. Taking image reconstruction as an example, +our approach can well recover the input image, significantly +outperforming BigBiGAN [17]. + +17 +MSE (IOD) +Corner Distance +Accuracy +Regression Error +Landmark Detection +Layout Prediction +Luminance Regression +Face Verification +Level Index +Level Index +Level Index +Level Index +Fig. 22. Comparison on the hierarchical property between using regularizer or not. y (in red color) and yreg (in blue color) denote the original +GH-Feat and GH-Feat with regularizer, respectively. +Fig. 23. Uncurated generated samples of StyleGAN model on ImageNet. + +0.06 +y +O1) +MSE +0.03 +2 +468101214 +LevelIndex0.08 +Corner Distance +Yreg +0.056 +2 +468101214 +LevelIndex0.7 +Accuracy +Yreg +0.5 +2 +4 +6 +8 +1012 +14 +Level Index25 +Error +21 +2 +4 +6 +8 +10 +12 +14 +Level Index \ No newline at end of file diff --git a/_9E4T4oBgHgl3EQf4w0P/content/tmp_files/load_file.txt b/_9E4T4oBgHgl3EQf4w0P/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..531a8d438dad5766804b8b67364cfdf0daec02d9 --- /dev/null +++ b/_9E4T4oBgHgl3EQf4w0P/content/tmp_files/load_file.txt @@ -0,0 +1,1613 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf,len=1612 +page_content='1 GH-Feat: Learning Versatile Generative Hierarchical Features from GANs Yinghao Xu, Yujun Shen, Jiapeng Zhu, Ceyuan Yang, and Bolei Zhou, Member, IEEE Abstract—Recent years witness the tremendous success of generative adversarial networks (GANs) in synthesizing photo-realistic images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' GAN generator learns to compose realistic images and reproduce the real data distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Through that, a hierarchical visual feature with multi-level semantics spontaneously emerges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' In this work we investigate that such a generative feature learned from image synthesis exhibits great potentials in solving a wide range of computer vision tasks, including both generative ones and more importantly discriminative ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' We first train an encoder by considering the pre-trained StyleGAN generator as a learned loss function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' The visual features produced by our encoder, termed as Generative Hierarchical Features (GH-Feat), highly align with the layer-wise GAN representations, and hence describe the input image adequately from the reconstruction perspective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Extensive experiments support the versatile transferability of GH-Feat across a range of applications, such as image editing, image processing, image harmonization, face verification, landmark detection, layout prediction, image retrieval, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' We further show that, through a proper spatial expansion, our developed GH-Feat can also facilitate fine-grained semantic segmentation using only a few annotations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Both qualitative and quantitative results demonstrate the appealing performance of GH-Feat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Code and models are available at https://genforce.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='io/ghfeat/.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Index Terms—Generative adversarial network, generative representation, feature learning, image editing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 1 INTRODUCTION R EPRESENTATION learning plays an essential role in the rise of deep learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' The learned representations are able to express the variation factors of the complex visual world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Accordingly, the performance of a deep learning algorithm largely depends on the features extracted from the input data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' As pointed out by Bengio et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' [1], a good representation is expected to have the following properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' First, it should capture multiple configurations of the input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Second, it should organize the explanatory factors of the input data as a hierarchy, where more abstract concepts are at a higher level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Third, it should have strong transferability, not only from datasets to datasets but also from tasks to tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Deep neural networks supervisedly trained for image classification on large-scale datasets (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', ImageNet [2] and Places [3]) have resulted in expressive and discriminative visual features [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' However, the developed features are heavily dependent on the training objective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' For example, the deep features learned for the object recognition task may give more attention to the shapes and parts of the objects while remain invariant to rotation [5], [6], and the deep features from a scene classification model may focus more on detecting the categorical objects (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', bed for bedroom and sofa for living room) [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Thus the discriminative features learned from solving high-level image classification tasks might not be necessarily good for other mid-level and low-level tasks, limiting their transferability [8], [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Besides, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Xu and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Yang are with the Department of Information Engineering, the Chinese University of Hong Kong, Hong Kong SAR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Shen is with Ant Research, China.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Zhu is with the School of Computer Science and Engineering, the Hong Kong University of Science and Technology, Hong Kong SAR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Zhou is with Computer Science Department, University of California, Los Angeles, USA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' it remains unknown how the discriminative features can be used in generative applications like image editing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' In contrast to discriminative models, generative models such as generative adversarial networks (GANs) [10] offer an alternative way for representation learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' A GAN is typically formulated to match the synthetic data distribution to the observed data distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Through adversarial training, the generator in GAN is required to capture the multi-level variation factors underlying the input data to the most extent, otherwise, the discrepancy between the real and synthesized data would be spotted by the discrim- inator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Recent studies have confirmed that the StyleGAN family [11], [12] spontaneously encodes rich semantics in a hierarchical manner [13], [14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' But the transferability of the per-layer representation learned by GANs is not fully verified in the literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Some attempts have been made to apply the generative representations (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', the representations emerging from solving generative tasks) to the high-level image classification task [15], [16], [17], yet leaving mid-level and low-level tasks less explored.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' In this work, we make a thorough investigation into the utility of GAN representations and demonstrate their wide applications to downstream tasks, including both generative ones and more importantly discriminative ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' To appropriately obtain the GAN-derived features from a given image, we train a hierarchical encoder using the pre-trained StyleGAN generator as a learned loss function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Through that way, our encoder works together with the generator to reconstruct the image, implicitly required to extract the variation factors that describe the input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' We call the output visual features as Generative Hierarchical Features (GH-Feat).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' We also observe in the encoder training that, only exploiting the supervision at the image level (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', the per- pixel reconstruction loss) may cause the overfitting of pixel arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='05315v1 [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='CV] 12 Jan 2023 2 values, severely limiting the transferability of the extracted representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' To mitigate such a negative effect, we intro- duce a training regularizer from the statistical perspective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' It alleviates the problem of distribution mismatching between the learned GH-Feat and the native GAN representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' After the encoder is well prepared, we evaluate the resulting GH-Feat on a broad range of downstream appli- cations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' On one hand, we verify that the representations learned by GANs naturally support various generative tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Concretely, to edit or process target images, we can simply modulate their corresponding features, and reuse the generator (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', the same as the one used in encoder training) as a renderer to decode features back to images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' The extensive experiments show that our approach achieves global and local image manipulation, transferring styles between two images, image colorization, image inpainting, image super-resolution, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Besides, our GH-Feat also allows fusing objects from an image into another as the application of image harmonization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' On the other hand, we are interested in the discriminative capability of the generative features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='For this purpose, we treat the features extracted by our encoder as the base representations, on top of which we learn different linear task heads for a range of high-level and middle-level tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Experiments on multiple datasets validate the effectiveness of GH-Feat on large- scale image classification, face verification, facial landmark detection, room layout prediction, transferring learning, image retrieval, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Furthermore, to enable dense prediction tasks, we manage to expand GH-Feat along spatial dimen- sions with an adequate modification of our encoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' The improved spatial-aware visual features suggest compelling performance on fine-grained semantic segmentation using only a few annotations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' The preliminary result of this work is published at [18] as oral presentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' We include the following new contents as the extension to the conference paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' (1) We find the limitation of only using image-level supervision for encoder training, and provide an effective solution by introducing a distribution-level regularizer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Analyses and improvements are illustrated in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' (2) We include two more image editing tasks, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' style transfer (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='4) and semantic manipulation (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='5), to validate that our GH-Feat can describe images moderately, aligning with human perception.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' (3) We confirm in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='6 that GH-Feat also facilitates conventional image processing tasks, including image colorization, image inpainting, and image super- resolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' (4) We include image retrieval as an addition discriminative task to verify the hierarchical property of GH-Feat, whose details are explained in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' (5) We propose a spatial expansion to our GH-Feat via learning a spatial-aware encoder, and show the great potential of the improved representations in data-efficient fine-grained semantic segmentation in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 2 RELATED WORK Visual Features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Visual Feature plays a fundamental role in the computer vision field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Traditional methods used manually designed features [19], [20], [21] for pattern matching and object detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' These features are signif- icantly improved by deep models [22], [23], [24], which automatically learn the feature extraction from large-scale datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' However, the features supervisedly learned for a particular task could be biased to the training task and hence become difficult to transfer to other tasks, especially when the target task is too far away from the base task [8], [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Unsupervised representation learning is widely explored to learn a more general and transferable feature [25], [26], [27], [28], [29], [30], [31], [32], [33], [34].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' However, most of existing unsupervised feature learning methods focus on evaluating their features on the tasks of image recognition, yet seldom evaluate them on other mid-level or low-level tasks, let alone generative tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Shocher et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' [35] discover the potential of discriminative features in image generation, but the transferability of such features are not fully verified.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Generative Adversarial Networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' GANs [10] are able to produce photo-realistic images via learning the underly- ing data distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' The recent advance of GANs [36], [37], [38] has significantly improved the synthesis quality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' StyleGAN [11] proposes a style-based generator with multi- level style codes and achieves the start-of-the-art generation performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' However, little work explores the represen- tation learned by GANs as well as how to apply such representation for other applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Some recent work interprets the semantics encoded in the internal represen- tation of GANs and applies them for image editing [13], [14], [39], [40], [41], [42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' But it remains much less explored whether the learned GAN representations are transferable to discriminative tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Adversarial Representation Learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' The main reason of hindering GANs from being applied to discriminative tasks comes from the lack of inference ability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' To fill this gap, prior work introduces an additional encoder to the GAN structure [15], [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Donahue and Simonyan [17] and Pidhorskyi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' [43] extend this idea to the state-of-the- art BigGAN [38] and StyleGAN [11] models respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' In this paper, we also study the representation learning using GANs, with following improvements compared to existing methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' First, we propose to treat the well-trained StyleGAN generator as a learned loss function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Second, instead of mapping the images to the initial GAN latent space, like most algorithms [15], [16], [17], [43] have done, we design a novel encoder to produce hierarchical features that well align with the layer-wise representation learned by StyleGAN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Third, besides the image classification task that is mainly targeted at by prior work [15], [16], [17], [43], we validate the transferability of our proposed GH-Feat on a range of generative and discriminative tasks, demonstrating its generalization ability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 3 METHODOLOGY This section introduces the encoder used to extract hierar- chical visual features from the input images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' This encoder is trained in an unsupervised manner using a well-prepared StyleGAN generator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='1 describes how we abstract the multi-level representation from StyleGAN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='2 presents the structure of the novel hierarchical encoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='4 describes the idea of using pre-trained StyleGAN generator as a learned loss function for representation learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='3 introduces the training regularizer to prevent the encoder from overfitting pixel values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 3 AdaIN Encoder GH-Feat Generator 𝐟!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 𝐟" AdaIN AdaIN AdaIN Discriminative Task Generative Task (3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Layout estimation (2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Segmentation (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Classification (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Semantic editing (2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Style transfer Dog (3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Image harmonization Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Framework of the GH-Feat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' This feature hierarchy highly aligns with the layer-wise representation (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', style codes of per-layer AdaIN) learned by the StyleGAN generator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Parameters in blue blocks are learnable while others are frozen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' TABLE 1 Encoder structure, which is based on ResNet-50 [24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Fully-connected (FC) layers are employed to map the feature maps produced by the Spatial Alignment Module (SAM) to our proposed Generative Hierarchical Features (GH-Feat).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' GH-Feat exactly align with the multi-scale style codes used in StyleGAN [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' The numbers in brackets indicate the dimension of features at each level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Stage Encoder Pathway Output Size SAM & Pool FC Dimension GH-Feat Style Code in StyleGAN input − 3 × 2562 conv1 7×7,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 64 64 × 1282 stride 2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 2 pool1 3×3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' max 64 × 642 stride 2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 2 res2 � 1×1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 64 3×3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 64 1×1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 256 � ×3 256 × 642 res3 � 1×1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 128 3×3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 128 1×1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 512 � ×4 512 × 322 512 × 42 8192×1792 Level 1-2 Layer 14-13 (128d × 2) Level 3-4 Layer 12-11 (256d × 2) Level 5-6 Layer 10-9 (512d × 2) res4 � 1×1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 256 3×3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 256 1×1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 1024 � ×6 1024 × 162 512 × 42 8192×4096 Level 7-8 Layer 8-7 (1024d × 2) Level 9-10 Layer 6-5 (1024d × 2) res5 � 1×1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 512 3×3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 512 1×1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 2048 � ×3 2048 × 82 512 × 42 8192×4096 Level 11-12 Layer 4-3 (1024d × 2) Level 13-14 Layer 2-1 (1024d × 2) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='1 Layer-wise Representation from StyleGAN The generator G(·) of GANs typically takes a latent code z ∈ Z as the input and is trained to synthesize a photo-realistic image x = G(z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' The recent state-of-the-art StyleGAN [11] proposes to first map z to a disentangled space W with w = f(z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Here, f(·) denotes the mapping implemented by multi-layer perceptron (MLP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' The w code is then projected to layer-wise style codes {y(ℓ)}L ℓ=1 ≜ {(y(ℓ) s , y(ℓ) b )}L ℓ=1 with affine transformations, where L is the number of convolutional layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' y(ℓ) s and y(ℓ) b correspond to the channel-wise scale and weight parameters in Adaptive Instance Normalization (AdaIN) [44].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' The space constructed by these layer-wise style parameters is named as Y space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' These style codes are used to modulate the output feature maps of each convolutional layer with AdaIN(x(ℓ) i , y(ℓ)) = y(ℓ) s,i x(ℓ) i − µ(x(ℓ) i ) σ(x(ℓ) i ) + y(ℓ) b,i , (1) MLP FC7 AdaIN FC1 AdaIN FC14 AdaIN ys,1 yb,1 ys,7 yb,7 ys,14 yb,14 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Multiple latent spaces of StyleGAN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' FC refers to the affine layer between W space and Y space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' where x(ℓ) i indicates the i-th channel of the output feature map from the ℓ-th layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' µ(·) and σ(·) denote the mean and variance respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 2 illustrates the Z, W and Y space of StyleGAN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Here, we treat the layer-wise style codes of Y space, {y(ℓ)}L ℓ=1, as the generative visual features that we would like to extract from the input image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' There are two YiEZ2W4 major advantages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' First, the synthesized image can be completely determined by these style codes without any other variations, making them suitable to express the information contained in the input data from the generative perspective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Second, these style codes are organized as a hierarchy where codes at different layers correspond to semantics at different levels [11], [14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' To the best of our knowledge, this is the first work that adopts the style codes for the per-layer AdaIN module as the learned representations of StyleGAN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Wu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' [45] also shows Y space can be leveraged for disentangled control of image editing, while our work explores the potential of generative representations in facilitating both generative and more importantly discriminative downstream tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='2 Hierarchical Encoder Based on the layer-wise representation described in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='1, we propose a novel encoder E(·) with a hierarchical structure to extract multi-level visual features from a given image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 1, the encoder is designed to best align with the StyleGAN generator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' In particular, the Generative Hierarchical Features (GH-Feat) produced by the encoder, {f (ℓ)}L ℓ=1 ≜ {(f (ℓ) s , f (ℓ) b )}L ℓ=1, are fed into the per- layer AdaIN module of the generator by replacing the style code y(L−ℓ+1) in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' We adopt ResNet [24] architecture as the encoder backbone and add an extra residual block to get an additional feature map with lower resolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='In fact, there are totally six stages in our encoder, where the first one is a convolutional layer (followed by a pooling layer) and each of the others consists of several residual blocks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Besides, we introduce a feature pyramid network [46] to learn the features from multiple levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' The output feature maps from the last three stages, {R4, R5, R6}, are used to produce GH- Feat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Taking a 14-layer StyleGAN generator as an instance, R4 aligns with layer 9-14, R5 with 5-8, while R6 with 1-4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Here, to bridge the feature map with each style code, we first downsample it to 4×4 resolution and then map it to a vector of the target dimension using a fully-connect (FC) layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' In addition, we introduce a lightweight Spatial Alignment Module (SAM) [47], [48] into the encoder structure to better capture the spatial information from the input image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' SAM works in a simple yet efficient way: Ri = Widown(Ri) + W6R6 i ∈ {4, 5}, where W4, W5, and W6 (all are implemented with an 1 × 1 convolutional layer) are used to project the feature maps R4, R5, and R6 to have the same number of feature channels respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' R4 and R5 are downsampled to the same resolution of R6 before fusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Encoder Structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Tab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 1 provides the detailed archi- tecture of our hierarchical encoder by taking a 14-layer StyleGAN [11] generator as an instance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Recall that the design of GH-Feat treats the layer-wise style codes used in the StyleGAN model (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', the code fed into the AdaIN module [44]) as generative features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Accordingly, GH-Feat consists of 14 levels that exactly align with the multi-scale style codes yet in a reverse order, as shown in the last two columns of Tab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='3 Statistical Training Regularizer As discussed in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='1, our approach aims at learning the style representations encoded in y, which are transformed from the w code using pre-layer linear projection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Y space is less constrained than W space and hence may suffer from the problem of overfitting pixel values, which further leads to poor transferability of the learned features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' To solve such a problem, we infer {y(ℓ) avg}L ℓ=1 from the averaged latent code (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', a statistics from the training stage), wavg, and propose to only learn the residual code at each layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Thus, we have E(x) = {∆y(ℓ)}L ℓ=1, which induces the final features as {y(ℓ) avg + ∆y(ℓ)}L ℓ=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' We then penalize the l2 norm of each residual code to prevent it from shifting too far from the native distribution, resulting in a training regularizer Lreg = L � ℓ=1 ∥∆y(ℓ)∥2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' (2) e4e [49] also regularizes the inversion space when training the encoder yet from a different aspect against GH-Feat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' In particular, the regularization in e4e [49] targets minimizing the latent code variation across layers (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', they expect the inverted codes regarding different layers to be close to each other) to reconstruct the input image from coarse to fine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Differently, the regularization in our work bonds the latent code close to the distribution center (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', the statistical average) to prevent the model from overfitting pixel values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' In this way, our approach could better represent an image from the semantic level, further facilitating downstream tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='4 StyleGAN Generator as Learned Loss We consider the pre-trained StyleGAN generator as a leaned loss function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Specifically, we employ a StyleGAN generator to supervise the encoder training with the objective of image reconstruction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' We also introduce a discriminator to compete with the encoder, following the formulation of GANs [10], to ensure the reconstruction quality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' To summarize, the encoder E(·) and the discriminator D(·) are jointly trained with min ΘE LE = ||x − G(E(x))||2 − λ1Ex[D(G(E(x)))] + λ2||F(x) − F(G(E(x)))||2 + λ3Lreg, (3) min ΘD LD = Ex[D(G(E(x)))] − Ex[D(x)] + λ4Ex[||∇xD(x)||2 2], (4) where || · ||2 denotes the l2 norm and λ1, λ2, λ3, λ4 are loss weights to balance different loss terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' The last term in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' (3) represents the perceptual loss [50] and F(·) denotes the conv4 3 output from a pre-trained VGG [23] model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 4 EXPERIMENTS We evaluate Generative Hierarchical Features (GH-Feat) on a wide range of downstream applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='1 introduces the experimental settings, such as implemen- tation details, datasets, and tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='2 presents the analysis of our approach including ablation study and the importance of the regularizer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='3 and Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='4 evaluate the applicability of GH-Feat on generative and 5 discriminative tasks respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='5 shows the results of the introduced spatial expansion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='1 Experimental Settings Implementation Details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' The loss weights are set as λ1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='1, λ2 = 5e−5, λ3 = 5e−4 and λ4 = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' We use Adam [51] optimizer, with β1 = 0 and β2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='99, to train both the encoder and the discriminator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' The learning rate is initially set as 1e−4 and exponentially decayed with the factor of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Datasets and Models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' We conduct experiments on four StyleGAN [11] models, pre-trained on MNIST [52], FF- HQ [11], LSUN bedrooms [53], and ImageNet [2] respec- tively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' The MNIST model is with 32 × 32 resolution and the remaining models are with 256 × 256 resolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Generative Tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' (1) Image editing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' It focuses on manip- ulating the image content or style, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', global editing, local editing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' (2) Image harmonization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' This task harmonizes a discontinuous image to produce a realistic output.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' (3) Style transfer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' This task focuses on transferring the style of the reference image to the source image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' (4) Semantic manipulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' It targets at modifying the semantic meaning of an object while preserving other characteristics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' (5) Image colorization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' It focuses on colorizing the grayscale image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' (6) Image inpainting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' This task reconstructs missing regions in an image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' (7) Image super-resolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' It aims at improving the resolution of the image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Discriminative Tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' (1) MNIST digit recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' It is a long-standing image classification task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' We report the Top-1 accuracy on the test set following [52].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' (2) Face verification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' It aims at distinguishing whether the given pair of faces come from the same identity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' We validate on the LFW dataset [54] following the standard protocol [54].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' (3) ImageNet classifi- cation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' This is a large-scale image classification dataset [2], consisting of over 1M training samples across 1,000 classes and 50K validation samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' We use Top-1 accuracy as the evaluation metric following existing work [15], [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' (4) Pose estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' This task targets at estimating the yaw pose of the input face.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 70K real faces on FF-HQ [11] are split into 60K training samples and 10K test samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' The ℓ1 regression error is used as the evaluation metric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' (5) Landmark detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' This task learns a set of semantic points with visual meaning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' We use FF-HQ [11] dataset and follow the standard MSE metric [55] to report performances in inter-ocular distance (IOD).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' (6) Layout prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' We extract the corner points of the layout line and convert the task to a landmark regression task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' The annotations of the collected 90K bedroom images (70K for training and 20K for validation) are obtained with [56].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Following [57], we report the corner distance as the metric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' (7) Face luminance regression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' It focuses on regressing the luminance of face images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' We use it as a low-level task on the FF-HQ [11] dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' (8) Image retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' It aims at retrieving the images with specific attributes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' (9) Data-efficient image segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' This task focuses on predicting the class of each spatial pixel with limited annotated data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='2 Analysis on GH-Feat 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='1 Ablation Study We make ablation studies on the training of encoder from two perspectives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' (1) We choose the layer-wise style codes TABLE 2 Ablation studies on the feature space and the SAM module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Space SAM Reg MSE↓ SSIM↑ FID↓ W \x13 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='0601 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='540 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='24 Y 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='0502 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='550 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='06 Y \x13 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='0464 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='558 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='48 Y \x13 \x13 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='0494 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='551 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='84 Input Training G & E together Ours Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Qualitative comparison on image reconstruction between training the generator from scratch together with the encoder, and our GH-Feat that treats the well-learned StyleGAN generator as a loss function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' y over the w codes as the representation from StyleGAN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' (2) We introduce Spatial Alignment Module (SAM) into the encoder to better handle the spatial information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' (3) We involve a regularizer in the training of encoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Since the encoder is trained with the objective of image reconstruction, we use mean square error (MSE), SSIM [58], and FID [59] to evaluate the encoder performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Tab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 2 shows the results where we can tell that our encoder benefits from the effective SAM module and that choosing an adequate representation space (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', the comparison between the first row and the last row) results in a better reconstruction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Introducing the regularizer alleviates the pixel value overfitting and improves the reconstruction quality at the distribution level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' More discussion on the differences between W space and Y space can be found in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Random Generator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Recall that, during the training of the encoder, we propose to treat the well-trained StyleGAN generator as a learned loss function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' In this part, we explore what will happen if we train the generator from scratch together with the encoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 3 and Tab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 3 show the qualitative and quantitative results respectively, which demonstrate the strong performance of GH-Feat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' It suggests that besides higher efficiency, reusing the knowledge from a well-trained generator can also bring better performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='2 Importance of Regularizer Although GH-Feat has achieved good results in image reconstruction, it cannot perform very well on image editing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Compared with the W space that previous attempts adopt as the inversion space, the Y space used by GH- Feat ignores the linear transformation between w code and y code, resulting in its flexibility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Hence, it is easier to overfit a given image through a simple combination of generative features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' This leads to a mismatch between the 6 Real Image w/o 𝐿!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' "# w/ 𝐿!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' "# Sampled Image Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Qualitative comparison on the style mixing task between using training regularizer or not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' The first row are the sampled images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' The second row shows the results mixed with the codes predicted by our encoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' The third row presents the mixing results with original latent code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Input ALAE e4e pSp GH-Feat GH-Feat-S Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Qualitative comparison on reconstructing real images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' GH-Feat-S denotes the spatial GH-Feat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Our GH-Feat and GH-Feat-S, which are built on StyleGAN, could get comparable and better performance as pSp [60] and e4e [49], which employ a more powerful StyleGAN2 generator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' TABLE 3 Quantitative comparison on image reconstruction between training the generator from scratch together with the encoder, and our GH-Feat that treats the well-learned StyleGAN generator as a loss function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' GH-Feat-R denotes GH-Feat trained with regularizer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' MSE↓ SSIM↑ FID↓ Training G(·) from Scratch 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='429 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='301 46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='20 GH-Feat (Ours) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='0464 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='558 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='48 GH-Feat-R 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='0494 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='551 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='84 TABLE 4 Cosine similarity of the encoder output and the native latent code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' w/o Lreg w/ Lreg FED 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='444 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='879 learned visual features and the latent space distribution of the generator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' We choose the task of global editing as a benchmark to explore the mismatch problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Specifically, we extract the generative features of the real image first and then randomly replace them with the randomly sampled features in the latent space at layers 0-4 to achieve global editing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' The results are shown in the 2nd row of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Besides, we also extract the visual feature of the sampled images and do the same operation to achieve the editing result in the third line of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Obviously, the mixed results by the two sets of features both extracted by the encoder are better, suggesting the domain shift between the visual features and the latent space of the generator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Based on this, we apply the constraints proposed in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 3 to the encoder training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' The right part of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 4 shows the editing results with the Lreg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' The global editing results with sampled and extracted features are very similar, and both are much better than the result without Lreg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' It demonstrates that the generative features learned with Lreg are more in line with its distribution of latent space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' To quantitatively measure the similarity between two domains, we use cosine distance between generative feature 7 and native code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Specifically, we sample 10k fake images and extract the corresponding GH-Feat by our encoder, and then cosine similarity is calculated for the two distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' As shown in Tab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 4, minimizing the variation of the generative features can improve the similarity from 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='444 to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='879, suggesting the effectiveness of this regularization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='3 Evaluation on Generative Tasks Thanks to using the StyleGAN as a learned loss function, a huge advantage of GH-Feat over existing unsupervised feature learning approaches [29], [30], [31], [32], [34], which mainly focus on the image classification task, is its generative capability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' In this section, we conduct a number of generative experiments to verify this point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='1 Image Reconstruction Image reconstruction is an important evaluation on whether the learned features can best represent the input image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' MSE and SSIM [58] are used as quantitative metrics to evaluate the reconstruction performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Tab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 5 and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 5 show the quantitative and qualitative comparison between our GH-Feat and other GAN inversion methods on FF- HQ faces [11] and LSUN bedrooms [53].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' The very recent work ALAE [43] also employs StyleGAN for representation learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' We have following differences from ALAE: (1) We use the Y space instead of the W space of StyleGAN as the representation space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' (2) We learn hierarchical features that highly align with the per-layer style codes in StyleGAN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' (3) Our encoder can be efficiently trained with a well-learned generator by treating StyleGAN as a loss function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' We can tell that GH-Feat better reconstructs the input by preserving more information, resulting a more expressiveness represen- tation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Besides pSp [60], e4e [49] and Restyle [62], we include the results of PTI [61] as well as the improved version of our GH-Feat (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', spatial expansion introduced in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' We also include the inference time to help evaluate the model efficiency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' We have three observations from the table below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' (1) Our GH-Feat, which is built on StyleGAN, could get comparable performance as pSp [60] and e4e [49], which employ a more powerful StyleGAN2 generator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' We surmise that such an advantage originates from the replacement from W space to Y space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' (2) Restyle [62] (which requires iterative refinement) and PTI [61] (which requires tuning of the weights of the generator) provide good reconstruction results but suffer from slow inference speed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' (3) Our improved version, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', Spatial GH-Feat, substantially im- proves the inversion quality without sacrificing the model efficiency, and achieves the best performance among all encoder-based methods without generator tuning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='2 Image Editing In this part, we evaluate GH-Feat on a number of image editing tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Different from the features learned from dis- criminative tasks [24], [31], our GH-Feat naturally supports sampling and enables creating new data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Style Mixing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' To achieve style mixing, we use the encoder to extract visual features from both the content image and the style image and swap these two features at some particular level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' The swapped features are then visualized by the generator, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' We can observe the compelling hierarchical property of the learned GH-Feat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' For example, by exchanging low-level features, only the image color tone and the skin color are changed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Meanwhile, mid-level features controls the expression, age, or even hair styles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Finally, high-level features correspond to the face shape and pose information (last two columns).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Global Editing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' The style mixing results have suggested the potential of GH-Feat in multi-level image stylization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Sometime, however, we may not have a target style image to use as the reference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Thanks to the design of the latent space in GANs [10], the generative representation naturally supports sampling, resulting in a strong creativity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' In other words, based on GH-Feat, we can arbitrarily sample meaningful visual features and use them for image editing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 7 presents some high-fidelity editing results at multiple levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' This benefits from the matching between the learned GH-Feat and the internal representation of StyleGAN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Local Editing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Besides global editing, our GH-Feat also facilitates editing the target image locally by deeply coop- erating with the generator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' In particular, instead of directly swapping features, we can exchange a certain region of the spatial feature map at some certain level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' In this way, only a local patch in the output image will be modified while other parts remain untouched.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 8, we can successfully manipulate the input face with different eyes, noses, and mouths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='3 Image Harmonization Our hierarchical encoder is robust such that it can extract reasonable visual features even from discontinuous image content.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' We copy the patches from other images onto the original image and feed the stitched image into our proposed encoder for feature extraction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' The extracted features are then visualized via the pre-trained generator, as in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' On the bedroom, we can see that the copied bed, window and ceiling light well blend into the “background”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' We also surprisingly find that when copying a window into the source image, the view from the original window and that from the new window highly align with each other (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', vegetation or ocean).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' On face image, besides eye, nose and mouth, GH-Feat also blends the glasses with the background very well, benefiting from the robust generative visual features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='4 Style Transfer Our GH-Feat can not only edit the image attributes by replacing the randomly sampling feature at a particular level but also can facilitate the editing with the given conditional input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Here, we take style transfer as an example, aiming to transfer the style of the given image to the source image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' We first extract the generative features of the content image Ic and style image Is, and then style-mixing is performed by replacing the visual features of Ic with the corresponding ones of Is at the layer 8- 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' We leverage the disentanglement of the generative features across different layers to perform style transfer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 10, our encoder can successfully transfer the style of the given image to the source images, suggesting the effectiveness of the generative features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' It is worth noting that although the texture of the given style images 8 TABLE 5 Quantitative comparison on reconstructing images from FF-HQ faces [11] and LSUN bedrooms [53].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' GH-Feat-S denotes the spatial GH-Feat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' bold ones rank the best among the methods w/o generator tuning and underlined ones are the second.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Face Bedroom Method MSE↓ SSIM↑ TIME↓ MSE↓ SSIM↑ w/ generator tuning PTI [61] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='009 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='74 58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='02 w/o generator tuning ALAE [43] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='182 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='40 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='023 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='275 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='32 pSp [60] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='034 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='56 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='063 e4e [49] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='052 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='063 Restyle [62] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='030 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='66 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='304 GH-Feat 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='046 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='56 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='035 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='068 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='52 GH-Feat-S 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='029 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='67 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='038 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='057 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='581 Content Image Level 0-1 Level 2-3 Level 4-5 Level 6-7 Level 8-9 Level 10-11 Level 12-13 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Style mixing results by exchanging the GH-Feat extracted from the content image and the style image (first row) at different levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Higher level corresponds to the high-level semantics like the face shape and pose information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Level 0-1 Level 2-5 Level 6-11 Level 12-13 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Global image editing achieved by GH-Feat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' On the left is the input image, while the others are generated by randomly sampling the visual feature at some particular level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Input Eyes Nose Mouth Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Local image editing achieved by GH-Feat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' On the left is the input image, while the others are generated by randomly sampling the visual feature and replacing the spatial feature map (for different regions) at some particular level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Zoom in for details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' rarely appears in the training dataset, our encoder can still reconstruct it and extract reasonable visual features with good disentangle properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' It also supports the robustness and generalization of the visual features extracted by our hierarchical encoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='5 Semantic Manipulation Here we explore the semantic editability of the generative features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' We utilize off-the-shelf semantic directions from InterFaceGAN [13] to edit the inversion results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 11 presents the results of the manipulated faces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Obviously, the learned generative features can preserve most other details when manipulating a particular facial attribute.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' These editing results demonstrate that generative features can not only reconstruct the given image in high quality, but also facilitate it with good semantic manipulation properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='6 Image Processing In this section, we demonstrate that our method facilitates various image processing tasks such as image colorization, image inpainting, and image super-resolution by utilizing the prior knowledge learned by GANs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Generally, these tasks can be formulated as follows: s∗ = arg min s∈S L(G(s), x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' (5) 9 Eye Nose Mouth Bed Window Ceiling Light Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Image harmonization on bedroom and face with GH-Feat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' The top left corner of the first and third rows are the original images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Pasting a target image patch onto the original image then feeding it as the input (first and third row), our hierarchical encoder is able to smooth the image content and produce a photo-realistic image (second and fourth row).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Source Image Transferring Results Style Image Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Style transfer results with GH-Feat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' GH-Feat can extract and then transfer the style of the reference image to the given image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' where s is the style code initialized by our encoder, L is the l2 loss function, and x is the reference image (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', gray- scale image for image colorization, corrupted image for the inpainting, and low-resolution image for super-resolution).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Image colorization tries to restore the original color of a gray-scale image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' The results from our method are listed in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 12a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Image inpainting aims at filling the missing pixels of the input images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 12b, when some pixels value of the input image is missing, our method still successfully recovers them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' The last one is super-resolution, which manages to generate a high-resolution image of the low-resolution one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 12c shows the super-resolution result scale 16 times using our method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='4 Evaluation on Discriminative Tasks In this part, we verify that even the proposed GH-Feat is learned from generative models, it can be applicable to a wide range of discriminative tasks with competitive performances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Here, we do not fine-tune the encoder for any certain task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' In particular, we choose multi-level down- stream applications, including image classification, face verification, pose estimation, layout prediction, landmark detection, and luminance regression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' For each task, we use our encoder to extract visual features from both the training and the test set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' A linear regression model (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', a fully- connected layer) is learned on the training set with ground- truth and then evaluated on the test set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Besides, we include image retrieval as an addition discriminative task to verify the hierarchical property of GH-Feat, whose details are explained in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='1 Discriminative and Hierarchical Property Recall that GH-Feat is a multi-scale representation learned by using StyleGAN as a loss function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' As a results, it consists of features from multiple levels, each of which correspond to a certain layer in the StyleGAN generator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Here, we would to explore how this feature hierarchy is organized as well as how they can facilitate multi-level 10 Input Inversion Semantic ++ Female Glasses Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Semantic Manipulation results with GH-Feat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' We utilize the off-the-shelf semantic directions from InterFaceGAN [13] to edit the gender and glasses of the given images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' (a) Colorization (b) Inpainting (c) Super-resolution Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Image processing with GH-Feat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' GH-Feat facilitates many image processing applications using the hierarchical encoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Performances on different discriminative tasks using GH-Feat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Left three columns enclose the comparisons between using different spaces of StyleGAN as the representation space, where Y space (in red color) shows stronger discriminative and hierarchical property than W space (in blue color).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' This is discussed in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' The last column compares the two different strategies used in the face verification task, which is explained in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' discriminative tasks, including face pose estimation, indoor scene layout prediction, and luminance1 regression from face images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' In particular, we evaluate GH-Feat on each task level by level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' As a comparison, we also train encoders by treating the w code, instead of the style code y, as the representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' From Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 13, we have three observations: (1) GH-Feat is discriminative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' (2) Features at lower level are more suitable for low-level tasks (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', luminance regression) and those at higher level better aid high-level tasks (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', pose estimation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' (3) Y space demonstrates a more obvious hierarchical property than W space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' The comparison on hierarchical property between using regularizer or not is included at Supplementay Material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='2 Digit Recognition & Face Verification Image classification is widely used to evaluate the perfor- mance of learned representations [17], [29], [30], [31], [32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' In this section, we first compare our proposed GH-Feat with 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' We convert images from RGB space to YUV space and use the mean value from Y space as the luminance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' other alternatives on a toy dataset, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', MNIST [52].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Then, we use a more challenging task, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', face verification, to evaluate the discriminative property of GH-Feat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' MNIST Digit Recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' We first show a toy example on MNIST following prior work [15], [43].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' We make a little modification to ResNet-18 like [63] which is widely used in literatures to handle samples from MNIST [52] in lower resolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' The Top-1 accuracy is reported in Tab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 6a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Our GH-Feat outperforms ALAE [43] and BiGAN [15] with 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='45% and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='92%, suggesting a stronger discriminative power.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Here, ResNet-18 [24] is employed as the backbone structure for both MoCo [31] and GH-Feat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' LFW Face Verification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' We directly use the proposed encoder, which is trained on FF-HQ [11], to extract GH- Feat from face images in LFW [54] and tries three different strategies on exploiting GH-Feat for face verification: (1) using a single level feature;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' (2) grouping multi-level features (starting from the highest level) together;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' (3) voting by choosing the largest face similarity across all levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 13 (last column) shows the results from the first two strategies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='08 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='04 W 2 4 6 8 10 12 Level Indexandmark DetectionMSE (IOD)0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='076 W 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='06 2 4 6 8 10 12 14 LevelIndexLayout PredictionCorner Distance26 y W 22 2 4 6 8 10 12 14 Level IndexLuminance RegressionRegression Error0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='7 Layer-wise Grouping 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='5 2 4 6 8 10 12 14 Level IndexFace VerificationAccuracyLevelIndex11 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Image reconstruction results on LFW [54].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' For each pair of images, left is the low-resolution input while right is reconstructed by GH-Feat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' All samples are with the same identity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Ours Input BigBiGAN Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Qualitative comparison between BigBiGAN [17] and GH-Feat on reconstructing images from ImageNet [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' TABLE 6 Quantitative comparison between our proposed GH-Feat and other alternatives on MNIST [52] and LFW [54].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' GH-Feat-R denotes GH-Feat trained with regularizer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' (a) Digit recognition on MNIST.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Methods Acc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' AE(ℓ1) [64] 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='43 AE(ℓ2) [64] 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='37 BiGAN [15] 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='14 ALAE [43] 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='61 MoCo-R18 [31] 95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='89 GH-Feat (Ours) 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='06 GH-Feat-R 98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='78 (b) Face verification on LFW.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Methods Acc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' VAE [65] 49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='3 MoCo-R50 [31] 48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='9 ALAE [43] 55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='7 GH-Feat (Grouping) 60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='1 GH-Feat (Layer-wise) 67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='5 GH-Feat (Voting) 69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='7 GH-Feat-R (Voting) 69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='1 Obviously, GH-Feat from the 5-th to the 9-th levels best preserve the identity information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Tab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 6b compares GH- Feat with other unsupervised feature learning methods, including VAE [65], MoCo [31], and ALAE [43].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' All these competitors are also trained on FF-HQ dataset [11] with optimally chosen hyper-parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' ResNet-50 [24] is em- ployed as the backbone for MoCo and GH-Feat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Our method with voting strategy achieves 69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='7% accuracy, surpassing other competitors by a large margin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' We also visualize some reconstructed LFW faces in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 14, where our GH-Feat well handles the domain gap (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', image resolution) and preserves the identity information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='3 Large-Scale Image Classification We further evaluate GH-Feat on the high-level image classification task using ImageNet [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Before the training of encoder, we first train a StyleGAN model, with 256 × 256 resolution, on the ImageNet training collection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' After that, we learn the hierarchical encoder by using the pre-trained generator as the supervision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' No labels are involved in the above training process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='2 For the image classification problem, we train a linear model on top of the features extracted from the training set with the softmax loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Then, this linear model is evaluated on the validation set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='3 Tab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 7 shows the comparison between GH-Feat and other unsupervised representation learning approaches [15], [17], [31], [32], [67], [68], where we beat most of the competitors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' The state-of-the-art MoCo [31] gives the most compelling performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' But different from the representations learned with contrastive learning, GH-Feat has huge advantages in generative tasks, as already discussed in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Among adversarial representation learning approaches, BigBiGAN [17] achieves the best performance, benefiting from the incredible large-scale training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' However, GH- Feat presents a stronger ability for image reconstruction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' BigBiGAN is learned by discriminating the data-latent joint distribution, while our GH-Feat targets image reconstruc- tion by treating a well-trained GAN generator as a learned loss function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Consequently, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 15, BigBiGAN can only recover the input images from the category level, instead, our approach can recover the inputs with much more details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' The reconstruction error in Tab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 8 conveys the same conclusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' This is also the reason why GH-Feat could facilitate various low-level and middle-level discriminative tasks beyond image classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' More details about Ima- geNet training can be found in Supplementary Material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='4 Transfer Learning In this part, we explore how GH-Feat can be transferred from one dataset to another.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Our encoder can be trained very efficiently, usually 3× faster than the GAN training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' During testing, we adopt the fully convolutional form as in [66] and average the scores at multiple scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' MGT589P12 FF-HQ CelebA Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Landmark detection results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' GH-Feat is trained on FF-HQ [11] dataset but can successfully handle the hard cases (large pose and low image quality) in MAFL dataset [55], a subset of CelebA [74].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Bedroom Kitchen Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Layout prediction results using feature learned by MoCo [31] (top row) and our GH-Feat (bottom row).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Both methods are trained on LSUN bedrooms [53] and then transferred to LSUN kitchens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' TABLE 7 Quantitative comparison on the ImageNet [2] classification task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Method Architecture Top-1 Acc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Motion Seg (MS) [69], [70] ResNet-101 27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='6 Exemplar (Ex) [70], [71] ResNet-101 31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='5 Relative Po (RP) [70], [72] ResNet-101 36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='2 Colorization (Col) [70], [73] ResNet-101 39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='6 Contrastive Learning InstDisc [67] ResNet-50 42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='5 CPC [32] ResNet-101 48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='7 MoCo [31] ResNet-50 60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='6 Generative Modeling BiGAN [15] AlexNet 31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='0 SS-GAN [68] ResNet-19 38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='3 BigBiGAN [17] ResNet-50 55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='4 GH-Feat (Ours) ResNet-50 51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='1 TABLE 8 Qualitative comparison between BigBiGAN [17] and GH-Feat on reconstructing images from ImageNet [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' MSE↓ SSIM↑ FID↓ BigBiGAN [17] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='363 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='236 33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='42 GH-Feat (Ours) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='078 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='431 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='70 Landmark Detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' We train a linear regression model using GH-Feat on FF-HQ [11] and test it on MAFL [55], which is a subset of CelebA [74].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' This two datasets have a large domain gap, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', faces in MAFL have larger poses yet lower image quality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 16, GH-Feat shows a strong transferability across these two datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' We compare our approach with some supervised and unsupervised alternatives [31], [55], [75], [76].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' CLIP [77] trained with 400,000,000 image-text paired samples is also included to serve as a strong baseline to compare with GH-Feat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' For a fair comparison, we try the multi-scale representations from MoCo [31] and CLIP [77] (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', Res2, Res3, Res4, and Res5 feature maps) and report the best results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Tab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 9 demonstrates the strong generalization ability of GH-Feat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' TABLE 9 Landmark detection results on MAFL [55].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' GH-Feat-R denotes GH-Feat trained with regularizer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Method Supervision MSE↓ TCDCN [55] \x13 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='95 MTCNN [75] \x13 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='39 Cond.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' ImGen [76] 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='95 ALAE [43].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='13 MoCo-R50 [31] 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='07 CLIP-R50 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='98 GH-Feat (Ours) 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='12 GH-Feat-R 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='92 In particular, it achieves on-par or better performance than the methods that are particular designed for this task [55], [75], [76].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Also, it outperforms MoCo [31] on this mid-level discriminative task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' As the Tab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 9 below suggests, GH- Feat achieves comparable performance as CLIP-R50 with significantly better data efficiency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Such a comparison is not 100% eye-to-eye because our approach is particularly trained on human faces while CLIP could cover a much larger data domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' But it still demonstrates, to some extent, that adequately leveraging the pre-trained GAN generator as a learned loss function yields a discriminative and transferable visual representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Layout Prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' We train the layout predictor on LSUN [53] bedrooms and test it on kitchens to validate how GH-Feat can be transferred from one scene category to an- other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Feature learned by MoCo [31] on the bedroom dataset is used for comparison.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' We can tell from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 17 that GH-Feat shows better predictions than MoCo, especially on the target set (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', kitchens), suggesting a stronger transferability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Like landmark detection, we also conduct experiments with the 4-level representations from MoCo [31] and select the best.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='5 Image Retrieval In this section, we verify the hierarchical property of the proposed GH-Feat with image retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Concretely, given a 13 Query Top-1 Top-2 Top-3 Top-4 High-Level Middle-Level Low-Level Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Retrieval results on LSUN bedroom [53].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' query image, we use encoder to extract its GH-Feat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Then, we use different levels of GH-Feat to perform retrieval from 10K real images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Note that GH-Feat from these 10K images are prepared in advance and ℓ1 distance is used as the metric for retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 18 shows the retrieval results on LSUN bedroom [53].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' We can tell that when we use higher level (first row) features for retrieval, all retrieved results are with the same layout as the query image, but they may have different lighting conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Meanwhile, when using lower level (bottom row) features for retrieval, the retrieved results are with similar lighting condition as the query image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='5 Spatial Expansion 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='1 Spatial GH-Feat Spatial-Aware Style Codes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Even though the layer-wise style codes can describe the global semantics of synthesized images, the fine-grained semantics cannot be expressed precisely because the style codes are too coarse to maintain spatial semantics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' To facilitate the style codes with semantic segmentation, we equip the layer-wise style codes with spatial dimension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' It is noteworthy that the introduced spatial dimension make the layer-wise representation more flexible for various of vision tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Spatial-Aware Encoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' For the vision tasks requiring the spatial-aware representation of the input image, a spatial- aware encoder is also needed to produce the spatial-aware style codes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' We inherit the backbone and FPN to fuse the semantics encoded at different level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' The last three stages feature maps {R4, R5, R6}, are used to produce spatial- aware GH-Feat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' We also use the same instantiation for the layer equipment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' But differently, we use an 1×1 convolution layer to embed the feature maps {R4, R5, R6} and an upsampler to match the spatial size of the corresponding convolution feature map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' It can be formulated as: GHj = up(WjRa[j], hCj/hRa[j]) j ∈ {1, N}, where GHj is the learned spatial-aware representation, Cj is the convolutional feature map, a[j] denotes the corresponding index of the output feature map from FPN, and hCj, hRa[j] denotes the spatial dimension of feature map Cj and Ra[j].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Ablation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' The proposed spatial generative feature is adopted to provide spatial information, and thus it is critical to the quality of the reconstructed image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' As shown in Tab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 10, the spatial generative feature can improve the TABLE 10 Quantitative comparison on image reconstruction between GH-Feat and spatial GH-Feat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' GH-Feat-R denotes GH-Feat trained with regularizer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Face Bedroom Method MSE↓ SSIM↑ MSE↓ SSIM↑ GH-Feat 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='046 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='56 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='068 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='52 GH-Feat-R 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='049 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='55 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='070 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='50 Spatial GH-Feat 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='029 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='67 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='057 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='58 reconstruction performance, and the qualitative results in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 21 present that the spatial GH-Feat is able to reconstruct the background and the out-of-the-distribution objects i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' hands and hats well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' It supports the effectiveness of the spatial-aware generative features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='2 Data-Efficient Semantic Segmentation Compared with classification, image segmentation needs more precise prediction along the spatial dimension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' How- ever, the generative features without spatial dimension cannot facilitate this task because they cannot be aware of the semantics for each pixel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' To enable this task, we use the spatial-aware encoder to obtain a set of generative features with spatial dimension, and a segmentation head i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' the Style Interpreter in [78] is followed to obtain the segmentation results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Because of the generalization of the spatial visual features, we only need a few samples to achieve a good segmentation head.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' In our experiment, we used 20 annotated samples for the training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' We visualize predictions learned from our visual features in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Obviously, the spatial-aware generative features provide precise information for dense pixels, facilitating image segmentation with a few annotations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' We include several extreme cases in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 20 to verify the robustness of the segmentation results achieved by GH-Feat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Concretely, we include samples under extreme poses, as well as samples containing out-of-distribution objects (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', the objects without annotations during the training of the segmentation branch).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' We have three observations: (1) Even there are few samples under extreme poses during training, our approach could still produce promising segmentation results on such challenging cases at the inference stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' (2) The model could well recognize the eyeglass frames yet perform poorly on eyeglass lens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' We guess this is caused by the overlap between lens and eyes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' (3) Hats (recognized as hair), earrings and microphones (recognized as background) could be regarded as failure cases, because our segmentation branch is learned with simple annotations (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', eyes, nose, cheek, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=').' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' A more competitive performance could be expected given richer segmentation labels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 5 CONCLUSION In this work, we consider the well-trained GAN generator as a learned loss function for learning multi-scale features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Unlike previous work, we treat layer-wise style codes in Y space as generative visual features rather than W space, resulting in better hierarchical properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' A distribution- level regularizer is introduced to overcome the limitation of only using image-level supervision for encoder training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' The resulting Generative Hierarchical Features are shown 14 Real Image Segmentation Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Data-efficient Image Segmentation with Spatial GH-Feat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' We use the spatial-aware encoder to obtain a set of generative features with spatial dimension and a segmentation head trained with limited annotated data to obtain segmentation results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Real Image Segmentation Extreme Poses Earrings Microphones Hats Sunglasses Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Extreme cases of data-efficient image segmentation with Spatial GH-Feat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' These extreme samples (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' extreme pose, hat, sunglasses, earrings as well as microphones) show the robustness of the segmentation head only trained with fewer annotated samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Input GH-Feat Spatial GH-Feat Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Qualitative comparison between GH-Feat and spatial GH-Feat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' to be generalizable to a wide range of vision tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Since GH-Feat only leverages the semantics learned in GANs, the features may lack the good properties of the discriminative model features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' In the future, we hope to learn deep representations by unifying discriminative and generative models that can complement each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' ACKNOWLEDGMENTS This work is supported in part by the Early Career Scheme (ECS) through the Research Grants Council (RGC) of Hong Kong under Grant No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='24206219, Grant No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='14204521, CUHK FoE RSFS Grant, and Centre for Perceptual and Interactive Intelligence (CPII) Ltd under the Innovation and Technology Fund.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' REFERENCES [1] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Bengio, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Courville, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Vincent, “Representation learning: A review and new perspectives,” IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Pattern Anal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Mach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Intell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 1 [2] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Deng, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Dong, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Socher, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Li, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Li, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Fei-Fei, “Imagenet: A large-scale hierarchical image database,” in IEEE Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Vis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Pattern Recog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 1, 5, 11, 12, 16 [3] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Zhou, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Lapedriza, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Khosla, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Oliva, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Torralba, “Places: A 10 million image database for scene recognition,” IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Pattern Anal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Mach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Intell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 1 [4] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Sharif Razavian, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Azizpour, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Sullivan, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Carlsson, “Cnn features off-the-shelf: an astounding baseline for recognition,” in IEEE Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Vis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Pattern Recog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Worksh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 1 [5] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Bau, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Zhou, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Khosla, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Oliva, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Torralba, “Network dissection: Quantifying interpretability of deep visual representa- tions,” in IEEE Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Vis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Pattern Recog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 1 [6] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Matthew and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Fergus, “Visualizing and understanding convolutional neural networks,” in IEEE Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Vis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Pattern Recog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 1 [7] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Zhou, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Khosla, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Lapedriza, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Oliva, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Torralba, “Object detectors emerge in deep scene cnns,” in Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Learn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Represent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 1 [8] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Yosinski, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Clune, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Bengio, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Lipson, “How transferable are features in deep neural networks?”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' in Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Neural Inform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Syst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 1, 2 [9] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Zhao, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Wu, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Lau, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Lin, “What makes in- stance discrimination good for transfer learning?”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' arXiv preprint arXiv:2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='06606, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 1, 2 [10] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Goodfellow, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Pouget-Abadie, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Mirza, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Xu, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Warde-Farley, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Ozair, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Courville, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Bengio, “Generative adversarial nets,” in Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Neural Inform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Syst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 1, 2, 4, 7 [11] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Karras, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Laine, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Aila, “A style-based generator architecture for generative adversarial networks,” in IEEE Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Vis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Pattern Recog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 1, 2, 3, 4, 5, 7, 8, 10, 11, 12 [12] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Karras, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Laine, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Aittala, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Hellsten, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Lehtinen, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Aila, “Analyzing and improving the image quality of stylegan,” in IEEE Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Vis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Pattern Recog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 8110–8119.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 1 [13] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Shen, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Yang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Tang, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Zhou, “Interfacegan: Interpreting the disentangled face representation learned by gans,” IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Pattern Anal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Mach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Intell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 1, 2, 8, 10 OLU二8二B15 [14] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Yang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Shen, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Zhou, “Semantic hierarchy emerges in deep generative representations for scene synthesis,” Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Vis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 1, 2, 4 [15] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Donahue, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Kr¨ahenb¨uhl, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Darrell, “Adversarial feature learning,” in Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Learn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Represent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 1, 2, 5, 10, 11, 12 [16] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Dumoulin, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Belghazi, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Poole, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Mastropietro, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Lamb, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Arjovsky, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Courville, “Adversarially learned inference,” in Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Learn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Represent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 1, 2 [17] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Donahue and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Simonyan, “Large scale adversarial representa- tion learning,” in Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Neural Inform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Syst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 1, 2, 5, 10, 11, 12, 16 [18] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Xu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Shen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Zhu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Yang, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Zhou, “Generative hierarchical features from synthesizing images,” in CVPR, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 2 [19] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Lowe, “Distinctive image features from scale-invariant keypoints,” Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Vis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 2 [20] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Bay, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Tuytelaars, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Van Gool, “Surf: Speeded up robust features,” in Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Vis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 2 [21] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Dalal and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Triggs, “Histograms of oriented gradients for human detection,” in IEEE Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Vis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Pattern Recog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 2 [22] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Krizhevsky, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Sutskever, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Hinton, “Imagenet classifi- cation with deep convolutional neural networks,” in Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Neural Inform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Syst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 2 [23] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Simonyan and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Zisserman, “Very deep convolutional net- works for large-scale image recognition,” in Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Learn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Represent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 2, 4 [24] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' He, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Zhang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Ren, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Sun, “Deep residual learning for image recognition,” in IEEE Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Vis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Pattern Recog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 2, 3, 4, 7, 10, 11, 16 [25] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Doersch and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Zisserman, “Multi-task self-supervised visual learning,” in Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Vis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 2 [26] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Zhang, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Isola, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Efros, “Split-brain autoencoders: Unsupervised learning by cross-channel prediction,” in IEEE Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Vis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Pattern Recog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 2 [27] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Wu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Xiong, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Yu, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Lin, “Unsupervised feature learning via non-parametric instance discrimination,” in IEEE Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Vis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Pattern Recog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 2 [28] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Gidaris, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Singh, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Komodakis, “Unsupervised represen- tation learning by predicting image rotations,” in Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Learn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Represent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 2 [29] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Hjelm, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Fedorov, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Lavoie-Marchildon, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Grewal, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Bach- man, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Trischler, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Bengio, “Learning deep representations by mutual information estimation and maximization,” in Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Learn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Represent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 2, 7, 10 [30] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Zhuang, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Zhai, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Yamins, “Local aggregation for unsupervised learning of visual embeddings,” in Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Vis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 2, 7, 10 [31] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' He, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Fan, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Wu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Xie, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Girshick, “Momentum contrast for unsupervised visual representation learning,” in IEEE Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Vis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Pattern Recog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 2, 7, 10, 11, 12 [32] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Oord, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Li, and O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Vinyals, “Representation learning with contrastive predictive coding,” arXiv preprint arXiv:1807.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='03748, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 2, 7, 10, 11, 12 [33] O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' H´enaff, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Srinivas, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' De Fauw, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Razavi, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Doersch, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Eslami, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Oord, “Data-efficient image recognition with contrastive predictive coding,” arXiv preprint arXiv:1905.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='09272, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 2 [34] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Tian, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Krishnan, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Isola, “Contrastive multiview coding,” arXiv preprint arXiv:1906.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='05849, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 2, 7 [35] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Shocher, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Gandelsman, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Mosseri, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Yarom, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Irani, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Freeman, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Dekel, “Semantic pyramid for image generation,” in IEEE Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Vis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Pattern Recog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 2 [36] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Radford, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Metz, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Chintala, “Unsupervised represen- tation learning with deep convolutional generative adversarial networks,” in Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Learn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Represent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 2 [37] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Karras, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Aila, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Laine, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Lehtinen, “Progressive growing of gans for improved quality, stability, and variation,” in Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Learn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Represent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 2 [38] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Brock, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Donahue, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Simonyan, “Large scale GAN training for high fidelity natural image synthesis,” in Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Learn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Represent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 2 [39] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Jahanian, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Chai, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Isola, “On the ”steerability” of generative adversarial networks,” in Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Learn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Represent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 2 [40] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Bau, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Zhu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Strobelt, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Zhou, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Tenenbaum, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Freeman, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Torralba, “Gan dissection: Visualizing and understanding generative adversarial networks,” in Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Learn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Represent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 2 [41] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Gu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Shen, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Zhou, “Image processing using multi-code gan prior,” in IEEE Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Vis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Pattern Recog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 2 [42] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Zhu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Shen, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Zhao, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Zhou, “In-domain gan inversion for real image editing,” in Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Vis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 2 [43] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Pidhorskyi, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Adjeroh, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Doretto, “Adversarial latent autoencoders,” in IEEE Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Vis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Pattern Recog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 2, 7, 8, 10, 11, 12 [44] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Huang and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Belongie, “Arbitrary style transfer in real-time with adaptive instance normalization,” in Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Vis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 3, 4 [45] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Wu, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Lischinski, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Shechtman, “Stylespace analysis: Disentangled controls for stylegan image generation,” in CVPR, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 4 [46] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Lin, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Doll´ar, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Girshick, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' He, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Hariharan, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Belongie, “Feature pyramid networks for object detection,” in IEEE Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Vis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Pattern Recog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 4 [47] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Yang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Xu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Shi, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Dai, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Zhou, “Temporal pyramid network for action recognition,” in IEEE Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Vis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Pattern Recog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 4 [48] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Liu, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Qi, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Qin, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Shi, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Jia, “Path aggregation network for instance segmentation,” in IEEE Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Vis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Pattern Recog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 4 [49] O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Tov, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Alaluf, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Nitzan, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Patashnik, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Cohen-Or, “Designing an encoder for StyleGAN image manipulation,” ACM Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 4, 6, 7, 8 [50] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Johnson, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Alahi, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Fei-Fei, “Perceptual losses for real- time style transfer and super-resolution,” in Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Vis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 4 [51] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Kingma and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Ba, “Adam: A method for stochastic optimization,” in Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Learn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Represent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 5 [52] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' LeCun, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Bottou, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Bengio, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Haffner, “Gradient-based learning applied to document recognition,” Proceedings of the IEEE, 1998.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 5, 10, 11 [53] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Yu, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Seff, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Zhang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Song, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Funkhouser, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Xiao, “Lsun: Construction of a large-scale image dataset using deep learning with humans in the loop,” arXiv preprint arXiv:1506.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='03365, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 5, 7, 8, 12, 13 [54] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Huang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Ramesh, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Berg, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Learned-Miller, “Labeled faces in the wild: A database for studying face recognition in unconstrained environments,” Technical Report 07-49, University of Massachusetts, Amherst, Tech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 5, 10, 11 [55] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Zhang, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Luo, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Loy, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Tang, “Facial landmark detection by deep multi-task learning,” in Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Vis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 5, 12 [56] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Zhang, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Zhang, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Gu, “Edge-semantic learning strategy for layout estimation in indoor environment,” Transactions On Cybernetics, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 5 [57] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Zou, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Colburn, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Shan, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Hoiem, “Layoutnet: Reconstructing the 3d room layout from a single rgb image,” in IEEE Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Vis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Pattern Recog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 5 [58] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Wang, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Bovik, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Sheikh, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Image Process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 5, 7 [59] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Heusel, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Ramsauer, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Unterthiner, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Nessler, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Hochre- iter, “Gans trained by a two time-scale update rule converge to a local nash equilibrium,” in Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Neural Inform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Syst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 5 [60] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Richardson, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Alaluf, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Patashnik, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Nitzan, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Azar, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Shapiro, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Cohen-Or, “Encoding in style: a StyleGAN encoder for image-to-image translation,” in IEEE Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Vis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Pattern Recog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 6, 7, 8 [61] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Roich, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Mokady, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Bermano, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Cohen-Or, “Pivotal tuning for latent-based editing of real images,” ACM Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 7, 8 [62] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Alaluf, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Patashnik, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Cohen-Or, “ReStyle: A residual- based StyleGAN encoder via iterative refinement,” in Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Vis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 7, 8 [63] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Liu, “Pyotrch cifar10,” https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='com/kuangliu/ pytorch-cifar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='git, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 10 [64] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Hinton and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Salakhutdinov, “Reducing the dimension- ality of data with neural networks,” Science, 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 11 [65] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Kingma and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Welling, “Auto-encoding variational bayes,” in Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Learn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Represent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 11 [66] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Szegedy, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Liu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Jia, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Sermanet, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Reed, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Anguelov, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Erhan, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Vanhoucke, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Rabinovich, “Going deeper with 16 convolutions,” in IEEE Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Vis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Pattern Recog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 11 [67] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Wu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Xiong, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Yu, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Lin, “Unsupervised feature learning via non-parametric instance discrimination,” in IEEE Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Vis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Pattern Recog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 11, 12 [68] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Chen, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Zhai, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Ritter, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Lucic, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Houlsby, “Self- supervised gans via auxiliary rotation loss,” in IEEE Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Vis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Pattern Recog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 11, 12 [69] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Pathak, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Girshick, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Doll´ar, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Darrell, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Hariharan, “Learning features by watching objects move,” in IEEE Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Vis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Pattern Recog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 12 [70] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Doersch and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Zisserman, “Multi-task self-supervised visual learning,” in Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Vis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 12 [71] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Dosovitskiy, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Springenberg, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Riedmiller, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Brox, “Discriminative unsupervised feature learning with convolutional neural networks,” in Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Neural Inform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Syst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 12 [72] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Doersch, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Gupta, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Efros, “Unsupervised visual representation learning by context prediction,” in Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Vis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 12 [73] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Zhang, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Isola, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Efros, “Colorful image colorization,” in Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Vis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 12 [74] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Liu, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Luo, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Wang, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Tang, “Deep learning face attributes in the wild,” in Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Vis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 12 [75] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Zhang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Zhang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Li, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Qiao, “Joint face detection and alignment using multitask cascaded convolutional networks,” IEEE Signal Processing Letters, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 12 [76] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Jakab, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Gupta, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Bilen, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Vedaldi, “Unsupervised learn- ing of object landmarks through conditional image generation,” in Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Neural Inform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Syst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 12 [77] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Radford, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Kim, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Hallacy, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Ramesh, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Goh, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Agarwal, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Sastry, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Askell, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Mishkin, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Clark et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', “Learning transferable visual models from natural language supervision,” in ICML, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 12 [78] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Zhang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Ling, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Gao, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Yin, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='-F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Lafleche, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Barriuso, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Torralba, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Fidler, “Datasetgan: Efficient labeled data factory with minimal human effort,” in CVPR, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 13 [79] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Karras, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Laine, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Aila, “Stylegan - official tensorflow implementation,” https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='com/NVlabs/stylegan, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 16 A1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' HIERARCHICAL PROPERTY We also re-evaluate the layer-wise representation on dif- ferent discriminative tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 22, the training regularizer improves the hierarchical property of the original GH-Feat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Since the training regularizer prevents the model from overfitting pixel values, the layer-wise representation is closer to the distribution center and achieve better hierarchical properties on the discriminative tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' A2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' EXPERIMENTS ON IMAGENET Training Details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' During the training of the StyleGAN model on the ImageNet dataset [2], we resize all images in the training set such that the short side of each image is 256, and then centrally crop them to 256 × 256 resolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' All training settings follow the StyleGAN official implemen- tation [79], including the progressive strategy, optimizer, learning rate, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' The generator and the discriminator are alternatively optimized until the discriminator have seen 250M real images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' After that, the generator is fixed and treated as a well-learned loss function to guide the training of the encoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' During the training of the hierarchical encoder, images in the training collection are pre-processed in the same way as mentioned above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' After the encoder is ready, we treat it as a feature extractor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' We use the output feature map at the “res5” stage, apply adaptively average pooling to obtain 2×2 spatial feature and vectorize it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' A linear classifier, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=', with one fully-connected layer, takes these extracted features as the inputs to learn the image classification task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' SGD optimizer, together with batch size 2048, is used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' The learning rate is initially set as 1 and decayed to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='1 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='01 at the 60-th and the 80-th epoch respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' During the training of the final classifier, ResNet-style data augmentation [24] is applied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' The FID score on ImageNet is 40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Fig 23 shows the uncurated samples of the pretrained ImageNet samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Al- though the synthesized samples are not very realistic, they can still help downstream tasks like ImageNet classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Discussion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' We have already shown in the main submission that GH-Feat achieves comparable accuracy to existing alternatives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Especially, among all methods based on gener- ative modeling, GH-Feat obtains second performance only to BigBiGAN [17], which requires incredible large-scale training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' However, as discussed in the main submission, our GH-Feat facilitates a wide rage of tasks besides image classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Taking image reconstruction as an example, our approach can well recover the input image, significantly outperforming BigBiGAN [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 17 MSE (IOD) Corner Distance Accuracy Regression Error Landmark Detection Layout Prediction Luminance Regression Face Verification Level Index Level Index Level Index Level Index Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Comparison on the hierarchical property between using regularizer or not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' y (in red color) and yreg (in blue color) denote the original GH-Feat and GH-Feat with regularizer, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' Uncurated generated samples of StyleGAN model on ImageNet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='06 y O1) MSE 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='03 2 468101214 LevelIndex0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='08 Corner Distance Yreg 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='056 2 468101214 LevelIndex0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='7 Accuracy Yreg 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} +page_content='5 2 4 6 8 1012 14 Level Index25 Error 21 2 4 6 8 10 12 14 Level Index' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_9E4T4oBgHgl3EQf4w0P/content/2301.05315v1.pdf'} diff --git a/_9FAT4oBgHgl3EQfrB3j/vector_store/index.pkl b/_9FAT4oBgHgl3EQfrB3j/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..3c60bd20fa7f9ec03e45f4c8a13ff29cdf9e8b18 --- /dev/null +++ b/_9FAT4oBgHgl3EQfrB3j/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:675f18a97c0f0521d70575a124ca1a1d671aa9dea1e3a3db042f7b2156de97ab +size 148226 diff --git a/_dE3T4oBgHgl3EQfsApn/vector_store/index.faiss b/_dE3T4oBgHgl3EQfsApn/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..6c9a3ca25bc40d2f9dfcbc4a8bb668ab2818f3db --- /dev/null +++ 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many emerging Internet of Things (IoT) appli- +cations, the freshness of the is an important design criterion. +Age of Information (AoI) quantifies the freshness of the received +information or status update. This work considers a setup of de- +ployed IoT devices in an IoT network; multiple unmanned aerial +vehicles (UAVs) serve as mobile relay nodes between the sensors +and the base station. We formulate an optimization problem to +jointly plan the UAVs’ trajectory, while minimizing the AoI of +the received messages and the devices’ energy consumption. The +solution accounts for the UAVs’ battery lifetime and flight time +to recharging depots to ensure the UAVs’ green operation. The +complex optimization problem is efficiently solved using a deep +reinforcement learning algorithm. In particular, we propose a +deep Q-network, which works as a function approximation to +estimate the state-action value function. The proposed scheme is +quick to converge and results in a lower ergodic age and ergodic +energy consumption when compared with benchmark algorithms +such as greedy algorithm (GA), nearest neighbour (NN), and +random-walk (RW). +Index Terms—Age of Information, deep reinforcement learn- +ing, energy efficiency, sustainability. +I. INTRODUCTION +The Internet of Things (IoT) era is allowing the implementa- +tion of new time-sensitive applications through the deployment +of sensor nodes to collect information in real-time. Use cases +include intelligent transportation, environmental monitoring, +and human safety. To address time sensitivity in such appli- +cations, a metric termed as Age of Information (AoI) was +introduced in [1] to quantify the degree of freshness of the +information about a certain process. It is defined as the time +elapsed since the generation of the packet that was most +recently delivered to the destination node. The application of +unmanned aerial vehicles (UAVs) as mobile relay units has +been proved to be very efficient in solving the problem of +minimizing the AoI while maintaining energy limitations [2]. +The UAV relays can reduce the transmission distance of IoT +nodes by moving close to the source nodes and then relaying +the transmitted information to the destination node [3]. This +facilitates communication and saves energy in remote areas, +where it is cumbersome to replace the batteries of the sensor +nodes. +Recently, learning schemes such as deep reinforcement +learning (DRL) have been extensively applied in solving the +This work has been partially supported by Academy of Finland 6G +Flagship program (Grant no. 346208), FIREMAN (Grant no. 326301), and +the European Commission through the Horizon Europe project Hexa-X (Grant +Agreement no. 101015956). +The authors are with Centre for Wireless Communications (CWC), Univer- +sity of Oulu, Finland. Email: firstname.lastname@oulu.fi. +problem of jointly minimizing the AoI and energy consump- +tion in IoT. However, the suitability of a DRL algorithm is +strongly conditioned on the dimension of action and state +spaces, which turns out to be a curse in massive scenarios [4]. +This issue can be handled by deploying multiple UAVs to +collect information along with device clustering to reduce the +state-action spaces. +Several works have considered the use of UAV for AoI +minimization. For instance, the authors in [5] jointly optimized +the scheduling policy and flight trajectory of the UAV to +minimize the weighted sum AoI. The work in [6] proposed +a DRL model to minimize the freshness of information in a +single-hop vehicular network. In [7], the authors presented a +multi-agent DRL solution to coordinate between the UAVs +to efficiently perform wireless energy transfer (WET) and +wireless information transfer (WIT). To minimize the AoI +in massive deployment up to fifty devices, the work in [8] +presented a model-free DRL solution, whereas the authors +in [9] formulated the problem as a mixed-integer program and +a convex-optimization-based solution. +To this end, the contributions of this paper are summarized +as follows: +• We propose a DRL solution to jointly minimize the +AoI and the devices energy consumption in a massive +deployment of up to hundred IoT devices. +• Our model accounts for UAVs battery constraints and +flying time to recharging depots. +• We apply k-means to perform device clustering, while +accounting for the UAVs scheduling capacity. +• Our approach outperforms the baseline RW, greedy and +NN models in terms of age and IoT energy consumption. +II. SYSTEM LAYOUT AND PROBLEM FORMULATION +A. System Model +We consider a 2D grid world of a set K = {1, 2, · · · , K} of +K low-power IoT devices. Each device is randomly distributed +in the grid world and is given a coordinate ck = (xk, yk) +after being projected to the 2D plane as in [10], [11]. The +IoT devices are served by a set U = {1, 2, · · · , U} of U +rotary-wing UAVs. Each UAV flies over the grid world to +collect information from the devices and relay the collected +information to the BS located at the center of the grid world +(i.e, at (0, 0)). The grid world has fixed charging depots D +located at the four corners. +Each UAV starts and ends its trajectory at one of the +charginf depots. The grid world is divided into square cells, +arXiv:2301.03423v1 [eess.SP] 9 Jan 2023 + +2 +IoT uplink +UAV to BS uplink +UAV charger +Base station +IoT device +Fig. 1: System model: IoT clusters are served by multiple UAVs. Each UAV +relays the information from the IoT clusters to the BS in the middle of the +map. +where the movement of each UAV occurs in four directions +(i.e, east, west, north, south) or preserving its location by not +moving at all (hovering). Time slots are discretely divided as +[τ, 2 τ, ...], where τ is the time that the UAV needs to move +from the center of one cell to the center of an adjacent cell. +The time unit τ is determined by calculating the ratio between +the distance between the centers of two adjacent cells dg and +the velocity of the UAV υt. The system model is illustrated +in Fig. 1. +B. Preliminaries +1) Energy Consumption: Consider that the scheduling pol- +icy of the IoT devices S(t) ∈ S = {0, 1, ..., K}, where S(t) = +(k1, k2, ...) means that the nodes k1, k2, ... are scheduled to +transmit at time slot t. Each UAV forwards the received packet +to the BS. We assume the presence of LOS communication +between the sensors and UAVs, and between the UAVs and +BS, therefore, the channel gain between UAV u and the BS +at time slot t is given by +gu,BS(t) = g0d−2 +u,BS = +g0 +|hu − hBS|2 + ||cu(t)||2 , +(1) +where g0 is the channel gain at the reference distance of 1 m, +du,BS is the distance between the UAV and the BS, hu is the +altitude of the UAV, hBS represents the height of the antennas +at the BS, and cu(t) is the position of UAV u at time instant +t [10]. Pk is the transmission power of an IoT device k and +it is calculated as follows +Pk = (2 +M +B − 1)σ2 +g0 +� +d2 +u,k + h2 +u +� +, +(2) +where M is the packet size of the sensor updates, B defines the +signal bandwidth, σ2 the noise power, and du,k is the distance +between UAV u and IoT device k [11]. +We discretize the battery capacity of each UAV Emax,u +into energy quanta Nu, where the amount of energy in each +energy quantum is given by the ratio Emax,u/Nu. Denote +the battery level of UAV u at time slot t as eu(t) ∈ Eu = +{0, 1, ..., eu,max}. The battery of the UAV is affected by the +energy consumed to relay an update packet to the BS eR +u (t) +and the energy consumed due to flying or hovering eF +u (υt). +The battery evolution of the UAVs can be described as +eu(t+1) = +� +eu(t) − ⌈eR +u (t) + eF +u (υt)⌉, +if S(t) = k, +eu(t) − ⌈eF +u (υt)⌉, +otherwise, +(3) +where ⌈ ⌉ is ceiling approximation. The energy consumed to +relay an update packet to the BS is given by +eR +u (t) = +Nu +Emax,u +Eu(t), +(4) +with +Eu(t) = +σ2 +gu,BS(t) +� +2 +M +B − 1 +� +, +(5) +whereas the energy consumed due to flying or hovering is +given by +eF +u (υt) = +Nu +Emax,u +Pu(υt), +(6) +where Pu(υt) is the power consumption of the UAVs when +moving or hovering and is formulated in [12] as +Pu(υt) = P0 +� +1 + 3υ2 +t +s2 +tip +� ++ P1 +�� +1 + υ4 +t +4s4 +0 +− υ2 +t +2s2 +0 +� 1 +2 ++1 +2d0ρµ0Zυ3 +t , +(7) +where P0 and P1 represent the blade profile power and derived +power when the UAVs are hovering, respectively, υt describes +the velocity of the UAVs and Stip depicts the tip speed of +the blade. Meanwhile, s0 is the mean rotor induced velocity +when hovering, d0 represents the fuselage drag radio, ρ is the +air density, µ0 represents the rotor solidity and Z the area of +the rotor disk. +2) AoI Calculation: We formulate the discrete AoI as the +time elapsed since the last time a device transmitted a packet. +The AoI is used as a degree of fairness in scheduling the +devices. If a device transmits an update packet, its AoI is reset +to one. The AoI of device k is given by +Ak(t+1) = +� +1, +if S(t) = k, +min{Amax, Ak(t) + 1}, +otherwise, +(8) +where Amax denotes the maximum allowed AoI in the model. +C. Problem Formulation +The main objective of the UAVs is to jointly minimize the +weighted average AoI and the transmission power of the IoT +devices. Hence, We the optimization problem is formulated as +follows +P1 : +min +l(t) +1 +T +T +� +t=1 +K +� +k=1 +δkAk(t) + λ +K +K +� +k=1 +Pk(t), +(9a) +s.t. +Tu +� +t +Pu(υt) ≤ eu(t), +(9b) +cu(1) = cd,u, +(9c) +where δk is the importance weight that denotes the importance +of device k and cd,u are the coordinates of the charging depot +where UAV u is going to take off. Here, λ is a multiplicative + +73 +variable that controls the trade-off between the AoI and the +transmission power. The larger the value of λ the more the +objective function cares about the power over the AoI. If λ = +0, the model learns to produce the best AoI without taking the +transmission power into account. The constraints of the given +optimization problem assure that the UAVs still have enough +energy to move and serve the devices and forcing the initial +and final positions of each UAV to be at one of the charging +depots. +The optimization problem (9) is a non-linear integer pro- +gramming optimization problem whose complexity grows with +the number of deployed devices. In addition, the UAV expe- +riences a large dimension of state space, which is almost a +continuous state space. To overcome the dimensionality curse, +we propose a DRL with a deep Q-network (DQN) approach, +which works as a function approximation to estimate the Q- +function and solve the given problem efficiently and feasibly. +III. THE PROPOSED DRL SOLUTION +A. Clustering and Rate-Mobility Characterization +Consider that each device k is assigned to a cluster l ∈ L, +where L = {1, 2, . . . , L} is a set of clusters of length n. We +call nl the number of devices on cluster l. A UAV will try +to communicate with all devices within a cluster l based on +a given policy. For this, before starting moving from one grid +position to another, the UAV will send an uplink grant to all +devices in the specified cluster. Thus, devices should be able +to transmit their updates before the UAV arrives at the next +position. Hence, the relation between the number of devices +on a cluster nl and the fixed transmission rate Rbl of devices +cluster l is given as nl ≤ +Rblτ +M . Thus, substituting τ = dg +υt , we +have +nl ≤ Rbldg +Mυt +. +(10) +Note that this number is directly related to the average rate, +and the speed of the UAV. The BS performs the clustering +using k-means according to the positions of the devices and by +setting the calculated maximum number of devices in a cluster +[13]. The scheduling policy can be redefined as S(t) ∈ S = +{0, 1, ..., L}, where S(t) = l means that the nodes in cluster +l are scheduled to transmit at time slot t. +B. Markov Decision Processes Formulation +We formulate the problem as a Markov Decision Process +(MDP) that is composed of the tuple ⟨s, a, r, p⟩, where s is +the state, a presents the action, r denotes the reward function, +and p describes the state transition probability. Hence, at time +instant t, the agent (UAV) observes the current state s(t) from +the environment and tries to follow the optimal policy by +selecting the best action a(t), which maximizes the reward +r(t) and transiting to the next state s(t+1) with a probability +p(s(t), s(t + 1)). For convenience, we propose an episodic +MDP, where an episode starts with each UAV at one of the +charging depots and ends when at least one UAV needs to +recharge its battery at the nearest charging depot. +1) State space: The state space of the system at time +slot t is defined as s(t) = (c(t), A(t), β(t)) where c(t) is +a vector containing the position of each UAV cu(t) ∈ C +at time slot t. A(t) = (A1(t), A2(t), ..., AL(t)) contains +the average AoI of the IoT devices in each cluster, where +Al(t) ∈ I = [1, 2, ..., Amax]. β(t) = (β1(t), β2(t), ..., βU(t)) +with βU(t) ∈ B, is a vector that contains the difference +between the battery status of each UAV and both the required +energy to arrive to the nearest charging depot d ∈ D and the +energy consumed by packet relays considering the worst case +when the UAVs relay packets in every time slot t. Finally, the +state space of the system is given by Σ = CU × IK × BU. +2) Action space: The action space at time slot t is defined +as a(t) = (Fu(t), Su(t), where fu(t) is the movement of UAV +u and Su(t) is the scheduling policy of UAV u. Each UAV u +selects a cluster l to serve all the devices within this particular +cluster. The action space is given by A = FU × SU. +3) Transition probability: The transition between states +relies on the 3 components of the state space. The AoI is +updated according to (8), the β is updated according to the +energy calculations discussed in II-B1. The position of each +UAV cu is updated according to the selected action fu(t), +where +cu(t + 1) = +� +� +� +� +� +� +� +� +� +� +� +� +� +� +� +cu(t) + (0, dg), +fu(t) = North, +cu(t) − (0, dg), +fu(t) = South, +cu(t) + (dg, 0), +fu(t) = East, +cu(t) − (dg, 0), +fu(t) = West, +cu(t), +Hovering. +(11) +4) Reward function: The reward system is defined to min- +imize the weighted sum of the age of information as well as +the average transmit power for all IoT devices. We define the +immediate reward ru for the u UAV at time instant t as +ru(t) = − +K +� +k=1 +δkAk(t) − λ 1 +K +K +� +k=1 +Pk, +(12) +which is the DRL version of the objective function in (9a). +C. DQN solution +The state-action value function (Q-function) Qπ(s, a) de- +scribes how good an action a is at state s while following the +policy π [14]. It can be updated each time instant as follows +Q (s (t) , a (t)) = Q (s (t) , a (t)) + +α +� +r (t) + γ max +a +Q (s (t + 1) , a) − Q (s (t) , a (t)) +� +, (13) +where α is the learning rate, r(t) is the immediate reward, +γ Q (s (t + 1) , a (t + 1)) is the discounted state-action value +at time instant t + 1, and γ is the discount factor. +The DQNs consist of two neural networks, where the first +network (current network) works as a Q-function estimator, +whereas the other (target network) works as a target Q- +function network [4]. This approach solves the problem of +large dimensionality in complex models. Moreover, the model +defines the exploration rate ϵ, which decays with time. To +break the correlation between samples and utilize past samples, +the DQN introduces experience replay, where it stores the past + +4 +Environment +Action a +New state s +Reward r +Agent +State s +Fig. 2: The DQN architecture. +Algorithm 1: The proposed DRL algorithm +1 Define parameters from table I. +2 Calculate nl using (10). +3 The number of clusters L = K +nl . +4 Apply k-means to perform clustering. +5 Initialize the replay buffer and t = 1. +6 Define ϵ, γ, α, O, and the number of episodes E. +7 Choose a value for λ in (12). +8 for e = 1,...,E do +9 +while No recharging needed (i.e. β1(t) > 0), do +10 +Explore a random action a with probability ϵ +or select optimal action a = maxa Q(s(t), a) +with probability 1 − ϵ. +11 +Save ⟨s(t), a(t), r(t), p(t)⟩ in the replay buffer. +12 +Sample a mini-batch from the buffer. +13 +Update the current network. +14 +Update the target network every O instants. +15 +t = t + 1. +16 +end +17 end +experiences ⟨s(t), a(t), r(t), s(t + 1)⟩ in a buffer and samples +a small batch randomly for training. Algorithm 1 summarizes +the proposed DRL framework and Fig. 2 illustrates the DQN +architecture and interaction with the environment. +IV. NUMERICAL RESULTS +In this section, we discuss the simulation results of the +proposed DRL algorithm and compare them to various base- +line models such as the GA, NN, RW. The GA tends to +minimize the age only by scheduling and moving towards +clusters with the highest age. This almost corresponds to the +case when λ = 0, and the UAV applies time division multiple +access (TDMA) to distribute resources fairly. The NN always +schedules the nearest cluster in order to minimize the transmit +power. We consider a grid world of 1100 m × 1100 m, which +is divided into 11 × 11 grids. The simulation parameters are +defined in Table I. +We build a DQN of five hidden layers (64,128,256,128,128 +neurons) with α = 0.0001, Adam optimizer, replay buffer +of size 100000, γ = 0.99, and 100000 trained episodes +using Pytorch framework on NIVIDIA Tesla V100 GPU. The +proposed DQN model has spatial complexity illustrated in +terms of the number of parameters (weights and biases) of +344, 290 parameters, which need around 30MB of memory. +In terms of the computational complexity, the model performs +170, 816 multiplications and additions. The time complexity to +TABLE I: UAV model parameters +Parameter +Value +Parameter +Value +Parameter +Value +Emax,u +10000 +emax,u +200 +Amax +30 +g0 +30 dB +hu +100 m +dg +100 m +B +1 MHz +M +5 Mb +σ2 +-100 dBm +C +4 +υt +25 m/s +stip +120 m/s +ρ +1.225 kg/m3 +P0 +99.66 W +P1 +120.16 W +d0 +0.48 +µ0 +0.0001 +Z +0.5 s2 +s0 +0.002 m/s +hBS +15 m +execute one episode using the proposed algorithm is 0.0918 s +compared to the 0.0665 s of the RW. Throughout this section, +the term ”ergodic” refers to time and statistical average. +Figure 3 presents an example trajectory path of two UAVs +for a trained episode. We can notice that with the NN in +Fig. 3a, the UAVs move randomly and schedule the nearest +devices. In Fig.3b, the GA chooses the devices with the highest +age careless of the large path losses. Fig. 3c shows the trained +DRL scheme. Since more devices are located in the right upper +section of the map, both UAVs tend to fly over the cluster +centroids close to this region, which indicates the learning +behaviour. Moreover, it is worth concluding that a free flight +passing above these centroids could be a low-complexity sub- +optimal trajectory. +Figure 4a depicts the accumulative reward for the DRL and +RW schemes for different values of λ. It is not a surprise that +higher λ values reflect lower accumulative rewards due to the +nature of the reward function in (12). However, we can see +that the DRL scheme offers a significant improvement in the +reward compared to the RW for all λ values. Looking at figures +4b and 4c, it was also expected that neither the age nor the +power consumption are affected by λ for all schemes expect +for the DRL. This present an aspect of adaptability for the +DRL scheme, where one can choose to prioritize the age or the +power consumption, and vice versa using the same algorithm. +Thus, it can achieve promising results on the age as the GA +scheme, or lower power consumption as the NN scheme. This +exchange can be observed in Fig. 5, where we observe the +achievable regions of age and power for the DRL scheme for +different values of λ values. We can see the DRL scheme as +lines, since it benefits from the variation of λ, where the other +schemes are just static points. Another important insight is +that increasing the number of UAVs as well as decreasing the +number of IoT devices improve the values of both age and +transmit power in the achievable region. +V. CONCLUSIONS +In this paper, we considered a relatively large IoT network, +where multiple UAVs serve as mobile relay nodes with the +objective of minimizing the age of information and the energy +consumption. The problem was formulated as an optimization +problem to plan the trajectory of the UAVs from one charg- +ing depot to another such that the ergodic age and energy +consumption of the network is minimized. We addressed the +problem by proposing a DRL-based solution, where the BS +clusters the IoT devices according to their positions and UAV +flight time between grids to improve the performance. Our +proposed approach outperforms other state-of-the-art solutions + +Hidden layer +Input +Output(pl) +(op) +(olb) +(cb) +loTuplink +UAV to BS uplink +(albi) +UAV charger +loTdevice +Base station5 +(a) NN +(b) GA +(c) DRL +Fig. 3: Trajectories for K = 100 and U = 2 at a trained episode. For the DRL scheme, λ = 25. The colored points represent IoT devices, where different +clusters are indicated by different colors. Crosses represent the cluster centroids. Circled points indicate the presence of multiple devices at those coordinates. +0 +20 +40 +-1500 +-1000 +-500 +0 +DRL, += 50 +RW, += 50 +DRL, += 100 +RW, += 100 +DRL, += 250 +RW, += 250 +(a) Accumulative reward +0 +100 +200 +300 +400 +5 +10 +15 +GA +DRL +NN +RW +(b) Ergodic age +0 +100 +200 +300 +400 +8 +10 +12 +14 +GA +DRL +NN +RW +(c) Ergodic power +Fig. 4: Accumulative reward, ergodic age, and ergodic power for the GA, DRL, NN, and RW schemes at K = 100, and U = 2. +9 +10 +11 +12 +13 +2 +4 +6 +8 +10 +12 +14 +16 +18 +2-UAVs, D = 50, C = 5 +2-UAVs, D = 70, C = 7 +2-UAVs, D = 100, C = 10 +1-UAV, D = 100, C = 10 +GA +NN +RW +Fig. 5: Achievable region of ergodic age and ergodic power for the DRL, GA, +NN, and RW schemes, adjusting the values of λ, U, D, and C. +such as GA, NN and RW. In particular, the proposed DRL- +based solution provides the best age-energy trade-off in a wide +range of scenarios involving different numbers of UAVs and +IoT nodes. Another contribution of this work is the simplicity +of the proposed solutions, which addresses the problem of high +dimensionality in the action space, thus enabling its application +in a massive IoT deployment scenario with the number of IoT +devices in the hundreds as a future extension. +REFERENCES +[1] S. Kaul, M. Gruteser, V. Rai, and J. Kenney, “Minimizing age of in- +formation in vehicular networks,” in 8th Annual IEEE Communications +Society Conference on Sensor, Mesh and Ad Hoc Communications and +Networks. +IEEE, 2011, pp. 350–358. +[2] H. Tang, J. Wang, L. Song, and J. Song, “Minimizing age of infor- +mation with power constraints: Multi-user opportunistic scheduling in +multi-state time-varying channels,” IEEE Journal on Selected Areas in +Communications, vol. 38, no. 5, pp. 854–868, 2020. +[3] M. Mozaffari et al., “A tutorial on UAVs for wireless networks: +Applications, challenges, and open problems,” IEEE communications +surveys & tutorials, vol. 21, no. 3, pp. 2334–2360, 2019. +[4] V. Mnih et al., “Human-level control through deep reinforcement learn- +ing,” Nature, vol. 518, pp. 529–33, 02 2015. +[5] M. A. Abd-Elmagid, A. Ferdowsi, H. S. Dhillon, and W. Saad, “Deep +reinforcement learning for minimizing age-of-information in UAV- +assisted networks,” in 2019 IEEE GLOBECOM, 2019, pp. 1–6. +[6] M. Samir et al., “Age of information aware trajectory planning of uavs +in intelligent transportation systems: A deep learning approach,” IEEE +Transactions on Vehicular Technology, vol. 69, no. 11, pp. 12 382– +12 395, 2020. +[7] O. S. Oubbati et al., “Synchronizing UAV Teams for Timely Data +Collection and Energy Transfer by Deep Reinforcement Learning,” IEEE +Transactions on Vehicular Technology, pp. 1–1, 2022. +[8] M. Samir, C. Assi, S. Sharafeddine, and A. Ghrayeb, “Online altitude +control and scheduling policy for minimizing AoI in UAV-assisted IoT +wireless networks,” IEEE Transactions on Mobile Computing, 2020. +[9] A. Ferdowsi et al, “Neural combinatorial deep reinforcement learning +for age-optimal joint trajectory and scheduling design in UAV-assisted +networks,” IEEE Journal on Selected Areas in Communications, vol. 39, +no. 5, pp. 1250–1265, 2021. +[10] M. A. Abd-Elmagid, A. Ferdowsi, H. S. Dhillon, and W. Saad, “Deep +reinforcement learning for minimizing age-of-information in UAV- +assisted networks,” in 2019 IEEE GLOBECOM, 2019, pp. 1–6. +[11] M. Yi et al., “Deep reinforcement learning for fresh data collection +in UAV-assisted IoT networks,” in IEEE INFOCOM Workshops 2020, +2020, pp. 716–721. +[12] Y. Zeng, J. Xu, and R. Zhang, “Energy minimization for wireless +communication with rotary-wing UAV,” IEEE Transactions on Wireless +Communications, vol. 18, no. 4, pp. 2329–2345, 2019. +[13] S. Na, L. Xumin, and G. Yong, “Research on k-means clustering +algorithm: An improved k-means clustering algorithm,” in 2010 Third +International Symposium on Intelligent Information Technology and +Security Informatics, 2010, pp. 63–67. +[14] K. Arulkumaran, M. P. Deisenroth, M. Brundage, and A. A. Bharath, +“Deep reinforcement learning: A brief survey,” IEEE Signal Processing +Magazine, vol. 34, no. 6, pp. 26–38, Nov. 2017. + +10 +9 +X +8 +X +X +7 +9 +5 +X +X +4 +3 +2 +X +X +1 +0 +0 +1 +2 +3 +4 +5 +6 +7 +8 +9 +1010 +9 +X +8 +X +X +7 +9 +5 +X +X +4 +3 +2 +X +X +1 +0 +0 +1 +2 +3 +4 +5 +6 +7 +8 +9 +1010 +9 +X +8 +X +X +7 +9 +5 +X +X +4 +3 +2 +X +X +1 +0 +0 +1 +2 +3 +4 +5 +6 +7 +8 +9 +10 \ No newline at end of file diff --git a/cdE1T4oBgHgl3EQfxgWe/content/tmp_files/load_file.txt b/cdE1T4oBgHgl3EQfxgWe/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..5a9a78d200a7b49b063f3ebc55e6e238c2352165 --- /dev/null +++ b/cdE1T4oBgHgl3EQfxgWe/content/tmp_files/load_file.txt @@ -0,0 +1,333 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf,len=332 +page_content='1 Multi-UAV Path Learning for Age and Power Optimization in IoT with UAV Battery Recharge Eslam Eldeeb, Jean Michel de Souza Sant’Ana, Dian Echevarr´ıa P´erez, Mohammad Shehab, Nurul Huda Mahmood, and Hirley Alves Abstract—In many emerging Internet of Things (IoT) appli- cations, the freshness of the is an important design criterion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Age of Information (AoI) quantifies the freshness of the received information or status update.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' This work considers a setup of de- ployed IoT devices in an IoT network;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' multiple unmanned aerial vehicles (UAVs) serve as mobile relay nodes between the sensors and the base station.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' We formulate an optimization problem to jointly plan the UAVs’ trajectory, while minimizing the AoI of the received messages and the devices’ energy consumption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' The solution accounts for the UAVs’ battery lifetime and flight time to recharging depots to ensure the UAVs’ green operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' The complex optimization problem is efficiently solved using a deep reinforcement learning algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' In particular, we propose a deep Q-network, which works as a function approximation to estimate the state-action value function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' The proposed scheme is quick to converge and results in a lower ergodic age and ergodic energy consumption when compared with benchmark algorithms such as greedy algorithm (GA), nearest neighbour (NN), and random-walk (RW).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Index Terms—Age of Information, deep reinforcement learn- ing, energy efficiency, sustainability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' INTRODUCTION The Internet of Things (IoT) era is allowing the implementa- tion of new time-sensitive applications through the deployment of sensor nodes to collect information in real-time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Use cases include intelligent transportation, environmental monitoring, and human safety.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' To address time sensitivity in such appli- cations, a metric termed as Age of Information (AoI) was introduced in [1] to quantify the degree of freshness of the information about a certain process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' It is defined as the time elapsed since the generation of the packet that was most recently delivered to the destination node.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' The application of unmanned aerial vehicles (UAVs) as mobile relay units has been proved to be very efficient in solving the problem of minimizing the AoI while maintaining energy limitations [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' The UAV relays can reduce the transmission distance of IoT nodes by moving close to the source nodes and then relaying the transmitted information to the destination node [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' This facilitates communication and saves energy in remote areas, where it is cumbersome to replace the batteries of the sensor nodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Recently, learning schemes such as deep reinforcement learning (DRL) have been extensively applied in solving the This work has been partially supported by Academy of Finland 6G Flagship program (Grant no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' 346208), FIREMAN (Grant no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' 326301), and the European Commission through the Horizon Europe project Hexa-X (Grant Agreement no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' 101015956).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' The authors are with Centre for Wireless Communications (CWC), Univer- sity of Oulu, Finland.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Email: firstname.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content='lastname@oulu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content='fi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' problem of jointly minimizing the AoI and energy consump- tion in IoT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' However, the suitability of a DRL algorithm is strongly conditioned on the dimension of action and state spaces, which turns out to be a curse in massive scenarios [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' This issue can be handled by deploying multiple UAVs to collect information along with device clustering to reduce the state-action spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Several works have considered the use of UAV for AoI minimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' For instance, the authors in [5] jointly optimized the scheduling policy and flight trajectory of the UAV to minimize the weighted sum AoI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' The work in [6] proposed a DRL model to minimize the freshness of information in a single-hop vehicular network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' In [7], the authors presented a multi-agent DRL solution to coordinate between the UAVs to efficiently perform wireless energy transfer (WET) and wireless information transfer (WIT).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' To minimize the AoI in massive deployment up to fifty devices, the work in [8] presented a model-free DRL solution, whereas the authors in [9] formulated the problem as a mixed-integer program and a convex-optimization-based solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' To this end, the contributions of this paper are summarized as follows: We propose a DRL solution to jointly minimize the AoI and the devices energy consumption in a massive deployment of up to hundred IoT devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Our model accounts for UAVs battery constraints and flying time to recharging depots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' We apply k-means to perform device clustering, while accounting for the UAVs scheduling capacity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Our approach outperforms the baseline RW, greedy and NN models in terms of age and IoT energy consumption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' SYSTEM LAYOUT AND PROBLEM FORMULATION A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' System Model We consider a 2D grid world of a set K = {1, 2, · · · , K} of K low-power IoT devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Each device is randomly distributed in the grid world and is given a coordinate ck = (xk, yk) after being projected to the 2D plane as in [10], [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' The IoT devices are served by a set U = {1, 2, · · · , U} of U rotary-wing UAVs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Each UAV flies over the grid world to collect information from the devices and relay the collected information to the BS located at the center of the grid world (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content='e, at (0, 0)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' The grid world has fixed charging depots D located at the four corners.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Each UAV starts and ends its trajectory at one of the charginf depots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' The grid world is divided into square cells, arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content='03423v1 [eess.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content='SP] 9 Jan 2023 2 IoT uplink UAV to BS uplink UAV charger Base station IoT device Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' 1: System model: IoT clusters are served by multiple UAVs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Each UAV relays the information from the IoT clusters to the BS in the middle of the map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' where the movement of each UAV occurs in four directions (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content='e, east, west, north, south) or preserving its location by not moving at all (hovering).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Time slots are discretely divided as [τ, 2 τ, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content='], where τ is the time that the UAV needs to move from the center of one cell to the center of an adjacent cell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' The time unit τ is determined by calculating the ratio between the distance between the centers of two adjacent cells dg and the velocity of the UAV υt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' The system model is illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Preliminaries 1) Energy Consumption: Consider that the scheduling pol- icy of the IoT devices S(t) ∈ S = {0, 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=', K}, where S(t) = (k1, k2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=') means that the nodes k1, k2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' are scheduled to transmit at time slot t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Each UAV forwards the received packet to the BS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' We assume the presence of LOS communication between the sensors and UAVs,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' and between the UAVs and BS,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' therefore,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' the channel gain between UAV u and the BS at time slot t is given by gu,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content='BS(t) = g0d−2 u,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content='BS = g0 |hu − hBS|2 + ||cu(t)||2 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' (1) where g0 is the channel gain at the reference distance of 1 m,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' du,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content='BS is the distance between the UAV and the BS,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' hu is the altitude of the UAV,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' hBS represents the height of the antennas at the BS,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' and cu(t) is the position of UAV u at time instant t [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Pk is the transmission power of an IoT device k and it is calculated as follows Pk = (2 M B − 1)σ2 g0 � d2 u,k + h2 u � , (2) where M is the packet size of the sensor updates, B defines the signal bandwidth, σ2 the noise power, and du,k is the distance between UAV u and IoT device k [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' We discretize the battery capacity of each UAV Emax,u into energy quanta Nu, where the amount of energy in each energy quantum is given by the ratio Emax,u/Nu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Denote the battery level of UAV u at time slot t as eu(t) ∈ Eu = {0, 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=', eu,max}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' The battery of the UAV is affected by the energy consumed to relay an update packet to the BS eR u (t) and the energy consumed due to flying or hovering eF u (υt).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' The battery evolution of the UAVs can be described as eu(t+1) = � eu(t) − ⌈eR u (t) + eF u (υt)⌉, if S(t) = k, eu(t) − ⌈eF u (υt)⌉, otherwise, (3) where ⌈ ⌉ is ceiling approximation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' The energy consumed to relay an update packet to the BS is given by eR u (t) = Nu Emax,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content='u Eu(t),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' (4) with Eu(t) = σ2 gu,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content='BS(t) � 2 M B − 1 � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' (5) whereas the energy consumed due to flying or hovering is given by eF u (υt) = Nu Emax,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content='u Pu(υt),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' (6) where Pu(υt) is the power consumption of the UAVs when moving or hovering and is formulated in [12] as Pu(υt) = P0 � 1 + 3υ2 t s2 tip � + P1 �� 1 + υ4 t 4s4 0 − υ2 t 2s2 0 � 1 2 +1 2d0ρµ0Zυ3 t ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' (7) where P0 and P1 represent the blade profile power and derived power when the UAVs are hovering,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' respectively,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' υt describes the velocity of the UAVs and Stip depicts the tip speed of the blade.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Meanwhile, s0 is the mean rotor induced velocity when hovering, d0 represents the fuselage drag radio, ρ is the air density, µ0 represents the rotor solidity and Z the area of the rotor disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' 2) AoI Calculation: We formulate the discrete AoI as the time elapsed since the last time a device transmitted a packet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' The AoI is used as a degree of fairness in scheduling the devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' If a device transmits an update packet, its AoI is reset to one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' The AoI of device k is given by Ak(t+1) = � 1, if S(t) = k, min{Amax, Ak(t) + 1}, otherwise, (8) where Amax denotes the maximum allowed AoI in the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Problem Formulation The main objective of the UAVs is to jointly minimize the weighted average AoI and the transmission power of the IoT devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Hence, We the optimization problem is formulated as follows P1 : min l(t) 1 T T � t=1 K � k=1 δkAk(t) + λ K K � k=1 Pk(t), (9a) s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Tu � t Pu(υt) ≤ eu(t), (9b) cu(1) = cd,u, (9c) where δk is the importance weight that denotes the importance of device k and cd,u are the coordinates of the charging depot where UAV u is going to take off.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Here, λ is a multiplicative 73 variable that controls the trade-off between the AoI and the transmission power.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' The larger the value of λ the more the objective function cares about the power over the AoI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' If λ = 0, the model learns to produce the best AoI without taking the transmission power into account.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' The constraints of the given optimization problem assure that the UAVs still have enough energy to move and serve the devices and forcing the initial and final positions of each UAV to be at one of the charging depots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' The optimization problem (9) is a non-linear integer pro- gramming optimization problem whose complexity grows with the number of deployed devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' In addition, the UAV expe- riences a large dimension of state space, which is almost a continuous state space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' To overcome the dimensionality curse, we propose a DRL with a deep Q-network (DQN) approach, which works as a function approximation to estimate the Q- function and solve the given problem efficiently and feasibly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' THE PROPOSED DRL SOLUTION A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Clustering and Rate-Mobility Characterization Consider that each device k is assigned to a cluster l ∈ L, where L = {1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' , L} is a set of clusters of length n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' We call nl the number of devices on cluster l.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' A UAV will try to communicate with all devices within a cluster l based on a given policy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' For this, before starting moving from one grid position to another, the UAV will send an uplink grant to all devices in the specified cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Thus, devices should be able to transmit their updates before the UAV arrives at the next position.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Hence, the relation between the number of devices on a cluster nl and the fixed transmission rate Rbl of devices cluster l is given as nl ≤ Rblτ M .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Thus, substituting τ = dg υt , we have nl ≤ Rbldg Mυt .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' (10) Note that this number is directly related to the average rate, and the speed of the UAV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' The BS performs the clustering using k-means according to the positions of the devices and by setting the calculated maximum number of devices in a cluster [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' The scheduling policy can be redefined as S(t) ∈ S = {0, 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=', L}, where S(t) = l means that the nodes in cluster l are scheduled to transmit at time slot t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Markov Decision Processes Formulation We formulate the problem as a Markov Decision Process (MDP) that is composed of the tuple ⟨s, a, r, p⟩, where s is the state, a presents the action, r denotes the reward function, and p describes the state transition probability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Hence, at time instant t, the agent (UAV) observes the current state s(t) from the environment and tries to follow the optimal policy by selecting the best action a(t), which maximizes the reward r(t) and transiting to the next state s(t+1) with a probability p(s(t), s(t + 1)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' For convenience, we propose an episodic MDP, where an episode starts with each UAV at one of the charging depots and ends when at least one UAV needs to recharge its battery at the nearest charging depot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' 1) State space: The state space of the system at time slot t is defined as s(t) = (c(t), A(t), β(t)) where c(t) is a vector containing the position of each UAV cu(t) ∈ C at time slot t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' A(t) = (A1(t), A2(t), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=', AL(t)) contains the average AoI of the IoT devices in each cluster, where Al(t) ∈ I = [1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=', Amax].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' β(t) = (β1(t), β2(t), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=', βU(t)) with βU(t) ∈ B, is a vector that contains the difference between the battery status of each UAV and both the required energy to arrive to the nearest charging depot d ∈ D and the energy consumed by packet relays considering the worst case when the UAVs relay packets in every time slot t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Finally, the state space of the system is given by Σ = CU × IK × BU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' 2) Action space: The action space at time slot t is defined as a(t) = (Fu(t), Su(t), where fu(t) is the movement of UAV u and Su(t) is the scheduling policy of UAV u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Each UAV u selects a cluster l to serve all the devices within this particular cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' The action space is given by A = FU × SU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' 3) Transition probability: The transition between states relies on the 3 components of the state space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' The AoI is updated according to (8), the β is updated according to the energy calculations discussed in II-B1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' The position of each UAV cu is updated according to the selected action fu(t), where cu(t + 1) = � � � � � � � � � � � � � � � cu(t) + (0, dg), fu(t) = North, cu(t) − (0, dg), fu(t) = South, cu(t) + (dg, 0), fu(t) = East, cu(t) − (dg, 0), fu(t) = West, cu(t), Hovering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' (11) 4) Reward function: The reward system is defined to min- imize the weighted sum of the age of information as well as the average transmit power for all IoT devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' We define the immediate reward ru for the u UAV at time instant t as ru(t) = − K � k=1 δkAk(t) − λ 1 K K � k=1 Pk, (12) which is the DRL version of the objective function in (9a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' DQN solution The state-action value function (Q-function) Qπ(s, a) de- scribes how good an action a is at state s while following the policy π [14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' It can be updated each time instant as follows Q (s (t) , a (t)) = Q (s (t) , a (t)) + α � r (t) + γ max a Q (s (t + 1) , a) − Q (s (t) , a (t)) � , (13) where α is the learning rate, r(t) is the immediate reward, γ Q (s (t + 1) , a (t + 1)) is the discounted state-action value at time instant t + 1, and γ is the discount factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' The DQNs consist of two neural networks, where the first network (current network) works as a Q-function estimator, whereas the other (target network) works as a target Q- function network [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' This approach solves the problem of large dimensionality in complex models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Moreover, the model defines the exploration rate ϵ, which decays with time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' To break the correlation between samples and utilize past samples, the DQN introduces experience replay, where it stores the past 4 Environment Action a New state s Reward r Agent State s Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' 2: The DQN architecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Algorithm 1: The proposed DRL algorithm 1 Define parameters from table I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' 2 Calculate nl using (10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' 3 The number of clusters L = K nl .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' 4 Apply k-means to perform clustering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' 5 Initialize the replay buffer and t = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' 6 Define ϵ, γ, α, O, and the number of episodes E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' 7 Choose a value for λ in (12).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' 8 for e = 1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=',E do 9 while No recharging needed (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' β1(t) > 0), do 10 Explore a random action a with probability ϵ or select optimal action a = maxa Q(s(t), a) with probability 1 − ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' 11 Save ⟨s(t), a(t), r(t), p(t)⟩ in the replay buffer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' 12 Sample a mini-batch from the buffer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' 13 Update the current network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' 14 Update the target network every O instants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' 15 t = t + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' 16 end 17 end experiences ⟨s(t), a(t), r(t), s(t + 1)⟩ in a buffer and samples a small batch randomly for training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Algorithm 1 summarizes the proposed DRL framework and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' 2 illustrates the DQN architecture and interaction with the environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' NUMERICAL RESULTS In this section, we discuss the simulation results of the proposed DRL algorithm and compare them to various base- line models such as the GA, NN, RW.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' The GA tends to minimize the age only by scheduling and moving towards clusters with the highest age.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' This almost corresponds to the case when λ = 0, and the UAV applies time division multiple access (TDMA) to distribute resources fairly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' The NN always schedules the nearest cluster in order to minimize the transmit power.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' We consider a grid world of 1100 m × 1100 m, which is divided into 11 × 11 grids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' The simulation parameters are defined in Table I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' We build a DQN of five hidden layers (64,128,256,128,128 neurons) with α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content='0001, Adam optimizer, replay buffer of size 100000, γ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content='99, and 100000 trained episodes using Pytorch framework on NIVIDIA Tesla V100 GPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' The proposed DQN model has spatial complexity illustrated in terms of the number of parameters (weights and biases) of 344, 290 parameters, which need around 30MB of memory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' In terms of the computational complexity, the model performs 170, 816 multiplications and additions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' The time complexity to TABLE I: UAV model parameters Parameter Value Parameter Value Parameter Value Emax,u 10000 emax,u 200 Amax 30 g0 30 dB hu 100 m dg 100 m B 1 MHz M 5 Mb σ2 100 dBm C 4 υt 25 m/s stip 120 m/s ρ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content='225 kg/m3 P0 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content='66 W P1 120.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content='16 W d0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content='48 µ0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content='0001 Z 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content='5 s2 s0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content='002 m/s hBS 15 m execute one episode using the proposed algorithm is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content='0918 s compared to the 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content='0665 s of the RW.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Throughout this section, the term ”ergodic” refers to time and statistical average.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Figure 3 presents an example trajectory path of two UAVs for a trained episode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' We can notice that with the NN in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' 3a, the UAVs move randomly and schedule the nearest devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content='3b, the GA chooses the devices with the highest age careless of the large path losses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' 3c shows the trained DRL scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Since more devices are located in the right upper section of the map, both UAVs tend to fly over the cluster centroids close to this region, which indicates the learning behaviour.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Moreover, it is worth concluding that a free flight passing above these centroids could be a low-complexity sub- optimal trajectory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Figure 4a depicts the accumulative reward for the DRL and RW schemes for different values of λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' It is not a surprise that higher λ values reflect lower accumulative rewards due to the nature of the reward function in (12).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' However, we can see that the DRL scheme offers a significant improvement in the reward compared to the RW for all λ values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Looking at figures 4b and 4c, it was also expected that neither the age nor the power consumption are affected by λ for all schemes expect for the DRL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' This present an aspect of adaptability for the DRL scheme, where one can choose to prioritize the age or the power consumption, and vice versa using the same algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Thus, it can achieve promising results on the age as the GA scheme, or lower power consumption as the NN scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' This exchange can be observed in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' 5, where we observe the achievable regions of age and power for the DRL scheme for different values of λ values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' We can see the DRL scheme as lines, since it benefits from the variation of λ, where the other schemes are just static points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Another important insight is that increasing the number of UAVs as well as decreasing the number of IoT devices improve the values of both age and transmit power in the achievable region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' CONCLUSIONS In this paper, we considered a relatively large IoT network, where multiple UAVs serve as mobile relay nodes with the objective of minimizing the age of information and the energy consumption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' The problem was formulated as an optimization problem to plan the trajectory of the UAVs from one charg- ing depot to another such that the ergodic age and energy consumption of the network is minimized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' We addressed the problem by proposing a DRL-based solution, where the BS clusters the IoT devices according to their positions and UAV flight time between grids to improve the performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Our proposed approach outperforms other state-of-the-art solutions Hidden layer Input Output(pl) (op) (olb) (cb) loTuplink UAV to BS uplink (albi) UAV charger loTdevice Base station5 (a) NN (b) GA (c) DRL Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' 3: Trajectories for K = 100 and U = 2 at a trained episode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' For the DRL scheme, λ = 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' The colored points represent IoT devices, where different clusters are indicated by different colors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Crosses represent the cluster centroids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Circled points indicate the presence of multiple devices at those coordinates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' 0 20 40 1500 1000 500 0 DRL, = 50 RW, = 50 DRL, = 100 RW, = 100 DRL, = 250 RW, = 250 (a) Accumulative reward 0 100 200 300 400 5 10 15 GA DRL NN RW (b) Ergodic age 0 100 200 300 400 8 10 12 14 GA DRL NN RW (c) Ergodic power Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' 4: Accumulative reward, ergodic age, and ergodic power for the GA, DRL, NN, and RW schemes at K = 100, and U = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' 9 10 11 12 13 2 4 6 8 10 12 14 16 18 2-UAVs, D = 50, C = 5 2-UAVs, D = 70, C = 7 2-UAVs, D = 100, C = 10 1-UAV, D = 100, C = 10 GA NN RW Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' 5: Achievable region of ergodic age and ergodic power for the DRL, GA, NN, and RW schemes, adjusting the values of λ, U, D, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' such as GA, NN and RW.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' In particular, the proposed DRL- based solution provides the best age-energy trade-off in a wide range of scenarios involving different numbers of UAVs and IoT nodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Another contribution of this work is the simplicity of the proposed solutions, which addresses the problem of high dimensionality in the action space, thus enabling its application in a massive IoT deployment scenario with the number of IoT devices in the hundreds as a future extension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' REFERENCES [1] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Kaul, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Gruteser, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Rai, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Kenney, “Minimizing age of in- formation in vehicular networks,” in 8th Annual IEEE Communications Society Conference on Sensor, Mesh and Ad Hoc Communications and Networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' IEEE, 2011, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' 350–358.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' [2] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Tang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Wang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Song, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Song, “Minimizing age of infor- mation with power constraints: Multi-user opportunistic scheduling in multi-state time-varying channels,” IEEE Journal on Selected Areas in Communications, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' 38, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' 5, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' 854–868, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' [3] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Mozaffari et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=', “A tutorial on UAVs for wireless networks: Applications, challenges, and open problems,” IEEE communications surveys & tutorials, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' 21, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' 2334–2360, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' [4] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Mnih et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=', “Human-level control through deep reinforcement learn- ing,” Nature, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' 518, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' 529–33, 02 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' [5] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Abd-Elmagid, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Ferdowsi, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Dhillon, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Saad, “Deep reinforcement learning for minimizing age-of-information in UAV- assisted networks,” in 2019 IEEE GLOBECOM, 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' 1–6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' [6] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Samir et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=', “Age of information aware trajectory planning of uavs in intelligent transportation systems: A deep learning approach,” IEEE Transactions on Vehicular Technology, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' 69, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' 11, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' 12 382– 12 395, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' [7] O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Oubbati et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=', “Synchronizing UAV Teams for Timely Data Collection and Energy Transfer by Deep Reinforcement Learning,” IEEE Transactions on Vehicular Technology, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' 1–1, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' [8] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Samir, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Assi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Sharafeddine, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Ghrayeb, “Online altitude control and scheduling policy for minimizing AoI in UAV-assisted IoT wireless networks,” IEEE Transactions on Mobile Computing, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' [9] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Ferdowsi et al, “Neural combinatorial deep reinforcement learning for age-optimal joint trajectory and scheduling design in UAV-assisted networks,” IEEE Journal on Selected Areas in Communications, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' 39, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' 5, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' 1250–1265, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' [10] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Abd-Elmagid, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Ferdowsi, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Dhillon, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Saad, “Deep reinforcement learning for minimizing age-of-information in UAV- assisted networks,” in 2019 IEEE GLOBECOM, 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' 1–6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' [11] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Yi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=', “Deep reinforcement learning for fresh data collection in UAV-assisted IoT networks,” in IEEE INFOCOM Workshops 2020, 2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' 716–721.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' [12] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Zeng, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Xu, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Zhang, “Energy minimization for wireless communication with rotary-wing UAV,” IEEE Transactions on Wireless Communications, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' 18, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' 4, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' 2329–2345, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' [13] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Na, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Xumin, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Yong, “Research on k-means clustering algorithm: An improved k-means clustering algorithm,” in 2010 Third International Symposium on Intelligent Information Technology and Security Informatics, 2010, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' 63–67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' [14] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Arulkumaran, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Deisenroth, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Brundage, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' Bharath, “Deep reinforcement learning: A brief survey,” IEEE Signal Processing Magazine, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' 34, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' 6, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' 26–38, Nov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} +page_content=' 10 9 X 8 X X 7 9 5 X X 4 3 2 X X 1 0 0 1 2 3 4 5 6 7 8 9 1010 9 X 8 X X 7 9 5 X X 4 3 2 X X 1 0 0 1 2 3 4 5 6 7 8 9 1010 9 X 8 X X 7 9 5 X X 4 3 2 X X 1 0 0 1 2 3 4 5 6 7 8 9 10' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE1T4oBgHgl3EQfxgWe/content/2301.03423v1.pdf'} diff --git a/cdE3T4oBgHgl3EQfeAov/content/tmp_files/2301.04539v1.pdf.txt b/cdE3T4oBgHgl3EQfeAov/content/tmp_files/2301.04539v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..64f52a61ee33c3065a40b421d7a617f4cc1a8ae7 --- /dev/null +++ b/cdE3T4oBgHgl3EQfeAov/content/tmp_files/2301.04539v1.pdf.txt @@ -0,0 +1,591 @@ +Draft version January 12, 2023 +Typeset using LATEX default style in AASTeX631 +Capturing Statistical Isotropy violation with generalized Isotropic Angular Correlation Functions of +CMB Anisotropy +Dipanshu +,1, 2 Tarun Souradeep +,1, 2, 3 and Shriya Hirve +1, 4 +1Department of Physics, Indian Institute of Science Education and Research, Pune 411008, India +2Raman Research Institute, Bangalore 560080, India +3Inter University Centre for Astronomy and Astrophysics, Post Bag 4, Ganeshkhind, Pune-411007, India +4Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803, USA +ABSTRACT +The exquisitely measured maps of fluctuations in the Cosmic Microwave Background (CMB) present +the possibility to test the principle of Statistical Isotropy (SI) of the Universe through systematic +observable measures for non-Statistical Isotropy (nSI) features in the data. +Recent measurements +of the CMB temperature field provide tantalizing evidence of the deviation from SI. A systematic +approach based on strong mathematical formulation allows any nSI feature to be traced to known +physical effects or observational artefacts. Unexplained nSI features could have immense cosmological +ramifications for the standard model of cosmology. BipoSH (Bipolar Spherical Harmonics) provides +a general formalism for quantifying the departure from statistical isotropy for a field on a 2D sphere. +We adopt a known reduction of the BipoSH functions, dubbed Minimal Harmonics (Manakov et al. +1996). We demonstrate that this reduction technique of BipoSH leads to a new generalized set of +isotropic angular correlation functions (mBipoSH) that are observable quantifications of nSI features +in a sky map. We show that any nSI feature in the CMB map captured by BipoSH at the bipolar +multiple L with projection M can be studied by (L+1) mBipoSH angular correlation functions in case +of even parity and by L functions in case of odd parity. We present in this letter a novel observable +quantification of deviation from statistical isotropy in terms of generalized angular correlation functions +that are compact and complementary to the BipoSH spectra that generalize angular power spectrum +CMB fluctuations. +Keywords: Spherical Harmonics, Correlation Function, CMB Anisotropy +1. INTRODUCTION +The CMB anisotropy measurements by WMAP (Hinshaw et al. 2009) and Planck (Aghanim et al. 2020) space +missions have ushered in the precision era of cosmology. Precise measurements enable cosmologists to pose queries +beyond the statistically isotropic two-point correlation function predicted by the fundamental assumption of homo- +geneity and isotropy based on the cosmological principle. Current observations are in good agreement with CMB +temperature anisotropies being Gaussian (Aghanim et al. 2020). In such a case, all the information encoded in the +CMB temperature field can be specified by a two-point correlation function. The WMAP and Planck collaboration +data release claimed significant deviation from SI in CMB maps. BipoSH provides an elegant and general formalism +for the two-point correlation function for a random field on a 2-sphere, where the statistical isotropy part is just a +subset in BipoSH basis (Hajian & Souradeep 2003). In this letter, we extend the BipoSH formalism to a new angle +dependent irreducible representation to be applicable in the real (angular) space instead of harmonic basis. Departures +from statistical isotropy can have its roots in known physical effects, and observational artefacts. Some known effects +include Doppler boost, Weak lensing of CMB photons by large scale structure, and systematics such as non-circular +Corresponding author: Dipanshu +garg.dipanshu@students.iiserpune.ac.in +arXiv:2301.04539v1 [astro-ph.CO] 11 Jan 2023 + +ID2 +Dipanshu et al. +beam have been studied in the BipoSH representation (Mitra et al. 2004; Joshi et al. 2010; Mukherjee et al. 2014; +Kumar et al. 2015). With upcoming missions with great precision, the study of SI violation has far-reaching implica- +tions in cosmology. Hence it is important to study crucial signatures of departure from statistical isotropy using an +appropriate mathematical construct. +2. BIPOSH FORMALISM +BipoSH (Bipolar Spherical Harmonics) provides a general formalism for quantifying the departure from the statistical +isotropy of CMB temperature field. Bipolar Spherical Harmonics form a complete and orthonormal basis in S2 × S2 +and thus have the bidirectional dependence. The most general two-point correlation function for a field defined on the +sphere can be obtained in terms of BipoSH basis as +C (ˆn1, ˆn2) = +� +L,M,l1,l2 +ALM +l1l2 {Yl1 (ˆn1) ⊗ Yl2 (ˆn2)}LM +(1) +where ALM +l1l2 are BipoSH coefficients and {Yl1 (ˆn1) ⊗ Yl2 (ˆn2)}LM are Bipolar Spherical Harmonic (BipoSH) functions. +BipoSH functions are tensor product of two spherical harmonics (SH) functions that can be expanded as +{Yl1 (ˆn1) ⊗ Yl2 (ˆn2)}LM = +� +m1m2 +CLM +l1m1l2−m2Yl1,m1(ˆn1)Yl2,m2(ˆn2) +(2) +where are CLM +l1m1l2−m2 are Clebsch Gordon (CG) coefficients. The indices of CG coefficients satisfy the triangularity +conditions as |l1 − l2| ≤ L ≤ l1 + l2 and m1 + m2 = M. +BipoSH coefficients are the natural generalization of CMB angular power spectrum. BipoSH coefficients carry crucial +signatures of SI violation describing direction-dependent statistics of CMB sky. Since the two-point correlation function +is a real measurable. BipoSH is widely used for characterizing different known sources of nSI effects and systematically +probing for non-statistical isotropy from the CMB maps. The L = 0 condition gives the isotropic part and higher L +values represent the corresponding bipolar multipole of nSI effects in the CMB Sky. +3. REDUCTION TECHNIQUE FOR BIPOLAR HARMONICS +In this section, we outline a mathematical construct for the reduction of Bipolar Harmonics as studied by Manakov +et al. (1996). In BipoSH basis, the rank L has values from 0,1,2,3.. and the internal ranks l, l +′ runs over all values from +0 to infinity for a given rank L constrained by the CG coefficients. In other words, the information at given Bipolar +multipole L could be spread over angular spectral range l. We show that the reduction to minimal Bipolar Spherical +Harmonics (mBipoSH) limits the spectral spread to L angular correlation functions with a dependence on ˆn1 · ˆn2. The +different mBipoSH functions represent the angle-dependent field correlation functions for the nSI map. +This above reduction follows from the justification that any irreducible tensor of rank L can be constructed using +L vectors of its arguments. Any Bipolar Harmonic with any possible internal rank l + l +′ can be constructed using +combination of L Minimal Harmonics defined as +Yk +LM(ˆn1, ˆn2) = Y L−k,k +LM +(ˆn1, ˆn2), where k = 0, 1....., L. +(3) +The above relation reduces our analysis to only a few internal ranks up to L. The tensor with rank l + l +′ ≥ L +can be written from L Minimal Harmonics and coefficients depending upon l, l +′and θ = cos−1(ˆn1.ˆn2). Mathematical +representation of the Minimal Harmonics from Manakov et al. (1996) can be written as +Y l1l2 +LM (ˆn1, ˆn2) = +L +� +λ=λp +aλ(l1, l2, L, cos θ)Y λ,L+λp−λ +LM +(ˆn1, ˆn2) +(4) +where +λp = +� +0 for even (l1 + l2 − L) +1 for odd (l1 + l2 − L) . +(5) +The parameter λp describes space inversion property of Spherical Harmonics. λp carries information about the parity +of BipoSH functions as discussed in Kamionkowski & Souradeep (2011). Which specifies the BipoSH function Y l1l2 +LM is +a tensor for even parity and pseudo tensor for odd parity. The coefficients aλ follows the symmetry relation given as +aλ(l1, l2, L, cos θ) = aL−λp−λ(l2, l1, L, cos θ). +(6) + +Minimal Harmonics +3 +The above-transformed set of Minimal Harmonics also forms a set of the complete basis for Bipolar Spherical Harmonics. +The coefficients aλ are functions of angle θ between two directions, and the BipoSH functions with dependence on +higher L values can be constructed using these coefficients with a finite set of Minimal Harmonics basis functions. +Considering the completeness property of BipoSH functions, the final expression for aλ can be written as +aλp +λ (l1, l2, L, cos θ) = iλp(−1)l2 +� 2L(2l1 + 1)(2l2 + 1)(2L + 1)!(l1 + l2 − L)!λ!(L − λ − λp)! +q!(L − l1 + l2)!(L − l2 + l1)!(2λ + 1)!!(2L − 2λ − 2λp + 1)!! +� +∗ +tmax +� +t=0 +(−1)λ+t +� (j−l1) +2 +t +��L − λp − t +λ +� +(q − λp)!! +(q − λp − 2t)!!P (L−t) +j−t−λ(cos θ) +(7) +where q = l1 + l2 + L + 1, j = L + l2 − λp, and tmax = min +� +L − λp − λ, j−l1 +2 +� +, +�m +n +� +is the binomial coefficient and +P (m) +n +(x) is the mth derivative of the Legendre polynomial Pn(x). Given that the functions follow the symmetry relation +given in Eq. (6). Henceforth to construct the mBipoSH coefficients, Eq. (7) is only referred for coefficients having +λ ≥ ( L +2 ) and the remaining coefficients can be computed using the symmetry relation for the aλ. This provides us with +a complete set of aλ functions for the reduction of Bipolar Harmonics with any rank L. It can be further analyzed +from the above set of Minimal Harmonics basis that the tensor Y l1l2 +LM has L + 1 − λp different basis components. +Using this reduction mechanism for Bipolar Harmonics, we can construct equivalent compact and complementary +angle-dependent mBipoSH functions for given any value of multipole L. +4. CONSTRUCTING MINIMAL BIPOSH FUNCTIONS +Employing the mechanism of reduction of Bipolar Harmonics basis discussed in previous section, we can construct the +nSI features in the CMB sky maps into angle-dependent correlation functions. The most general two-point correlation +function from Eq.(1) and Eq.(4) can be expanded in the form of mBipoSH angular correlation functions as +C (ˆn1, ˆn2) = +� +L,M,l1,l2 +ALM +l1l2 +L +� +λ=λp +aλ(l1, l2, L, cos θ)Y λ,L+λp−λ +LM +(ˆn1, ˆn2). +(8) +Where in the case of SI, the above equation gets reduced to C (ˆn1.ˆn2) = C(θ). Simplifying the above equation in the +case of even parity i.e. substituting λp = 0, the equation reduces to +C(ˆn1, ˆn2) = +� +L,M +L +� +λ=0 +� +�� +l1,l2 +ALM +l1l2 aλ(l1, l2, L, cos θ) +� +� Y λ,L−λ +LM +(ˆn1, ˆn2). +(9) +We conclude from the above expression that the correlation function for any particular multipole L can be represented +with a sum over a few Bipolar functions and referring the expression inside the bracket as minimal BipoSH coefficients. +Hence, mBipoSH coefficients can be written as +αL,M +λ +(cos θ) = +� +l1l2 +ALM +l1l2 aλ(l1, l2, L, cos θ), +(10) +these are the angle-dependent coefficients in our new reduced Bipolar basis. From the definition of BipoSH coefficients +in Hajian & Souradeep (2003), minimal BipoSH coefficients could be expressed in terms of covariance matrix computed +through CMB maps as +αL,M +λ +(cos θ) = +� +l1l2 +� +m1m2 +al1m1a∗ +l2m2(−1)m2CLM +l1m1l2−m2aλ(l1, l2, L, cos θ) +(11) +Since alms are measurable from the CMB temperature maps. It is crucial to study of CMB sky using mBipoSH +coefficients representing real space quantities. It can be emphasized from the above relations that minimal BipoSH +coefficients are a set of different θ dependent correlation functions defined for specific nSI feature in a CMB map. +For L = 0, we recover the isotropic two-point correlation function known as CMB angular power spectrum, which is +extensively studied in cosmology literature and has been source of vast information. But angle dependent isotropic + +4 +Dipanshu et al. +correlation function for a SI violated CMB map hasn’t been studied earlier. This mathematical exercise gives an easy +and compact way to study higher multipole angular correlation functions in the case of nSI CMB maps. +It can be observed from the analysis that L + 1 different angle-dependent correlation functions completely capture +the anisotropy of multipole L with projection M in case of even parity and L correlation functions in case of odd +parity. +The mBipoSH functions can be summed over to construct cos θ dependent spectrum at each point on the 2D sphere. +ζλ(ˆn1, cos θ) = +� +LM +αLM +λ +(cos θ)YLM(ˆn1) +(12) +These defined functions form a basis in S2 × S1 and can minimally represent the anisotropy pattern in the CMB map. +This mathematical structure opens a new avenue for constructing and analyzing CMB temperature maps. +5. ILLUSTRATIVE EXAMPLE +Precise measurements from WMAP and Planck have signaled various sources of SI violation in the CMB data. Our +mathematical representation uses harmonic space decomposed alm to compute mBipoSH coefficients. These functions +represent the angle-dependent real space correlation functions for SI violated map. We study one case of nSI map due +to Doppler Boost with the mBipoSH angular correlations functions that have come under discussion due to results +obtained by recent experiments. +5.1. Doppler Boost +Our motion today with respect to the cosmic rest frame causes dipole anisotropy in the CMB temperature and +polarization fields. Doppler boost of CMB with velocity (β ≡ |v|/c = 1.23 × 10−3) induces non-zero dipolar (L = 1) +signatures in the CMB maps as shown by Mukherjee et al. (2014). +Doppler boost leads to two kinds of effects, +modulation, and aberration of the CMB temperature field. +This effect is studied via the l , l +1 correlations of SH space covariance matrix, which is related to the L = 1 +BipoSH spectra. The BipoSH coefficients for the Doppler Boost could be written as +˜A1M +ll+1|T T = β1MDT T +l +Πll+1 +Π1 +C10 +l 0 l+1 0, +(13) +where BipoSH spectra is defined as +DT T +l += +1 +√ +4π +� +(l + bν)CT T +l +− (l + 2 − bν)CT T +l+1 +� +(14) +where, β refers to the boost velocity vector and bν is the frequency dependent effect on Doppler boost given by +bν = ν +ν0 +coth +� ν +2ν0 +� +− 1, +(15) +the local velocity β1M defined as according to Planck Collaboration et al. (2014) +β1M = +� +β.ˆnY ∗ +1M(ˆn)dˆn +(16) +with the notation Πl1 l2...ln = +� +(2l1 + 1)(2l2 + 1) . . . (2ln + 1). The minimal BipoSH coefficients for Doppler Boost +can be constructed using the method used in the above section as +α1M +λ +(cos θ) = +� +l +A1M +ll+1aλ(l, l + 1, 1, cos θ). +(17) +The above reduction process for the Doppler Boost (L = 1) can be simplified in terms of the correlation function as +C (ˆn1, ˆn2) = CnSI(ˆn1, ˆn2) + CSI(cos θ). +(18) +Where the nSI correlation function corresponding to Doppler Boost (L = 1) along the β direction in terms of angular +correlation functions as +CnSI (ˆn1, ˆn2) = +1 +� +λ=0 +Cλ(cos θ)fλ (ˆn1, ˆn2) , +(19) + +Minimal Harmonics +5 +where Cλ(cos θ) represents the two different angular correlation functions for the Doppler-boosted CMB temperature +map and fλ (ˆn1, ˆn2) are the functions of directions, which for the L = 1 case, are [ˆn1]10 = ˆn1. ˆd and [ˆn2]10 = ˆn2. ˆd +respectively, the indices representing the zeroth component of rank 1 tensor, specifying the projection of the respective +vector along the ( ˆd) boost direction. +Simplifying the equation becomes +CnSI (ˆn1, ˆn2) = C0(cos θ) ˆn1. ˆd + C1(cos θ) ˆn1. ˆd +(20) +The explicit form of these functions can be written as +C0(θ) = +� +l +DT T +l +Πll+1 +Π1 +C10 +l 0 l+1 0 +� +− +√ +3 +4π +√ +l + 1(−1)lP (1) +l +(cos θ) +� +(21) +C1(θ) = +� +l +DT T +l +Πll+1 +Π1 +C10 +l 0 l+1 0 +� +− +√ +3 +4π +√ +l + 1(−1)l+1P (1) +l+1(cos θ) +� +. +(22) +Naively, we can see both angular correlation functions depend upon the first derivative of Legendre polynomials +P (1) +ℓ +(cos θ). This attributes to the generalization of well-studied statistical isotropic correlation function CSI(cos θ). +Noting that the magnitude of both correlation functions is not exactly the same, they differ a little as their mathematical +expression suggests. +Figure 1 represents the theoretical and simulated plots of angular correlation functions for the CMB map having +anisotropy corresponding to L = 1 Doppler Boost. +Figure 1. +The left panel displays theoretical correlation function CSI(θ) plot for Isotropic L = 0 part, C0(θ) and C1(θ) +correlation functions for Doppler Boost with bν = 3 for ν = 217 GHz with β = 1.23 × 10−3 using the best-fit ΛCDM CT T +l +generated from CAMB (Lewis & Challinor 2011). The right panel presents the C0(θ) and C1(θ) plots obtained from 1000 +realizations of Doppler Boosted maps using the same parameters. +The above plots show that temperature fluctuations in a Doppler-boosted map are correlated at very small angles +only. We conclude that correlation length in fluctuations in such a case is non-zero for an angle less than 1◦. Right +panel in Figure 1 displays an error bar plot for 1000 simulated maps with such nSI effect. From the plot, we conclude +that Planck mission (Planck Collaboration et al. 2014) with much improved resolution could manifest the doppler boost +velocity signal with greater efficiency as compared to WMAP (Hinshaw et al. 2013) due to signal strength relevant +at very small angles only. We used the CoNIGS code discussed in Mukherjee & Souradeep (2014) for generating nSI +maps for Doppler boost. +5.2. Estimation + +10000 +(0 = 7)/S(0) +Co()(L = 1) +8000 +Ci(0)(L = 1) +6000 +(μk2) +4000 +Correlation +2000 +0 +-2000 +-4000 +-6000 +10-2 +10-1 +100 +101 +102 +Angle in degreesPlanck +WMAP +10000 +Co(o) using Doppler Boosted Map +Ci(0) using Doppler Boosted Map +7500 +Co(0) using Sl Map +Ci(0) using SI Map +5000 +Correlation (μuk2) +2500 +0 +-2500 +-5000 +-7500 +-10000 +10-2 +10-1 +100 +101 +102 +Angle in degrees6 +Dipanshu et al. +We discuss here the estimation of signal strength of the source of nSI effects using the real space angular correlation +mBipoSH functions. The estimation of the mBipoSH functions could be written as +ˆαLM +λ +(cos θ) = αLM +λ +(cos θ) + ΓLMGL +λ(cos θ) , +(23) +where, ˆαLM +λ +(cos θ) is the observed mBipoSH coefficient and αLM +λ +(cos θ) is the mBipoSH coefficient for a SI field, +which on average over an ensemble is zero for L ̸= 0. ΓLMGL +λ is the source of SI violation with GL +λ(cos θ) as the +shape factor and ΓLM is the signal strength of nSI effects like weak lensing, doppler boost, etc. This estimator is +an extension of the estimator defined by Hu & Okamoto (2002), Hanson et al. (2009) for angle-dependent real space +mBipoSH coefficients. +For the the doppler boost case, to measure the β1M , we define estimator, ˆβLM for L = 1 as +ˆβ1M = +� +θ +α1M +λ +(cos θ) +G1 +λ(cos θ) + β1M . +(24) +Where, shape factor for λ = 1 is defined as +G1 +1(cos θ) = +� +l +Πl,l+1 +√ +12π [(l + b) Cl − (l + 2 − b) Cl+1] C10 +l0l+10 +� +− +√ +3 +4π +√ +l + 1(−1)lP (1) +l +(cos θ) +� +(25) +To arrive at the minimum variance estimator, using the appropriate weights, we can write +ˆβ1M = +� +θ +w1 +λ(cos θ)α1M +λ +(cos θ) +G1 +λ(cos θ) + β1M , +(26) +where w1 +λ(cos θ) are the weights such that � +θ wL +λ (cos θ) = 1. These weight factors should be chosen such that it +minimizes the reconstruction noise. This presents us with a unique estimator for the nSI effects. +6. DISCUSSIONS +In this letter, we proposed a natural generalization of the well-known angular correlation function that can capture +non-Statistical Isotropy in sky maps of the CMB temperature fluctuations. We invoke a reduction technique for Bipolar +Spherical Harmonics that lead to new measures called Minimal Harmonics. These new measures depict the real space +angular correlation functions from the nSI sky termed as mBipoSH coefficients. In the limits of SI, we recover the +well-studied statistical isotropic correlation function of the CMB data. +As an illustrative example, we present the exact relations having mBipoSH angular correlations for the popular effect +of nSI feature as doppler boost. We systematically construct mBipoSH functions for this case, concluding in such case +of nSI effect, temperature fluctuations have correlation length at very small angles only. Through this systematic +study, we have proposed that this method can be used to quantify various other signatures of SI violation in CMB +data. +DG would like to thank Debabrata Adak, Rajorshi Chandra, Ritam Pal, Sayan Saha, and Shabbir Shaikh for helpful +discussions during the course of this project. We also acknowledge the use of Healpix (Gorski et al. 2005), CoNIGS +Code (Mukherjee & Souradeep 2014), BipoSH code with various contributions mentioned in (Das 2019), CAMB (Lewis +& Challinor 2011), Numpy (Harris et al. 2020), Scipy (Virtanen et al. 2020), Matplotlib (Hunter 2007). The work of +D.G is supported by CSIR-SRF Fellowship. S.H is partially supported by DST-Inspire fellowship. +1 +2 +3 +4 +5 +REFERENCES +Aghanim, N., et al. 2020, Astron. Astrophys., 641, A1, +doi: 10.1051/0004-6361/201833880 +Copi, C. J., Huterer, D., Schwarz, D. J., & Starkman, G. D. +2010, Adv. Astron., 2010, 847541, +doi: 10.1155/2010/847541 +Das, S. 2019, arXiv preprint arXiv:1902.02328 + +Minimal Harmonics +7 +Gorski, K. M., Hivon, E., Banday, A. J., et al. 2005, The +Astrophysical Journal, 622, 759 +Hajian, A., & Souradeep, T. 2003, The Astrophysical +Journal, 597, L5, doi: 10.1086/379757 +Hanson, D., Rocha, G., & G´orski, K. 2009, Monthly +Notices of the Royal Astronomical Society, 400, 2169 +Harris, C. R., Millman, K. J., van der Walt, S. J., et al. +2020, Nature, 585, 357, doi: 10.1038/s41586-020-2649-2 +Hinshaw, G., et al. 2009, Astrophys. J. Suppl., 180, 225, +doi: 10.1088/0067-0049/180/2/225 +Hinshaw, G., Larson, D., Komatsu, E., et al. 2013, The +Astrophysical Journal Supplement Series, 208, 19 +Hu, W., & Okamoto, T. 2002, The Astrophysical Journal, +574, 566 +Hunter, J. D. 2007, Computing in Science & Engineering, 9, +90, doi: 10.1109/MCSE.2007.55 +Joshi, N., Jhingan, S., Souradeep, T., & Hajian, A. 2010, +Phys. Rev. D, 81, 083012, +doi: 10.1103/PhysRevD.81.083012 +Kamionkowski, M., & Souradeep, T. 2011, Phys. Rev. D, +83, 027301, doi: 10.1103/PhysRevD.83.027301 +Kumar, S., Rotti, A., Aich, M., et al. 2015, Phys. Rev. D, +91, 043501, doi: 10.1103/PhysRevD.91.043501 +Lewis, A., & Challinor, A. 2011, CAMB: Code for +Anisotropies in the Microwave Background, Astrophysics +Source Code Library, record ascl:1102.026. +http://ascl.net/1102.026 +Manakov, N. L., Marmo, S. I., & Meremianin, A. V. 1996, +Journal of Physics B: Atomic, Molecular and Optical +Physics, 29, 2711, doi: 10.1088/0953-4075/29/13/010 +Mitra, S., Sengupta, A. S., & Souradeep, T. 2004, Phys. +Rev. D, 70, 103002, doi: 10.1103/PhysRevD.70.103002 +Mukherjee, S., De, A., & Souradeep, T. 2014, Phys. Rev. D, +89, 083005, doi: 10.1103/PhysRevD.89.083005 +Mukherjee, S., & Souradeep, T. 2014, Phys. Rev. D, 89, +063013, doi: 10.1103/PhysRevD.89.063013 +Planck Collaboration, Aghanim, N., Armitage-Caplan, C., +et al. 2014, A&A, 571, A27, +doi: 10.1051/0004-6361/201321556 +Saha, S., Shaikh, S., Mukherjee, S., Souradeep, T., & +Wandelt, B. D. 2021, JCAP, 10, 072, +doi: 10.1088/1475-7516/2021/10/072 +Varshalovich, D. A., Moskalev, A. N., & Khersonskii, V. K. +1988, Quantum Theory of Angular Momentum +(Singapore: World Scientific) +Virtanen, P., Gommers, R., Oliphant, T. E., et al. 2020, +Nature Methods, 17, 261, doi: 10.1038/s41592-019-0686-2 + diff --git a/cdE3T4oBgHgl3EQfeAov/content/tmp_files/load_file.txt b/cdE3T4oBgHgl3EQfeAov/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..6239e0e3ab3c9ee85dcd28b7c9a97d207f030920 --- /dev/null +++ b/cdE3T4oBgHgl3EQfeAov/content/tmp_files/load_file.txt @@ -0,0 +1,354 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf,len=353 +page_content='Draft version January 12,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' 2023 Typeset using LATEX default style in AASTeX631 Capturing Statistical Isotropy violation with generalized Isotropic Angular Correlation Functions of CMB Anisotropy Dipanshu ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content='1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' 2 Tarun Souradeep ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content='1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' 2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' 3 and Shriya Hirve 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' 4 1Department of Physics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' Indian Institute of Science Education and Research,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' Pune 411008,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' India 2Raman Research Institute,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' Bangalore 560080,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' India 3Inter University Centre for Astronomy and Astrophysics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' Post Bag 4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' Ganeshkhind,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' Pune-411007,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' India 4Department of Physics and Astronomy,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' Louisiana State University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' Baton Rouge,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' LA 70803,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' USA ABSTRACT The exquisitely measured maps of fluctuations in the Cosmic Microwave Background (CMB) present the possibility to test the principle of Statistical Isotropy (SI) of the Universe through systematic observable measures for non-Statistical Isotropy (nSI) features in the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' Recent measurements of the CMB temperature field provide tantalizing evidence of the deviation from SI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' A systematic approach based on strong mathematical formulation allows any nSI feature to be traced to known physical effects or observational artefacts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' Unexplained nSI features could have immense cosmological ramifications for the standard model of cosmology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' BipoSH (Bipolar Spherical Harmonics) provides a general formalism for quantifying the departure from statistical isotropy for a field on a 2D sphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' We adopt a known reduction of the BipoSH functions, dubbed Minimal Harmonics (Manakov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' 1996).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' We demonstrate that this reduction technique of BipoSH leads to a new generalized set of isotropic angular correlation functions (mBipoSH) that are observable quantifications of nSI features in a sky map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' We show that any nSI feature in the CMB map captured by BipoSH at the bipolar multiple L with projection M can be studied by (L+1) mBipoSH angular correlation functions in case of even parity and by L functions in case of odd parity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' We present in this letter a novel observable quantification of deviation from statistical isotropy in terms of generalized angular correlation functions that are compact and complementary to the BipoSH spectra that generalize angular power spectrum CMB fluctuations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' Keywords: Spherical Harmonics, Correlation Function, CMB Anisotropy 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' INTRODUCTION The CMB anisotropy measurements by WMAP (Hinshaw et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' 2009) and Planck (Aghanim et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' 2020) space missions have ushered in the precision era of cosmology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' Precise measurements enable cosmologists to pose queries beyond the statistically isotropic two-point correlation function predicted by the fundamental assumption of homo- geneity and isotropy based on the cosmological principle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' Current observations are in good agreement with CMB temperature anisotropies being Gaussian (Aghanim et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' In such a case, all the information encoded in the CMB temperature field can be specified by a two-point correlation function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' The WMAP and Planck collaboration data release claimed significant deviation from SI in CMB maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' BipoSH provides an elegant and general formalism for the two-point correlation function for a random field on a 2-sphere, where the statistical isotropy part is just a subset in BipoSH basis (Hajian & Souradeep 2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' In this letter, we extend the BipoSH formalism to a new angle dependent irreducible representation to be applicable in the real (angular) space instead of harmonic basis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' Departures from statistical isotropy can have its roots in known physical effects, and observational artefacts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' Some known effects include Doppler boost, Weak lensing of CMB photons by large scale structure, and systematics such as non-circular Corresponding author: Dipanshu garg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content='dipanshu@students.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content='iiserpune.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content='in arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content='04539v1 [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content='CO] 11 Jan 2023 ID2 Dipanshu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' beam have been studied in the BipoSH representation (Mitra et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' 2004;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' Joshi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' Mukherjee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' Kumar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' With upcoming missions with great precision, the study of SI violation has far-reaching implica- tions in cosmology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' Hence it is important to study crucial signatures of departure from statistical isotropy using an appropriate mathematical construct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' BIPOSH FORMALISM BipoSH (Bipolar Spherical Harmonics) provides a general formalism for quantifying the departure from the statistical isotropy of CMB temperature field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' Bipolar Spherical Harmonics form a complete and orthonormal basis in S2 × S2 and thus have the bidirectional dependence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' The most general two-point correlation function for a field defined on the sphere can be obtained in terms of BipoSH basis as C (ˆn1, ˆn2) = � L,M,l1,l2 ALM l1l2 {Yl1 (ˆn1) ⊗ Yl2 (ˆn2)}LM (1) where ALM l1l2 are BipoSH coefficients and {Yl1 (ˆn1) ⊗ Yl2 (ˆn2)}LM are Bipolar Spherical Harmonic (BipoSH) functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' BipoSH functions are tensor product of two spherical harmonics (SH) functions that can be expanded as {Yl1 (ˆn1) ⊗ Yl2 (ˆn2)}LM = � m1m2 CLM l1m1l2−m2Yl1,m1(ˆn1)Yl2,m2(ˆn2) (2) where are CLM l1m1l2−m2 are Clebsch Gordon (CG) coefficients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' The indices of CG coefficients satisfy the triangularity conditions as |l1 − l2| ≤ L ≤ l1 + l2 and m1 + m2 = M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' BipoSH coefficients are the natural generalization of CMB angular power spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' BipoSH coefficients carry crucial signatures of SI violation describing direction-dependent statistics of CMB sky.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' Since the two-point correlation function is a real measurable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' BipoSH is widely used for characterizing different known sources of nSI effects and systematically probing for non-statistical isotropy from the CMB maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' The L = 0 condition gives the isotropic part and higher L values represent the corresponding bipolar multipole of nSI effects in the CMB Sky.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' REDUCTION TECHNIQUE FOR BIPOLAR HARMONICS In this section, we outline a mathematical construct for the reduction of Bipolar Harmonics as studied by Manakov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' (1996).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' In BipoSH basis, the rank L has values from 0,1,2,3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content='. and the internal ranks l, l ′ runs over all values from 0 to infinity for a given rank L constrained by the CG coefficients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' In other words, the information at given Bipolar multipole L could be spread over angular spectral range l.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' We show that the reduction to minimal Bipolar Spherical Harmonics (mBipoSH) limits the spectral spread to L angular correlation functions with a dependence on ˆn1 · ˆn2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' The different mBipoSH functions represent the angle-dependent field correlation functions for the nSI map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' This above reduction follows from the justification that any irreducible tensor of rank L can be constructed using L vectors of its arguments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' Any Bipolar Harmonic with any possible internal rank l + l ′ can be constructed using combination of L Minimal Harmonics defined as Yk LM(ˆn1, ˆn2) = Y L−k,k LM (ˆn1, ˆn2), where k = 0, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=', L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' (3) The above relation reduces our analysis to only a few internal ranks up to L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' The tensor with rank l + l ′ ≥ L can be written from L Minimal Harmonics and coefficients depending upon l, l ′and θ = cos−1(ˆn1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content='ˆn2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' Mathematical representation of the Minimal Harmonics from Manakov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' (1996) can be written as Y l1l2 LM (ˆn1, ˆn2) = L � λ=λp aλ(l1, l2, L, cos θ)Y λ,L+λp−λ LM (ˆn1, ˆn2) (4) where λp = � 0 for even (l1 + l2 − L) 1 for odd (l1 + l2 − L) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' (5) The parameter λp describes space inversion property of Spherical Harmonics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' λp carries information about the parity of BipoSH functions as discussed in Kamionkowski & Souradeep (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' Which specifies the BipoSH function Y l1l2 LM is a tensor for even parity and pseudo tensor for odd parity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' The coefficients aλ follows the symmetry relation given as aλ(l1, l2, L, cos θ) = aL−λp−λ(l2, l1, L, cos θ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' (6) Minimal Harmonics 3 The above-transformed set of Minimal Harmonics also forms a set of the complete basis for Bipolar Spherical Harmonics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' The coefficients aλ are functions of angle θ between two directions, and the BipoSH functions with dependence on higher L values can be constructed using these coefficients with a finite set of Minimal Harmonics basis functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' Considering the completeness property of BipoSH functions, the final expression for aλ can be written as aλp λ (l1, l2, L, cos θ) = iλp(−1)l2 � 2L(2l1 + 1)(2l2 + 1)(2L + 1)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' (l1 + l2 − L)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content='λ!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' (L − λ − λp)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' q!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' (L − l1 + l2)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' (L − l2 + l1)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' (2λ + 1)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content='!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' (2L − 2λ − 2λp + 1)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' � ∗ tmax � t=0 (−1)λ+t � (j−l1) 2 t ��L − λp − t λ � (q − λp)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' (q − λp − 2t)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content='P (L−t) j−t−λ(cos θ) (7) where q = l1 + l2 + L + 1, j = L + l2 − λp, and tmax = min � L − λp − λ, j−l1 2 � , �m n � is the binomial coefficient and P (m) n (x) is the mth derivative of the Legendre polynomial Pn(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' Given that the functions follow the symmetry relation given in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' (6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' Henceforth to construct the mBipoSH coefficients, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' (7) is only referred for coefficients having λ ≥ ( L 2 ) and the remaining coefficients can be computed using the symmetry relation for the aλ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' This provides us with a complete set of aλ functions for the reduction of Bipolar Harmonics with any rank L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' It can be further analyzed from the above set of Minimal Harmonics basis that the tensor Y l1l2 LM has L + 1 − λp different basis components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' Using this reduction mechanism for Bipolar Harmonics, we can construct equivalent compact and complementary angle-dependent mBipoSH functions for given any value of multipole L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' CONSTRUCTING MINIMAL BIPOSH FUNCTIONS Employing the mechanism of reduction of Bipolar Harmonics basis discussed in previous section, we can construct the nSI features in the CMB sky maps into angle-dependent correlation functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' The most general two-point correlation function from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' (1) and Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' (4) can be expanded in the form of mBipoSH angular correlation functions as C (ˆn1, ˆn2) = � L,M,l1,l2 ALM l1l2 L � λ=λp aλ(l1, l2, L, cos θ)Y λ,L+λp−λ LM (ˆn1, ˆn2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' (8) Where in the case of SI, the above equation gets reduced to C (ˆn1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content='ˆn2) = C(θ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' Simplifying the above equation in the case of even parity i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' substituting λp = 0, the equation reduces to C(ˆn1, ˆn2) = � L,M L � λ=0 � �� l1,l2 ALM l1l2 aλ(l1, l2, L, cos θ) � � Y λ,L−λ LM (ˆn1, ˆn2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' (9) We conclude from the above expression that the correlation function for any particular multipole L can be represented with a sum over a few Bipolar functions and referring the expression inside the bracket as minimal BipoSH coefficients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' Hence, mBipoSH coefficients can be written as αL,M λ (cos θ) = � l1l2 ALM l1l2 aλ(l1, l2, L, cos θ), (10) these are the angle-dependent coefficients in our new reduced Bipolar basis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' From the definition of BipoSH coefficients in Hajian & Souradeep (2003), minimal BipoSH coefficients could be expressed in terms of covariance matrix computed through CMB maps as αL,M λ (cos θ) = � l1l2 � m1m2 al1m1a∗ l2m2(−1)m2CLM l1m1l2−m2aλ(l1, l2, L, cos θ) (11) Since alms are measurable from the CMB temperature maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' It is crucial to study of CMB sky using mBipoSH coefficients representing real space quantities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' It can be emphasized from the above relations that minimal BipoSH coefficients are a set of different θ dependent correlation functions defined for specific nSI feature in a CMB map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' For L = 0, we recover the isotropic two-point correlation function known as CMB angular power spectrum, which is extensively studied in cosmology literature and has been source of vast information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' But angle dependent isotropic 4 Dipanshu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' correlation function for a SI violated CMB map hasn’t been studied earlier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' This mathematical exercise gives an easy and compact way to study higher multipole angular correlation functions in the case of nSI CMB maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' It can be observed from the analysis that L + 1 different angle-dependent correlation functions completely capture the anisotropy of multipole L with projection M in case of even parity and L correlation functions in case of odd parity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' The mBipoSH functions can be summed over to construct cos θ dependent spectrum at each point on the 2D sphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' ζλ(ˆn1, cos θ) = � LM αLM λ (cos θ)YLM(ˆn1) (12) These defined functions form a basis in S2 × S1 and can minimally represent the anisotropy pattern in the CMB map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' This mathematical structure opens a new avenue for constructing and analyzing CMB temperature maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' ILLUSTRATIVE EXAMPLE Precise measurements from WMAP and Planck have signaled various sources of SI violation in the CMB data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' Our mathematical representation uses harmonic space decomposed alm to compute mBipoSH coefficients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' These functions represent the angle-dependent real space correlation functions for SI violated map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' We study one case of nSI map due to Doppler Boost with the mBipoSH angular correlations functions that have come under discussion due to results obtained by recent experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' Doppler Boost Our motion today with respect to the cosmic rest frame causes dipole anisotropy in the CMB temperature and polarization fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' Doppler boost of CMB with velocity (β ≡ |v|/c = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content='23 × 10−3) induces non-zero dipolar (L = 1) signatures in the CMB maps as shown by Mukherjee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' Doppler boost leads to two kinds of effects, modulation, and aberration of the CMB temperature field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' This effect is studied via the l , l +1 correlations of SH space covariance matrix, which is related to the L = 1 BipoSH spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' The BipoSH coefficients for the Doppler Boost could be written as ˜A1M ll+1|T T = β1MDT T l Πll+1 Π1 C10 l 0 l+1 0, (13) where BipoSH spectra is defined as DT T l = 1 √ 4π � (l + bν)CT T l − (l + 2 − bν)CT T l+1 � (14) where, β refers to the boost velocity vector and bν is the frequency dependent effect on Doppler boost given by bν = ν ν0 coth � ν 2ν0 � − 1, (15) the local velocity β1M defined as according to Planck Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' (2014) β1M = � β.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content='ˆnY ∗ 1M(ˆn)dˆn (16) with the notation Πl1 l2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content='ln = � (2l1 + 1)(2l2 + 1) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' (2ln + 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' The minimal BipoSH coefficients for Doppler Boost can be constructed using the method used in the above section as α1M λ (cos θ) = � l A1M ll+1aλ(l, l + 1, 1, cos θ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' (17) The above reduction process for the Doppler Boost (L = 1) can be simplified in terms of the correlation function as C (ˆn1, ˆn2) = CnSI(ˆn1, ˆn2) + CSI(cos θ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' (18) Where the nSI correlation function corresponding to Doppler Boost (L = 1) along the β direction in terms of angular correlation functions as CnSI (ˆn1, ˆn2) = 1 � λ=0 Cλ(cos θ)fλ (ˆn1, ˆn2) , (19) Minimal Harmonics 5 where Cλ(cos θ) represents the two different angular correlation functions for the Doppler-boosted CMB temperature map and fλ (ˆn1, ˆn2) are the functions of directions, which for the L = 1 case, are [ˆn1]10 = ˆn1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' ˆd and [ˆn2]10 = ˆn2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' ˆd respectively, the indices representing the zeroth component of rank 1 tensor, specifying the projection of the respective vector along the ( ˆd) boost direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' Simplifying the equation becomes CnSI (ˆn1, ˆn2) = C0(cos θ) ˆn1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' ˆd + C1(cos θ) ˆn1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' ˆd (20) The explicit form of these functions can be written as C0(θ) = � l DT T l Πll+1 Π1 C10 l 0 l+1 0 � − √ 3 4π √ l + 1(−1)lP (1) l (cos θ) � (21) C1(θ) = � l DT T l Πll+1 Π1 C10 l 0 l+1 0 � − √ 3 4π √ l + 1(−1)l+1P (1) l+1(cos θ) � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' (22) Naively, we can see both angular correlation functions depend upon the first derivative of Legendre polynomials P (1) ℓ (cos θ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' This attributes to the generalization of well-studied statistical isotropic correlation function CSI(cos θ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' Noting that the magnitude of both correlation functions is not exactly the same, they differ a little as their mathematical expression suggests.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' Figure 1 represents the theoretical and simulated plots of angular correlation functions for the CMB map having anisotropy corresponding to L = 1 Doppler Boost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' The left panel displays theoretical correlation function CSI(θ) plot for Isotropic L = 0 part, C0(θ) and C1(θ) correlation functions for Doppler Boost with bν = 3 for ν = 217 GHz with β = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content='23 × 10−3 using the best-fit ΛCDM CT T l generated from CAMB (Lewis & Challinor 2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' The right panel presents the C0(θ) and C1(θ) plots obtained from 1000 realizations of Doppler Boosted maps using the same parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' The above plots show that temperature fluctuations in a Doppler-boosted map are correlated at very small angles only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' We conclude that correlation length in fluctuations in such a case is non-zero for an angle less than 1◦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' Right panel in Figure 1 displays an error bar plot for 1000 simulated maps with such nSI effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' From the plot, we conclude that Planck mission (Planck Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' 2014) with much improved resolution could manifest the doppler boost velocity signal with greater efficiency as compared to WMAP (Hinshaw et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' 2013) due to signal strength relevant at very small angles only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' We used the CoNIGS code discussed in Mukherjee & Souradeep (2014) for generating nSI maps for Doppler boost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' Estimation 10000 (0 = 7)/S(0) Co()(L = 1) 8000 Ci(0)(L = 1) 6000 (μk2) 4000 Correlation 2000 0 2000 4000 6000 10-2 10-1 100 101 102 Angle in degreesPlanck WMAP 10000 Co(o) using Doppler Boosted Map Ci(0) using Doppler Boosted Map 7500 Co(0) using Sl Map Ci(0) using SI Map 5000 Correlation (μuk2) 2500 0 2500 5000 7500 10000 10-2 10-1 100 101 102 Angle in degrees6 Dipanshu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' We discuss here the estimation of signal strength of the source of nSI effects using the real space angular correlation mBipoSH functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' The estimation of the mBipoSH functions could be written as ˆαLM λ (cos θ) = αLM λ (cos θ) + ΓLMGL λ(cos θ) , (23) where, ˆαLM λ (cos θ) is the observed mBipoSH coefficient and αLM λ (cos θ) is the mBipoSH coefficient for a SI field, which on average over an ensemble is zero for L ̸= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' ΓLMGL λ is the source of SI violation with GL λ(cos θ) as the shape factor and ΓLM is the signal strength of nSI effects like weak lensing, doppler boost, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' This estimator is an extension of the estimator defined by Hu & Okamoto (2002), Hanson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' (2009) for angle-dependent real space mBipoSH coefficients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' For the the doppler boost case, to measure the β1M , we define estimator, ˆβLM for L = 1 as ˆβ1M = � θ α1M λ (cos θ) G1 λ(cos θ) + β1M .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' (24) Where, shape factor for λ = 1 is defined as G1 1(cos θ) = � l Πl,l+1 √ 12π [(l + b) Cl − (l + 2 − b) Cl+1] C10 l0l+10 � − √ 3 4π √ l + 1(−1)lP (1) l (cos θ) � (25) To arrive at the minimum variance estimator, using the appropriate weights, we can write ˆβ1M = � θ w1 λ(cos θ)α1M λ (cos θ) G1 λ(cos θ) + β1M , (26) where w1 λ(cos θ) are the weights such that � θ wL λ (cos θ) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' These weight factors should be chosen such that it minimizes the reconstruction noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' This presents us with a unique estimator for the nSI effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' DISCUSSIONS In this letter, we proposed a natural generalization of the well-known angular correlation function that can capture non-Statistical Isotropy in sky maps of the CMB temperature fluctuations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' We invoke a reduction technique for Bipolar Spherical Harmonics that lead to new measures called Minimal Harmonics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' These new measures depict the real space angular correlation functions from the nSI sky termed as mBipoSH coefficients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' In the limits of SI, we recover the well-studied statistical isotropic correlation function of the CMB data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' As an illustrative example, we present the exact relations having mBipoSH angular correlations for the popular effect of nSI feature as doppler boost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' We systematically construct mBipoSH functions for this case, concluding in such case of nSI effect, temperature fluctuations have correlation length at very small angles only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' Through this systematic study, we have proposed that this method can be used to quantify various other signatures of SI violation in CMB data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' DG would like to thank Debabrata Adak, Rajorshi Chandra, Ritam Pal, Sayan Saha, and Shabbir Shaikh for helpful discussions during the course of this project.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' We also acknowledge the use of Healpix (Gorski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' 2005), CoNIGS Code (Mukherjee & Souradeep 2014), BipoSH code with various contributions mentioned in (Das 2019), CAMB (Lewis & Challinor 2011), Numpy (Harris et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' 2020), Scipy (Virtanen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' 2020), Matplotlib (Hunter 2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' The work of D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content='G is supported by CSIR-SRF Fellowship.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content='H is partially supported by DST-Inspire fellowship.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' 1 2 3 4 5 REFERENCES Aghanim, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' 2020, Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=', 641, A1, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content='1051/0004-6361/201833880 Copi, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=', Huterer, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=', Schwarz, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=', & Starkman, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' 2010, Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=', 2010, 847541, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content='1155/2010/847541 Das, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' 2019, arXiv preprint arXiv:1902.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content='02328 Minimal Harmonics 7 Gorski, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=', Hivon, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=', Banday, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' 2005, The Astrophysical Journal, 622, 759 Hajian, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=', & Souradeep, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' 2003, The Astrophysical Journal, 597, L5, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content='1086/379757 Hanson, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=', Rocha, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=', & G´orski, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' 2009, Monthly Notices of the Royal Astronomical Society, 400, 2169 Harris, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=', Millman, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=', van der Walt, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' 2020, Nature, 585, 357, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content='1038/s41586-020-2649-2 Hinshaw, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' 2009, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' Suppl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=', 180, 225, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content='1088/0067-0049/180/2/225 Hinshaw, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=', Larson, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=', Komatsu, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' 2013, The Astrophysical Journal Supplement Series, 208, 19 Hu, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=', & Okamoto, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' 2002, The Astrophysical Journal, 574, 566 Hunter, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' 2007, Computing in Science & Engineering, 9, 90, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content='1109/MCSE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content='2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content='55 Joshi, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=', Jhingan, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=', Souradeep, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=', & Hajian, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' 2010, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' D, 81, 083012, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content='1103/PhysRevD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content='81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content='083012 Kamionkowski, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=', & Souradeep, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' 2011, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' D, 83, 027301, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content='1103/PhysRevD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content='83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content='027301 Kumar, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=', Rotti, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=', Aich, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' 2015, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' D, 91, 043501, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content='1103/PhysRevD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content='91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content='043501 Lewis, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=', & Challinor, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' 2011, CAMB: Code for Anisotropies in the Microwave Background, Astrophysics Source Code Library, record ascl:1102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content='026.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' http://ascl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content='net/1102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content='026 Manakov, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=', Marmo, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=', & Meremianin, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' 1996, Journal of Physics B: Atomic, Molecular and Optical Physics, 29, 2711, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content='1088/0953-4075/29/13/010 Mitra, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=', Sengupta, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=', & Souradeep, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' 2004, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' D, 70, 103002, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content='1103/PhysRevD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content='70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content='103002 Mukherjee, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=', De, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=', & Souradeep, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' 2014, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' D, 89, 083005, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content='1103/PhysRevD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content='89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content='083005 Mukherjee, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=', & Souradeep, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' 2014, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' D, 89, 063013, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content='1103/PhysRevD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content='89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content='063013 Planck Collaboration, Aghanim, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=', Armitage-Caplan, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' 2014, A&A, 571, A27, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content='1051/0004-6361/201321556 Saha, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=', Shaikh, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=', Mukherjee, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=', Souradeep, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=', & Wandelt, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' 2021, JCAP, 10, 072, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content='1088/1475-7516/2021/10/072 Varshalovich, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=', Moskalev, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=', & Khersonskii, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' 1988, Quantum Theory of Angular Momentum (Singapore: World Scientific) Virtanen, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=', Gommers, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=', Oliphant, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content=' 2020, Nature Methods, 17, 261, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} +page_content='1038/s41592-019-0686-2' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/cdE3T4oBgHgl3EQfeAov/content/2301.04539v1.pdf'} diff --git a/etAzT4oBgHgl3EQfL_vx/content/tmp_files/2301.01126v1.pdf.txt b/etAzT4oBgHgl3EQfL_vx/content/tmp_files/2301.01126v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..67d5d1fb25f4ed1311ac288ac513a395891d5420 --- /dev/null +++ b/etAzT4oBgHgl3EQfL_vx/content/tmp_files/2301.01126v1.pdf.txt @@ -0,0 +1,1530 @@ +Orbital Hall physics in two-dimensional Dirac materials +Armando Pezo,∗ Diego Garc´ıa Ovalle, and Aur´elien Manchon† +Aix-Marseille Universit´e, CNRS, CINaM, Marseille, France. +(Dated: January 4, 2023) +Orbitronics has recently emerged as a very active research topic after several proposals aiming to +exploit the orbital degree of freedom for charge-free electronics. In this communication, we investi- +gate orbital transport in selected two-dimensional systems to better understand which parameters +govern the intra-atomic and inter-atomic contributions to the orbital Hall effect. +We study the +impact of the gap, the role of the materials’ topology and the influence of the disorder on spin and +orbital Hall transport. Starting from the Kane-Mele model, we describe how the orbital moment +behaves depending on the material’s topology and clarify the influence of the gap on the orbital +Hall conductivity. We then extend the study to realistic topologically trivial and non-trivial ma- +terials, and find that the topology has little qualitative influence on the orbital Hall conductivity. +In contrast, we observe that the energy dispersion has a more dramatic impact, especially in the +presence of disorder. Remarkably, our results suggest that the intra-atomic orbital Hall current is +more robust against scattering than the inter-atomic one, without further impact of the topological +properties of the system under consideration. +I. +INTRODUCTION +Recent theoretical and experimental efforts suggest +that the orbital angular momentum of electrons can be +used as an alternative degree of freedom to the spin an- +gular momentum [1–6]. In contrast with the generation +of spin currents that necessitates either a ferromagnet +or a heavy metal, orbital currents can be induced elec- +trically using light metals, thereby presenting a poten- +tial technical advantage in terms of materials scarcity +[1, 3]. Current research is being developed along two di- +rections. A first direction takes advantage of the vast ex- +perience acquired on spin transport in transition metal +heterostructures [7, 8]. +Tight-binding and first princi- +ples calculations have suggested that certain light metals +such as V, Cr or Cu can host large orbital Hall effect +[5, 9], resulting in the experimental demonstration of or- +bital torque and magnetoresistance [10–13]. In the last +years new experimental developments have unlocked the +synthesis of two-dimensional materials opening new pos- +sibilities for spintronics [14]. To date, most of the atten- +tion has been focused on graphene and transition metal +dichalcogenides, where valley Hall effect and orbital Hall +effect coexist [15–18]. +In most early theoretical studies on the orbital Hall +effect, the orbital moment was assumed to be mostly of +intra-atomic origin, adopting the so-called atom-centered +approximation (ACA) [1, 2, 5, 9, 17, 19]. However, im- +portant developments in the theory of orbital magnetism +have demonstrated that ACA is not sufficient to properly +describe the orbital motion of quasiparticles in solids and +that the inter-atomic contribution cannot be neglected +[20–23]. +Whereas the inter-atomic orbital moment is +small in the case of bulk transition metals [23], it is par- +ticularly significant in materials like graphene where the +∗ armando-arquimedes.pezo-lopez@univ-amu.fr +† aurelien.manchon@univ-amu.fr +intra-atomic orbital character of the conduction electrons +vanishes [24]. Extending the ”modern theory” of orbital +magnetization to the orbital Hall effect, it recently ap- +peared that the inter-atomic contribution cannot be ne- +glected in general [6, 16, 18]. +Building on our previous work on the modern theory +of orbital Hall effect in realistic materials [6], we inves- +tigate orbital transport in selected two-dimensional sys- +tems to better understand which parameters govern the +intra-atomic and inter-atomic contributions to the orbital +Hall effect in these systems. +In particular, we investi- +gate the impact of the gap, the role of the materials +topology and the influence of the disorder on spin and +orbital Hall transport. We find that whereas the topol- +ogy has little influence on the orbital Hall effect itself, +the orbital transport exhibits markedly distinct behav- +ior depending on the nature of the gap (spin-orbit cou- +pling, staggered potential) and systematically increases +upon reducing the gap size. Our results also show that +the intra-atomic and inter-atomic orbital Hall conduc- +tivities experience different robustness against disorder. +Whereas the inter-atomic orbital Hall contribution sys- +tematically decreases upon increasing impurity scatter- +ing, the intra-atomic contribution remains mostly unaf- +fected in the gap region and decreases in the metallic +regime, suggesting that overall the intra-atomic contribu- +tion is more robust against disorder than the inter-atomic +one. +This work is organized as follows. In Section II, we +briefly remind the concepts of the modern theory of the +orbital Hall effect and use the two-dimensional Kane- +Mele model to determine the influence of the lattice +topology on the spin and orbital Hall transport. In Sec- +tion III, we investigate the spin and orbital Hall effects +in selected two-dimensional lattices computed using den- +sity functional theory (DFT) and show that orbital Hall +transport is substantially influenced by the proximity to +the gap and by the nature of the energy dispersion. Then, +in Section IV, we investigate the impact of the Anderson- +arXiv:2301.01126v1 [cond-mat.mes-hall] 3 Jan 2023 + +2 +type disorder on the orbital Hall effect and show that +intra-atomic and inter-atomic contributions behave dif- +ferently. Conclusions and perspectives are given in Sec- +tion V. +II. +THEORY AND CONCEPTS +A. +Modern theory of the orbital Hall effect +Let us remind the concepts related to the modern the- +ory of orbital magnetization and its extension to the or- +bital Hall effect. In crystals, the orbital motion of an elec- +tron arises from the self-rotation of the wavepacket in the +unit cell which includes both the intra-atomic and inter- +atomic contributions as mentioned above. In equilibrium, +this self-rotation gives rise to the orbital magnetization as +long as the time-reversal symmetry is broken [20, 22]. In +contrast, for materials with time-reversal symmetry, an +orbital magnetization can be generated out of equilibrium +as long as inversion symmetry is broken [25]. When both +time-reversal symmetry and inversion symmetry are pre- +served though, no orbital magnetization can be induced, +and only the orbital Hall effect survives. +Let us start with the real space definition of the orbital +moment, ˆL = (ˆr× ˆp− ˆp׈r)/4. Under the parallel trans- +port gauge condition applied on non-degenerate bands +(i.e., ⟨n| ˙n⟩ = 0), this expression can be projected on the +Bloch states |un +k⟩ and recasted in the form (see [16, 26]) +⟨un +k|ˆL|up +k⟩ = +e +2gLµB Im⟨∂kun +k| × Hk|∂kup +k⟩ +− +e +4gLµB (εn +k + εp +k)Im⟨∂kun +k| × |∂kup +k⟩. (1) +Here, |un +k⟩ is the periodic part of the Bloch state asso- +ciated with the energy εn +k, ˆv = ℏ−1∂kHk is the velocity +operator, Hk being the Hamiltonian in momentum space, +µB = eℏ/2me is Bohr’s magneton and gL = 1 is Land´e’s +g-factor. This expression can be further formulated in a +more tractable identity given by +⟨un +k|ˆL|up +k⟩ = eℏ2 +4µB +Im +� +q̸=n,p +� +1 +εq +k − εn +k ++ +1 +εq +k − εp +k +� +⟨un +k|ˆv|uq +k⟩ × ⟨uq +k|ˆv|up +k⟩ . +(2) +In the Bloch state basis, the matrix element of the +orbital current operator, defined as J γ +i += 1/2{Lγ, vi}, +reads +⟨un +k|J γ +i |um +k ⟩ = 1 +2 +� +p +(⟨un +k|ˆvi|up +k⟩⟨up +k|Lγ|um +k ⟩ ++⟨un +k|Lγ|up +k⟩⟨up +k|ˆvi|um +k ⟩) , +(3) +where the orbital moment Lγ is either the atomic or- +bital moment operator (intra-atomic orbital current) or +Eq. (2) (total orbital current). In the following, we will +take Lγ = Lz since we focus on two-dimensional lattices. +In the linear response theory, spin and orbital currents +are time-reversal symmetric which allows one to consider +the intrinsic Fermi sea contribution of the Kubo formula +[27]. The orbital conductivity reads +σz +ij = −2ℏe +� +BZ +d3k +(2π)3 +� +n +fn(k)× +Im +� +m̸=n +⟨un +k|J z +i |um +k ⟩ ⟨um +k |ˆvj|un +k⟩ +(εn +k − εm +k )2 +, +(4) +where fn(k) is the equilibrium Fermi distribution func- +tion. +The quantity that multiplies the Fermi function +is usually referred to as the orbital Berry curvature, in +analogy with the conventional Berry curvature where the +orbital current operator is replaced by the velocity oper- +ator [3, 17, 28]. +B. +Orbital Hall effect in Kane-Mele model +FIG. 1. Kane-Mele model band structure for the trivial phase +with the Berry curvature displayed in the color bar (a). The +orbital moment plotted for trivial (∆ = 0.25t, λSOC = 0) (b) +and topological (∆ = 0, λSOC = 0.25t) (c) phases for the +two valence energy bands. The black (red) curve refers to the +lowest (highest) valence band. +Due to the ubiquitous presence of spin-orbit coupling +in real materials, orbital currents usually coexist with +spin currents and probing orbital-only responses is exper- +imentally challenging. +To overcome this difficulty, one +usually relies on materials with vanishing or low spin- +orbit coupling so that spin currents can be neglected +[11, 29]. In topological materials though, the topologi- +cal transition is mostly driven by the strong spin-orbit +coupling of the heavy elements, so that spin and orbital +currents are entangled. A pedagogical tool to evaluate +how these two effects behave in two-dimensional topolog- +ical materials is the Kane-Mele Hamiltonian [30]. This +model features a two-dimensional honeycomb lattice with +spin-orbit coupling and its Hamiltonian reads +H = t +� +⟨ij⟩ +c† +icj + iλSOC +� +⟨⟨ij⟩⟩ +νijc† +iszcj + ∆ +� +i +ϵic† +ici, (5) + +300 +(a) +(b) +200 +3 +100 +20 +0 +2 +-100 +10 +-200 +(n : +-300 +a +300 +a +0 +(c) +200 +L +100 +-1 +-10 +0 +no(a.l +-100 +-20 +-200 +-3 +-300 +K +M +Ki +一 +K +M +K13 +FIG. 2. (Color online) (a) Orbital Hall conductivity of the Kane-Mele model as function of ∆ for fixed values of the λSOC [0.25t +(black), 1.0t (red) and 1.5t (green)]. (b) Orbital Hall conductivity as function of λSOC with fixed values of ∆ [0.25t (black), +1.0t (red) and 1.5t (green)]. (c) Phase diagram for the orbital Hall conductivity as function of both ∆ and λSOC. Whenever +|3 +√ +3λSOC| > |∆|, the orbital Hall effect is larger than for the opposite situation. (d) Orbital Hall conductivity in the center of +the band gap as a function of ∆ (black) and λSOC (red). +where the creation and annihilation operators ci, c† +i +are spinors representing the spin degree of freedom. The +first term is the usual nearest neighbour hopping (t), the +second term is the spin-orbit coupling term (λSOC) act- +ing on the next-nearest neighbours and the last term is +the on-site staggered potential term (ϵi∆, ϵi = ±1 on +the different sublattices), also called Semenoff mass gap +[31]. This last term leads to the appearance of an orbital +magnetic moment as pointed out in Refs. [16, 28]. To il- +lustrate the connection between the Berry curvature, the +orbital magnetic moment and the orbital Hall effect, let +us consider the effective Hamiltonian of the Kane-Mele +model, valid close to the neutrality point at K and K’ +points in the Brillouin zone. In the absence of Rashba +interaction, the Kane-Mele model can be thought of as +a double copy of the Haldane model [32], each copy cor- +responding to a spin sector described by the two-band +Hamiltonian +Hηs = vF (ηkxσx + kyσy) + (∆ + ηs˜λSOC)σz, +(6) +where ˜λSOC = 3 +√ +3λSOC, σ is the pseudospin in the sub- +lattice space, s = ±1 refers to the spin projection and +η = ±1 to the K and K’ valleys, respectively. The gap is +given by ∆ηs = ∆+ηs˜λSOC so that the non-trivial regime +is reached whenever |˜λSOC| > |∆|. This Hamiltonian can +be written [25, 33] +Hηs = ˆIϵηs +k + ˆσ · dηs +k , +(7) +where ϵηs +k is the energy dispersion of the individual bands +and dηs +k +describes the hybridization between bands. +Therefore the Berry curvature and orbital magnetic mo- +ment read [25] +Ωηs +k,i = ± +εijk +2(dηs +k )3 dηs +k · +�∂dηs +k +∂kj +× ∂dηs +k +∂kk +� +, +(8) +mo,ηs +k,i += − e +ℏ +εijk +2(dηs +k )2 dηs +k · +�∂dηs +k +∂kj +× ∂dηs +k +∂kk +� +, +(9) +with ± referring to the conduction and valence band, re- +spectively and dηs +k = |dηs +k |. Equations (8) and (9) show +that the Berry curvature and the orbital magnetic mo- +ment possess a very similar structure in momentum space +[16, 20], revealing that the orbital motion finds it origin in +the Berry curvature of the Bloch states. Since the Kane- +Mele model, Eq. +(5), describes an effective four-band +model taking into account the spin degree of freedom, +the Bloch state does not carry any atomic orbital mo- +mentum (in other words, in this model the Bloch states +are typically s or pz). For this reason, the orbital moment +comes entirely from the details of the band structure in- +timately correlated to the Berry curvature, as displayed +as a color gradient in Fig. 1(a). Using the effective two- +band Hamiltonian, one obtains +Ωηs +k,z = ± +ηv2 +F ∆ηs +2(∆2ηs + v2 +F k2)3/2 , +(10) +mo,ηs +k,z = − e +2ℏ +ηv2 +F ∆ηs +∆2ηs + v2 +F k2 . +(11) +One sees that both the Berry curvature and the orbital +magnetic moment are inversely proportional to the band +gap [16]. +The Berry curvature hot-spots appearing at + +1.5 +101 +(a) +(c) +人人人人人 +1.0 +0.5 +10° +一 +0.1 +△(t) +COH( +)HO0 +LL +0.0 +10-1 +0.5 +0.01 +LL +-1.0 +1 +0.001 +10-2 +.2 +-1 +0 +1 +2 +-1.5 +-1.5 +-1.0 +0.5 +0.0 +0.5 +1.0 +1.5 +△(t) +3/3 asoc(t) +(b) +(p) +人人人人 +-)HO0 +COH( +0.1 +0.1 +soc = 0 +△=0 +0.01 +0.01 +0.001 +-1 +0 +2 +1 +2 +0.1 +1 +Λsoc, 4 +different valleys characterize the topological transition: +in the non-trivial phase both spin partners at the same +inequivalent point (K or K’) display opposite values of +the orbital moment, while they have the same sign in the +trivial regime, as seen in Fig. 1(b). +Following the procedure outlined by Bhowal and Vi- +gnale [16], the orbital Hall conductivity for spin s and +valley η reads +σηs +OH = +� e +2π +� � mev2 +F +6ℏ2gL +� +∆2 +ηs +(∆2ηs + v2 +F k2)3/2 , +(12) +Therefore, the total orbital Hall conductivity is the sum +of individuals contributions, σOH = � +η ση +OH. +In the +middle of the gap (k → 0), one retrieves the constant +value pointed out by Bhowal and Vignale [16], +σOH = +� e +2π +� � mev2 +F +3ℏ2gL +� � +1 +|∆ + ˜λSOC| ++ +1 +|∆ − ˜λSOC| +� +. +(13) +This expression indicates that the orbital Hall conductiv- +ity decreases when increasing the gap, independently of +the topological nature of the gap. To assess the interplay +between the spin-orbit coupling strength λSOC and the +staggered potential ∆, Fig. 2(a) [Fig. 2(b)] shows the or- +bital Hall conductivity as a function of ∆ (λSOC) for dif- +ferent values of λSOC (∆). We find that the orbital Hall +conductivity reaches a maximum whenever ∆ ≈ ˜λSOC, +i.e., at the topological phase transition. We note that the +orbital Hall conductivity tends to be larger in the triv- +ial phase than in the topological phase, as confirmed by +the phase diagram presented in Fig. 2(c). In this panel, +brighter regions correspond to larger values of the orbital +Hall conductivity, located in the topologically-trivial re- +gions, |∆| > |˜λSOC|. +Finally, in order to establish a connection between the +Kane-Mele model and the realistic two-dimensional ma- +terials discussed in the next section, we report the orbital +Hall conductivity as a function of the gap size in Fig. +2(d). Our calculations confirm that the orbital Hall con- +ductivity systematically decreases with the size for the +gap, be it driven by ∆ or by ˜λSOC consistently with Eq. +(13). However, we notice that when further increasing +the spin-orbit coupling above t, the orbital Hall conduc- +tivity increases again which is understood by consider- +ing the change of the band structure depicted in Fig. +3. When the staggered potential is turned off, at small +˜λSOC, the gap is located close to K and K’ points and +Eq. (13) applies. However, in the larger spin-orbit cou- +pling limit, i.e., ˜λSOC ≈ t, the gap has moved to the M +point. In this case, increasing spin-orbit coupling reduces +the gap, which leads to an enhancement of the orbital +Hall effect, as depicted in Fig. 2(d). The two situations +reported in Fig. 3 are representative of the case of ger- +manene (small ˜λSOC, Dirac cones at K and K’ points) +and bismuthene (large ˜λSOC, Dirac cone at Γ point) dis- +cussed below. +FIG. 3. Band structure for the Kane-Mele model with differ- +ent values of λSOC. In the non-trivial phase, the increasing of +spin orbit coupling not necessarily leads to the increase of the +gap, this is in connection to what is depicted in Fig. 2 (d). +III. +ORBITAL TRANSPORT IN REALISTIC 2D +MATERIALS +We now turn to the simulations performed in realistic +two-dimensional materials presenting different topologi- +cal characters. For the trivial systems, we consider two +cases: h-BN/graphene bilayer where the proximity effects +lead to the breaking of inversion symmetry [34, 35], as +well as hydrogene-decorated graphene in which a colos- +sal enhancement of the spin-orbit coupling has been pre- +dicted [36]. +For the non-trivial systems, we have se- +lected bismuthene, proven to be a topological insulator +with a sizeable gap in its buckled hexagonal structure +[37], and germanene, characterized by a buckled structure +and a large enough spin-orbit coupling capable to open +a topological gap [38, 39]. +For the DFT [40, 41] sim- +ulations, we used the Perdew-Burke-Ernzerhof [42, 43] +exchange-correlation functional. +We performed the re- +laxation with the plane-wave basis as implemented in the +Vienna Ab-initio Simulation Package (VASP) [44, 45], +and employ a plane-wave expansion cutoff of 400 eV +along with a force criterion of 0.2×10−2 eV/˚Awith a +(15 × 15 × 1) k-points sampling of the Brillouin zone. +The ionic potentials were described using the projector +augmented-wave (PAW) method [46]. Finally, the Hamil- +tonian matrix was obtained through the Wannier90 pack- +age [47]. +1. +h-BN/graphene and graphene+H +The recent proposal suggesting gapped graphene as +an orbital Hall insulator has shed light on the nature +of the valley Hall effect [16]. +Motivated by this real- +ization, we present the results on h-BN/graphene het- +erostructures. This system has been extensively studied +in the last years in several contexts [34, 48, 49]. While +free-standing graphene is a topological semimetal that +possesses a robust band structure protected by inversion + +4 +3 +2 +1 +E-Ef(a.u +asoc = 0.05t +0 +Λsoc = 0.75t +-1 +-2 +-3 +-4 +K +M +K15 +FIG. 4. (a) h-BN/graphene heterostructure electronic band structure, (b) spin Hall, (c) intra-atomic orbital Hall and (d) total +orbital Hall conductivities. The grey shaded region in (a) corresponds to the energy window where the Hall conductivities were +calculated. +symmetry, it loses this symmetry by proximity with a ma- +terial like h-BN. The whole heterostructure resembles a +Kane-Mele model in the trivial phase with a gap opening +whose size is given by the interaction with h-BN. Theo- +retically it has been shown that spin manipulation would +be possible in this scenario [35]. Most importantly for our +purpose, graphene acquires a px-py orbital hybridization +when interfaced with h-BN, which promotes the onset of +intra-atomic orbital Hall effect. The Hall conductivities +are shown in Fig. 4 where a small spin Hall effect is ob- +served [Fig. 4(b)], whereas the orbital Hall response is +one to two orders of magnitude larger. In particular, the +intra-atomic orbital Hall effect [Fig. 4(c)] displays a mod- +erate value within the energy window around the charge +neutrality point while the total orbital Hall effect, which +contains both intra- and inter-atomic contributions, [Fig. +4(d)] attains the largest value of the three Hall responses. +Notice that the energy profile of the Hall responses are +similar, as both spin and orbital Hall effects are driven +by proximity with h-BN. +We now consider graphene decorated with hydro- +gen. +The inclusion of hydrogen is enough to enhance +graphene’s spin-orbit splitting up to 100 µeV locally +[36, 50]. For this system, we have considered a 5 × 5 su- +percell with a single hydrogen atom on top at the center +of the graphene flake. The band structure is presented in +Fig. 5(a) where spin-orbit coupling was also taken into +account, showing a good agreement with previous reports +[50]. The orbital and spin textures are shown in Fig. 5(b) +and (c) respectively, for the most energetic valence bands +closer to the hydrogen states, well localized in the spec- +trum. Our results suggest a large imprinted px-py hy- +bridization which leads to the large value of the atomic +orbital momentum Lz having hot spots at inequivalent +points in the hexagonal Brillouin zone. This is encourag- +ing from the orbital transport perspective. Our calcula- +tions show that the intra-atomic orbital Hall conductiv- +ity (ACA) is around 0.6 (e/2π) whereas the total (intra- +FIG. 5. Graphene+H electronic band structure considering +spin-orbit coupling (a). Orbital texture (b) and spin texture +(b) for the most energetic valence band. +In this case the +isolated flat bands come from the Hydrogen atom. +and inter-atomic) orbital Hall conductivity is about 2.1 +(e/2π), which is comparable to the h-BN/graphene case +discussed above. In contrast, the spin Hall conductivity +is about ≈ 0.15 (e/2π), still much smaller than the or- +bital Hall effect, but one order of magnitude larger than +the spin Hall effect computed in h-BN/graphene, demon- +strating the large spin-orbit coupling enhancement in this +heterostructure. This result is remarkable especially con- +sidering that it solely arises from the interaction between +graphene and hydrogen. On the other hand, the spin tex- +ture induces a local magnetic moment of ∼1 µB, leading +to a large spin splitting. The orbital Hall effect will also + +1.5 +3 +(a) +(b) +(c) +(d) +1.0 - +2 +0.5 +1 +(eV +EF +0.0 +0 +E +-1 +-0.5 +-2 +-1.0 +-3 +-1.5 +0.00 +0.02 +0.04 +0.552 0.554 0.556 0.558 0.560 +M +K +2.54 2.55 2.56 2.57 2.58 +sz(e/2元) +Total(e/2元) +(e/2元) +Xy +xy(a) +2 +1 +E-Er(eV) +0 +E +-1 - +-2 +M +K +(b) +(c) +0.6 +0.6 +0.4 +0.4 +0.4 +0.4 +0.2 +0.2 +0.2 +0.2 - +0.0 +0.0 +0.0 - +0.0 +-0.2 +-0.2 +-0.2 +-0.2 +-0.4 - +-0.4 - +-0.4 +-0.4 +-0.6 +-0.6 +-0.5 +0.0 +0.5 +-0.5 +0.0 +0.5 +k, +1k +Nx +x6 +appear in other graphene-based heterostructures whose +band structure is tuned by proximity effects [14, 51, 52]. +2. +Germanene and bismuthene +FIG. 6. (a) Germanene projected density of states showing +the pz (green), px , py (orange) and s (blue) states as a func- +tion of the Fermi level. (b) Corresponding orbital texture for +the most energetic valence band. (c) Germanene electronic +band structure, and (d) spin (blue), intra-atomic (black) and +total orbital Hall conductivities (green). +The next material we consider is germanene which pos- +sesses a narrow gap and has a buckled structure that fa- +vors a sp3 hybridization inducing a px-py hybridization +away from the neutrality point [Fig. 6(a)] which results +in an orbital texture in momentum space [Fig. +6(b)]. +Alike Kane-Mele model with small spin-orbit coupling, +germanene possesses slightly gapped Dirac cones located +at K and K’ points [Fig. +6(c)]. +The Hall conductivi- +ties are depicted in Fig. 6(d) where the spin Hall effect +(blue) reaches a (narrow) quantized plateau at the Fermi +level, associated with the non-trivial phase. Whereas the +spin Hall conductivity is peaked close to the gap, where +the spin Berry curvature is maximum, the non-vanishing +orbital texture in germanene leads to a finite value of +the orbital Hall conductivity (intra-atomic contribution +in black, total contribution in green) on a much broader +range of energy around the gap. Notice that the total +orbital Hall effect remains smaller than the intra-atomic +Hall effect, which implies that inter-atomic and intra- +atomic contributions partially cancel each other. A par- +ticular feature of germanene (and bismuthene, see below) +is that inversion symmetry is preserved, and therefore +the total orbital Hall response has its origin in the non- +abelian nature of the Berry curvature as already shown +[18]. +FIG. 7. (a) Bismuthene electronic band structure. (b) Spin +(blue), intra-atomic (black) and total orbital Hall conductiv- +ities (green). (c) Orbital moment calculated for the two most +(red and black) and two less energetic (blue and green) bands +along the M − K − Γ − M kpath. +The last system we consider is buckled bismuthene, +which displays a much larger gap than germanene due +to a much larger spin-orbit coupling [Fig. +7(a)]. +In +this crystalline phase, bismuthene’s band character is in- +verted at Γ point due to spin-orbit coupling, following +the same process as described in the Bernevig-Hughes- +Zhang model [53, 54], exemplified above by the Kane- +Mele model with strong spin-orbit coupling (see Fig. 3). +This change in the band structure allows for a strong +s-character at this point in reciprocal space leading to +a quenched orbital texture [55]. The spin, intra-atomic +and total orbital Hall conductivities are displayed on Fig. +7(b). The absence of an orbital texture in terms of the +px and py near the gap leads to a vanishingly smaller +intra-atomic orbital Hall effect (black), which increases +away from the gap due to enhanced px-py hybridization. +In contrast, the total orbital Hall conductivity reaches +a large value (green), even larger than that of the spin +Hall conductivity (blue). These larger values can be un- +derstood by looking at the orbital moment distribution +along the momentum path M −K −Γ−M shown in Fig. +7(c). The hot-spots located at the Γ-point lead to a larger +value of the total orbital Hall conductivity compared to + +(b) +Pz +0.7 +0.4 +0.75 +px + p. +0.6 +0.50 +s +0.2 +0.5 +DoS(a.u) +0.25 +0.4 +1 ( +0.00 +0.0 +'y +0.3 +-0.25 +-0.2 +0.2 +-0.50 +0.1 +-0.75 +-0.4 +0.0 +-2 +-1 +0 +1 +2 +-0.5 +0,0 +0.5 +(c) +(d) +1.5 +1.5 +6000000000000000000 +1.0 +1.0 +0.5 +0.5 +0.0 +0.0 +E +-0.5 +0.5 +0000000000000d +-1.0 +1.0 +0000000 +-1.5 +r +M +K +-2 +-1 +0 +2 +Spin/Orbital Hall Conductivity(e/2rt)1.5 +1.5 +(a) +(b) +1.0 - +1.0 +0.5 +0.5 +E-Ef(eV) +0.0 - +0.0 - +E +-0.5 +0.5 +-1.0 +1.0 +-1.5 +1.5 +M +r +K +0 +1 +2 +3 +Spin/Orbital Hall Conductivity(e/2r) +(c) +250 +200 +150 +2 +100 +mo(eV.A2 +50 +0 +- +50 +-100 +M +K +L +M7 +the spin one. Notice that the spin conductivity is quan- +tized, whereas the total orbital conductivity is not. We +mention in passing that it has been recently suggested +that such non-quantized plateaus are related to high- +order topological insulating behavior [56]. +Hence, the +overall scenario in bismuthene contrasts markedly with +that in germanene and follows the situation discussed in +the previous section using the Kane-Mele model. Con- +sequently, from a materials’ perspective, we are able to +draw differences on the orbital response based on details +of their band structures and orbital character. +IV. +IMPACT OF DISORDER ON ORBITAL +HALL TRANSPORT +An important question that remains unanswered at +this point is the impact of disorder-induced scattering on +the orbital conductivity. As a matter of fact, a simple- +minded rationale suggests that the intra-atomic orbital +Hall effect, which arises from the atomic orbital moment, +would be less sensitive to momentum scattering than the +inter-atomic orbital Hall effect, which arises from self- +rotation of the electron wave packet in the unit cell. +To investigate the impact of disorder, we consider three +different systems: germanene, h-BN/graphene, the two +narrow-gap semiconductors studied above, and MoS2, a +large band gap semiconductor that has been predicted +to be an orbital Hall insulator [6, 17]. From the tight- +binding basis obtained by ab initio simulations, we in- +troduce disorder by the inclusion of an on-site Anderson +disorder which can be expressed mathematically like +H = H0 + +� +i +Vi, +(14) +where H0 is the bare Hamiltonian corresponding to a +10 × 10 supercell and Vi is an onsite potential acting on +the i site with values [−1, 1]eV . We calculated the Hall +conductivity for 40 random realizations of every fixed set +of parameters. +The +results +obtained +for +germanene +and +h- +BN/graphene are depicted in Fig. +8 (a,b) and (c,d), +respectively. +To understand how disorder affects the +orbital transport, +we have considered two different +transport regimes: (i) the single band case, where the +carrier’s energy to close to the gap, ε = 0.1 eV (solid +lines), and (ii) the multiband case, where the carrier’s +energy is far from the gap, ε = −3.0 eV (dashed lines). +In the former, the band dispersion is mostly linear +and the longitudinal conductivity of germanene (a) +and h-BN/graphene (c) slowly decays as a function of +disorder due to enhanced scattering. In contrast, when +the energy lies far from the gap, in the multiband case +(dashed), the conductivity decay is more dramatic, as +expected in conventional metals. We have also computed +the intra-atomic and total orbital Hall conductivities +for these different situations (b, d). To better visualize +the effect of disorder, we report the ratio between +FIG. 8. (a,c) Longitudinal conductivity and (b,d) orbital Hall +conductivity near the Fermi level (ε = 0.1 eV) for germanene +(a,b) and h-BN/graphene (c,d) as a function of the disorder +concentration, the values plot correspond to the ratio orbital +Hall conductivity over its maximum value σ0 +OH in the pristine +case. We computed both the intra-atomic (ACA - red) and +total contributions (green). The inset in (a) shows a sketch +of a disorder realization in the lattice. +the Hall conductivities with and without disorder, +σOH/σ0 +OH. In the single band transport regime, we find +that the intra-atomic conductivity (red) is mostly flat, +independent on the disorder. +Nonetheless, the total +orbital Hall effect (green), which contrains both intra- +and inter-atomic contributions, is as a whole much +more sensitive to disorder and decreases continuously. +In fact, the intra-atomic Hall effect is controlled by +the orbital Berry curvature of the single band and is +therefore expected to be rather robust against disorder +whereas the inter-atomic Hall effect, which arises from +self-rotation of the wave packet in the unit cell is much +more sensitive to onsite energy fluctuations brought by +Anderson disorder. +In the multiband transport regime (dashed lines), we +find that both the intra-atomic and total orbital Hall ef- +fect decay at a similar rate. This distinct behavior sug- +gests that the linear dispersion of the single band trans- +port regime has a strong impact on the robustness of the +intra-atomic orbital Hall effect. In contrast, the total or- +bital Hall effect, that contains the inter-atomic contribu- +tion, is much more sensitive to Anderson-type disorder. +We must note that the intra-atomic contribution is larger +than the total one in the case of germanene while the op- +posite is true for h-BN/graphene. This result indicates +that the inter-atomic contribution is much more sensitive +to disorder than the intra-atomic one, irrespective of the +transport regime. +We now turn our attention to MoS2, a large band gap +orbital Hall insulator studied previously [6, 19]. +The +band structure and orbital Hall conductivity are reported +in insert for reference. Here, we fix the carrier’s energy +at ε=1.5 eV above the center of the gap in a region where +the energy dispersion is quadratic. The value of the con- + +1.0 +(a) +(b) +1.4 +0.8 +H1.2 +0.6 +6 +1.0 +0.4 +6 +0.8 +0.2 +0.6 - +0.0 +0 +20 +40 +60 +80 +100 +0 +20 +40 +60 +80 +100 +0.6 +(c) +(d) 1.4 +0.5 +H1.2 +0.4 +6 +1.0 +0.3 +6 +0.2 +0.8 +0.1 +0.6 +0.0 +20 +0 +40 +60 +80 +100 +20 +40 +60 +0 +80 +100 +Disorder (%) +Disorder (%)8 +FIG. 9. +(a) Longitudinal conductivity for an energy of 1.5 eV +with respect to the zero energy (middle of the gap) defined +as the Fermi level. (b) Orbital Hall conductivities over the +maximum value (σ0 +OH)in the pristine system, calculated by +the Kubo formula in a 10×10 supercell containing Anderson +type disorder, intra-atomic Hall conductivity (ACA) and total +orbital Hall conductivity are depicted with dashed lines for +an energy of 1.5 eV with respect to the zero energy defined +as the Fermi level. +The solid lines correspond to the Hall +conductivites calculated the Fermi level. The inset shows the +actual values of the orbital conductivity for both intra-atomic +and total responses. +ductivity decreases rapidly with increasing the impurity +concentration, as expected in a conventional, leading to +a decay over about two orders of magnitude, quite differ- +ent from linearly dispersing narrow-gap germanene and +graphene/hBN. The behaviour of the (normalized) or- +bital Hall conductivities is depicted in Fig. 9(b) where +dashed lines correspond to a transport energy of ε=1.5 +eV and the solid lines correspond to a transport energy +taken in the middle of the gap. The inset shows the ab- +solute values for reference. +The behavior we obtain is +qualitatively similar to the one observed in the narrow- +gap semiconductors discussed previously. In the gap, the +intra-atomic orbital Hall conductivity (solid red) is in- +sensitive to disorder, as expected from a Berry-curvature +driven effect, whereas the total orbital Hall conductivity +decays. It has been argued recently that the in-gap intra- +atomic orbital Hall conductivity is associated with intra- +atomic orbital polarized edge states [17, 19] that remain +insensitive to the disorder, although this picture might +change when considering open boundary conditions like +in nanoribbons for instance [57]. This contrasts to what +we find for the total Hall response where a drop of nearly +half of the initial value is observed. When the energy +is set in the conduction band, one finds that both intra- +atomic and total orbital Hall conductivities decrease with +a similar rate, as already observed in narrow-gap semi- +conductors. +V. +CONCLUSION +To summarize, we have explored the microscopic ori- +gin of the orbital Hall effect in model and realistic two- +dimensional Dirac materials. Since the orbital Hall ef- +fect is intimately connected with the Berry curvature of +the material, we first investigated the inter-atomic orbital +Hall contribution in the Kane-Mele model, that accom- +modates topological phase transition and in which the +intra-atomic contribution is absent. We found that al- +though the orbital moment itself behaves differently in +the topologically trivial and non-trivial phases, the re- +sulting orbital Hall conductivity is rather controlled by +the size of the gap, irrespective of its topological nature. +We then studied the orbital Hall effect in selected two- +dimensional materials, starting with graphene. Whereas +orbital Hall effect is absent of pristine graphene, it can +be turned on by inducing a global or local gap, either +interfacing graphene with h-BN or by using hydrogen +adatoms, respectively. In these cases, the emergence of +orbital and spin textures in reciprocal space stand out +as key ingredients for the generation of orbital and spin +polarized Hall currents. These predictions are particu- +larly intriguing given that these two systems are made +out of light elements unable to portray a sizeable spin- +orbit coupling by their own. +We then moved on to investigate the orbital Hall cur- +rents in two selected two-dimensional topological insu- +lators, germanene and bismuthene, which represent two +distinct realizations of the Kane-Mele model, with weak +and strong spin-orbit coupling, respectively. +In ger- +manene, we have found that the intra-atomic orbital Hall +contribution displays a larger value than of the total or- +bital Hall one, resembling the weakly spin-orbit coupled +non-trivial phase of the Kane-Mele model (small spin- +orbit gaps at K and K’ points). +The existence of the +quantum spin Hall effect in germanene is corroborated +with a narrow plateau appearing for the spin Hall con- +ductivity while the values for the orbital Hall effect re- +mains larger in a broader energy window. In bismuthene, +besides the spin Hall effect, we have found a large orbital +Hall conductivity coming from the orbital moment car- +ried out by the bands near the Fermi level. This situa- +tion resembles the strongly spin-orbit coupled non-trivial +phase of the Kane-Mele model (large spin-orbit gap at M +point). +Finally, we investigated the impact of disorder on the +intra-atomic and inter-atomic contributions of the or- + +(a) +0.4 +(eV) +— ACA +0.3 - +0 +_ Total +1 +-2 +0.2 +3 +M +-2.5 +0.0 +2.5 +5.0 +7.5 +10.0 +OHC(e/2) +0.1 +0.0 - +0 +20 +40 +60 +80 +100 +(b) +6 +3.0 +4 +2.5 +ACA +3 +2 + Total +2.0 - +1 +0 +-1 +1.5 +-2 +20 +40 +60 +80 +100 +Disorder (%) +1.0 +0.5 +0.0 +0 +20 +40 +60 +80 +100 +Disorder (%)9 +bital Hall effect in two-dimensional systems featuring +very different transport regimes (insulating, single-band +and multiband metallic regimes). We find that the intra- +atomic orbital Hall effect tends to be less affected by +disorder than the total orbital Hall effect, especially in +the insulating and single-band regimes, i.e., in situa- +tions where the orbital Berry curvature is smooth and +well-defined. +In contrast, in the multiband transport +regime, both intra-atomic contribution and total orbital +conductivity. These results suggest that irrespective of +the transport regime, the intra-atomic part of the orbital +Hall effect is more robust than the inter-atomic part. +The present work sheds light on the mechanisms re- +sponsible for orbital Hall effect in two-dimensional mate- +rials, and in particular clarifies the role of the gap. The +intimate connection between the orbital Hall transport +and the Berry curvature of the band structure opens in- +teresting perspectives for the external control of the or- +bital transport through interfacial engineering or strain, +as demonstrated in Ref.[58]. From this standpoint Van +der Waals heterostructures made of light materials, such +as graphene and h-BN for instance, could be used for +the realization of nonlocal orbital devices, akin to the +all-electric valley or spin Hall transistor [59, 60]. In this +context, a more comprehensive understanding of the or- +bital relaxation induced by momentum scattering is nec- +essary. +VI. +ACKNOWLEDGMENTS +This work was supported by the ANR ORION project, +grant ANR-20-CE30-0022-01 of the French Agence Na- +tionale de la Recherche. D. G.O. and A. M. acknowl- +edge support from the Excellence Initiative of Aix- +Marseille Universit´e - A*Midex, a French ”Investisse- +ments d’Avenir” program. +[1] B. A. Bernevig, T. L. Hughes, and S.-c. Zhang, Physical +Review Letters 95, 066601 (2005). +[2] H. Kontani, T. Tanaka, D. Hirashima, K. Yamada, and +J. Inoue, Physical Review Letters 102, 016601 (2009). +[3] D. Go, D. Jo, C. Kim, and H. W. Lee, Physical Review +Letters 121, 086602 (2018). +[4] M. Hayashi, J. Ieda, Y. Yamane, J.-i. Ohe, Y. K. Taka- +hashi, S. Mitani, and S. Maekawa, Physical Review Let- +ters 108, 147202 (2012). +[5] L. Salemi and P. M. Oppeneer, Physical Review Materials +6, 095001 (2022), arXiv:2203.17037. +[6] A. Pezo, D. Garc´ıa Ovalle, and A. Manchon, Phys. Rev. +B 106, 104414 (2022). +[7] E. Y. Vedmedenko, R. K. Kawakami, D. D. Sheka, +P. Gambardella, A. Kirilyuk, A. Hirohata, C. Binek, +O. Chubykalo-Fesenko, S. Sanvito, B. J. Kirby, J. Grol- +lier, K. Everschor-Sitte, T. Kampfrath, C. Y. You, and +A. Berger, Journal of Physics D: Applied Physics 53, +453001 (2020). +[8] A. V. Chumak, V. I. Vasyuchka, A. A. Serga, +and +B. Hillebrands, Nature Physics 11, 453 (2015). +[9] D. Jo, D. Go, +and H.-w. Lee, Physical Review B 98, +214405 (2018). +[10] D. Go and H.-w. Lee, Physical Review Research 2, 13177 +(2020). +[11] S. Ding, A. Ross, D. Go, L. Baldrati, Z. Ren, F. Freimuth, +S. +Becker, +F. +Kammerbauer, +J. +Yang, +G. +Jakob, +Y. Mokrousov, +and M. Kl¨aui, Physical Review Letters +125, 177201 (2020), arXiv:2006.03649. +[12] D. Lee, D. Go, H. J. Park, W. Jeong, H. W. Ko, D. Yun, +D. Jo, S. Lee, G. Go, J. H. Oh, K. J. Kim, B. G. Park, +B. C. Min, H. C. Koo, H. W. Lee, O. J. Lee, and K. J. +Lee, Nature Communications 12, 6710 (2021). +[13] S. Ding, Z. Liang, D. Go, C. Yun, M. Xue, Z. Liu, +S. Becker, W. Yang, H. Du, C. Wang, Y. Yang, G. Jakob, +M. Kl¨aui, Y. Mokrousov, and J. Yang, Physical Review +Letters 128, 067201 (2022), arXiv:2105.04495. +[14] S. Roche, +J. ˚Akerman, +B. Beschoten, +J. C. Char- +lier, M. Chshiev, S. P. Dash, B. Dlubak, J. Fabian, +A. Fert, +M. Guimar˜aes, +F. Guinea, +I. Grigorieva, +C. Sch¨onenberger, P. Seneor, C. Stampfer, S. O. Valen- +zuela, X. Waintal, +and B. Van Wees, 2D Materials 2, +030202 (2015). +[15] D. Xiao, G.-B. Liu, W. Feng, X. Xu, and W. Yao, Phys- +ical Review Letters 108, 196802 (2012). +[16] S. Bhowal and G. Vignale, Physical Review B 103, +195309 (2021), arXiv:2103.03148. +[17] T. P. Cysne, M. Costa, L. M. Canonico, M. Buon- +giorno +Nardelli, +R. +B. +Muniz, +and +T. +G. +Rap- +poport, Physical Review Letters 127, 056601 (2021), +arXiv:arXiv:2010.07894v2. +[18] T. P. Cysne, +S. Bhowal, +G. Vignale, +and T. G. +Rappoport, Physical Review B 105, 195421 (2022), +arXiv:2201.03491. +[19] L. M. Canonico, T. P. Cysne, A. Molina-Sanchez, R. B. +Muniz, and T. G. Rappoport, Physical Review B 101, +161409(R) (2020), arXiv:2001.03592. +[20] T. +Thonhauser, +D. +Ceresoli, +D. +Vanderbilt, +and +R. Resta, Physical Review Letters 95, 137205 (2005), +arXiv:0505518 [cond-mat]. +[21] D. Ceresoli, T. Thonhauser, D. Vanderbilt, and R. Resta, +Physical Review B 74, 024408 (2006), arXiv:0512142 +[cond-mat]. +[22] J. Shi, G. Vignale, D. Xiao, and Q. Niu, Physical Review +Letters 99, 197202 (2007). +[23] J. Hanke, F. Freimuth, A. K. Nandy, H. Zhang, S. Bl, +Y. Mokrousov, +and P. Gr, Physical Review B 94, +121114(R) (2016). +[24] J. Liu and X. Dai, Nature Reviews Physics 3, 367 (2021). +[25] T. Yoda, T. Yokoyama, and S. Murakami, Nano Letters +18, 916 (2018). +[26] E. I. Blount, Solid State Physics 13, 305 (1962). +[27] V. Bonbien and A. Manchon, Physical Review B 102, +085113 (2020). +[28] S. Bhowal and S. Satpathy, Physical Review B 101, +121112(R) (2020). +[29] S. Ding, Z. Liang, D. Go, C. Yun, M. Xue, Z. Liu, +S. Becker, W. Yang, H. Du, C. Wang, Y. Yang, G. Jakob, + +10 +M. Kl¨aui, Y. Mokrousov, +and J. Yang, arXiv preprint +arxiv:2105.04495 (2021), arXiv:2105.04495. +[30] C. L. Kane and E. J. Mele, Physical Review Letters 95, +226801 (2005). +[31] G. W. Semenoff, Phys. Rev. Lett. 53, 2449 (1984). +[32] F. Haldane, Physical Review Letters 61, 2015 (1988). +[33] X.-L. Qi, Y.-S. Wu, and S.-C. Zhang, Phys. Rev. B 74, +085308 (2006). +[34] J. Wang, F. Ma, and M. Sun, RSC Adv. 7, 16801 (2017). +[35] K. Zollner, A. W. Cummings, S. Roche, and J. Fabian, +Phys. Rev. B 103, 075129 (2021). +[36] M. Gmitra, D. Kochan, and J. Fabian, Phys. Rev. Lett. +110, 246602 (2013). +[37] Y. Guo, F. Pan, M. Ye, X. Sun, Y. Wang, J. Li, X. Zhang, +H. Zhang, Y. Pan, Z. Song, J. Yang, +and J. Lu, ACS +Applied Materials and Interfaces 9, 23128 (2017). +[38] A. Acun, L. Zhang, P. Bampoulis, M. Farmanbar, A. Van +Houselt, A. N. Rudenko, M. Lingenfelder, G. Brocks, +B. Poelsema, M. I. Katsnelson, +and H. J. Zandvliet, +Journal of Physics Condensed Matter 27, 443002 (2015). +[39] M. Ezawa, Journal of the Physical Society of Japan 84, +1 (2015), arXiv:1503.0891. +[40] P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 +(1964). +[41] W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965). +[42] J. P. Perdew, J. A. Chevary, S. H. Vosko, K. A. Jackson, +M. R. Pederson, D. J. Singh, and C. Fiolhais, Phys. Rev. +B 46, 6671 (1992). +[43] J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. +Lett. 77, 3865 (1996). +[44] G. Kresse and J. Furthm¨uller, Comput. Mater. Sci. 6, 15 +(1996). +[45] G. Kresse and J. Furthm¨uller, Phys. Rev. B 54, 11169 +(1996). +[46] G. Kresse and D. Joubert, Phys. Rev. B 59, 1758 (1999). +[47] G. Pizzi, V. Vitale, R. Arita, S. Bl¨ugel, F. Freimuth, +G. G´eranton, M. Gibertini, D. Gresch, C. Johnson, +T. Koretsune, J. Ibanez-Azpiroz, H. Lee, J. M. Lihm, +D. Marchand, A. Marrazzo, Y. Mokrousov, J. I. Mustafa, +Y. Nohara, Y. Nomura, L. Paulatto, S. Ponc´e, T. Pon- +weiser, J. Qiao, F. Th¨ole, S. S. Tsirkin, M. Wierzbowska, +N. Marzari, D. Vanderbilt, I. Souza, A. A. Mostofi, and +J. R. Yates, Journal of Physics Condensed Matter 32, +165902 (2020), arXiv:1907.09788. +[48] X. Sun, S. Zhang, Z. Liu, H. Zhu, J. Huang, K. Yuan, +Z. Wang, K. Watanabe, T. Taniguchi, X. Li, M. Zhu, +J. Mao, T. Yang, J. Kang, J. Liu, Y. Ye, Z. V. Han, and +Z. Zhang, Nature Communications 12, 7196 (2021). +[49] J. +Salvador-S´anchez, +L. +M. +Canonico, +A. +P´erez- +Rodr´ıguez, T. P. Cysne, Y. Baba, V. Cleric`o, M. Vila, +D. +Vaquero, +J. +A. +Delgado-Notario, +J. +M. +Cari- +dad, +K. +Watanabe, +T. +Taniguchi, +R. +A. +Molina, +F. Dom´ınguez-Adame, S. Roche, E. Diez, T. G. Rap- +poport, and M. Amado, “Generation and control of non- +local chiral currents in graphene superlattices by orbital +hall effect,” (2022). +[50] D. Soriano, D. V. Tuan, S. M.-M. Dubois, M. Gmitra, +A. W. Cummings, D. Kochan, F. Ortmann, J.-C. Char- +lier, J. Fabian, +and S. Roche, 2D Materials 2, 022002 +(2015). +[51] W. Han, R. K. Kawakami, M. Gmitra, +and J. Fabian, +Nature nanotechnology 9, 794 (2014). +[52] A. Pezo, Z. Zanolli, N. Wittemeier, P. Ordej´on, A. Fazzio, +S. Roche, +and J. H. Garcia, 2D Materials 9, 015008 +(2021). +[53] B. A. Bernevig, T. L. Hughes, and S.-C. Zhang, Science +314, 1757 (2006). +[54] A. Zhao and B. Wang, APL Materials 8, 030701 (2020), +https://doi.org/10.1063/1.5135984. +[55] G. Li, W. Hanke, E. M. Hankiewicz, F. Reis, J. Sch¨afer, +R. Claessen, C. Wu, and R. Thomale, Phys. Rev. B 98, +165146 (2018). +[56] M. Costa, B. Focassio, T. P. Cysne, L. M. Canon- +ico, G. R. Schleder, R. B. Muniz, A. Fazzio, +and +T. G. Rappoport, “Connecting higher-order topology +with the orbital hall effect in monolayers of transition +metal dichalcogenides,” (2022). +[57] A. Pezo, M. P. Lima, M. Costa, +and A. Fazzio, Phys. +Chem. Chem. Phys. 21, 11359 (2019). +[58] J. Son, K. H. Kim, Y. H. Ahn, H. W. Lee, +and +J. Lee, Physical Review Letters 123, 36806 (2019), +arXiv:1907.00010. +[59] R. V. Gorbachev, J. C. W. Song, G. L. Yu, a. V. Kretinin, +F. Withers, Y. Cao, A. Mishchenko, I. V. Grigorieva, +K. S. Novoselov, L. S. Levitov, and a. K. Geim, Science +(New York, N.Y.) 346, 448 (2014). +[60] W. Y. Choi, H.-j. Kim, J. Chang, S. H. Han, A. Abbout, +H. Ben, M. Saidaoui, K.-j. Lee, +and H. C. Koo, Nano +Letters 18, 7998 (2018). + diff --git a/etAzT4oBgHgl3EQfL_vx/content/tmp_files/load_file.txt b/etAzT4oBgHgl3EQfL_vx/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..8151cef14a20090332e313dee0c19883ea552371 --- /dev/null +++ b/etAzT4oBgHgl3EQfL_vx/content/tmp_files/load_file.txt @@ -0,0 +1,1066 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf,len=1065 +page_content='Orbital Hall physics in two-dimensional Dirac materials Armando Pezo,∗ Diego Garc´ıa Ovalle, and Aur´elien Manchon† Aix-Marseille Universit´e, CNRS, CINaM, Marseille, France.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' (Dated: January 4, 2023) Orbitronics has recently emerged as a very active research topic after several proposals aiming to exploit the orbital degree of freedom for charge-free electronics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' In this communication, we investi- gate orbital transport in selected two-dimensional systems to better understand which parameters govern the intra-atomic and inter-atomic contributions to the orbital Hall effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' We study the impact of the gap, the role of the materials’ topology and the influence of the disorder on spin and orbital Hall transport.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Starting from the Kane-Mele model, we describe how the orbital moment behaves depending on the material’s topology and clarify the influence of the gap on the orbital Hall conductivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' We then extend the study to realistic topologically trivial and non-trivial ma- terials, and find that the topology has little qualitative influence on the orbital Hall conductivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' In contrast, we observe that the energy dispersion has a more dramatic impact, especially in the presence of disorder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Remarkably, our results suggest that the intra-atomic orbital Hall current is more robust against scattering than the inter-atomic one, without further impact of the topological properties of the system under consideration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' INTRODUCTION Recent theoretical and experimental efforts suggest that the orbital angular momentum of electrons can be used as an alternative degree of freedom to the spin an- gular momentum [1–6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' In contrast with the generation of spin currents that necessitates either a ferromagnet or a heavy metal, orbital currents can be induced elec- trically using light metals, thereby presenting a poten- tial technical advantage in terms of materials scarcity [1, 3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Current research is being developed along two di- rections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' A first direction takes advantage of the vast ex- perience acquired on spin transport in transition metal heterostructures [7, 8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Tight-binding and first princi- ples calculations have suggested that certain light metals such as V, Cr or Cu can host large orbital Hall effect [5, 9], resulting in the experimental demonstration of or- bital torque and magnetoresistance [10–13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' In the last years new experimental developments have unlocked the synthesis of two-dimensional materials opening new pos- sibilities for spintronics [14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' To date, most of the atten- tion has been focused on graphene and transition metal dichalcogenides, where valley Hall effect and orbital Hall effect coexist [15–18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' In most early theoretical studies on the orbital Hall effect, the orbital moment was assumed to be mostly of intra-atomic origin, adopting the so-called atom-centered approximation (ACA) [1, 2, 5, 9, 17, 19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' However, im- portant developments in the theory of orbital magnetism have demonstrated that ACA is not sufficient to properly describe the orbital motion of quasiparticles in solids and that the inter-atomic contribution cannot be neglected [20–23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Whereas the inter-atomic orbital moment is small in the case of bulk transition metals [23], it is par- ticularly significant in materials like graphene where the ∗ armando-arquimedes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='pezo-lopez@univ-amu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='fr † aurelien.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='manchon@univ-amu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='fr intra-atomic orbital character of the conduction electrons vanishes [24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Extending the ”modern theory” of orbital magnetization to the orbital Hall effect, it recently ap- peared that the inter-atomic contribution cannot be ne- glected in general [6, 16, 18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Building on our previous work on the modern theory of orbital Hall effect in realistic materials [6], we inves- tigate orbital transport in selected two-dimensional sys- tems to better understand which parameters govern the intra-atomic and inter-atomic contributions to the orbital Hall effect in these systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' In particular, we investi- gate the impact of the gap, the role of the materials topology and the influence of the disorder on spin and orbital Hall transport.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' We find that whereas the topol- ogy has little influence on the orbital Hall effect itself, the orbital transport exhibits markedly distinct behav- ior depending on the nature of the gap (spin-orbit cou- pling, staggered potential) and systematically increases upon reducing the gap size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Our results also show that the intra-atomic and inter-atomic orbital Hall conduc- tivities experience different robustness against disorder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Whereas the inter-atomic orbital Hall contribution sys- tematically decreases upon increasing impurity scatter- ing, the intra-atomic contribution remains mostly unaf- fected in the gap region and decreases in the metallic regime, suggesting that overall the intra-atomic contribu- tion is more robust against disorder than the inter-atomic one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' This work is organized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' In Section II, we briefly remind the concepts of the modern theory of the orbital Hall effect and use the two-dimensional Kane- Mele model to determine the influence of the lattice topology on the spin and orbital Hall transport.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' In Sec- tion III, we investigate the spin and orbital Hall effects in selected two-dimensional lattices computed using den- sity functional theory (DFT) and show that orbital Hall transport is substantially influenced by the proximity to the gap and by the nature of the energy dispersion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Then, in Section IV, we investigate the impact of the Anderson- arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='01126v1 [cond-mat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='mes-hall] 3 Jan 2023 2 type disorder on the orbital Hall effect and show that intra-atomic and inter-atomic contributions behave dif- ferently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Conclusions and perspectives are given in Sec- tion V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' THEORY AND CONCEPTS A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Modern theory of the orbital Hall effect Let us remind the concepts related to the modern the- ory of orbital magnetization and its extension to the or- bital Hall effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' In crystals, the orbital motion of an elec- tron arises from the self-rotation of the wavepacket in the unit cell which includes both the intra-atomic and inter- atomic contributions as mentioned above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' In equilibrium, this self-rotation gives rise to the orbital magnetization as long as the time-reversal symmetry is broken [20, 22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' In contrast, for materials with time-reversal symmetry, an orbital magnetization can be generated out of equilibrium as long as inversion symmetry is broken [25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' When both time-reversal symmetry and inversion symmetry are pre- served though, no orbital magnetization can be induced, and only the orbital Hall effect survives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Let us start with the real space definition of the orbital moment, ˆL = (ˆr× ˆp− ˆp׈r)/4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Under the parallel trans- port gauge condition applied on non-degenerate bands (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=', ⟨n| ˙n⟩ = 0), this expression can be projected on the Bloch states |un k⟩ and recasted in the form (see [16, 26]) ⟨un k|ˆL|up k⟩ = e 2gLµB Im⟨∂kun k| × Hk|∂kup k⟩ − e 4gLµB (εn k + εp k)Im⟨∂kun k| × |∂kup k⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' (1) Here, |un k⟩ is the periodic part of the Bloch state asso- ciated with the energy εn k, ˆv = ℏ−1∂kHk is the velocity operator, Hk being the Hamiltonian in momentum space, µB = eℏ/2me is Bohr’s magneton and gL = 1 is Land´e’s g-factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' This expression can be further formulated in a more tractable identity given by ⟨un k|ˆL|up k⟩ = eℏ2 4µB Im � q̸=n,p � 1 εq k − εn k + 1 εq k − εp k � ⟨un k|ˆv|uq k⟩ × ⟨uq k|ˆv|up k⟩ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' (2) In the Bloch state basis, the matrix element of the orbital current operator, defined as J γ i = 1/2{Lγ, vi}, reads ⟨un k|J γ i |um k ⟩ = 1 2 � p (⟨un k|ˆvi|up k⟩⟨up k|Lγ|um k ⟩ +⟨un k|Lγ|up k⟩⟨up k|ˆvi|um k ⟩) , (3) where the orbital moment Lγ is either the atomic or- bital moment operator (intra-atomic orbital current) or Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' (2) (total orbital current).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' In the following, we will take Lγ = Lz since we focus on two-dimensional lattices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' In the linear response theory, spin and orbital currents are time-reversal symmetric which allows one to consider the intrinsic Fermi sea contribution of the Kubo formula [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' The orbital conductivity reads σz ij = −2ℏe � BZ d3k (2π)3 � n fn(k)× Im � m̸=n ⟨un k|J z i |um k ⟩ ⟨um k |ˆvj|un k⟩ (εn k − εm k )2 , (4) where fn(k) is the equilibrium Fermi distribution func- tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' The quantity that multiplies the Fermi function is usually referred to as the orbital Berry curvature, in analogy with the conventional Berry curvature where the orbital current operator is replaced by the velocity oper- ator [3, 17, 28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Orbital Hall effect in Kane-Mele model FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Kane-Mele model band structure for the trivial phase with the Berry curvature displayed in the color bar (a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' The orbital moment plotted for trivial (∆ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='25t, λSOC = 0) (b) and topological (∆ = 0, λSOC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='25t) (c) phases for the two valence energy bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' The black (red) curve refers to the lowest (highest) valence band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Due to the ubiquitous presence of spin-orbit coupling in real materials, orbital currents usually coexist with spin currents and probing orbital-only responses is exper- imentally challenging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' To overcome this difficulty, one usually relies on materials with vanishing or low spin- orbit coupling so that spin currents can be neglected [11, 29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' In topological materials though, the topologi- cal transition is mostly driven by the strong spin-orbit coupling of the heavy elements, so that spin and orbital currents are entangled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' A pedagogical tool to evaluate how these two effects behave in two-dimensional topolog- ical materials is the Kane-Mele Hamiltonian [30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' This model features a two-dimensional honeycomb lattice with spin-orbit coupling and its Hamiltonian reads H = t � ⟨ij⟩ c† icj + iλSOC � ⟨⟨ij⟩⟩ νijc† iszcj + ∆ � i ϵic† ici, (5) 300 (a) (b) 200 3 100 20 0 2 100 10 200 (n : 300 a 300 a 0 (c) 200 L 100 1 10 0 no(a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='l 100 20 200 3 300 K M Ki 一 K M K13 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' (Color online) (a) Orbital Hall conductivity of the Kane-Mele model as function of ∆ for fixed values of the λSOC [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='25t (black), 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='0t (red) and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='5t (green)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' (b) Orbital Hall conductivity as function of λSOC with fixed values of ∆ [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='25t (black), 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='0t (red) and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='5t (green)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' (c) Phase diagram for the orbital Hall conductivity as function of both ∆ and λSOC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Whenever |3 √ 3λSOC| > |∆|, the orbital Hall effect is larger than for the opposite situation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' (d) Orbital Hall conductivity in the center of the band gap as a function of ∆ (black) and λSOC (red).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' where the creation and annihilation operators ci, c† i are spinors representing the spin degree of freedom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' The first term is the usual nearest neighbour hopping (t), the second term is the spin-orbit coupling term (λSOC) act- ing on the next-nearest neighbours and the last term is the on-site staggered potential term (ϵi∆, ϵi = ±1 on the different sublattices), also called Semenoff mass gap [31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' This last term leads to the appearance of an orbital magnetic moment as pointed out in Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' [16, 28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' To il- lustrate the connection between the Berry curvature, the orbital magnetic moment and the orbital Hall effect, let us consider the effective Hamiltonian of the Kane-Mele model, valid close to the neutrality point at K and K’ points in the Brillouin zone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' In the absence of Rashba interaction, the Kane-Mele model can be thought of as a double copy of the Haldane model [32], each copy cor- responding to a spin sector described by the two-band Hamiltonian Hηs = vF (ηkxσx + kyσy) + (∆ + ηs˜λSOC)σz, (6) where ˜λSOC = 3 √ 3λSOC, σ is the pseudospin in the sub- lattice space, s = ±1 refers to the spin projection and η = ±1 to the K and K’ valleys, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' The gap is given by ∆ηs = ∆+ηs˜λSOC so that the non-trivial regime is reached whenever |˜λSOC| > |∆|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' This Hamiltonian can be written [25, 33] Hηs = ˆIϵηs k + ˆσ · dηs k , (7) where ϵηs k is the energy dispersion of the individual bands and dηs k describes the hybridization between bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Therefore the Berry curvature and orbital magnetic mo- ment read [25] Ωηs k,i = ± εijk 2(dηs k )3 dηs k · �∂dηs k ∂kj × ∂dηs k ∂kk � , (8) mo,ηs k,i = − e ℏ εijk 2(dηs k )2 dηs k · �∂dηs k ∂kj × ∂dηs k ∂kk � , (9) with ± referring to the conduction and valence band, re- spectively and dηs k = |dηs k |.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Equations (8) and (9) show that the Berry curvature and the orbital magnetic mo- ment possess a very similar structure in momentum space [16, 20], revealing that the orbital motion finds it origin in the Berry curvature of the Bloch states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Since the Kane- Mele model, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' (5), describes an effective four-band model taking into account the spin degree of freedom, the Bloch state does not carry any atomic orbital mo- mentum (in other words, in this model the Bloch states are typically s or pz).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' For this reason, the orbital moment comes entirely from the details of the band structure in- timately correlated to the Berry curvature, as displayed as a color gradient in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' 1(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Using the effective two- band Hamiltonian, one obtains Ωηs k,z = ± ηv2 F ∆ηs 2(∆2ηs + v2 F k2)3/2 , (10) mo,ηs k,z = − e 2ℏ ηv2 F ∆ηs ∆2ηs + v2 F k2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' (11) One sees that both the Berry curvature and the orbital magnetic moment are inversely proportional to the band gap [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' The Berry curvature hot-spots appearing at 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='5 101 (a) (c) 人人人人人 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='5 10° 一 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='1 △(t) COH( )HO0 LL 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='0 10-1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='01 LL 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='0 1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='001 10-2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='2 1 0 1 2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='5 △(t) 3/3 asoc(t) (b) (p) 人人人人 )HO0 COH( 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='1 soc = 0 △=0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='001 1 0 2 1 2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='1 1 Λsoc, 4 different valleys characterize the topological transition: in the non-trivial phase both spin partners at the same inequivalent point (K or K’) display opposite values of the orbital moment, while they have the same sign in the trivial regime, as seen in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' 1(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Following the procedure outlined by Bhowal and Vi- gnale [16], the orbital Hall conductivity for spin s and valley η reads σηs OH = � e 2π � � mev2 F 6ℏ2gL � ∆2 ηs (∆2ηs + v2 F k2)3/2 , (12) Therefore, the total orbital Hall conductivity is the sum of individuals contributions, σOH = � η ση OH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' In the middle of the gap (k → 0), one retrieves the constant value pointed out by Bhowal and Vignale [16], σOH = � e 2π � � mev2 F 3ℏ2gL � � 1 |∆ + ˜λSOC| + 1 |∆ − ˜λSOC| � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' (13) This expression indicates that the orbital Hall conductiv- ity decreases when increasing the gap, independently of the topological nature of the gap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' To assess the interplay between the spin-orbit coupling strength λSOC and the staggered potential ∆, Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' 2(a) [Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' 2(b)] shows the or- bital Hall conductivity as a function of ∆ (λSOC) for dif- ferent values of λSOC (∆).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' We find that the orbital Hall conductivity reaches a maximum whenever ∆ ≈ ˜λSOC, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=', at the topological phase transition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' We note that the orbital Hall conductivity tends to be larger in the triv- ial phase than in the topological phase, as confirmed by the phase diagram presented in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' 2(c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' In this panel, brighter regions correspond to larger values of the orbital Hall conductivity, located in the topologically-trivial re- gions, |∆| > |˜λSOC|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Finally, in order to establish a connection between the Kane-Mele model and the realistic two-dimensional ma- terials discussed in the next section, we report the orbital Hall conductivity as a function of the gap size in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' 2(d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Our calculations confirm that the orbital Hall con- ductivity systematically decreases with the size for the gap, be it driven by ∆ or by ˜λSOC consistently with Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' (13).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' However, we notice that when further increasing the spin-orbit coupling above t, the orbital Hall conduc- tivity increases again which is understood by consider- ing the change of the band structure depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' When the staggered potential is turned off, at small ˜λSOC, the gap is located close to K and K’ points and Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' (13) applies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' However, in the larger spin-orbit cou- pling limit, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=', ˜λSOC ≈ t, the gap has moved to the M point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' In this case, increasing spin-orbit coupling reduces the gap, which leads to an enhancement of the orbital Hall effect, as depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' 2(d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' The two situations reported in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' 3 are representative of the case of ger- manene (small ˜λSOC, Dirac cones at K and K’ points) and bismuthene (large ˜λSOC, Dirac cone at Γ point) dis- cussed below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Band structure for the Kane-Mele model with differ- ent values of λSOC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' In the non-trivial phase, the increasing of spin orbit coupling not necessarily leads to the increase of the gap, this is in connection to what is depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' 2 (d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' ORBITAL TRANSPORT IN REALISTIC 2D MATERIALS We now turn to the simulations performed in realistic two-dimensional materials presenting different topologi- cal characters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' For the trivial systems, we consider two cases: h-BN/graphene bilayer where the proximity effects lead to the breaking of inversion symmetry [34, 35], as well as hydrogene-decorated graphene in which a colos- sal enhancement of the spin-orbit coupling has been pre- dicted [36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' For the non-trivial systems, we have se- lected bismuthene, proven to be a topological insulator with a sizeable gap in its buckled hexagonal structure [37], and germanene, characterized by a buckled structure and a large enough spin-orbit coupling capable to open a topological gap [38, 39].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' For the DFT [40, 41] sim- ulations, we used the Perdew-Burke-Ernzerhof [42, 43] exchange-correlation functional.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' We performed the re- laxation with the plane-wave basis as implemented in the Vienna Ab-initio Simulation Package (VASP) [44, 45], and employ a plane-wave expansion cutoff of 400 eV along with a force criterion of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='2×10−2 eV/˚Awith a (15 × 15 × 1) k-points sampling of the Brillouin zone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' The ionic potentials were described using the projector augmented-wave (PAW) method [46].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Finally, the Hamil- tonian matrix was obtained through the Wannier90 pack- age [47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' h-BN/graphene and graphene+H The recent proposal suggesting gapped graphene as an orbital Hall insulator has shed light on the nature of the valley Hall effect [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Motivated by this real- ization, we present the results on h-BN/graphene het- erostructures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' This system has been extensively studied in the last years in several contexts [34, 48, 49].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' While free-standing graphene is a topological semimetal that possesses a robust band structure protected by inversion 4 3 2 1 E-Ef(a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='u asoc = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='05t 0 Λsoc = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='75t 1 2 3 4 K M K15 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' (a) h-BN/graphene heterostructure electronic band structure, (b) spin Hall, (c) intra-atomic orbital Hall and (d) total orbital Hall conductivities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' The grey shaded region in (a) corresponds to the energy window where the Hall conductivities were calculated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' symmetry, it loses this symmetry by proximity with a ma- terial like h-BN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' The whole heterostructure resembles a Kane-Mele model in the trivial phase with a gap opening whose size is given by the interaction with h-BN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Theo- retically it has been shown that spin manipulation would be possible in this scenario [35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Most importantly for our purpose, graphene acquires a px-py orbital hybridization when interfaced with h-BN, which promotes the onset of intra-atomic orbital Hall effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' The Hall conductivities are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' 4 where a small spin Hall effect is ob- served [Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' 4(b)], whereas the orbital Hall response is one to two orders of magnitude larger.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' In particular, the intra-atomic orbital Hall effect [Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' 4(c)] displays a mod- erate value within the energy window around the charge neutrality point while the total orbital Hall effect, which contains both intra- and inter-atomic contributions, [Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' 4(d)] attains the largest value of the three Hall responses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Notice that the energy profile of the Hall responses are similar, as both spin and orbital Hall effects are driven by proximity with h-BN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' We now consider graphene decorated with hydro- gen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' The inclusion of hydrogen is enough to enhance graphene’s spin-orbit splitting up to 100 µeV locally [36, 50].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' For this system, we have considered a 5 × 5 su- percell with a single hydrogen atom on top at the center of the graphene flake.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' The band structure is presented in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' 5(a) where spin-orbit coupling was also taken into account, showing a good agreement with previous reports [50].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' The orbital and spin textures are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' 5(b) and (c) respectively, for the most energetic valence bands closer to the hydrogen states, well localized in the spec- trum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Our results suggest a large imprinted px-py hy- bridization which leads to the large value of the atomic orbital momentum Lz having hot spots at inequivalent points in the hexagonal Brillouin zone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' This is encourag- ing from the orbital transport perspective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Our calcula- tions show that the intra-atomic orbital Hall conductiv- ity (ACA) is around 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='6 (e/2π) whereas the total (intra- FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Graphene+H electronic band structure considering spin-orbit coupling (a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Orbital texture (b) and spin texture (b) for the most energetic valence band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' In this case the isolated flat bands come from the Hydrogen atom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' and inter-atomic) orbital Hall conductivity is about 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='1 (e/2π), which is comparable to the h-BN/graphene case discussed above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' In contrast, the spin Hall conductivity is about ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='15 (e/2π), still much smaller than the or- bital Hall effect, but one order of magnitude larger than the spin Hall effect computed in h-BN/graphene, demon- strating the large spin-orbit coupling enhancement in this heterostructure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' This result is remarkable especially con- sidering that it solely arises from the interaction between graphene and hydrogen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' On the other hand, the spin tex- ture induces a local magnetic moment of ∼1 µB, leading to a large spin splitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' The orbital Hall effect will also 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='5 3 (a) (b) (c) (d) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='0 - 2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='5 1 (eV EF 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='0 0 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='5 k, 1k Nx x6 appear in other graphene-based heterostructures whose band structure is tuned by proximity effects [14, 51, 52].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Germanene and bismuthene FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' (a) Germanene projected density of states showing the pz (green), px , py (orange) and s (blue) states as a func- tion of the Fermi level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' (b) Corresponding orbital texture for the most energetic valence band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' (c) Germanene electronic band structure, and (d) spin (blue), intra-atomic (black) and total orbital Hall conductivities (green).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' The next material we consider is germanene which pos- sesses a narrow gap and has a buckled structure that fa- vors a sp3 hybridization inducing a px-py hybridization away from the neutrality point [Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' 6(a)] which results in an orbital texture in momentum space [Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' 6(b)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Alike Kane-Mele model with small spin-orbit coupling, germanene possesses slightly gapped Dirac cones located at K and K’ points [Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' 6(c)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' The Hall conductivi- ties are depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' 6(d) where the spin Hall effect (blue) reaches a (narrow) quantized plateau at the Fermi level, associated with the non-trivial phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Whereas the spin Hall conductivity is peaked close to the gap, where the spin Berry curvature is maximum, the non-vanishing orbital texture in germanene leads to a finite value of the orbital Hall conductivity (intra-atomic contribution in black, total contribution in green) on a much broader range of energy around the gap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Notice that the total orbital Hall effect remains smaller than the intra-atomic Hall effect, which implies that inter-atomic and intra- atomic contributions partially cancel each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' A par- ticular feature of germanene (and bismuthene, see below) is that inversion symmetry is preserved, and therefore the total orbital Hall response has its origin in the non- abelian nature of the Berry curvature as already shown [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' (a) Bismuthene electronic band structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' (b) Spin (blue), intra-atomic (black) and total orbital Hall conductiv- ities (green).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' (c) Orbital moment calculated for the two most (red and black) and two less energetic (blue and green) bands along the M − K − Γ − M kpath.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' The last system we consider is buckled bismuthene, which displays a much larger gap than germanene due to a much larger spin-orbit coupling [Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' 7(a)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' In this crystalline phase, bismuthene’s band character is in- verted at Γ point due to spin-orbit coupling, following the same process as described in the Bernevig-Hughes- Zhang model [53, 54], exemplified above by the Kane- Mele model with strong spin-orbit coupling (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' This change in the band structure allows for a strong s-character at this point in reciprocal space leading to a quenched orbital texture [55].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' The spin, intra-atomic and total orbital Hall conductivities are displayed on Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' 7(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' The absence of an orbital texture in terms of the px and py near the gap leads to a vanishingly smaller intra-atomic orbital Hall effect (black), which increases away from the gap due to enhanced px-py hybridization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' In contrast, the total orbital Hall conductivity reaches a large value (green), even larger than that of the spin Hall conductivity (blue).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' These larger values can be un- derstood by looking at the orbital moment distribution along the momentum path M −K −Γ−M shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' 7(c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' The hot-spots located at the Γ-point lead to a larger value of the total orbital Hall conductivity compared to (b) Pz 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='4 0.' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='0 E 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='5 0000000000000d 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='0 0000000 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='5 r M K 2 1 0 2 Spin/Orbital Hall Conductivity(e/2rt)1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='5 (a) (b) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='0 - 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='5 E-Ef(eV) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='0 - 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='0 - E 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='5 M r K 0 1 2 3 Spin/Orbital Hall Conductivity(e/2r) (c) 250 200 150 2 100 mo(eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='A2 50 0 50 100 M K L M7 the spin one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Notice that the spin conductivity is quan- tized, whereas the total orbital conductivity is not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' We mention in passing that it has been recently suggested that such non-quantized plateaus are related to high- order topological insulating behavior [56].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Hence, the overall scenario in bismuthene contrasts markedly with that in germanene and follows the situation discussed in the previous section using the Kane-Mele model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Con- sequently, from a materials’ perspective, we are able to draw differences on the orbital response based on details of their band structures and orbital character.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' IMPACT OF DISORDER ON ORBITAL HALL TRANSPORT An important question that remains unanswered at this point is the impact of disorder-induced scattering on the orbital conductivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' As a matter of fact, a simple- minded rationale suggests that the intra-atomic orbital Hall effect, which arises from the atomic orbital moment, would be less sensitive to momentum scattering than the inter-atomic orbital Hall effect, which arises from self- rotation of the electron wave packet in the unit cell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' To investigate the impact of disorder, we consider three different systems: germanene, h-BN/graphene, the two narrow-gap semiconductors studied above, and MoS2, a large band gap semiconductor that has been predicted to be an orbital Hall insulator [6, 17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' From the tight- binding basis obtained by ab initio simulations, we in- troduce disorder by the inclusion of an on-site Anderson disorder which can be expressed mathematically like H = H0 + � i Vi, (14) where H0 is the bare Hamiltonian corresponding to a 10 × 10 supercell and Vi is an onsite potential acting on the i site with values [−1, 1]eV .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' We calculated the Hall conductivity for 40 random realizations of every fixed set of parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' The results obtained for germanene and h- BN/graphene are depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' 8 (a,b) and (c,d), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' To understand how disorder affects the orbital transport, we have considered two different transport regimes: (i) the single band case, where the carrier’s energy to close to the gap, ε = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='1 eV (solid lines), and (ii) the multiband case, where the carrier’s energy is far from the gap, ε = −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='0 eV (dashed lines).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' In the former, the band dispersion is mostly linear and the longitudinal conductivity of germanene (a) and h-BN/graphene (c) slowly decays as a function of disorder due to enhanced scattering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' In contrast, when the energy lies far from the gap, in the multiband case (dashed), the conductivity decay is more dramatic, as expected in conventional metals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' We have also computed the intra-atomic and total orbital Hall conductivities for these different situations (b, d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' To better visualize the effect of disorder, we report the ratio between FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' (a,c) Longitudinal conductivity and (b,d) orbital Hall conductivity near the Fermi level (ε = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='1 eV) for germanene (a,b) and h-BN/graphene (c,d) as a function of the disorder concentration, the values plot correspond to the ratio orbital Hall conductivity over its maximum value σ0 OH in the pristine case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' We computed both the intra-atomic (ACA - red) and total contributions (green).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' The inset in (a) shows a sketch of a disorder realization in the lattice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' the Hall conductivities with and without disorder, σOH/σ0 OH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' In the single band transport regime, we find that the intra-atomic conductivity (red) is mostly flat, independent on the disorder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Nonetheless, the total orbital Hall effect (green), which contrains both intra- and inter-atomic contributions, is as a whole much more sensitive to disorder and decreases continuously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' In fact, the intra-atomic Hall effect is controlled by the orbital Berry curvature of the single band and is therefore expected to be rather robust against disorder whereas the inter-atomic Hall effect, which arises from self-rotation of the wave packet in the unit cell is much more sensitive to onsite energy fluctuations brought by Anderson disorder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' In the multiband transport regime (dashed lines), we find that both the intra-atomic and total orbital Hall ef- fect decay at a similar rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' This distinct behavior sug- gests that the linear dispersion of the single band trans- port regime has a strong impact on the robustness of the intra-atomic orbital Hall effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' In contrast, the total or- bital Hall effect, that contains the inter-atomic contribu- tion, is much more sensitive to Anderson-type disorder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' We must note that the intra-atomic contribution is larger than the total one in the case of germanene while the op- posite is true for h-BN/graphene.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' This result indicates that the inter-atomic contribution is much more sensitive to disorder than the intra-atomic one, irrespective of the transport regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' We now turn our attention to MoS2, a large band gap orbital Hall insulator studied previously [6, 19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' The band structure and orbital Hall conductivity are reported in insert for reference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Here, we fix the carrier’s energy at ε=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='5 eV above the center of the gap in a region where the energy dispersion is quadratic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' The value of the con- 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='0 (a) (b) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='8 H1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='6 6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='4 6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='6 - 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='0 0 20 40 60 80 100 0 20 40 60 80 100 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='6 (c) (d) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='5 H1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='4 6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='3 6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='0 20 0 40 60 80 100 20 40 60 0 80 100 Disorder (%) Disorder (%)8 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' (a) Longitudinal conductivity for an energy of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='5 eV with respect to the zero energy (middle of the gap) defined as the Fermi level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' (b) Orbital Hall conductivities over the maximum value (σ0 OH)in the pristine system, calculated by the Kubo formula in a 10×10 supercell containing Anderson type disorder, intra-atomic Hall conductivity (ACA) and total orbital Hall conductivity are depicted with dashed lines for an energy of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='5 eV with respect to the zero energy defined as the Fermi level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' The solid lines correspond to the Hall conductivites calculated the Fermi level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' The inset shows the actual values of the orbital conductivity for both intra-atomic and total responses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' ductivity decreases rapidly with increasing the impurity concentration, as expected in a conventional, leading to a decay over about two orders of magnitude, quite differ- ent from linearly dispersing narrow-gap germanene and graphene/hBN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' The behaviour of the (normalized) or- bital Hall conductivities is depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' 9(b) where dashed lines correspond to a transport energy of ε=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='5 eV and the solid lines correspond to a transport energy taken in the middle of the gap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' The inset shows the ab- solute values for reference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' The behavior we obtain is qualitatively similar to the one observed in the narrow- gap semiconductors discussed previously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' In the gap, the intra-atomic orbital Hall conductivity (solid red) is in- sensitive to disorder, as expected from a Berry-curvature driven effect, whereas the total orbital Hall conductivity decays.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' It has been argued recently that the in-gap intra- atomic orbital Hall conductivity is associated with intra- atomic orbital polarized edge states [17, 19] that remain insensitive to the disorder, although this picture might change when considering open boundary conditions like in nanoribbons for instance [57].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' This contrasts to what we find for the total Hall response where a drop of nearly half of the initial value is observed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' When the energy is set in the conduction band, one finds that both intra- atomic and total orbital Hall conductivities decrease with a similar rate, as already observed in narrow-gap semi- conductors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' CONCLUSION To summarize, we have explored the microscopic ori- gin of the orbital Hall effect in model and realistic two- dimensional Dirac materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Since the orbital Hall ef- fect is intimately connected with the Berry curvature of the material, we first investigated the inter-atomic orbital Hall contribution in the Kane-Mele model, that accom- modates topological phase transition and in which the intra-atomic contribution is absent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' We found that al- though the orbital moment itself behaves differently in the topologically trivial and non-trivial phases, the re- sulting orbital Hall conductivity is rather controlled by the size of the gap, irrespective of its topological nature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' We then studied the orbital Hall effect in selected two- dimensional materials, starting with graphene.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Whereas orbital Hall effect is absent of pristine graphene, it can be turned on by inducing a global or local gap, either interfacing graphene with h-BN or by using hydrogen adatoms, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' In these cases, the emergence of orbital and spin textures in reciprocal space stand out as key ingredients for the generation of orbital and spin polarized Hall currents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' These predictions are particu- larly intriguing given that these two systems are made out of light elements unable to portray a sizeable spin- orbit coupling by their own.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' We then moved on to investigate the orbital Hall cur- rents in two selected two-dimensional topological insu- lators, germanene and bismuthene, which represent two distinct realizations of the Kane-Mele model, with weak and strong spin-orbit coupling, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' In ger- manene, we have found that the intra-atomic orbital Hall contribution displays a larger value than of the total or- bital Hall one, resembling the weakly spin-orbit coupled non-trivial phase of the Kane-Mele model (small spin- orbit gaps at K and K’ points).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' The existence of the quantum spin Hall effect in germanene is corroborated with a narrow plateau appearing for the spin Hall con- ductivity while the values for the orbital Hall effect re- mains larger in a broader energy window.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' In bismuthene, besides the spin Hall effect, we have found a large orbital Hall conductivity coming from the orbital moment car- ried out by the bands near the Fermi level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' This situa- tion resembles the strongly spin-orbit coupled non-trivial phase of the Kane-Mele model (large spin-orbit gap at M point).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Finally, we investigated the impact of disorder on the intra-atomic and inter-atomic contributions of the or- (a) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='4 (eV) — ACA 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='3 - 0 _ Total 1 2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='2 3 M 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='5 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='0 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='5 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='0 OHC(e/2) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='0 - 0 20 40 60 80 100 (b) 6 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='0 4 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='5 ACA 3 2 Total 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='0 - 1 0 1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='5 2 20 40 60 80 100 Disorder (%) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='0 0 20 40 60 80 100 Disorder (%)9 bital Hall effect in two-dimensional systems featuring very different transport regimes (insulating, single-band and multiband metallic regimes).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' We find that the intra- atomic orbital Hall effect tends to be less affected by disorder than the total orbital Hall effect, especially in the insulating and single-band regimes, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=', in situa- tions where the orbital Berry curvature is smooth and well-defined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' In contrast, in the multiband transport regime, both intra-atomic contribution and total orbital conductivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' These results suggest that irrespective of the transport regime, the intra-atomic part of the orbital Hall effect is more robust than the inter-atomic part.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' The present work sheds light on the mechanisms re- sponsible for orbital Hall effect in two-dimensional mate- rials, and in particular clarifies the role of the gap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' The intimate connection between the orbital Hall transport and the Berry curvature of the band structure opens in- teresting perspectives for the external control of the or- bital transport through interfacial engineering or strain, as demonstrated in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='[58].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' From this standpoint Van der Waals heterostructures made of light materials, such as graphene and h-BN for instance, could be used for the realization of nonlocal orbital devices, akin to the all-electric valley or spin Hall transistor [59, 60].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' In this context, a more comprehensive understanding of the or- bital relaxation induced by momentum scattering is nec- essary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' ACKNOWLEDGMENTS This work was supported by the ANR ORION project, grant ANR-20-CE30-0022-01 of the French Agence Na- tionale de la Recherche.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' acknowl- edge support from the Excellence Initiative of Aix- Marseille Universit´e - A*Midex, a French ”Investisse- ments d’Avenir” program.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' [1] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Bernevig, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Hughes, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='-c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Zhang, Physical Review Letters 95, 066601 (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' [2] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Kontani, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Tanaka, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Hirashima, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Yamada, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Inoue, Physical Review Letters 102, 016601 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' [3] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Go, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Jo, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Kim, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Lee, Physical Review Letters 121, 086602 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' [4] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Hayashi, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Ieda, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Yamane, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='-i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Ohe, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Taka- hashi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Mitani, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Maekawa, Physical Review Let- ters 108, 147202 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' [5] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Salemi and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Oppeneer, Physical Review Materials 6, 095001 (2022), arXiv:2203.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='17037.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' [6] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Pezo, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Garc´ıa Ovalle, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Manchon, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' B 106, 104414 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' [7] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Vedmedenko, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Kawakami, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Sheka, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Gambardella, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Kirilyuk, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Hirohata, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Binek, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Chubykalo-Fesenko, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Sanvito, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Kirby, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Grol- lier, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Everschor-Sitte, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Kampfrath, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' You, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Berger, Journal of Physics D: Applied Physics 53, 453001 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' [8] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Chumak, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Vasyuchka, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Serga, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Hillebrands, Nature Physics 11, 453 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' [9] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Jo, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Go, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='-w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Lee, Physical Review B 98, 214405 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' [10] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Go and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='-w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Lee, Physical Review Research 2, 13177 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' [11] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Ding, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Ross, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Go, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Baldrati, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Ren, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Freimuth, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Becker, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Kammerbauer, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Yang, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Jakob, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Mokrousov, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Kl¨aui, Physical Review Letters 125, 177201 (2020), arXiv:2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='03649.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' [12] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Lee, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Go, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Park, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Jeong, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Ko, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Yun, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Jo, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Lee, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Go, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Oh, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Kim, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Park, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Min, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Koo, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Lee, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Lee, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Lee, Nature Communications 12, 6710 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' [13] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Ding, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Liang, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Go, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Yun, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Xue, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Liu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Becker, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Yang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Du, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Wang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Yang, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Jakob, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Kl¨aui, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Mokrousov, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Yang, Physical Review Letters 128, 067201 (2022), arXiv:2105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='04495.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' [14] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Roche, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' ˚Akerman, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Beschoten, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Char- lier, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Chshiev, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Dash, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Dlubak, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Fabian, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Fert, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Guimar˜aes, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Guinea, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Grigorieva, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Sch¨onenberger, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Seneor, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Stampfer, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Valen- zuela, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Waintal, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Van Wees, 2D Materials 2, 030202 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' [15] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Xiao, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='-B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Liu, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Feng, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Xu, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Yao, Phys- ical Review Letters 108, 196802 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' [16] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Bhowal and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Vignale, Physical Review B 103, 195309 (2021), arXiv:2103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='03148.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' [17] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Cysne, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Costa, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Canonico, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Buon- giorno Nardelli, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Muniz, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Rap- poport, Physical Review Letters 127, 056601 (2021), arXiv:arXiv:2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='07894v2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' [18] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Cysne, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Bhowal, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Vignale, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Rappoport, Physical Review B 105, 195421 (2022), arXiv:2201.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='03491.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' [19] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Canonico, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Cysne, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Molina-Sanchez, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Muniz, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Rappoport, Physical Review B 101, 161409(R) (2020), arXiv:2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='03592.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' [20] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Thonhauser, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Ceresoli, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Vanderbilt, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Resta, Physical Review Letters 95, 137205 (2005), arXiv:0505518 [cond-mat].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' [21] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Ceresoli, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Thonhauser, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Vanderbilt, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Resta, Physical Review B 74, 024408 (2006), arXiv:0512142 [cond-mat].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' [22] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Shi, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Vignale, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Xiao, and Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Niu, Physical Review Letters 99, 197202 (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' [23] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Hanke, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Freimuth, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Nandy, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Zhang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Bl, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Mokrousov, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Gr, Physical Review B 94, 121114(R) (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' [24] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Liu and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Dai, Nature Reviews Physics 3, 367 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' [25] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Yoda, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Yokoyama, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Murakami, Nano Letters 18, 916 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' [26] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Blount, Solid State Physics 13, 305 (1962).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' [27] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Bonbien and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Manchon, Physical Review B 102, 085113 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' [28] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Bhowal and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Satpathy, Physical Review B 101, 121112(R) (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' [29] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Ding, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Liang, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Go, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Yun, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Xue, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Liu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Becker, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Yang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Du, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Wang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Yang, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Jakob, 10 M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Kl¨aui, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Mokrousov, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Yang, arXiv preprint arxiv:2105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='04495 (2021), arXiv:2105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='04495.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' [30] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Kane and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Mele, Physical Review Letters 95, 226801 (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' [31] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Semenoff, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' 53, 2449 (1984).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' [32] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Haldane, Physical Review Letters 61, 2015 (1988).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' [33] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Qi, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Wu, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Zhang, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' B 74, 085308 (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' [34] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Wang, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Ma, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Sun, RSC Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' 7, 16801 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' [35] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Zollner, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Cummings, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Roche, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Fabian, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' B 103, 075129 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' [36] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Gmitra, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Kochan, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Fabian, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' 110, 246602 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' [37] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Guo, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Pan, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Ye, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Sun, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Wang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Li, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Zhang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Zhang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Pan, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Song, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Yang, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Lu, ACS Applied Materials and Interfaces 9, 23128 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' [38] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Acun, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Zhang, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Bampoulis, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Farmanbar, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Van Houselt, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Rudenko, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Lingenfelder, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Brocks, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Poelsema, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Katsnelson, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Zandvliet, Journal of Physics Condensed Matter 27, 443002 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' [39] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Ezawa, Journal of the Physical Society of Japan 84, 1 (2015), arXiv:1503.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='0891.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' [40] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Hohenberg and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Kohn, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' 136, B864 (1964).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' [41] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Kohn and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Sham, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' 140, A1133 (1965).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' [42] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Perdew, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Chevary, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Vosko, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Jackson, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Pederson, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Singh, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Fiolhais, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' B 46, 6671 (1992).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' [43] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Perdew, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Burke, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Ernzerhof, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' 77, 3865 (1996).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' [44] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Kresse and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Furthm¨uller, Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Mater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' 6, 15 (1996).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' [45] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Kresse and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Furthm¨uller, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' B 54, 11169 (1996).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' [46] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Kresse and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Joubert, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' B 59, 1758 (1999).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' [47] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Pizzi, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Vitale, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Arita, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Bl¨ugel, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Freimuth, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' G´eranton, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Gibertini, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Gresch, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Johnson, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Koretsune, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Ibanez-Azpiroz, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Lee, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Lihm, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Marchand, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Marrazzo, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Mokrousov, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Mustafa, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Nohara, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Nomura, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Paulatto, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Ponc´e, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Pon- weiser, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Qiao, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Th¨ole, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Tsirkin, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Wierzbowska, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Marzari, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Vanderbilt, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Souza, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Mostofi, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Yates, Journal of Physics Condensed Matter 32, 165902 (2020), arXiv:1907.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='09788.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' [48] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Sun, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Zhang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Liu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Zhu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Huang, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Yuan, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Wang, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Watanabe, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Taniguchi, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Li, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Zhu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Mao, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Yang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Kang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Liu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Ye, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Han, and Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Zhang, Nature Communications 12, 7196 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' [49] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Salvador-S´anchez, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Canonico, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' P´erez- Rodr´ıguez, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Cysne, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Baba, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Cleric`o, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Vila, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Vaquero, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Delgado-Notario, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Cari- dad, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Watanabe, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Taniguchi, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Molina, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Dom´ınguez-Adame, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Roche, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Diez, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Rap- poport, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Amado, “Generation and control of non- local chiral currents in graphene superlattices by orbital hall effect,” (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' [50] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Soriano, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Tuan, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='-M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Dubois, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Gmitra, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Cummings, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Kochan, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Ortmann, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Char- lier, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Fabian, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Roche, 2D Materials 2, 022002 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' [51] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Han, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Kawakami, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Gmitra, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Fabian, Nature nanotechnology 9, 794 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' [52] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Pezo, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Zanolli, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Wittemeier, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Ordej´on, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Fazzio, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Roche, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Garcia, 2D Materials 9, 015008 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' [53] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Bernevig, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Hughes, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Zhang, Science 314, 1757 (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' [54] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Zhao and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Wang, APL Materials 8, 030701 (2020), https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='5135984.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' [55] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Li, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Hanke, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Hankiewicz, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Reis, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Sch¨afer, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Claessen, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Wu, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Thomale, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' B 98, 165146 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' [56] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Costa, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Focassio, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Cysne, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Canon- ico, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Schleder, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Muniz, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Fazzio, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Rappoport, “Connecting higher-order topology with the orbital hall effect in monolayers of transition metal dichalcogenides,” (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' [57] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Pezo, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Lima, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Costa, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Fazzio, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' 21, 11359 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' [58] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Son, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Kim, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Ahn, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Lee, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Lee, Physical Review Letters 123, 36806 (2019), arXiv:1907.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='00010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' [59] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Gorbachev, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Song, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Yu, a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Kretinin, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Withers, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Cao, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Mishchenko, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Grigorieva, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Novoselov, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Levitov, and a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Geim, Science (New York, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=') 346, 448 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' [60] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Choi, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='-j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Kim, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Chang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Han, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Abbout, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Ben, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Saidaoui, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content='-j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Lee, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} +page_content=' Koo, Nano Letters 18, 7998 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/etAzT4oBgHgl3EQfL_vx/content/2301.01126v1.pdf'} diff --git a/ftE1T4oBgHgl3EQfywUm/content/2301.03436v1.pdf b/ftE1T4oBgHgl3EQfywUm/content/2301.03436v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..f8130e91af1a63e7ef8347614fd9e30ddfc8beab --- /dev/null +++ b/ftE1T4oBgHgl3EQfywUm/content/2301.03436v1.pdf @@ -0,0 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453581 diff --git a/g9FMT4oBgHgl3EQf3DHu/vector_store/index.pkl b/g9FMT4oBgHgl3EQf3DHu/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..17458ddcc4c75687139f5ffdeff22e21917504f4 --- /dev/null +++ b/g9FMT4oBgHgl3EQf3DHu/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:c4e5e65439635f6ec9c0cda28314c2209e1081cc323516b68df1ddab9837a758 +size 191194 diff --git a/gNAzT4oBgHgl3EQfavxL/content/tmp_files/2301.01373v1.pdf.txt b/gNAzT4oBgHgl3EQfavxL/content/tmp_files/2301.01373v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..12b2bd238dddcd329ef809a5640082dac785dc03 --- /dev/null +++ b/gNAzT4oBgHgl3EQfavxL/content/tmp_files/2301.01373v1.pdf.txt @@ -0,0 +1,2730 @@ +COVARIATE-GUIDED BAYESIAN MIXTURE OF SPLINE EXPERTS +FOR THE ANALYSIS OF MULTIVARIATE TIME SERIES +Haoyi Fu +Department of Biostatistics +University of Pittsburgh +Pittsburgh, PA, USA +haf48@pitt.edu +Lu Tang +Department of Biostatistics +University of Pittsburgh +Pittsburgh, PA, USA +Ori Rosen +Department of Mathematical Sciences +University of Texas at El Paso +El Paso, TX, USA +Alison E. Hipwell +Department of Psychiatry +University of Pittsburgh +Pittsburgh, PA, USA +Theodore J. Huppert +Department of Electrical and Computer Engineering +University of Pittsburgh +Pittsburgh, PA, USA +Robert T. Krafty +Department of Biostatistics and Bioinformatics +Emory University +Atlanta, GA, USA +ABSTRACT +With rapid development of techniques to measure brain activity and structure, statistical methods +for analyzing modern brain-imaging play an important role in the advancement of science. Imaging +data that measure brain function are usually multivariate time series and are heterogeneous across +both imaging sources and subjects, which lead to various statistical and computational challenges. +In this paper, we propose a group-based method to cluster a collection of multivariate time series +via a Bayesian mixture of smoothing splines. Our method assumes each multivariate time series is +a mixture of multiple components with different mixing weights. Time-independent covariates are +assumed to be associated with the mixture components and are incorporated via logistic weights of a +mixture-of-experts model. We formulate this approach under a fully Bayesian framework using Gibbs +sampling where the number of components is selected based on a deviance information criterion. The +proposed method is compared to existing methods via simulation studies and is applied to a study on +functional near-infrared spectroscopy (fNIRS), which aims to understand infant emotional reactivity +and recovery from stress. The results reveal distinct patterns of brain activity, as well as associations +between these patterns and selected covariates. +Keywords Bayesian mixture model · Brain-imaging · Functional near-infrared spectroscopy · Model-based clustering · +Multivariate time series · Smoothing splines · Face-to-face still-face +1 +Introduction +Time series are realizations of random processes. Obtaining estimated time series trajectories may provide insights into +many practical problems. Functional near-infrared spectroscopy (fNIRS) is a noninvasive brain imaging technique that +measures changes in both oxy- and deoxy-hemoglobin using near-infrared light (Jobsis, 1977). In fNIRS, processed data +are nonstationary multivariate time series with a non-constant mean and high variability across time, which pose many +statistical challenges in inference and estimation. In the case of fNIRS, different subjects could have distinct patterns of +multivariate time series trajectories, which could be associated with certain clinical or demographic characteristics. +arXiv:2301.01373v1 [stat.ME] 3 Jan 2023 + +Covariate-guided Bayesian mixture model for multivariate time series +The analysis of fNIRS data requires an appropriate method for the analysis of a collection of multivariate time series +observed from different subjects, which is often referred to as a replicated multivariate time series setting. +Cluster analysis is often used to address the issue of heterogeneity and identify subgroups from collections of time +series observed from different subjects. Time series clustering has been used in diverse scientific areas to discover +trajectory patterns, which can uncover valuable information from complex and massive datasets (Liao, 2005). Time +series clustering partitions the entire collection of data into different groups such that homogeneous time series are +grouped together based on a certain similarity measure. Challenges in time-series clustering include computational +issues due to high-dimensionality and the selection of proper similarity measures (Lin and others, 2003; Keogh and +Pazzani, 2000). Several authors have proposed clustering algorithms for multivariate time series. Kakizawa and +others (1998) used Kullback-Leibler discrimination information as the minimum discrimination criterion for clustering +multivariate Gaussian time series. Wang and others (2007) used a modified K-means clustering algorithm for clustering +multivariate time series based on univariate structures. A variety of papers have established different model-based +clustering methods for clustering multivariate time series, such as multivariate autoregressive models (Maharaj, 1999; +He and others, 2022), a hidden Markov model (Li and others, 2001) and smoothing splines (Krafty and others, 2017; +Li and Krafty, 2019). Comprehensive review of methods for time series clustering can be found in Liao (2005) and in +Maharaj and others (2019). +Covariate-dependent structures can often be associated with the mixture components from a clustering of time +series. Bertolacci and others (2022) presented an analysis of multiple nonstationary time series by using a covariate- +dependent infinite mixture with logistic stick-breaking weights, where mixing weights are computed based on covariates. +The mixture-of-experts model (Jacobs and others, 1991) assigns weights to each expert via a covariate-dependent +multinomial logists. Huerta and others (2003) addressed the issue of time series model mixing based on covariates +using the hierarchical mixture-of-experts (Jordan and Jacobs, 1994). +Smoothing splines, which are nonparametric methods that utilize roughness-based penalties, have been widely used in +the analysis of time series (Wang, 2011; Gu, 2013). Bayesian interpretations of smoothing splines were first discussed +by Kimeldorf and Wahba (1970). Wahba (1978) showed that the solution to the smoothing splines objective function is +equivalent to Bayesian estimation with a partially diffuse prior. Speckman and Sun (2003) adopted a fully Bayesian +approach for implementing smoothing splines with a noninformative prior on the variance component, as well as +derived necessary and sufficient conditions for the propriety of the posterior. Smoothing splines require estimation of +a large number of coefficients, which might be impractical in high-dimensional settings. Gu and Kim (2002) used a +subset of reproducing kernel functions to achieve a low-dimensional approximation. Wood and others (2002) obtained +a subset of basis functions using the eigen-decomposition of the Gaussian kernel. Krafty and others (2017) proposed a +tensor-product model for the analysis of replicated multivariate time series which decomposes the power spectrum into +products of univariate outcomes and frequencies. +Our goal in this paper is to perform a covariate-guided clustering of multivariate time series that can capture trajectory +patterns of mixture components and evaluate the relationship between covariates and trajectory patterns. To this end, +each mixture component is modeled via smoothing splines, and time-independent covariates are incorporated into the +mixture model via the mixing weights. The method is formulated in a fully Bayesian framework. The rest of this paper +is organized as follows. In Section 2 we introduce the motivating study. Sections 3 and 4 present the proposed model +and priors. Section 5 introduces the sampling scheme. In Section 6 we report simulation results under different settings +and Section 7 illustrates our proposed method with application to the motivating study. Section 8 concludes the paper +with a discussion. +2 +Motivating Study +Our motivating study aims to understand patterns of infant’s brain activity before, during and after an emotionally +stressful probe called face-to-face still-face (FFSF) (Tronick and others, 1978). Participant mothers in this study were +recruited from the longitudinal Pittsburgh Girls Study (PGS), a population-based study of 2,450 girls who were recruited +in the city of Pittsburgh between the ages of 5 and 8 (Keenan and others, 2010). In 2016, a large-scale sub-study of +the PGS was initiated to investigate how environmental factors, such as psychological stressors experienced during +childhood and adolescence, affect later maternal pregnancy and child health. The study is part of the National Institutes +of Health Environmental Influences of Child Health Outcomes (ECHO) program, which examines different impacts of +prenatal environmental exposures across biological, chemical, physical and social domains on offspring health and +development (Gillman and Blaisdell, 2018). The PGS-ECHO study enrolls PGS participants as they become pregnant +or recently deliver a live birth. Participants complete multiple prenatal lab visits and the children are followed from +ages 6 to 36 months. The lab protocol includes interviews and interaction tasks to assess contextual stressors, health, +mood, lifestyle behaviors and offspring behavioral and emotional development. +2 + +Covariate-guided Bayesian mixture model for multivariate time series +Face-to-face interactions between mothers and infants are essential to the development of infants with respect to +communication and social skills, as well as the regulation of emotion and temperament (Hipwell and others, 2019). +The FFSF paradigm is a widely used stress task (a violation of the expectation of social interaction) that allows for +biobehavioral measurement of individual differences in infant response and recovery. The FFSF comprises of three +phases: interact (or baseline), still-face and recovery (Adamson and Frick, 2003). In phase 1, mothers perform normal +interactions with infants without the use of toys; this phase serves as the baseline. In phase 2, mothers adopt a neutral +facial expression (still-face with no facial or oral communication) to infants, followed by phase 3, where mothers +resume normal interactions with their infants. Prior to the start of the FFSF, an fNIRS cap is fitted on the infant’s head +to measure the level of and change in brain activation across the three phases. +PGS-ECHO fNIRS still-face data are recorded using a continuous NIRS imaging system (NIRScout; NIRx Medical +Technologies, Berlin, Germany) at the sampling rate of 7.8125 Hz and using the NIRStart acquisition software. The +data are measured simultaneously at two wavelengths (760 nm and 850 nm). As shown in Figure 1(a), this fNIRS probe +consists of 12 channels from 8 sources and 4 detectors. +In the current study, we measured infant brain activity using the above fNIRS probe (roughly 120 seconds of measure- +ments for each phase). At the end of 2021, recorded fNIRS still-face data had been collected from 155 infant subjects. +Demographic variables of infants and mothers such as gestational age, infant age, sex, birth weight, head circumference, +along with parent reports on the Infant Behavior Questionnaire-Revised (IBQ-R) (Gartstein and Rothbart, 2003) were +also collected. By removing infants who did not complete the three phases of the still-face paradigm, who had large +outliers based on leverage and who had a very short period of measurements in any of the three still-face phases, +there were a total of 82 subjects with complete fNIRS still-face data available for future analysis. The above quality +control steps were performed by the NIRS brain AnalyzIR toolbox in MATLAB (Santosa and others, 2018). Moreover, +additional data pre-processing steps were performed in R software, including data interpolation and rescaling. Finally, +processed fNIRS data had a total of 1,500 measurement points for each subject and each channel, where each phase +consisted of 500 points. All measurements and sampling times were rescaled to be between 0 and 1, with the interact +phase occurring between time 0 to 1/3, still-face between 1/3 to 2/3, and recovery between 2/3 to 1. An example of +processed fNIRS time series from two selected subjects and four selected channels is displayed in Figure 2. +The goals of our analysis are to identify distinct patterns of brain activity trajectories from multiple fNIRS channels +represented by the relative concentration of oxy-hemoglobin, and to assess the association between trajectory patterns +and relevant covariates. +3 +Model +In this section, we provide a detailed description of our proposed covariate-guided Bayesian mixture of spline experts +model. The proposed model consists of spline components whose mixing weights depend on covariates. +3.1 +Mixture of splines model +We propose a tensor-product mixture of splines model for multivariate time series. For each subject i = 1, . . . , N, let +yi = (y′ +i1, . . . , y′ +ik, . . . , y′ +iK)′ be the nK-vector corresponding to the K-dimensional time series for k = 1, . . . , K, +where yik = +� +yik(t1), . . . , yik(tj), . . . , yik(tn) +�′ contains the trajectory of measurements on the kth entry of the time +series evaluated over a grid of n time points for j = 1, . . . , n, and ϵi = (ϵ′ +i1, . . . , ϵ′ +iK)′ is the nK-vector of errors. +Following the model representation of Krafty and others (2017), the tensor-product model for the K-dimensional +multivariate time series, conditional on component g, g = 1, . . . , G, can be written as: +{yi | zig = 1} = (IK ⊗ X)αg + (IK ⊗ W )βg + ϵi, +(1) +where {zig}G +g=1 are latent indicators as described in Section 3.3, αg = (α′ +g1, . . . , α′ +gK)′ is a 2K-vector of intercepts +and slopes, βg = (β′ +g1, . . . , β′ +gK)′ is a mK-vector of basis function coefficients as described in Section 4.1, IK is a +K × K identity matrix and ⊗ denotes a tensor product. The matrix X is given by X = +� +1 +1 +. . . +1 +t1 +t2 +. . . +tn +�′ +and the +m columns of the matrix W are smoothing splines basis functions as described in Section 4.1. We assume the error +vector ϵi follows a MVN(0, Ψg ⊗ U) distribution, where U = In is the n × n identity matrix, and Ψg = diag(σ2 +g) is +a K × K diagonal matrix with the error variances σ2 +g = (σ2 +g1, . . . , σ2 +gK)′. We assume each subject has a common grid +of time points across all K entries, such that X and W are common to all subjects, although our proposed method +can be generalized to the case where subjects are observed at different grids of time points. In addition, we assume +E(yik, yih) = 0n×n for k ̸= h. +3 + +Covariate-guided Bayesian mixture model for multivariate time series +To simplify notation, we let S = [X W ] and θg = (α′ +g1, β′ +g1, . . . , α′ +gK, β′ +gK)′. Equation (1) can then be rewritten as: +{yi | zig = 1} = (IK ⊗ S)θg + ϵi. +(2) +3.2 +Model for the mixing weights +The mixture-of-experts model (Jacobs and others, 1991) is applied to form a covariate-guided structure for our proposed +model, where the mixing weights are multinomial logits that are functions of selected covariates. As in Sun and others +(2007), the mixing weights are expressed as +πig(V i) = +exp(V ′ +iδg + ζig) +�G +h=1 exp(V ′ +iδh + ζih) +, +(3) +where V i = (1, Vi1, · · · , ViP )′ is a vector of length (P + 1) containing values of P covariates for subject i, and +δg = (δg0, δg1, · · · , δgP )′ is the corresponding coefficient vector. For identifiability, we set δG = 0. Equation (3) +differs slightly from the weights in the traditional mixture of experts model in that it includes a random term ζig for each +subject. This term accounts for unmeasured factors beyond the observed covariates, and enhances model performance +and inference of the mixing weights. +3.3 +Augmented likelihood +To account for heterogeneity across subjects, we assume that the kth entry of the multivariate time series, yik, comes +from a mixture model with G components, i.e., +yik ∼ +G +� +g=1 +πigfgk(yik | µgk, σ2 +gkIn), +(4) +where fgk(yik | µgk, σ2 +gkIn) is the probability density function of the multivariate normal distribution with mean +vector µgk = Xαgk + W βgk and covariance matrix σ2 +gkIn for the gth component and the kth entry. The πig are +mixing weights that depend on covariates as described in Section 3.2. +As is common in mixture models, augmenting the likelihood with latent variables indicating the component from which +a time series originates simplifies the computation greatly (Dempster and others, 1977). In particular, let zig = 1 +if the ith multivariate time series belongs to the gth component and zig = 0, otherwise. Let y = (y1, . . . , yN)′ +be all observed multivariate time series and Θgk be the aggregation of all parameters for component g and entry k. +The parameter vector for all components and all entries is then denoted by Θ = (Θ′ +11, . . . , Θ′ +GK)′. The augmented +likelihood of all N multivariate time series is given by +L(Θ | y, Z) = +N +� +i=1 +G +� +g=1 +� +πig +K +� +k=1 +fgk(yik | Θgk) +�zig +, +(5) +where fgk(yik | Θgk) is the probability density function as appeared in the (4). From Bayes’ rule, the distribution of +the latent indicators zig is given by +p(zig = 1 | y, S, Θ, πig) = +πig +�K +k=1 fgk(yik | Θgk) +�G +h=1 πih +�K +k=1 fhk(yik | Θhk) +. +(6) +4 +Priors +In this section, the priors on the model parameters are introduced. +4.1 +Smoothing splines prior +The conditional expectation of a mixture component in model (4) is given by E(yik | zig = 1) = Xαgk + W βgk. +We place a smoothing spline prior on βgk and let Hgk = W βgk, where Hgk = +� +Hgk(t1), . . . , Hgk(tn) +�′ is a +zero-mean Gaussian process with variance covariance matrix τ 2 +gkΦ (Wahba, 1980; Wood and others, 2002), such that +cov +� +Hgk(tr), Hgk(th) +� += τ 2 +gkφrh, τ 2 +gk is a smoothing parameter for component g and entry k, and the (r, h)th element +4 + +Covariate-guided Bayesian mixture model for multivariate time series +of Φ is given by φrh = 1 +2t2 +r(th − tr +3 ) for tr ≤ th. The matrix Φ is common to all subjects since all entries of the +multivariate time series are observed at common time points. +As seen above, the matrix Φ is n × n, and to avoid the computational burden for large n, a low-rank approximation +is often adopted. To facilitate this approximation, we obtain basis functions via the spectral decomposition of Φ, as +has been proposed in Wood and others (2002) and used in Rosen and others (2009, 2012); Krafty and others (2011). +In particular, the matrix W consists of m basis functions evaluated at times t1, . . . , tn, and βgk is an m-dimensional +vector of basis function coefficients. These basis functions are obtained by applying the spectral decomposition to +Φ such that Φ = QΓQT , where Q is the matrix of eigenvectors of Φ, and Γ is a diagonal matrix containing the +eigenvalues of Φ. We then let the design matrix W = QΓ1/2 and place a normal prior N(0, τ 2 +gkIn) on βgk, which +leads to Hgk or W βgk ∼ N(0, τ 2 +gkΦ) as mentioned above. +By using the low-rank approximation, the number of columns of W is reduced from n to m (m < n), which greatly +reduces the computational burden without sacrificing the model fit (Wahba, 1980; Wood, 2006). Eubank (1999) +indicated that the eigenvalues in the diagonal matrix Γ decay rapidly as m increases. Thus, we can achieve a good +approximation by selecting a relatively small number m of basis functions. The number of basis functions m is set to +10 in simulation studies as described in Section 6, which has been shown (Krafty and others 2011) to explain more than +98% of the total variability. +The prior on θg is thus θg ∼ N(0, Dg), where Dg = diag(σ2 +α112, τ 2 +g11m, . . . , σ2 +αK12, τ 2 +gK1m) is the covariance +matrix of θg. The vector (σ2 +α1, . . . , σ2 +αK)′ contains fixed prior variances for the regression coefficients αgk, common to +all components and entries. In particular, we fix the common prior variance σ2 +α = 100. The vector τ 2 +g = (τ 2 +g1, . . . , τ 2 +gK)′ +contains the smoothing parameters for the gth mixture component and 1m is an m-vector of ones. We assume +independence between the regression coefficients αgk and the basis function coefficients βgk. +4.2 +Priors on the smoothing parameters +We assume the smoothing parameters τ 2 +g = (τ 2 +g1, . . . , τ 2 +gK)′ vary across components g and entries k. Although the most +common choice for the prior on a variance parameter is the inverse gamma distribution, Gelman (2006) and Wand and +others (2011) suggested that a half-t prior on the standard deviation can reflect lack of information on a scale parameter. +The half-t is a family of heavy-tailed distributions and has a good shrinkage performance. It can be expressed as a scale +mixture of inverse gamma random variables using a latent variable which follows an inverse gamma distribution (Wand +and others, 2011). Thus, we assume a half-t distribution such that τgk ∼ t+ +ντ (0, Aτ), where ντ is a degrees of freedom +parameter, and Aτ is a scale parameter. We set ντ = 3 and Aτ = 10 for all components and entries. +4.3 +Priors on the error variances +We assume σgk +i.i.d +∼ t+ +νσ(0, Aσ) and set νσ = 3 and Aσ = 10 for all components and entries. +4.4 +Priors on the logistic parameters and the variances of random intercepts +This section provides details on the prior distributions placed on the parameters of the logistic weights (3). For ease of +notation, we denote δ∗ +g = (δT +g , ζT +g )T , where ζg = (ζ1g, · · · , ζNg)T , g = 1, . . . , G. We let V ∗ +i = (V ′ +i, e′ +i)′ where ei is +a vector of all zeros except for a single 1 in the ith position, and V ∗ is a matrix consisting of the rows V ∗T +i , i = 1, . . . , N. +Gaussian priors are placed on the logistic parameters, i.e., δ∗ +g ∼ N(0, Bg), where Bg = diag(σ2 +δg1P+1, κ2 +ζg1N), and +the priors on the random intercepts satisfy ζg ∼ N(0, κ2 +ζgIN). As for the hyperparameters, we assume σ2 +δg = 10 for +all components and covariates, and κζg ∼ t+ +νκ(0, Aκ), where νκ = 3 and Aκ = 10 for all components. +To sample the logistic parameters, Polson and others (2013) proposed a data augmentation scheme incorporating +Pólya-Gamma latent variables, which facilitates Gibbs steps. Details on sampling the logistic parameters are provided +in the Supplementary Material. +5 +Sampling scheme +This section outlines the Gibbs steps for sampling from the conditional posterior distributions of all the model parameters. +More details are given in Supplementary Material. +5 + +Covariate-guided Bayesian mixture model for multivariate time series +5.1 +Gibbs sampling steps +Letting ℓ denote the current Gibbs sampling iteration, parameter values at the (ℓ + 1)th iteration are drawn according to +the following steps. +1. Draw θ(ℓ+1) +gk +from (θ(ℓ+1) +gk +| y, S, τ 2(ℓ) +gk , σ2(ℓ) +gk ) ∼ N(ugk, σ2 +gkΛgk), where ugk and Λgk are mean vectors and +covariance matrices. +2. Draw σ2(ℓ+1) +gk +from (σ2(ℓ+1) +gk +| ϵ(ℓ+1) +igk +, a(ℓ+1) +σgk +) ∼ IG +� +(nN (ℓ) +g ++ νσ)/2, �N +i=1 zigϵ′ +igkϵigk/2 + νσ/aσgk +� +, +where N (ℓ) +g +is the current number of subjects in the gth component, ϵigk is the error vector for the gth +component, the ith subject and the kth entry, and aσgk is a latent variable in the IG scale mixture underlying +the half-t distribution. +3. Draw τ 2(ℓ+1) +gk +from (τ 2(ℓ+1) +gk +| β(ℓ+1) +gk +, a(ℓ+1) +τgk +) ∼ IG +� +(ντ + m)/2, β′ +gkβgk/2 + ντ/aτgk +� +, where aτgk is a +latent variable as in 2. +4. Draw δ∗(ℓ+1) +g +from (δ∗(ℓ+1) +g +| V ∗, z(ℓ) +ig , ω(ℓ+1) +ig +, κ2(ℓ) +ζg ) ∼ N(M g, Σg), where ω(ℓ+1) +ig +is a Pólya-Gamma latent +variable in the augmentation described in Section 4.4. +5. Draw κ2(ℓ+1) +ζg +from (κ2(ℓ+1) +ζg +| ζ(ℓ+1) +g +, a(ℓ+1) +κg +) ∼ IG +� +νκ/2, ζ′ +gζg/2 + (νκ + N)/aκg +� +, where aκg is a latent +variable as in 2 and 3. +6. The mixing weights π(ℓ+1) +ig +are obtained by computing p(π(ℓ+1) +ig +| V ∗, δ∗(ℓ+1) +g +, z(ℓ) +ig ) from Equation (3). +7. Draw z(ℓ+1) +ig +∼ p(z(ℓ+1) +ig += 1 | y, S, θ(ℓ+1) +gk +, σ2(ℓ+1) +gk +, π(ℓ+1) +ig +) according to Equation (6). +5.2 +Selecting the number of components +Spiegelhalter and others (2002) suggested the use of the deviance information criterion (DIC) for model selection +based on the effective number of parameters. Gelman and others (2003) introduced an alternative measure of effective +number of parameters based on the variance of the log predictive density across MCMC iterations. This measure is +robust and more accurate than the original one. Moreover, it has the advantages of always being positive and invariant +to reparameterizations (Gelman and others, 2003). +In this paper, we use DIC to select the number of components for our proposed mixture model. +6 +Simulation studies +To demonstrate the performance of the proposed method, we conduct simulation studies by generating data sets from +the proposed model under two scenarios: two-component mixture (G = 2) of trivariate time series (K = 3) and +four-component mixture (G = 4) of bivariate time series (K = 2). We simulate 100 replicates in each simulation +setting with N = 150 time series of length n = 50. A total of 20, 000 Gibbs sampling iterations are run with a burn-in +of 4, 000. In all simulation settings, the hyperparameters are assigned the same values, given in Section 4. +6.1 +Two-component trivariate model +In this scenario, we consider the two-component trivariate model. From Equation (1), the gth component of the proposed +mixture model is given by +{y(tj) | zig = 1} = α0g + α1gtj + +m +� +q=1 +wq(tj)βgq + ϵgtj, +j = 1, . . . , n, g = 1, . . . , G, +(7) +where y(tj) is the trivariate time series evaluated at time tj, α01 = (1, −3, −2)′, α02 = (5, 4, 3)′ and α11 = +(−2, 2, 0.5)′, α12 = (1, −1, −0.5)′ are independent intercepts and slopes for each component, respectively. The vector +βgq consists of the qth spline coefficients of all variates for component g, and wq(tj) is the qth spline basis function eval- +uated at time tj. The ϵgtj are independent zero-mean error terms, distributed as ϵgtj ∼ MVN +� +0, diag(σ2 +g1, σ2 +g2, σ2 +g3) +� +, +where σ2 +1 = (σ2 +11, σ2 +12, σ2 +13)′ = (3, 5, 4.5)′ and σ2 +2 = (σ2 +21, σ2 +22, σ2 +23)′ = (4, 3.5, 4)′. The smoothing parameters are set +to τ 2 +1 = (τ 2 +11, τ 2 +12, τ 2 +13)′ = (3.5, 5, 8.5)′ and τ 2 +2 = (τ 2 +21, τ 2 +22, τ 2 +23)′ = (6, 2.5, 1.5)′. +6 + +Covariate-guided Bayesian mixture model for multivariate time series +We investigate the performance of the trajectory and logistic parameter (see Equation (3)) estimates. For the former, we +calculate the averaged root square error (ARSE) of each mixture component g +ARSEg = +� +� +� +� 1 +nK +n +� +j=1 +K +� +k=1 +� +µgk(tj) − ˆµgk(tj) +�2 +, +where µgk(tj) is the expectation of yk(tj) according to the gth component, and yk(tj) is the kth entry of the time series +evaluated at time tj. The ˆµgk(tj) are the estimated posterior means of µgk(tj) for k = 1, . . . , K and j = 1, . . . , n. +To handle a potential label switching across mixture components, we compute ARSEg as the minimum value across all +components, by using the estimate of the gth component and the truth of each group, g = 1, . . . , G. After obtaining +correct component labels by evaluating ARSE, we also report the averaged bias (A-bias) and the variance of the bias +(V-bias) of each mixture component g, where +A-biasg = +1 +nK +n +� +j=1 +K +� +k=1 +� +ˆµgk(tj) − µgk(tj) +� +, +and V-biasg is computed by calculating the sample variance of the bias over entries and time points. +For each replicate, time series trajectories are estimated by three methods: the proposed method, the R package gbmt +(Magrini, 2022) and the TRAJ procedure in SAS (Nagin and others, 2018). Boxplots of ARSE, A-bias and V-bias of +each component are given in Figure 3. Notably, TRAJ is able to fit a regression spline model by treating basis functions +as time-varying covariates, while gbmt is only able to fit a cubic model. Our proposed method fits a penalized spline +model under the Bayesian framework and is able to outperform both gbmt and TRAJ in terms of ARSE and V-bias for +both components. A-biases are close to zero and comparable for all three methods. These findings demonstrate that +all three methods are able to achieve a reasonable fit to group-based trajectories since bias over the entire time series +is close to zero. Our proposed method is able to obtain more precise estimates of trajectories as is evident from the +smaller V-biases. +To evaluate the performances of the logistic parameters, we compute the root mean squared error (RMSE) for each +logistic parameter using the proposed method and TRAJ. Notably, gbmt is not able to incorporate covariates into the +computation of mixing weights. Results of RMSEs of each logistic parameter are given in Table 1. We also compare +RMSEs between the proposed method and TRAJ under four settings of different combinations of N = 150, 250 and +n = 50, 70. Our proposed method yields smaller RMSEs of the logistic parameters in all cases, especially for the +intercept δ0 and the first covariate δ1. This is to be expected since TRAJ uses a multinomial logistic model, which may +result in inflated parameter estimates in cases of unbalanced outcomes or perfect separation, while our proposed method +is able to obtain a shrinkage result using the penalization method. +6.2 +Four-component bivariate model +In this scenario, we consider the four-component bivariate model whose gth component is given in Equation (7), +where the values of the intercepts and slopes are α01 = (1, −2)′, α02 = (5, 3)′, α03 = (−3, 5.5)′, α04 = (4, −1)′, +α11 = (−3, 0)′, α12 = (2, −3.5)′, α13 = (2.5, 2)′ and α14 = (−3, 1.5)′. By analogy to the two-component +trivariate model, the errors ϵgtj are independent zero-mean bivariate Gaussian random variables, distributed as ϵgtj ∼ +MVN +� +0, diag(σ2 +g1, σ2 +g2) +� +, where σ2 +1 = (σ2 +11, σ2 +12)′ = (6, 9)′, σ2 +2 = (σ2 +21, σ2 +22)′ = (8, 7.5)′, σ2 +3 = (σ2 +31, σ2 +32)′ = +(10, 6.5)′ and σ2 +4 = (σ2 +41, σ2 +42)′ = (7, 8.5)′. +The performances of the estimated trajectories and logistic parameters for this scenario are displayed in Figure 4 and +Table 2. As in the first scenario, our proposed method outperforms both gbmt and TRAJ in terms of ARSE and V-bias +for all components. Notably, TRAJ fails to yield precise estimates in several replicates and thus results in larger mean +ARSE and V-bias. In terms of the logistic parameters, the proposed method performs well with smaller RMSEs in +almost all cases, especially for δ0 and δ1. More simulation results based on different values of N and n under the two +scenarios considered above are presented in the Supplementary Material. +7 +Real data application +We apply our proposed method to the analysis of the fNIRS still-face study introduced in Section 2. Six covariates +are considered in our covariate-guided model, including Infant Behavior Questionnaire-Revised negative emotionality +(IBQ-NE) score, Infant Behavior Questionnaire-Revised effortful control (IBQ-EC) score, gestational age (in Days), +7 + +Covariate-guided Bayesian mixture model for multivariate time series +infant age (in Months), head circumference (in cm) and sex. All continuous covariates are centered and scaled. We set +the number of basis functions at m = 20 and run a total of 30, 000 Gibbs iterations with a burn-in period of 6, 000. The +values of the hyperparameters are the same as the ones used in the simulation studies. +The IBQ-NE construct combines data from the following subscales: Sadness, Distress to Limitations, Fear, and Falling +Reactivity/Rate of Recovery from Distress. IBQ-EC refers to the ability to inhibit a dominant response to perform a +subdominant one and has been shown to be protective against a myriad of difficulties (Gartstein and others, 2013). +Finally, the data consist of 79 subjects with complete fNIRS and covariate values. We present results based on analyzing +one set of four-channels. Additional results based on analyzing another set of four channels and all channels are given +in the Supplementary Material. The four channels are S1D1, S2D2, S5D3 and S6D4. Channels S1D1 and S5D3 are in +the central prefrontal region, while channels S2D2 and S6D4 are in the left and right prefrontal region, respectively. We +fit our proposed model with the number of components varying from 2 to 6. Based on values of DIC introduced in +Section 5.2, the two-component model is selected as the best model for this four-channel analysis. +Figure 5 presents the estimated trajectories of the two-component model fitted to the four channels. We are interested in +brain activation signals in the still-face period while the interact period is used as the reference level. For component +1, a decreasing trajectory is observed for the still-face period in all four channels. In contrast, an increasing trend is +observed for the still-face period in all four channels for component 2. After fitting the mixture model and finding +above trajectory patterns, we define component 1 as the no response component and component 2 as the response +component based on trajectory patterns in the still-face period. Figure 6 displays the logistic parameter estimates for all +covariates in the 2-component model, where component 2 is used as the reference. There is evidence that IBQ-NE +scores differ between the two components as its 95% credible interval does not include zero. A positive coefficient of +IBQ-NE indicates that a higher IBQ-NE score is associated with component 1, which has decreased brain activation +levels in the still-face period for all four channels. Though other logistic coefficients have 95% credible intervals that +include zero, the negative posterior mean estimate of the IBQ-EC score could still indicate that a high IBQ-EC is +associated with an increased brain activation as shown for component 2. These conclusions are consistent with findings +in Gartstein and others (2013) that IBQ-NE is negatively associated with IBQ-EC. Enlow and others (2016) reported +a negative association between activity level and IBQ-NE among infants whose families encourage a high level of +activities. Furthermore, a negative posterior mean of logistic coefficient of infant age suggests that younger infant tends +to have a decreasing brain activation level in the still-face period. +8 +Discussion +The proposed covariate-guided Bayesian mixture of spline experts model aims to perform a model-based clustering of +multivariate time series from multiple subjects. The mixture components in this model are penalized splines, and the +mixing weights incorporate covariates. Our proposed method is compared to two commonly used methods through +simulation studies which demonstrate a better performance of our method under different scenarios. We apply our +proposed method to a fNIRS still-face study and find distinct patterns of components of time series trajectories, as well +as an association between IBQ-NE score and a pattern of decreased brain activity in the still-face period. To the best of +our knowledge, this is the first still-face study using fNIRS whose purpose is to identify trajectory components. +Our proposed method has some limitations. First, as in any mixture models, label switching may occur, especially in +the real-data application. We have adopted the Equivalence Classes Representatives (ECR) algorithm proposed by +Papastamoulis and Iliopoulos (2010) to make the components interpretable, but other methods may be considered. +Second, the proposed method assumes independence among the entries of the time series and does not allow spatial +dependence. Spatial correlations of fNIRS are correlations among fNIRS channels based on the placements and +locations of each source and detector. An extension to a multilevel multivariate model would be possible by considering +spatial correlations among time series entries. Lastly, our proposed method uses DIC to select the number of components +which might be sub-optimal. Bayesian model averaging and reversible jump MCMC (RJMCMC) methods could be +considered, but trans-dimensional sampling methods would pose challenges in providing interpretable components. +9 +Software +Software in the form of R codes, together with an example data, is available at https://github.com/HaoyiFu1993/ +CBMOSE. +8 + +Covariate-guided Bayesian mixture model for multivariate time series +References +ADAMSON, LAUREN B AND FRICK, JANET E. (2003). The still face: A history of a shared experimental paradigm. +Infancy 4(4), 451–473. +BERTOLACCI, MICHAEL, ROSEN, ORI, CRIPPS, EDWARD AND CRIPPS, SALLY. (2022). Adaptspec-x: Covariate- +dependent spectral modeling of multiple nonstationary time series. Journal of Computational and Graphical +Statistics 31(2), 436–454. +DEMPSTER, ARTHUR P, LAIRD, NAN M AND RUBIN, DONALD B. (1977). Maximum likelihood from incomplete +data via the em algorithm. Journal of the Royal Statistical Society: Series B (Methodological) 39(1), 1–22. +ENLOW, MICHELLE BOSQUET, WHITE, MATTHEW T, HAILS, KATHERINE, CABRERA, IVAN AND WRIGHT, ROS- +ALIND J. (2016). The infant behavior questionnaire-revised: Factor structure in a culturally and sociodemographically +diverse sample in the united states. Infant Behavior and Development 43, 24–35. +EUBANK, RANDALL L. (1999). Nonparametric regression and spline smoothing. CRC press. +GARTSTEIN, MARIA A, BRIDGETT, DAVID J, YOUNG, BRANDI N, PANKSEPP, JAAK AND POWER, THOMAS. +(2013). Origins of effortful control: Infant and parent contributions. Infancy 18(2), 149–183. +GARTSTEIN, MARIA A AND ROTHBART, MARY K. (2003). Studying infant temperament via the revised infant +behavior questionnaire. Infant behavior and development 26(1), 64–86. +GELMAN, ANDREW. (2006). Prior distributions for variance parameters in hierarchical models (comment on article by +browne and draper). Bayesian analysis 1(3), 515–534. +GELMAN, A, CARLIN, JB, STERN, HS, RUBIN, DB and others. (2003). Bayesian data analysis. +GILLMAN, MATTHEW W AND BLAISDELL, CAROL J. (2018). Environmental influences on child health outcomes, a +research program of the nih. Current opinion in pediatrics 30(2), 260. +GU, CHONG. (2013). Smoothing spline ANOVA models, Volume 297. Springer. +GU, CHONG AND KIM, YOUNG-JU. (2002). Penalized likelihood regression: General formulation and efficient +approximation. Canadian Journal of Statistics 30(4), 619–628. +HE, LINCHEN, WANG, CHAN, HU, JIYUAN, GAO, ZHAN, FALCONE, EMILIA, HOLLAND, STEVEN M, BLASER, +MARTIN J AND LI, HUILIN. (2022). Arzimm: A novel analytic platform for the inference of microbial interactions +and community stability from longitudinal microbiome study. Frontiers in genetics 13. +HIPWELL, ALISON E, TUNG, IRENE, NORTHRUP, JESSIE AND KEENAN, KATE. (2019). Transgenerational asso- +ciations between maternal childhood stress exposure and profiles of infant emotional reactivity. Development and +psychopathology 31(3), 887–898. +HUERTA, GABRIEL, JIANG, WENXIN AND TANNER, MARTIN A. (2003). Time series modeling via hierarchical +mixtures. Statistica Sinica, 1097–1118. +JACOBS, ROBERT A, JORDAN, MICHAEL I, NOWLAN, STEVEN J AND HINTON, GEOFFREY E. (1991). Adaptive +mixtures of local experts. Neural computation 3(1), 79–87. +JOBSIS, FRANS F. (1977). Noninvasive, infrared monitoring of cerebral and myocardial oxygen sufficiency and +circulatory parameters. Science 198(4323), 1264–1267. +JORDAN, MICHAEL I AND JACOBS, ROBERT A. (1994). Hierarchical mixtures of experts and the em algorithm. +Neural computation 6(2), 181–214. +KAKIZAWA, YOSHIHIDE, SHUMWAY, ROBERT H AND TANIGUCHI, MASANOBU. (1998). Discrimination and +clustering for multivariate time series. Journal of the American Statistical Association 93(441), 328–340. +KEENAN, KATE, HIPWELL, ALISON, CHUNG, TAMMY, STEPP, STEPHANIE, STOUTHAMER-LOEBER, MAGDA, +LOEBER, ROLF AND MCTIGUE, KATHLEEN. (2010). The pittsburgh girls study: overview and initial findings. +Journal of Clinical Child & Adolescent Psychology 39(4), 506–521. +KEOGH, EAMONN J AND PAZZANI, MICHAEL J. (2000). A simple dimensionality reduction technique for fast +similarity search in large time series databases. In: Pacific-Asia conference on knowledge discovery and data mining. +Springer. pp. 122–133. +KIMELDORF, GEORGE S AND WAHBA, GRACE. (1970). A correspondence between bayesian estimation on stochastic +processes and smoothing by splines. The Annals of Mathematical Statistics 41(2), 495–502. +KRAFTY, ROBERT T, HALL, MARTICA AND GUO, WENSHENG. (2011). Functional mixed effects spectral analysis. +Biometrika 98(3), 583–598. +9 + +Covariate-guided Bayesian mixture model for multivariate time series +KRAFTY, ROBERT T, ROSEN, ORI, STOFFER, DAVID S, BUYSSE, DANIEL J AND HALL, MARTICA H. (2017). +Conditional spectral analysis of replicated multiple time series with application to nocturnal physiology. Journal of +the American Statistical Association 112(520), 1405–1416. +LI, CEN, BISWAS, GAUTAM, DALE, MIKE AND DALE, PAT. (2001). Building models of ecological dynamics using +hmm based temporal data clustering—a preliminary study. In: International Symposium on Intelligent Data Analysis. +Springer. pp. 53–62. +LI, ZEDA AND KRAFTY, ROBERT T. (2019). Adaptive bayesian time–frequency analysis of multivariate time series. +Journal of the American Statistical Association 114(525), 453–465. +LIAO, T WARREN. (2005). Clustering of time series data—a survey. Pattern recognition 38(11), 1857–1874. +LIN, JESSICA, KEOGH, EAMONN AND TRUPPEL, WAGNER. (2003). Clustering of streaming time series is meaningless. +In: Proceedings of the 8th ACM SIGMOD workshop on Research issues in data mining and knowledge discovery. pp. +56–65. +MAGRINI, ALESSANDRO. (2022). Assessment of agricultural sustainability in european union countries: a group-based +multivariate trajectory approach. AStA Advances in Statistical Analysis, 1–31. +MAHARAJ, ELIZABETH ANN. (1999). Comparison and classification of stationary multivariate time series. Pattern +Recognition 32(7), 1129–1138. +MAHARAJ, ELIZABEH ANN, D’URSO, PIERPAOLO AND CAIADO, JORGE. (2019). Time Series Clustering and +Classification. chapman and hall/CRC. +NAGIN, DANIEL S, JONES, BOBBY L, PASSOS, VALERIA LIMA AND TREMBLAY, RICHARD E. (2018). Group-based +multi-trajectory modeling. Statistical methods in medical research 27(7), 2015–2023. +PAPASTAMOULIS, PANAGIOTIS AND ILIOPOULOS, GEORGE. (2010). An artificial allocations based solution to the +label switching problem in bayesian analysis of mixtures of distributions. Journal of Computational and Graphical +Statistics 19(2), 313–331. +POLSON, NICHOLAS G, SCOTT, JAMES G AND WINDLE, JESSE. (2013). Bayesian inference for logistic models using +pólya–gamma latent variables. Journal of the American statistical Association 108(504), 1339–1349. +ROSEN, ORI, STOFFER, DAVID S AND WOOD, SALLY. (2009). Local spectral analysis via a bayesian mixture of +smoothing splines. Journal of the American Statistical Association 104(485), 249–262. +ROSEN, ORI, WOOD, SALLY AND STOFFER, DAVID S. (2012). Adaptspec: Adaptive spectral estimation for +nonstationary time series. Journal of the American Statistical Association 107(500), 1575–1589. +SANTOSA, HENDRIK, ZHAI, XUETONG, FISHBURN, FRANK AND HUPPERT, THEODORE. (2018). The nirs brain +analyzir toolbox. Algorithms 11(5), 73. +SPECKMAN, PAUL L AND SUN, DONGCHU. (2003). Fully bayesian spline smoothing and intrinsic autoregressive +priors. Biometrika 90(2), 289–302. +SPIEGELHALTER, DAVID J, BEST, NICOLA G, CARLIN, BRADLEY P AND VAN DER LINDE, ANGELIKA. (2002). +Bayesian measures of model complexity and fit. Journal of the royal statistical society: Series b (statistical +methodology) 64(4), 583–639. +SUN, ZHUOXIN, ROSEN, ORI AND SAMPSON, ALLAN R. (2007). Multivariate bernoulli mixture models with +application to postmortem tissue studies in schizophrenia. Biometrics 63(3), 901–909. +TRONICK, EDWARD, ALS, HEIDELISE, ADAMSON, LAUREN, WISE, SUSAN AND BRAZELTON, T BERRY. (1978). +The infant’s response to entrapment between contradictory messages in face-to-face interaction. Journal of the +American Academy of Child psychiatry 17(1), 1–13. +WAHBA, GRACE. (1978). Improper priors, spline smoothing and the problem of guarding against model errors in +regression. Journal of the Royal Statistical Society: Series B (Methodological) 40(3), 364–372. +WAHBA, GRACE. (1980). Automatic smoothing of the log periodogram. Journal of the American Statistical Associa- +tion 75(369), 122–132. +WAND, MATTHEW P, ORMEROD, JOHN T, PADOAN, SIMONE A AND FRÜHWIRTH, RUDOLF. (2011). Mean field +variational bayes for elaborate distributions. Bayesian Analysis 6(4), 847–900. +WANG, XIAOZHE, WIRTH, ANTHONY AND WANG, LIANG. (2007). Structure-based statistical features and multi- +variate time series clustering. In: Seventh IEEE international conference on data mining (ICDM 2007). IEEE. pp. +351–360. +WANG, YUEDONG. (2011). Smoothing splines: methods and applications. CRC press. +10 + +Covariate-guided Bayesian mixture model for multivariate time series +WOOD, SALLY A, JIANG, WENXIN AND TANNER, MARTIN. (2002). Bayesian mixture of splines for spatially +adaptive nonparametric regression. Biometrika 89(3), 513–528. +WOOD, SIMON N. (2006). Generalized additive models: an introduction with R. chapman and hall/CRC. +11 + +Covariate-guided Bayesian mixture model for multivariate time series +Figure 1: fNIRS probe configuration. (a) Positioning of 8 sources, 4 detectors and 12 channels. A channel is connected +by one source and one detector (blue line). (b) Brodmann areas covered by fNIRS probe. +Figure 2: An example of processed fNIRS time series from two selected subjects and four selected channels. The +measurements are the relative concentration of oxy-hemoglobin. +12 + +(a) +(b) +BA-9L +BA-44L +BA-45L +BA-46L +BA-9R +BA-45R +BA-46R +Source +Detector +ChannelChannel1 +Channel2 +Channel3 +Channel4 +1.00 +0.75 +Subject 1 +0.50 +series +0.25 +0.00 +Time +1.00 +0.75 +Subject 2 +0.50- +0.25 +0.00 +00 +50 +75 +25 +TimeCovariate-guided Bayesian mixture model for multivariate time series +Figure 3: Boxplots of the averaged root square error (ARSE), the averaged bias (A-bias) and the variance of bias +(V-bias) of estimated trajectories for each component from 100 replicates of 150 two-component trivariate time series of +length 50. The proposed method was compared to R package gbmt and TRAJ procedure in SAS. The diamond markers +denote the mean statistics of each method and component. +Table 1: Root mean square errors (RMSEs) of each logistic parameter for the two-component trivariate model from 100 +replicates of N two-component trivariate time series of length n. RMSEs of the proposed method were compared to +TRAJ procedure in SAS. Parameters δ0, δ1, δ2 and δ3 are intercept, first, second and third logistic parameters, respectively. +The true values of logistic parameters are 5, −3.5, 1, 0.1, respectively +n +N +Method +δ0 +δ1 +δ2 +δ3 +50 +150 +Proposed +0.89 +0.52 +0.29 +0.32 +TRAJ +1.57 +0.87 +0.36 +0.34 +70 +150 +Proposed +0.86 +0.50 +0.29 +0.31 +TRAJ +1.55 +0.86 +0.36 +0.34 +50 +250 +Proposed +0.77 +0.40 +0.22 +0.23 +TRAJ +0.96 +0.50 +0.23 +0.24 +70 +250 +Proposed +0.77 +0.41 +0.22 +0.23 +TRAJ +0.97 +0.51 +0.24 +0.24 +13 + +0.04 +0.150 +0.02 +0.02 +0.125 +0.00 +RSE +A-bias +V-bias +AR +0.100 +0.02 +0.01 +0.075 +0.04 +0.050 +2 +2 +Component +Component +Component +MethodProposed +gbmt TRAJCovariate-guided Bayesian mixture model for multivariate time series +Figure 4: Boxplots of the averaged root square error (ARSE), the averaged bias (A-bias) and the variance of bias +(V-bias) of estimated trajectories for each component from 100 replicates of 150 four-component bivariate time series of +length 50. The proposed method was compared to R package gbmt and TRAJ procedure in SAS. The diamond markers +denote the mean statistics of each method and component. All boxplots are zoomed in for better visualization. +Table 2: Root mean square errors (RMSEs) of each logistic parameter for the four-component bivariate model from 100 +replicates of 150 four-component bivariate time series of length 50. RMSEs of the proposed method were compared to +TRAJ procedure in SAS. Parameters δ0, δ1, δ2 and δ3 are intercept, first, second and third logistic parameters, respectively. +The fourth component was used as the reference component. The true values of logistic parameters are 5, −3.5, 1, 0.1 +(first component), −4, 2.5, −2, −0.2 (second component), 3, −2, 0.8, 0.2 (third component). C1, C2, C3 and C4 denote +first, second, third and fourth component, respectively. +n +N +Method +Comparison +δ0 +δ1 +δ2 +δ3 +50 +150 +Proposed +C1 vs C4 +0.81 +0.53 +0.30 +0.39 +C2 vs C4 +1.11 +0.46 +0.42 +0.36 +C3 vs C4 +0.89 +0.42 +0.28 +0.34 +TRAJ +C1 vs C4 +1.20 +0.74 +0.35 +0.41 +C2 vs C4 +3.81 +2.27 +1.33 +0.49 +C3 vs C4 +2.07 +1.33 +0.76 +0.32 +14 + +0.08 +0.20 +0.020 +0.15 +0.04 +0.015 +RSE +ias +sel +AR +0.10 +0.00 +0.010 +0.05 +-0.04 +0.005 +0.00 +0.000 +0.08 +4 +2 +3 +4 +3 +4 +Component +Component +Component +Method +dProposed +gbmt +TRAJCovariate-guided Bayesian mixture model for multivariate time series +Figure 5: Estimated trajectories of the two-component model with four selected channels. I: Interact S: Still-face R: +Recovery. Red curves are posterior mean and two green dashed curves are 95% pointwise credible intervals. +15 + +S1D1 +S2D2 +S5D3 +S6D4 +0.7 +S +R +... +S +.. +R +S +R +.. +S +.. +R +0.6 +Component1 +0.5 +Itrajectory +.......... +0.4 +.......... +..-. +0.3 +.. +Estimated +0.7 +........... +S +R +S +.-. +R +.-.. +S +... +R +- + + +S +.-.. +R +0.6 +Component2 +0.5 +0.4 +...... +0.3 +00 +00 +20 +0000 +25 +.00 +.25 +50 +15 +.75 +00 +0. +Time +Component 1:No response +Component2:ResponseCovariate-guided Bayesian mixture model for multivariate time series +Figure 6: Logistic coefficient estimates and 95% credible intervals for each covariate of the two-component model. +16 + +(Intercept) +IBQ-NE +IBQ-EC +Infant age +Gestational days +Head circumference +Sex +-5.0 +-2.5 +0.0 +2.5 +5.0 +Coefficient estimateCovariate-guided Bayesian mixture model for multivariate time series +10 +Supplemental material +Appendix A: Details of the sampling scheme +As described in Section 5 of the paper, Gibbs sampling is used to facilitate Bayesian inference. We denote by +Θgk = (θ′ +gk, τ 2 +gk, σ2 +gk, δ∗′ +g , κ2 +ζg)′ the parameters for the gth component and the kth entry, and the parameters in this +vector are drawn from the corresponding conditional posterior distributions. Let ℓ be the current Gibbs sampling +iteration; detailed Gibbs sampling steps for drawing the parameters at the (ℓ + 1)th iteration are given below. +1. Sampling the basis function coefficients +For each component g and time series entry k, based on the augmented likelihood in Section 3.3 and the +priors on θgk = (α′ +gk, β′ +gk)′ described in Section 4.1, the conditional posterior distribution of (θ(ℓ+1) +gk +| +y, S, τ 2(ℓ) +gk , σ2(ℓ) +gk ) is: +p(θ(ℓ+1) +gk +| y, S,τ 2(ℓ) +gk , σ2(ℓ) +gk ) ∝ p(y | S, θ(ℓ+1) +gk +, σ2(ℓ) +gk ) · p(θ(ℓ+1) +gk +| τ 2(ℓ) +gk ) +∝ +N +� +i=1 +� +(σ2 +gk)−n/2 exp +� +− +1 +2σ2 +gk +(yik − Sθgk)′(yik − Sθgk) +��zig +× |Dgk|−1/2 exp +� +− 1 +2θgkD−1 +gk θgk +� +∝ exp +� +− +1 +2σ2 +gk +� N +� +i=1 +zig(yik − Sθgk)′(yik − Sθgk) + θ′ +gkσ2 +gkD−1 +gk θgk +�� +∝ exp +� +− +1 +2σ2 +gk +(θgk − ugk)′(Λgk)−1(θgk − ugk) +� +∼ N(ugk, σ2 +gkΛgk), +where Λgk = (N (ℓ) +g S′S + σ2 +gkD−1 +gk )−1, ugk = Λgk +�N +i=1 zigS′yik, N (ℓ) +g +is the current number of subjects +in the gth component, Dgk = diag(σ2 +α12, τ 2 +gk1m) is the prior covariance matrix for θgk. Hence, for each +component g and entry k, we draw θ(ℓ+1) +gk +from (θ(ℓ+1) +gk +| y, S, τ 2(ℓ) +gk , σ2(ℓ) +gk ) ∼ N(ugk, σ2 +gkΛgk). +2. Sampling the error variances +Gelman (2006) proposed using the half-t distribution as the prior on scale parameters. We follow Wand and +others (2011) and express the half-t prior of Section 4.3 as a scale mixture of inverse Gamma distributions as +follows +(σ2 +gk | aσgk) ∼ IG +�νσ +2 , νσ +aσgk +� +, aσgk ∼ IG +�1 +2, 1 +A2σ +� +. +Therefore, the conditional posterior distribution of the latent variable aσgk is +p(a(ℓ+1) +σgk +| σ2(ℓ) +gk ) ∝ exp +� +− +1 +aσgk +� νσ +σ2 +gk ++ 1 +A2σ +�� +× (aσgk)−( 1 +2 +1+ νσ +2 ), +which is IG +� +νσ+1 +2 +, νσ +σ2 +gk + +1 +A2σ +� +. Denoting by ϵigk the error vector of time series yik for component g, we +have ϵigk = yik − Sθgk, where ϵigk ∼ N(0, σ2 +gkIn). The conditional distribution of the error variance is +p(σ2(ℓ+1) +gk +| ϵ(ℓ+1) +igk +, a(ℓ+1) +σgk +) ∝ p(ϵ(ℓ+1) +igk +| σ2(ℓ+1) +gk +) · p(a(ℓ+1) +σgk +| σ2(ℓ+1) +gk +) · p(σ2(ℓ+1) +gk +) +∝ +N +� +i=1 +� +(σ2 +gk)− n +2 exp +� +− +1 +2σ2 +gk +ϵ′ +igkϵigk +��zig +× (σ2 +gk)−( νσ +2 +1) exp +� +− +νσ +σ2 +gkaσgk +� +∝ (σ2 +gk)−( n +2 N (ℓ) +g ++ νσ +2 +1) exp +� +− +1 +σ2 +gk +��N +i=1 zigϵ′ +igkϵigk +2 ++ νσ +aσgk +�� +, +which is IG +� nN (ℓ) +g ++νσ +2 +, +�N +i=1 zigϵ′ +igkϵigk +2 ++ +νσ +aσgk +� +. The sampling scheme proceeds by first sampling (a(ℓ+1) +σgk +| +σ2(ℓ) +gk ) and then (σ2(ℓ+1) +gk +| ϵ(ℓ+1) +igk +, a(ℓ+1) +σgk +). +17 + +Covariate-guided Bayesian mixture model for multivariate time series +3. Sampling the smoothing parameters +The smoothing parameters τ 2 +gk are drawn by analogy to the error variances. We first draw (a(ℓ+1) +τgk +| τ 2(ℓ) +gk ) ∼ +IG +� +ντ +1 +2 +, ντ +τ 2 +gk + +1 +A2τ +� +. The conditional posterior distribution of the smoothing parameters is +p(τ 2(ℓ+1) +gk +| β(ℓ+1) +gk +, a(ℓ+1) +τgk +) ∝ p(β(ℓ+1) +gk +| τ 2(ℓ+1) +gk +) · p(a(ℓ+1) +τgk +| τ 2(ℓ+1) +gk +) · p(τ 2(ℓ+1) +gk +) +∝ (τ 2 +gk)− m+ντ +2 +exp +� +− 1 +τ 2 +gk +� ντ +aτgk ++ β′ +gkβgk +2 +�� +, +which is IG +� +ντ +m +2 +, +β′ +gkβgk +2 ++ +ντ +aτgk +� +. The sampling scheme proceeds by first sampling (a(ℓ+1) +τgk +| τ 2(ℓ) +gk ) and +then (τ 2(ℓ+1) +gk +| β(ℓ+1) +gk +, a(ℓ+1) +τgk +). +4. Sampling the logistic parameters +Let δ∗ +g = (δT +g , ζT +g )T be the aggregation of the logistic parameters and all random intercepts for the gth +component. Based on the logits of Section 3.2 and the corresponding priors described in Section 4.4, the +conditional posterior distribution of (δ∗(ℓ+1) +g +| V ∗, z(ℓ) +ig , κ2(ℓ) +ζg ) is +p(δ∗(ℓ+1) +g +| V ∗, z(ℓ) +ig , κ2(ℓ) +ζg ) ∝ p(z(ℓ) +ig = 1 | V ∗, δ∗(ℓ+1) +g +) · p(δ∗(ℓ+1) +g +| κ2(ℓ) +ζg ) += +N +� +i=1 +� +exp(V ∗′ +i δ∗ +g) +�G +h=1 exp(V ∗′ +i δ∗ +h) +�zig +p(δ∗(ℓ+1) +g +| κ2(ℓ) +ζg ), +where V ∗ = (V ∗ +1, . . . , V ∗ +N)′ is a N ×(P +1) matrix with V ∗ +i representing all covariates (including intercepts) +for subject i. To sample from the posterior distribution of p(δ∗(ℓ+1) +g +| V ∗, z(ℓ) +ig , κ2(ℓ) +ζg ), we adopt the Póyla- +Gamma data augmentation strategy of Polson and others (2013) by introducing a latent variable ωig coming +from the Pólya-Gamma distribution. Thus, the conditional posterior distributions of the logistic parameters are +p(δ∗(ℓ+1) +g +| V ∗, z(ℓ) +ig , ω(ℓ+1) +ig +, κ2(ℓ) +ζg ) ∝ p(z(ℓ) +ig = 1 | V ∗, ω(ℓ+1) +ig +, δ∗(ℓ+1) +g +) · p(ω(ℓ+1) +ig +| V ∗, δ∗(ℓ) +g +) +· p(δ∗(ℓ+1) +g +| κ2(ℓ) +ζg ) +∝ exp +� +− ωigη2 +ig +2 +� +· p(ωig | 1, 0)|Bg|−P/2 exp +� +− 1 +2δ∗′ +g B−1 +g δ∗ +g +� +, +where ηig = V ∗′ +i δ∗ +g − Cig and Cig = log � +h̸=j exp(V ∗′ +i δ∗ +h), p(ωig | 1, 0) is the Pólya-gamma dis- +tribution PG(b, c) with b = 1 and c = 0, Bg is the prior covariance matrix of Section 4.4 and +Bg = diag(σ2 +δg1P +1, κ2 +ζg1N). By assuming the conjugate prior N(0, Bg) on δ∗ +g, the posterior distribu- +tion of the Pólya-gamma latent variable is +(ω(ℓ+1) +ig +| V ∗, δ∗(ℓ) +g +) ∼ PG(1, ηig). +Thus, the conditional distributions of the logistic parameters (including the random intercepts) are +(δ∗(ℓ+1) +g +| V ∗, z(ℓ) +ig , ω(ℓ+1) +ig +, κ2(ℓ) +ζg ) ∼ N(M g, Σg), +where Σg = (V ∗′ΩgV ∗ + B−1 +g )−1, M g = Σg +� +V ∗′(ΩgCg + ξg) +� +, Ωg = diag(ω1g, · · · , ωNg), Cg = +(C1g, · · · , CNg)′, and ξg = (ξ1g, · · · , ξNg)′, with ξig = zig − 1 +2. Thus, δ∗(ℓ+1) +g +is drawn by first sampling +(ω(ℓ+1) +ig +| V ∗, δ∗(ℓ) +g +) and then (δ∗(ℓ+1) +g +| V ∗, z(ℓ) +ig , ω(ℓ+1) +ig +, κ2(ℓ) +ζg ). +5. Sampling the variances of the random intercepts +By analogy with sampling the error variances and sthe moothing parameters, we first draw (a(ℓ+1) +κg +| κ2(ℓ) +ζg ) ∼ +IG +� +νκ+1 +2 +, νκ +κ2 +ζg + +1 +A2κ +� +. The conditional posterior distributions of the variances of the random intercepts are +p(κ2(ℓ+1) +ζg +| ζ(ℓ+1) +g +, a(ℓ+1) +κg +) ∝ p(ζ(ℓ+1) +g +| κ2(ℓ+1) +ζg +) · p(a(ℓ+1) +κg +| κ2(ℓ+1) +ζg +) · p(κ2(ℓ+1) +ζg +) +∝ (κ2 +ζg)− N+νκ +2 ++1 exp +� +− +1 +κ2 +ζg +� νκ +aκg ++ ζT +g ζg +2 +�� +, +which is IG +� +νκ+N +2 +, +ζT +g ζg +2 ++ νκ +aκg +� +. The sampling scheme proceeds by first sampling (a(ℓ+1) +κg +| κ2(ℓ) +ζg ) and then +(κ2(ℓ+1) +ζg +| ζ(ℓ+1) +g +, a(ℓ+1) +κg +). +18 + +Covariate-guided Bayesian mixture model for multivariate time series +6. Computing the mixing weights +After drawing the δ∗ +g, the mixing weights π(ℓ+1) +ig +for each component, given the design matrix V ∗ +i , are computed +by +p(π(ℓ+1) +ig +| V ∗ +i , δ∗(ℓ+1) +g +) = +exp(V ∗T +i δ∗ +g) +�G +h=1 exp(V ∗T +i δ∗ +h) +. +7. Sampling the latent indicators +After sampling all parameters and computing the mixing weights, the final Gibbs step is to allocate subjects to +different components by drawing the latent indicators zig. As in Section 3.3, the conditional posterior of these +indicators is +p(z(ℓ+1) +ig += 1 | y, S, Θ(ℓ+1), π(ℓ+1) +ig +) = +πig +�K +k=1 fgk(yik | Θgk) +�G +h=1 πih +�K +k=1 fhk(yik | Θhk) +, +and the indicators are drawn from the multinomial distribution. +Appendix B: Additional simulation results +Appendix B adds more simulation results in addition to simulation results in the paper itself. To further demonstrate the +performance of the proposed method, we conduct simulation studies under two scenarios: two-component mixture of +trivariate time series and four-component mixture of bivariate time series. The model formula is displayed in Section +6.1 of the paper. We investigate the performance of our proposed method in terms of estimated trajectories and logistic +parameters. +Mean(SD) of the ARSE, A-bias and V-bias for each component of the two-component trivariate model are given in +Table 3. To demonstrate the performance of the proposed method in various settings, we look at combinations of the +number of multivariate time series (N = 150, 250) and the length of each time series (n = 50, 70), and compare our +proposed method to two existing methods: gbmt package in R (Magrini, 2022) and TRAJ procedure in SAS (Nagin and +others, 2018). The case of n = 50 and N = 150 in Table 3 corresponds to Figure 3 in the main paper. The performance +of the logistic parameters (RMSEs) with different values of n and N are given in Table 1 of the paper. +The Mean(SD) of the ARSE, A-bias and V-bias for each component of the N = 150 four-component mixture of +bivariate time series of length n = 50 are given in Table 4, which corresponds to Figure 4 in the main paper. RMSEs of +the logistic parameters for this setting are listed in Table 2 of the paper. Tables 5 - 10 present performance measures of +the estimated trajectories and logistic parameters for combinations of different lengths of time series n and numbers of +time series N, under the scenario of the four-component bivariate model. +As expected, our proposed method outperforms the two existing methods in terms of the estimated trajectories for +each component under different settings (different values of n and N, for both the two-component trivariate and the +four-component bivariate scenarios). The proposed method is able to achieve smaller ARSE and V-bias, while all three +methods are able to obtain estimated trajectories with a very small bias. Notably, for the four-component bivariate +scenario, TRAJ gives larger values of mean ARSE, A-bias and V-bias, which result from imprecise estimates of several +replicates due to convergence issues. In terms of the logistic parameters, our proposed method outperforms TRAJ in +almost all comparisons, especially for the intercept δ0 and the slope of the first covariate δ1. Our proposed method +yields shrinkage estimates for the logistic parameters due to using a Bayesian method, while the multinomial logistic +regression used in TRAJ gives inflated parameter estimates in case of perfect separations and unbalanced designs. +Appendix C: Additional real-data results +Appendix C describes more real-data results in addition to those in Section 7 of the main paper. Our motivating study is +described in Section 2 of the paper. Figure 7 shows the estimated trajectories of the three-component model for another +set of four channels (S1D3, S3D2, S5D4, and S7D4). Based on the selection criterion DIC introduced in Section 5.2 of +the main paper, the three-component model was selected as the best model. We named the second component as the +mixture response component because it involves both increased and decreased brain activity or hemoglobin level for the +still-face period for different channels. In addition, Figure 8 displays the logistic coefficient estimates and 95% credible +intervals corresponding to each covariate. The last component (third component) is always used as the reference. We +reach the same conclusion with positive estimates of IBQ-NE scores and negative estimates of IBQ-EC scores for both +components (component 1 vs. 3, component 2 vs. 3). +In addition to the four-channel analyses, we also present results from all channels (twelve channels). Figures 9, 10, 11 +present the estimated trajectories of the first, second and third component for the three-component model with all twelve +19 + +Covariate-guided Bayesian mixture model for multivariate time series +Table 3: Mean (standard deviation) of the averaged root square error (ARSE), the averaged bias (A-bias) and the +variance of bias (V-bias) of estimated trajectories for each component from 100 replicates of N two-component trivariate +time series of length n. The proposed method was compared to R package gbmt and TRAJ procedure in SAS. C1 and C2 +denote first and second components. Means were calculated by averaging over estimates of 100 replicates. Standard +deviations are Monte Carlo standard deviations from estimates of 100 replicates. Each value was reported ×102. +n +N +Method +ARSE C1 +A-bias C1 +V-bias C1 +ARSE C2 +A-bias C2 +V-bias C2 +50 +150 +Proposed +8.35 +(1.26) +0.03 +(1.83) +0.68 +(0.22) +7.65 +(1.38) +0.10 +(1.76) +0.58 +(0.22) +gbmt +10.67 +(1.91) +0.03 +(1.83) +1.15 +(0.42) +9.08 +(1.72) +0.10 +(1.76) +0.83 +(0.33) +TRAJ +11.06 +(1.48) +0.03 +(1.83) +1.22 +(0.33) +10.59 +(1.52) +0.10 +(1.76) +1.12 +(0.34) +70 +150 +Proposed +7.16 +(1.04) +0.24 +(1.38) +0.51 +(0.16) +6.53 +(1.07) +-0.11 +(1.42) +0.42 +(0.14) +gbmt +9.91 +(1.96) +0.24 +(1.38) +1.01 +(0.40) +8.19 +(1.65) +-0.11 +(1.42) +0.68 +(0.29) +TRAJ +9.34 +(1.10) +0.24 +(1.38) +0.87 +(0.22) +8.95 +(1.13) +-0.11 +(1.42) +0.80 +(0.20) +50 +250 +Proposed +6.81 +(1.02) +0.07 +(1.33) +0.46 +(0.14) +6.22 +(0.94) +0.02 +(1.31) +0.38 +(0.12) +gbmt +9.79 +(1.91) +0.07 +(1.33) +0.98 +(0.40) +8.00 +(1.53) +0.02 +(1.31) +0.65 +(0.26) +TRAJ +8.70 +(1.18) +0.07 +(1.33) +0.76 +(0.21) +8.20 +(1.03) +0.02 +(1.31) +0.67 +(0.17) +70 +250 +Proposed +5.65 +(0.84) +0.08 +(1.00) +0.32 +(0.10) +5.27 +(0.82) +-0.06 +(1.42) +0.27 +(0.09) +gbmt +9.15 +(1.96) +0.08 +(1.00) +0.87 +(0.38) +7.43 +(1.60) +-0.06 +(1.42) +0.56 +(0.26) +TRAJ +7.18 +(0.94) +0.08 +(1.00) +0.52 +(0.14) +6.80 +(0.77) +-0.06 +(1.42) +0.45 +(0.10) +Table 4: Mean (standard deviation) of the averaged root square error (ARSE), the averaged bias (A-bias) and the +variance of bias (V-bias) of estimated trajectories for each component from 100 replicates of 150 four-component +bivariate time series of length 50. The proposed method was compared to R package gbmt and TRAJ procedure in +SAS. C1, C2, C3 and C4 denote first, second, third and fourth component, respectively. Means were calculated by +averaging over estimates of 100 replicates. Standard deviations are Monte Carlo standard deviations from estimates of +100 replicates. Each value was reported ×102. +n +N +Method +ARSE C1 +A-bias C1 +V-bias C1 +ARSE C2 +A-bias C2 +V-bias C2 +50 +150 +Proposed +4.38 +(1.04) +0.38 +(1.59) +0.18 +(0.08) +3.76 +(0.87) +-0.01 +(1.37) +0.13 +(0.06) +gbmt +4.75 +(1.04) +0.38 +(1.59) +0.21 +(0.09) +4.79 +(1.17) +0.01 +(1.65) +0.22 +(0.11) +TRAJ +13.87 +(15.59) +0.62 +(9.91) +3.39 +(9.24) +12.41 +(13.42) +0.08 +(9.74) +2.41 +(5.37) +n +N +Method +ARSE C3 +A-bias C3 +V-bias C3 +ARSE C4 +A-bias C4 +V-bias C4 +50 +150 +Proposed +4.69 +(1.14) +-0.11 +(1.83) +0.20 +(0.12) +3.88 +(1.15) +-0.09 +(1.56) +0.14 +(0.08) +gbmt +5.08 +(1.12) +-0.12 +(1.83) +0.24 +(0.12) +4.70 +(1.32) +-0.09 +(1.78) +0.21 +(0.12) +TRAJ +14.55 +(14.82) +-1.58 +(10.31) +3.24 +(7.35) +14.36 +(17.01) +0.12 +(9.92) +3.99 +(10.70) +20 + +Covariate-guided Bayesian mixture model for multivariate time series +Table 5: Mean (standard deviation) of the averaged root square error (ARSE), the averaged bias (A-bias) and the +variance of bias (V-bias) of estimated trajectories for each component from 100 replicates of 150 four-component +bivariate time series of length 70. The proposed method was compared to R package gbmt and TRAJ procedure in +SAS. C1, C2, C3 and C4 denote first, second, third and fourth component, respectively. Means were calculated by +averaging over estimates of 100 replicates. Standard deviations are Monte Carlo standard deviations from estimates of +100 replicates. Each value was reported ×102. +n +N +Method +ARSE C1 +A-bias C1 +V-bias C1 +ARSE C2 +A-bias C2 +V-bias C2 +70 +150 +Proposed +3.82 +(0.95) +0.44 +(1.30) +0.14 +(0.07) +3.22 +(0.85) +-0.07 +(0.95) +0.10 +(0.06) +gbmt +4.05 +(0.97) +0.44 +(1.30) +0.16 +(0.08) +4.11 +(1.12) +-0.08 +(1.15) +0.17 +(0.10) +TRAJ +13.51 +(17.04) +-0.30 +(9.34) +3.86 +(10.73) +10.00 +(10.11) +-0.25 +(6.21) +1.64 +(4.02) +n +N +Method +ARSE C3 +A-bias C3 +V-bias C3 +ARSE C4 +A-bias C4 +V-bias C4 +70 +150 +Proposed +4.12 +(0.90) +-0.29 +(1.69) +0.15 +(0.06) +3.52 +(0.85) +0.24 +(1.22) +0.12 +(0.06) +gbmt +4.38 +(1.01) +-0.29 +(1.69) +0.17 +(0.07) +4.13 +(0.99) +0.27 +(1.40) +0.16 +(0.09) +TRAJ +13.03 +(17.04) +0.30 +(10.49) +3.86 +(10.73) +11.77 +(13.78) +0.39 +(8.49) +2.57 +(6.45) +Table 6: Root mean square errors (RMSEs) of each logistic parameter for the four-component bivariate model from 100 +replicates of 150 four-component bivariate time series of length 70. RMSEs of the proposed method were compared to +TRAJ procedure in SAS. Parameters δ0, δ1, δ2 and δ3 are intercept, first, second and third logistic parameters, respectively. +The fourth component was used as the reference component. The true values of logistic parameters are 5, −3.5, 1, 0.1 +(first component), −4, 2.5, −2, −0.2 (second component), 3, −2, 0.8, 0.2 (third component). C1, C2, C3 and C4 denote +first, second, third and fourth component, respectively. +n +N +Method +Comparison +δ0 +δ1 +δ2 +δ3 +70 +150 +Proposed +C1 vs C4 +0.81 +0.51 +0.29 +0.41 +C2 vs C4 +1.42 +0.73 +0.58 +0.36 +C3 vs C4 +1.05 +0.58 +0.37 +0.31 +TRAJ +C1 vs C4 +1.13 +0.66 +0.31 +0.45 +C2 vs C4 +3.12 +1.66 +0.99 +0.55 +C3 vs C4 +1.15 +0.74 +0.48 +0.35 +Table 7: Mean (standard deviation) of the averaged root square error (ARSE), the averaged bias (A-bias) and the +variance of bias (V-bias) of estimated trajectories for each component from 100 replicates of 250 four-component +bivariate time series of length 50. The proposed method was compared to R package gbmt and TRAJ procedure in +SAS. C1, C2, C3 and C4 denote first, second, third and fourth component, respectively. Means were calculated by +averaging over estimates of 100 replicates. Standard deviations are Monte Carlo standard deviations from estimates of +100 replicates. Each value was reported ×102. +n +N +Method +ARSE C1 +A-bias C1 +V-bias C1 +ARSE C2 +A-bias C2 +V-bias C2 +50 +250 +Proposed +3.42 +(0.78) +0.18 +(1.19) +0.11 +(0.05) +2.86 +(0.61) +-0.14 +(0.98) +0.08 +(0.04) +gbmt +3.57 +(0.85) +0.18 +(1.19) +0.12 +(0.06) +3.68 +(0.79) +-0.15 +(1.20) +0.13 +(0.06) +TRAJ +11.66 +(15.03) +0.53 +(10.63) +2.50 +(6.30) +8.90 +(9.38) +1.47 +(7.81) +1.05 +(2.16) +n +N +Method +ARSE C3 +A-bias C3 +V-bias C3 +ARSE C4 +A-bias C4 +V-bias C4 +50 +250 +Proposed +3.93 +(0.92) +-0.06 +(1.48) +0.14 +(0.07) +3.28 +(0.76) +-0.10 +(1.19) +0.10 +(0.05) +gbmt +4.16 +(0.95) +-0.06 +(1.49) +0.16 +(0.07) +3.83 +(0.83) +-0.13 +(1.36) +0.14 +(0.06) +TRAJ +10.80 +(9.92) +0.49 +(5.78) +1.83 +(3.70) +10.17 +(12.54) +-0.17 +(8.83) +1.84 +(5.20) +21 + +Covariate-guided Bayesian mixture model for multivariate time series +Table 8: Root mean square errors (RMSEs) of each logistic parameter for the four-component bivariate model from 100 +replicates of 250 four-component bivariate time series of length 50. RMSEs of the proposed method were compared to +TRAJ procedure in SAS. Parameters δ0, δ1, δ2 and δ3 are intercept, first, second and third logistic parameters, respectively. +The fourth component was used as the reference component. The true values of logistic parameters are 5, −3.5, 1, 0.1 +(first component), −4, 2.5, −2, −0.2 (second component), 3, −2, 0.8, 0.2 (third component). C1, C2, C3 and C4 denote +first, second, third and fourth component, respectively. +n +N +Method +Comparison +δ0 +δ1 +δ2 +δ3 +50 +250 +Proposed +C1 vs C4 +0.63 +0.41 +0.26 +0.29 +C2 vs C4 +1.00 +0.46 +0.40 +0.27 +C3 vs C4 +0.63 +0.33 +0.23 +0.24 +TRAJ +C1 vs C4 +0.91 +0.56 +0.30 +0.28 +C2 vs C4 +1.40 +0.86 +0.61 +0.35 +C3 vs C4 +2.24 +1.40 +0.85 +0.27 +Table 9: Mean (standard deviation) of the averaged root square error (ARSE), the averaged bias (A-bias) and the +variance of bias (V-bias) of estimated trajectories for each component from 100 replicates of 250 four-component +bivariate time series of length 70. The proposed method was compared to R package gbmt and TRAJ procedure in +SAS. C1, C2, C3 and C4 denote first, second, third and fourth component, respectively. Means were calculated by +averaging over estimates of 100 replicates. Standard deviations are Monte Carlo standard deviations from estimates of +100 replicates. Each value was reported ×102. +n +N +Method +ARSE C1 +A-bias C1 +V-bias C1 +ARSE C2 +A-bias C2 +V-bias C2 +70 +250 +Proposed +2.94 +(0.60) +-0.04 +(1.06) +0.08 +(0.04) +2.61 +(0.57) +-0.01 +(0.87) +0.06 +(0.03) +gbmt +3.10 +(0.63) +-0.04 +(1.06) +0.09 +(0.04) +3.18 +(0.70) +0.01 +(1.05) +0.10 +(0.05) +TRAJ +13.52 +(17.70) +-1.58 +(11.09) +3.71 +(8.80) +11.51 +(14.85) +-0.19 +(9.98) +2.54 +(7.10) +n +N +Method +ARSE C3 +A-bias C3 +V-bias C3 +ARSE C4 +A-bias C4 +V-bias C4 +70 +250 +Proposed +3.30 +(0.76) +-0.02 +(1.21) +0.10 +(0.05) +2.85 +(0.73) +-0.07 +(0.97) +0.08 +(0.04) +gbmt +3.51 +(0.79) +-0.01 +(1.21) +0.12 +(0.06) +3.26 +(0.80) +-0.09 +(1.06) +0.10 +(0.05) +TRAJ +13.07 +(15.21) +1.48 +(10.52) +2.90 +(7.11) +10.68 +(12.93) +0.65 +(8.11) +2.16 +(5.66) +Table 10: Root mean square errors (RMSEs) of each logistic parameter for the four-component bivariate model from 100 +replicates of 250 four-component bivariate time series of length 70. RMSEs of the proposed method were compared to +TRAJ procedure in SAS. Parameters δ0, δ1, δ2 and δ3 are intercept, first, second and third logistic parameters, respectively. +The fourth component was used as the reference component. The true values of logistic parameters are 5, −3.5, 1, 0.1 +(first component), −4, 2.5, −2, −0.2 (second component), 3, −2, 0.8, 0.2 (third component). C1, C2, C3 and C4 denote +first, second, third and fourth component, respectively. +n +N +Method +Comparison +δ0 +δ1 +δ2 +δ3 +70 +250 +Proposed +C1 vs C4 +0.64 +0.40 +0.26 +0.28 +C2 vs C4 +0.92 +0.42 +0.41 +0.28 +C3 vs C4 +0.63 +0.31 +0.23 +0.23 +TRAJ +C1 vs C4 +0.82 +0.50 +0.27 +0.28 +C2 vs C4 +1.47 +0.86 +0.61 +0.36 +C3 vs C4 +1.60 +0.96 +0.57 +0.25 +22 + +Covariate-guided Bayesian mixture model for multivariate time series +channels, respectively. The three-component model was selected as the best model for the twelve-channel analysis +based on the adjusted DIC. We named the three components no response, mixture response, and response component, +respectively. Figure 12 displays the logistic coefficient estimates and 95 % credible intervals corresponding to each +covariate. +23 + +Covariate-guided Bayesian mixture model for multivariate time series +Figure 7: Estimated trajectories of the three-component model with four selected channels. I: Interact S: Still-face R: +Recovery. Red curves are posterior means and the two green dashed curves are 95% pointwise credible intervals. +24 + +S1D3 +S3D2 +S5D4 +S7D4 +0.7 +S +R +S +R +S +R +S +R +0.6 +Component 1 +0.5 +0.4 +....... +...... +0.3 +I trajectory +0.7 +S +R +S +R +S +R +S +R +0.6 +Component2 +Estimated +0.5 +0.4 +....... +0.3 +0.7 +.... +S +R +S +R +S +R +S +R +... +0.6 +Component3 +0.5 +0.4 +... +...... +0.3 +- +0.00 +0.25 +S20 +2 +0.50 +.50 +100 +00 +15 +00 +0.5 +O. +O +0.25 +O. +Time +Component1:Noresponse +Component 3: ResponseCovariate-guided Bayesian mixture model for multivariate time series +Figure 8: Logistic coefficient estimates and 95% credible intervals corresponding to each covariate of the three- +component model. +25 + +(Intercept) +IBQ-NE +IBQ-EC +model +Infant age +Component 1 +Component 2 +Gestational days +HeadCircumference +Sex +0 +4 +Coefficient estimateCovariate-guided Bayesian mixture model for multivariate time series +Figure 9: Estimated trajectories of the first component for the three-component model with all twelve channels. I: +Interact S: Still-face R: Recovery. Red curves are posterior mean and two green dashed curves are 95% pointwise +credible intervals. +26 + +S1D1 +S1D2 +S1D3 +S2D2 +0.7 +S +R +S +R +S +R +S +.. +R +0.6 +0.5 +0.4 +0.3 +jectory +S3D2 +S4D2 +S5D1 +S5D3 +0.7 +R +S +R +traj +0.6 +Estimated +0.5 +0.4 +... +0.3 +S5D4 +S6D4 +S7D4 +S8D4 +0.7 +S +R +S +R +S +R +: +S +R +0.6 +0.5 +0.4 +0.3 +00 +0 +5 +0. +0 +Time +Component1:NoresponseCovariate-guided Bayesian mixture model for multivariate time series +Figure 10: Estimated trajectories of the second component for the three-component model with all twelve channels. +I: Interact S: Still-face R: Recovery. Red curves are posterior mean and two green dashed curves are 95% pointwise +credible intervals. +27 + +S1D1 +S1D2 +S1D3 +S2D2 +0.7 +Rn +R +AR +0.6 +0.5 +0.4 +0.3 +trajectory +S3D2 +S4D2 +S5D1 +S5D3 +0.7 +S +B +S +R +S +R +S +R +0.6 +Estimated +0.5 +- +0.4 +0.3 +S5D4 +S6D4 +S7D4 +S8D4 +0.7 +R +R +S +- +R +R +0.6 +0.5 +0.4 +0.3 +.00 +22 +22 +50 +Time +Component 2: Mixture responseCovariate-guided Bayesian mixture model for multivariate time series +Figure 11: Estimated trajectories of the third component for the three-component model with all twelve channels. I: +Interact S: Still-face R: Recovery. Red curves are posterior mean and two green dashed curves are 95% pointwise +credible intervals. +28 + +S1D1 +S1D2 +S1D3 +S2D2 +0.7 +S +R +0.6 +0.5 +0.4 +0.3 +trajectory +S3D2 +S4D2 +S5D1 +S5D3 +0.7 +S +B +B +B +S +R +0.6 +Estimated +0.5 +0.4 +..-. +0.3 +S5D4 +S6D4 +S7D4 +S8D4 +0.7 +R +TR +0.6 +0.5 +0.4 +0.3 +00 +0 +00 +Time +Component 3:ResponseCovariate-guided Bayesian mixture model for multivariate time series +Figure 12: Logistic coefficient estimates and 95% credible intervals for each covariate of the three-component model +for all twelve channels. +29 + +(Intercept) +IBQ-NE +IBQ-EC +model +Infant age +Component 1 +Component 2 +Gestational days +HeadCircumference +Sex +4 +0 +4 +Coefficient estimate \ No newline at end of file diff --git a/gNAzT4oBgHgl3EQfavxL/content/tmp_files/load_file.txt b/gNAzT4oBgHgl3EQfavxL/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..565f6cc0b0ad6f328c3b6139064bc61044dd9ffe --- /dev/null +++ b/gNAzT4oBgHgl3EQfavxL/content/tmp_files/load_file.txt @@ -0,0 +1,1541 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf,len=1540 +page_content='COVARIATE-GUIDED BAYESIAN MIXTURE OF SPLINE EXPERTS FOR THE ANALYSIS OF MULTIVARIATE TIME SERIES Haoyi Fu Department of Biostatistics University of Pittsburgh Pittsburgh, PA, USA haf48@pitt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='edu Lu Tang Department of Biostatistics University of Pittsburgh Pittsburgh, PA, USA Ori Rosen Department of Mathematical Sciences University of Texas at El Paso El Paso, TX, USA Alison E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Hipwell Department of Psychiatry University of Pittsburgh Pittsburgh, PA, USA Theodore J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Huppert Department of Electrical and Computer Engineering University of Pittsburgh Pittsburgh, PA, USA Robert T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Krafty Department of Biostatistics and Bioinformatics Emory University Atlanta, GA, USA ABSTRACT With rapid development of techniques to measure brain activity and structure, statistical methods for analyzing modern brain-imaging play an important role in the advancement of science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Imaging data that measure brain function are usually multivariate time series and are heterogeneous across both imaging sources and subjects, which lead to various statistical and computational challenges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' In this paper, we propose a group-based method to cluster a collection of multivariate time series via a Bayesian mixture of smoothing splines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Our method assumes each multivariate time series is a mixture of multiple components with different mixing weights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Time-independent covariates are assumed to be associated with the mixture components and are incorporated via logistic weights of a mixture-of-experts model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' We formulate this approach under a fully Bayesian framework using Gibbs sampling where the number of components is selected based on a deviance information criterion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The proposed method is compared to existing methods via simulation studies and is applied to a study on functional near-infrared spectroscopy (fNIRS), which aims to understand infant emotional reactivity and recovery from stress.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The results reveal distinct patterns of brain activity, as well as associations between these patterns and selected covariates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Keywords Bayesian mixture model · Brain-imaging · Functional near-infrared spectroscopy · Model-based clustering · Multivariate time series · Smoothing splines · Face-to-face still-face 1 Introduction Time series are realizations of random processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Obtaining estimated time series trajectories may provide insights into many practical problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Functional near-infrared spectroscopy (fNIRS) is a noninvasive brain imaging technique that measures changes in both oxy- and deoxy-hemoglobin using near-infrared light (Jobsis, 1977).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' In fNIRS, processed data are nonstationary multivariate time series with a non-constant mean and high variability across time, which pose many statistical challenges in inference and estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' In the case of fNIRS, different subjects could have distinct patterns of multivariate time series trajectories, which could be associated with certain clinical or demographic characteristics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='01373v1 [stat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='ME] 3 Jan 2023 Covariate-guided Bayesian mixture model for multivariate time series The analysis of fNIRS data requires an appropriate method for the analysis of a collection of multivariate time series observed from different subjects, which is often referred to as a replicated multivariate time series setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Cluster analysis is often used to address the issue of heterogeneity and identify subgroups from collections of time series observed from different subjects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Time series clustering has been used in diverse scientific areas to discover trajectory patterns, which can uncover valuable information from complex and massive datasets (Liao, 2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Time series clustering partitions the entire collection of data into different groups such that homogeneous time series are grouped together based on a certain similarity measure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Challenges in time-series clustering include computational issues due to high-dimensionality and the selection of proper similarity measures (Lin and others, 2003;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Keogh and Pazzani, 2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Several authors have proposed clustering algorithms for multivariate time series.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Kakizawa and others (1998) used Kullback-Leibler discrimination information as the minimum discrimination criterion for clustering multivariate Gaussian time series.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Wang and others (2007) used a modified K-means clustering algorithm for clustering multivariate time series based on univariate structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' A variety of papers have established different model-based clustering methods for clustering multivariate time series, such as multivariate autoregressive models (Maharaj, 1999;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' He and others, 2022), a hidden Markov model (Li and others, 2001) and smoothing splines (Krafty and others, 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Li and Krafty, 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Comprehensive review of methods for time series clustering can be found in Liao (2005) and in Maharaj and others (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Covariate-dependent structures can often be associated with the mixture components from a clustering of time series.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Bertolacci and others (2022) presented an analysis of multiple nonstationary time series by using a covariate- dependent infinite mixture with logistic stick-breaking weights, where mixing weights are computed based on covariates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The mixture-of-experts model (Jacobs and others, 1991) assigns weights to each expert via a covariate-dependent multinomial logists.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Huerta and others (2003) addressed the issue of time series model mixing based on covariates using the hierarchical mixture-of-experts (Jordan and Jacobs, 1994).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Smoothing splines, which are nonparametric methods that utilize roughness-based penalties, have been widely used in the analysis of time series (Wang, 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Gu, 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Bayesian interpretations of smoothing splines were first discussed by Kimeldorf and Wahba (1970).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Wahba (1978) showed that the solution to the smoothing splines objective function is equivalent to Bayesian estimation with a partially diffuse prior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Speckman and Sun (2003) adopted a fully Bayesian approach for implementing smoothing splines with a noninformative prior on the variance component, as well as derived necessary and sufficient conditions for the propriety of the posterior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Smoothing splines require estimation of a large number of coefficients, which might be impractical in high-dimensional settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Gu and Kim (2002) used a subset of reproducing kernel functions to achieve a low-dimensional approximation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Wood and others (2002) obtained a subset of basis functions using the eigen-decomposition of the Gaussian kernel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Krafty and others (2017) proposed a tensor-product model for the analysis of replicated multivariate time series which decomposes the power spectrum into products of univariate outcomes and frequencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Our goal in this paper is to perform a covariate-guided clustering of multivariate time series that can capture trajectory patterns of mixture components and evaluate the relationship between covariates and trajectory patterns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' To this end, each mixture component is modeled via smoothing splines, and time-independent covariates are incorporated into the mixture model via the mixing weights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The method is formulated in a fully Bayesian framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The rest of this paper is organized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' In Section 2 we introduce the motivating study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Sections 3 and 4 present the proposed model and priors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Section 5 introduces the sampling scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' In Section 6 we report simulation results under different settings and Section 7 illustrates our proposed method with application to the motivating study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Section 8 concludes the paper with a discussion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' 2 Motivating Study Our motivating study aims to understand patterns of infant’s brain activity before, during and after an emotionally stressful probe called face-to-face still-face (FFSF) (Tronick and others, 1978).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Participant mothers in this study were recruited from the longitudinal Pittsburgh Girls Study (PGS), a population-based study of 2,450 girls who were recruited in the city of Pittsburgh between the ages of 5 and 8 (Keenan and others, 2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' In 2016, a large-scale sub-study of the PGS was initiated to investigate how environmental factors, such as psychological stressors experienced during childhood and adolescence, affect later maternal pregnancy and child health.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The study is part of the National Institutes of Health Environmental Influences of Child Health Outcomes (ECHO) program, which examines different impacts of prenatal environmental exposures across biological, chemical, physical and social domains on offspring health and development (Gillman and Blaisdell, 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The PGS-ECHO study enrolls PGS participants as they become pregnant or recently deliver a live birth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Participants complete multiple prenatal lab visits and the children are followed from ages 6 to 36 months.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The lab protocol includes interviews and interaction tasks to assess contextual stressors, health, mood, lifestyle behaviors and offspring behavioral and emotional development.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' 2 Covariate-guided Bayesian mixture model for multivariate time series Face-to-face interactions between mothers and infants are essential to the development of infants with respect to communication and social skills, as well as the regulation of emotion and temperament (Hipwell and others, 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The FFSF paradigm is a widely used stress task (a violation of the expectation of social interaction) that allows for biobehavioral measurement of individual differences in infant response and recovery.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The FFSF comprises of three phases: interact (or baseline), still-face and recovery (Adamson and Frick, 2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' In phase 1, mothers perform normal interactions with infants without the use of toys;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' this phase serves as the baseline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' In phase 2, mothers adopt a neutral facial expression (still-face with no facial or oral communication) to infants, followed by phase 3, where mothers resume normal interactions with their infants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Prior to the start of the FFSF, an fNIRS cap is fitted on the infant’s head to measure the level of and change in brain activation across the three phases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' PGS-ECHO fNIRS still-face data are recorded using a continuous NIRS imaging system (NIRScout;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' NIRx Medical Technologies, Berlin, Germany) at the sampling rate of 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='8125 Hz and using the NIRStart acquisition software.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The data are measured simultaneously at two wavelengths (760 nm and 850 nm).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' As shown in Figure 1(a), this fNIRS probe consists of 12 channels from 8 sources and 4 detectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' In the current study, we measured infant brain activity using the above fNIRS probe (roughly 120 seconds of measure- ments for each phase).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' At the end of 2021, recorded fNIRS still-face data had been collected from 155 infant subjects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Demographic variables of infants and mothers such as gestational age, infant age, sex, birth weight, head circumference, along with parent reports on the Infant Behavior Questionnaire-Revised (IBQ-R) (Gartstein and Rothbart, 2003) were also collected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' By removing infants who did not complete the three phases of the still-face paradigm, who had large outliers based on leverage and who had a very short period of measurements in any of the three still-face phases, there were a total of 82 subjects with complete fNIRS still-face data available for future analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The above quality control steps were performed by the NIRS brain AnalyzIR toolbox in MATLAB (Santosa and others, 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Moreover, additional data pre-processing steps were performed in R software, including data interpolation and rescaling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Finally, processed fNIRS data had a total of 1,500 measurement points for each subject and each channel, where each phase consisted of 500 points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' All measurements and sampling times were rescaled to be between 0 and 1, with the interact phase occurring between time 0 to 1/3, still-face between 1/3 to 2/3, and recovery between 2/3 to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' An example of processed fNIRS time series from two selected subjects and four selected channels is displayed in Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The goals of our analysis are to identify distinct patterns of brain activity trajectories from multiple fNIRS channels represented by the relative concentration of oxy-hemoglobin, and to assess the association between trajectory patterns and relevant covariates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' 3 Model In this section, we provide a detailed description of our proposed covariate-guided Bayesian mixture of spline experts model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The proposed model consists of spline components whose mixing weights depend on covariates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='1 Mixture of splines model We propose a tensor-product mixture of splines model for multivariate time series.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' For each subject i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' , N, let yi = (y′ i1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' , y′ ik, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' , y′ iK)′ be the nK-vector corresponding to the K-dimensional time series for k = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' , K, where yik = � yik(t1), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' , yik(tj), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' , yik(tn) �′ contains the trajectory of measurements on the kth entry of the time series evaluated over a grid of n time points for j = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' , n, and ϵi = (ϵ′ i1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' , ϵ′ iK)′ is the nK-vector of errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Following the model representation of Krafty and others (2017), the tensor-product model for the K-dimensional multivariate time series, conditional on component g, g = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' , G, can be written as: {yi | zig = 1} = (IK ⊗ X)αg + (IK ⊗ W )βg + ϵi, (1) where {zig}G g=1 are latent indicators as described in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='3, αg = (α′ g1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' , α′ gK)′ is a 2K-vector of intercepts and slopes, βg = (β′ g1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' , β′ gK)′ is a mK-vector of basis function coefficients as described in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='1, IK is a K × K identity matrix and ⊗ denotes a tensor product.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The matrix X is given by X = � 1 1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' 1 t1 t2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' tn �′ and the m columns of the matrix W are smoothing splines basis functions as described in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' We assume the error vector ϵi follows a MVN(0, Ψg ⊗ U) distribution, where U = In is the n × n identity matrix, and Ψg = diag(σ2 g) is a K × K diagonal matrix with the error variances σ2 g = (σ2 g1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' , σ2 gK)′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' We assume each subject has a common grid of time points across all K entries, such that X and W are common to all subjects, although our proposed method can be generalized to the case where subjects are observed at different grids of time points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' In addition, we assume E(yik, yih) = 0n×n for k ̸= h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' 3 Covariate-guided Bayesian mixture model for multivariate time series To simplify notation, we let S = [X W ] and θg = (α′ g1, β′ g1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' , α′ gK, β′ gK)′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Equation (1) can then be rewritten as: {yi | zig = 1} = (IK ⊗ S)θg + ϵi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' (2) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='2 Model for the mixing weights The mixture-of-experts model (Jacobs and others, 1991) is applied to form a covariate-guided structure for our proposed model, where the mixing weights are multinomial logits that are functions of selected covariates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' As in Sun and others (2007), the mixing weights are expressed as πig(V i) = exp(V ′ iδg + ζig) �G h=1 exp(V ′ iδh + ζih) , (3) where V i = (1, Vi1, · · · , ViP )′ is a vector of length (P + 1) containing values of P covariates for subject i, and δg = (δg0, δg1, · · · , δgP )′ is the corresponding coefficient vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' For identifiability, we set δG = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Equation (3) differs slightly from the weights in the traditional mixture of experts model in that it includes a random term ζig for each subject.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' This term accounts for unmeasured factors beyond the observed covariates, and enhances model performance and inference of the mixing weights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='3 Augmented likelihood To account for heterogeneity across subjects, we assume that the kth entry of the multivariate time series, yik, comes from a mixture model with G components, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=', yik ∼ G � g=1 πigfgk(yik | µgk, σ2 gkIn), (4) where fgk(yik | µgk, σ2 gkIn) is the probability density function of the multivariate normal distribution with mean vector µgk = Xαgk + W βgk and covariance matrix σ2 gkIn for the gth component and the kth entry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The πig are mixing weights that depend on covariates as described in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' As is common in mixture models, augmenting the likelihood with latent variables indicating the component from which a time series originates simplifies the computation greatly (Dempster and others, 1977).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' In particular, let zig = 1 if the ith multivariate time series belongs to the gth component and zig = 0, otherwise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Let y = (y1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' , yN)′ be all observed multivariate time series and Θgk be the aggregation of all parameters for component g and entry k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The parameter vector for all components and all entries is then denoted by Θ = (Θ′ 11, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' , Θ′ GK)′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The augmented likelihood of all N multivariate time series is given by L(Θ | y, Z) = N � i=1 G � g=1 � πig K � k=1 fgk(yik | Θgk) �zig , (5) where fgk(yik | Θgk) is the probability density function as appeared in the (4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' From Bayes’ rule, the distribution of the latent indicators zig is given by p(zig = 1 | y, S, Θ, πig) = πig �K k=1 fgk(yik | Θgk) �G h=1 πih �K k=1 fhk(yik | Θhk) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' (6) 4 Priors In this section, the priors on the model parameters are introduced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='1 Smoothing splines prior The conditional expectation of a mixture component in model (4) is given by E(yik | zig = 1) = Xαgk + W βgk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' We place a smoothing spline prior on βgk and let Hgk = W βgk, where Hgk = � Hgk(t1), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' , Hgk(tn) �′ is a zero-mean Gaussian process with variance covariance matrix τ 2 gkΦ (Wahba, 1980;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Wood and others, 2002), such that cov � Hgk(tr), Hgk(th) � = τ 2 gkφrh, τ 2 gk is a smoothing parameter for component g and entry k, and the (r, h)th element 4 Covariate-guided Bayesian mixture model for multivariate time series of Φ is given by φrh = 1 2t2 r(th − tr 3 ) for tr ≤ th.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The matrix Φ is common to all subjects since all entries of the multivariate time series are observed at common time points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' As seen above, the matrix Φ is n × n, and to avoid the computational burden for large n, a low-rank approximation is often adopted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' To facilitate this approximation, we obtain basis functions via the spectral decomposition of Φ, as has been proposed in Wood and others (2002) and used in Rosen and others (2009, 2012);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Krafty and others (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' In particular, the matrix W consists of m basis functions evaluated at times t1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' , tn, and βgk is an m-dimensional vector of basis function coefficients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' These basis functions are obtained by applying the spectral decomposition to Φ such that Φ = QΓQT , where Q is the matrix of eigenvectors of Φ, and Γ is a diagonal matrix containing the eigenvalues of Φ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' We then let the design matrix W = QΓ1/2 and place a normal prior N(0, τ 2 gkIn) on βgk, which leads to Hgk or W βgk ∼ N(0, τ 2 gkΦ) as mentioned above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' By using the low-rank approximation, the number of columns of W is reduced from n to m (m < n), which greatly reduces the computational burden without sacrificing the model fit (Wahba, 1980;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Wood, 2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Eubank (1999) indicated that the eigenvalues in the diagonal matrix Γ decay rapidly as m increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Thus, we can achieve a good approximation by selecting a relatively small number m of basis functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The number of basis functions m is set to 10 in simulation studies as described in Section 6, which has been shown (Krafty and others 2011) to explain more than 98% of the total variability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The prior on θg is thus θg ∼ N(0, Dg), where Dg = diag(σ2 α112, τ 2 g11m, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' , σ2 αK12, τ 2 gK1m) is the covariance matrix of θg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The vector (σ2 α1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' , σ2 αK)′ contains fixed prior variances for the regression coefficients αgk, common to all components and entries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' In particular, we fix the common prior variance σ2 α = 100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The vector τ 2 g = (τ 2 g1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' , τ 2 gK)′ contains the smoothing parameters for the gth mixture component and 1m is an m-vector of ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' We assume independence between the regression coefficients αgk and the basis function coefficients βgk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='2 Priors on the smoothing parameters We assume the smoothing parameters τ 2 g = (τ 2 g1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' , τ 2 gK)′ vary across components g and entries k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Although the most common choice for the prior on a variance parameter is the inverse gamma distribution, Gelman (2006) and Wand and others (2011) suggested that a half-t prior on the standard deviation can reflect lack of information on a scale parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The half-t is a family of heavy-tailed distributions and has a good shrinkage performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' It can be expressed as a scale mixture of inverse gamma random variables using a latent variable which follows an inverse gamma distribution (Wand and others, 2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Thus, we assume a half-t distribution such that τgk ∼ t+ ντ (0, Aτ), where ντ is a degrees of freedom parameter, and Aτ is a scale parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' We set ντ = 3 and Aτ = 10 for all components and entries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='3 Priors on the error variances We assume σgk i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='d ∼ t+ νσ(0, Aσ) and set νσ = 3 and Aσ = 10 for all components and entries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='4 Priors on the logistic parameters and the variances of random intercepts This section provides details on the prior distributions placed on the parameters of the logistic weights (3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' For ease of notation, we denote δ∗ g = (δT g , ζT g )T , where ζg = (ζ1g, · · · , ζNg)T , g = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' , G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' We let V ∗ i = (V ′ i, e′ i)′ where ei is a vector of all zeros except for a single 1 in the ith position, and V ∗ is a matrix consisting of the rows V ∗T i , i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' , N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Gaussian priors are placed on the logistic parameters, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=', δ∗ g ∼ N(0, Bg), where Bg = diag(σ2 δg1P+1, κ2 ζg1N), and the priors on the random intercepts satisfy ζg ∼ N(0, κ2 ζgIN).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' As for the hyperparameters, we assume σ2 δg = 10 for all components and covariates, and κζg ∼ t+ νκ(0, Aκ), where νκ = 3 and Aκ = 10 for all components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' To sample the logistic parameters, Polson and others (2013) proposed a data augmentation scheme incorporating Pólya-Gamma latent variables, which facilitates Gibbs steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Details on sampling the logistic parameters are provided in the Supplementary Material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' 5 Sampling scheme This section outlines the Gibbs steps for sampling from the conditional posterior distributions of all the model parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' More details are given in Supplementary Material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' 5 Covariate-guided Bayesian mixture model for multivariate time series 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='1 Gibbs sampling steps Letting ℓ denote the current Gibbs sampling iteration, parameter values at the (ℓ + 1)th iteration are drawn according to the following steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Draw θ(ℓ+1) gk from (θ(ℓ+1) gk | y, S, τ 2(ℓ) gk , σ2(ℓ) gk ) ∼ N(ugk, σ2 gkΛgk), where ugk and Λgk are mean vectors and covariance matrices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Draw σ2(ℓ+1) gk from (σ2(ℓ+1) gk | ϵ(ℓ+1) igk , a(ℓ+1) σgk ) ∼ IG � (nN (ℓ) g + νσ)/2, �N i=1 zigϵ′ igkϵigk/2 + νσ/aσgk � , where N (ℓ) g is the current number of subjects in the gth component, ϵigk is the error vector for the gth component, the ith subject and the kth entry, and aσgk is a latent variable in the IG scale mixture underlying the half-t distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Draw τ 2(ℓ+1) gk from (τ 2(ℓ+1) gk | β(ℓ+1) gk , a(ℓ+1) τgk ) ∼ IG � (ντ + m)/2, β′ gkβgk/2 + ντ/aτgk � , where aτgk is a latent variable as in 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Draw δ∗(ℓ+1) g from (δ∗(ℓ+1) g | V ∗, z(ℓ) ig , ω(ℓ+1) ig , κ2(ℓ) ζg ) ∼ N(M g, Σg), where ω(ℓ+1) ig is a Pólya-Gamma latent variable in the augmentation described in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Draw κ2(ℓ+1) ζg from (κ2(ℓ+1) ζg | ζ(ℓ+1) g , a(ℓ+1) κg ) ∼ IG � νκ/2, ζ′ gζg/2 + (νκ + N)/aκg � , where aκg is a latent variable as in 2 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The mixing weights π(ℓ+1) ig are obtained by computing p(π(ℓ+1) ig | V ∗, δ∗(ℓ+1) g , z(ℓ) ig ) from Equation (3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Draw z(ℓ+1) ig ∼ p(z(ℓ+1) ig = 1 | y, S, θ(ℓ+1) gk , σ2(ℓ+1) gk , π(ℓ+1) ig ) according to Equation (6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='2 Selecting the number of components Spiegelhalter and others (2002) suggested the use of the deviance information criterion (DIC) for model selection based on the effective number of parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Gelman and others (2003) introduced an alternative measure of effective number of parameters based on the variance of the log predictive density across MCMC iterations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' This measure is robust and more accurate than the original one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Moreover, it has the advantages of always being positive and invariant to reparameterizations (Gelman and others, 2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' In this paper, we use DIC to select the number of components for our proposed mixture model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' 6 Simulation studies To demonstrate the performance of the proposed method, we conduct simulation studies by generating data sets from the proposed model under two scenarios: two-component mixture (G = 2) of trivariate time series (K = 3) and four-component mixture (G = 4) of bivariate time series (K = 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' We simulate 100 replicates in each simulation setting with N = 150 time series of length n = 50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' A total of 20, 000 Gibbs sampling iterations are run with a burn-in of 4, 000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' In all simulation settings, the hyperparameters are assigned the same values, given in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='1 Two-component trivariate model In this scenario, we consider the two-component trivariate model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' From Equation (1), the gth component of the proposed mixture model is given by {y(tj) | zig = 1} = α0g + α1gtj + m � q=1 wq(tj)βgq + ϵgtj, j = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' , n, g = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' , G, (7) where y(tj) is the trivariate time series evaluated at time tj, α01 = (1, −3, −2)′, α02 = (5, 4, 3)′ and α11 = (−2, 2, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='5)′, α12 = (1, −1, −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='5)′ are independent intercepts and slopes for each component, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The vector βgq consists of the qth spline coefficients of all variates for component g, and wq(tj) is the qth spline basis function eval- uated at time tj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The ϵgtj are independent zero-mean error terms, distributed as ϵgtj ∼ MVN � 0, diag(σ2 g1, σ2 g2, σ2 g3) � , where σ2 1 = (σ2 11, σ2 12, σ2 13)′ = (3, 5, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='5)′ and σ2 2 = (σ2 21, σ2 22, σ2 23)′ = (4, 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='5, 4)′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The smoothing parameters are set to τ 2 1 = (τ 2 11, τ 2 12, τ 2 13)′ = (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='5, 5, 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='5)′ and τ 2 2 = (τ 2 21, τ 2 22, τ 2 23)′ = (6, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='5, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='5)′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' 6 Covariate-guided Bayesian mixture model for multivariate time series We investigate the performance of the trajectory and logistic parameter (see Equation (3)) estimates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' For the former, we calculate the averaged root square error (ARSE) of each mixture component g ARSEg = � � � � 1 nK n � j=1 K � k=1 � µgk(tj) − ˆµgk(tj) �2 , where µgk(tj) is the expectation of yk(tj) according to the gth component, and yk(tj) is the kth entry of the time series evaluated at time tj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The ˆµgk(tj) are the estimated posterior means of µgk(tj) for k = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' , K and j = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' , n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' To handle a potential label switching across mixture components, we compute ARSEg as the minimum value across all components, by using the estimate of the gth component and the truth of each group, g = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' , G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' After obtaining correct component labels by evaluating ARSE, we also report the averaged bias (A-bias) and the variance of the bias (V-bias) of each mixture component g, where A-biasg = 1 nK n � j=1 K � k=1 � ˆµgk(tj) − µgk(tj) � , and V-biasg is computed by calculating the sample variance of the bias over entries and time points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' For each replicate, time series trajectories are estimated by three methods: the proposed method, the R package gbmt (Magrini, 2022) and the TRAJ procedure in SAS (Nagin and others, 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Boxplots of ARSE, A-bias and V-bias of each component are given in Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Notably, TRAJ is able to fit a regression spline model by treating basis functions as time-varying covariates, while gbmt is only able to fit a cubic model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Our proposed method fits a penalized spline model under the Bayesian framework and is able to outperform both gbmt and TRAJ in terms of ARSE and V-bias for both components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' A-biases are close to zero and comparable for all three methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' These findings demonstrate that all three methods are able to achieve a reasonable fit to group-based trajectories since bias over the entire time series is close to zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Our proposed method is able to obtain more precise estimates of trajectories as is evident from the smaller V-biases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' To evaluate the performances of the logistic parameters, we compute the root mean squared error (RMSE) for each logistic parameter using the proposed method and TRAJ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Notably, gbmt is not able to incorporate covariates into the computation of mixing weights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Results of RMSEs of each logistic parameter are given in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' We also compare RMSEs between the proposed method and TRAJ under four settings of different combinations of N = 150, 250 and n = 50, 70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Our proposed method yields smaller RMSEs of the logistic parameters in all cases, especially for the intercept δ0 and the first covariate δ1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' This is to be expected since TRAJ uses a multinomial logistic model, which may result in inflated parameter estimates in cases of unbalanced outcomes or perfect separation, while our proposed method is able to obtain a shrinkage result using the penalization method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='2 Four-component bivariate model In this scenario, we consider the four-component bivariate model whose gth component is given in Equation (7), where the values of the intercepts and slopes are α01 = (1, −2)′, α02 = (5, 3)′, α03 = (−3, 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='5)′, α04 = (4, −1)′, α11 = (−3, 0)′, α12 = (2, −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='5)′, α13 = (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='5, 2)′ and α14 = (−3, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='5)′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' By analogy to the two-component trivariate model, the errors ϵgtj are independent zero-mean bivariate Gaussian random variables, distributed as ϵgtj ∼ MVN � 0, diag(σ2 g1, σ2 g2) � , where σ2 1 = (σ2 11, σ2 12)′ = (6, 9)′, σ2 2 = (σ2 21, σ2 22)′ = (8, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='5)′, σ2 3 = (σ2 31, σ2 32)′ = (10, 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='5)′ and σ2 4 = (σ2 41, σ2 42)′ = (7, 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='5)′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The performances of the estimated trajectories and logistic parameters for this scenario are displayed in Figure 4 and Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' As in the first scenario, our proposed method outperforms both gbmt and TRAJ in terms of ARSE and V-bias for all components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Notably, TRAJ fails to yield precise estimates in several replicates and thus results in larger mean ARSE and V-bias.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' In terms of the logistic parameters, the proposed method performs well with smaller RMSEs in almost all cases, especially for δ0 and δ1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' More simulation results based on different values of N and n under the two scenarios considered above are presented in the Supplementary Material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' 7 Real data application We apply our proposed method to the analysis of the fNIRS still-face study introduced in Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Six covariates are considered in our covariate-guided model, including Infant Behavior Questionnaire-Revised negative emotionality (IBQ-NE) score, Infant Behavior Questionnaire-Revised effortful control (IBQ-EC) score, gestational age (in Days), 7 Covariate-guided Bayesian mixture model for multivariate time series infant age (in Months), head circumference (in cm) and sex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' All continuous covariates are centered and scaled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' We set the number of basis functions at m = 20 and run a total of 30, 000 Gibbs iterations with a burn-in period of 6, 000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The values of the hyperparameters are the same as the ones used in the simulation studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The IBQ-NE construct combines data from the following subscales: Sadness, Distress to Limitations, Fear, and Falling Reactivity/Rate of Recovery from Distress.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' IBQ-EC refers to the ability to inhibit a dominant response to perform a subdominant one and has been shown to be protective against a myriad of difficulties (Gartstein and others, 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Finally, the data consist of 79 subjects with complete fNIRS and covariate values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' We present results based on analyzing one set of four-channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Additional results based on analyzing another set of four channels and all channels are given in the Supplementary Material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The four channels are S1D1, S2D2, S5D3 and S6D4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Channels S1D1 and S5D3 are in the central prefrontal region, while channels S2D2 and S6D4 are in the left and right prefrontal region, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' We fit our proposed model with the number of components varying from 2 to 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Based on values of DIC introduced in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='2, the two-component model is selected as the best model for this four-channel analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Figure 5 presents the estimated trajectories of the two-component model fitted to the four channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' We are interested in brain activation signals in the still-face period while the interact period is used as the reference level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' For component 1, a decreasing trajectory is observed for the still-face period in all four channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' In contrast, an increasing trend is observed for the still-face period in all four channels for component 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' After fitting the mixture model and finding above trajectory patterns, we define component 1 as the no response component and component 2 as the response component based on trajectory patterns in the still-face period.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Figure 6 displays the logistic parameter estimates for all covariates in the 2-component model, where component 2 is used as the reference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' There is evidence that IBQ-NE scores differ between the two components as its 95% credible interval does not include zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' A positive coefficient of IBQ-NE indicates that a higher IBQ-NE score is associated with component 1, which has decreased brain activation levels in the still-face period for all four channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Though other logistic coefficients have 95% credible intervals that include zero, the negative posterior mean estimate of the IBQ-EC score could still indicate that a high IBQ-EC is associated with an increased brain activation as shown for component 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' These conclusions are consistent with findings in Gartstein and others (2013) that IBQ-NE is negatively associated with IBQ-EC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Enlow and others (2016) reported a negative association between activity level and IBQ-NE among infants whose families encourage a high level of activities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Furthermore, a negative posterior mean of logistic coefficient of infant age suggests that younger infant tends to have a decreasing brain activation level in the still-face period.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' 8 Discussion The proposed covariate-guided Bayesian mixture of spline experts model aims to perform a model-based clustering of multivariate time series from multiple subjects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The mixture components in this model are penalized splines, and the mixing weights incorporate covariates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Our proposed method is compared to two commonly used methods through simulation studies which demonstrate a better performance of our method under different scenarios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' We apply our proposed method to a fNIRS still-face study and find distinct patterns of components of time series trajectories, as well as an association between IBQ-NE score and a pattern of decreased brain activity in the still-face period.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' To the best of our knowledge, this is the first still-face study using fNIRS whose purpose is to identify trajectory components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Our proposed method has some limitations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' First, as in any mixture models, label switching may occur, especially in the real-data application.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' We have adopted the Equivalence Classes Representatives (ECR) algorithm proposed by Papastamoulis and Iliopoulos (2010) to make the components interpretable, but other methods may be considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Second, the proposed method assumes independence among the entries of the time series and does not allow spatial dependence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Spatial correlations of fNIRS are correlations among fNIRS channels based on the placements and locations of each source and detector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' An extension to a multilevel multivariate model would be possible by considering spatial correlations among time series entries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Lastly, our proposed method uses DIC to select the number of components which might be sub-optimal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Bayesian model averaging and reversible jump MCMC (RJMCMC) methods could be considered, but trans-dimensional sampling methods would pose challenges in providing interpretable components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' 9 Software Software in the form of R codes, together with an example data, is available at https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='com/HaoyiFu1993/ CBMOSE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' 8 Covariate-guided Bayesian mixture model for multivariate time series References ADAMSON, LAUREN B AND FRICK, JANET E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The still face: A history of a shared experimental paradigm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Infancy 4(4), 451–473.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' BERTOLACCI, MICHAEL, ROSEN, ORI, CRIPPS, EDWARD AND CRIPPS, SALLY.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Adaptspec-x: Covariate- dependent spectral modeling of multiple nonstationary time series.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Journal of Computational and Graphical Statistics 31(2), 436–454.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' DEMPSTER, ARTHUR P, LAIRD, NAN M AND RUBIN, DONALD B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' (1977).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Maximum likelihood from incomplete data via the em algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Journal of the Royal Statistical Society: Series B (Methodological) 39(1), 1–22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' ENLOW, MICHELLE BOSQUET, WHITE, MATTHEW T, HAILS, KATHERINE, CABRERA, IVAN AND WRIGHT, ROS- ALIND J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The infant behavior questionnaire-revised: Factor structure in a culturally and sociodemographically diverse sample in the united states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Infant Behavior and Development 43, 24–35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' EUBANK, RANDALL L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' (1999).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Nonparametric regression and spline smoothing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' CRC press.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' GARTSTEIN, MARIA A, BRIDGETT, DAVID J, YOUNG, BRANDI N, PANKSEPP, JAAK AND POWER, THOMAS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Origins of effortful control: Infant and parent contributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Infancy 18(2), 149–183.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' GARTSTEIN, MARIA A AND ROTHBART, MARY K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Studying infant temperament via the revised infant behavior questionnaire.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Infant behavior and development 26(1), 64–86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' GELMAN, ANDREW.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Prior distributions for variance parameters in hierarchical models (comment on article by browne and draper).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Bayesian analysis 1(3), 515–534.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' GELMAN, A, CARLIN, JB, STERN, HS, RUBIN, DB and others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Bayesian data analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' GILLMAN, MATTHEW W AND BLAISDELL, CAROL J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Environmental influences on child health outcomes, a research program of the nih.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Current opinion in pediatrics 30(2), 260.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' GU, CHONG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Smoothing spline ANOVA models, Volume 297.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Springer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' GU, CHONG AND KIM, YOUNG-JU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' (2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Penalized likelihood regression: General formulation and efficient approximation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Canadian Journal of Statistics 30(4), 619–628.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' HE, LINCHEN, WANG, CHAN, HU, JIYUAN, GAO, ZHAN, FALCONE, EMILIA, HOLLAND, STEVEN M, BLASER, MARTIN J AND LI, HUILIN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Arzimm: A novel analytic platform for the inference of microbial interactions and community stability from longitudinal microbiome study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Frontiers in genetics 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' HIPWELL, ALISON E, TUNG, IRENE, NORTHRUP, JESSIE AND KEENAN, KATE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Transgenerational asso- ciations between maternal childhood stress exposure and profiles of infant emotional reactivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Development and psychopathology 31(3), 887–898.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' HUERTA, GABRIEL, JIANG, WENXIN AND TANNER, MARTIN A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Time series modeling via hierarchical mixtures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Statistica Sinica, 1097–1118.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' JACOBS, ROBERT A, JORDAN, MICHAEL I, NOWLAN, STEVEN J AND HINTON, GEOFFREY E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' (1991).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Adaptive mixtures of local experts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Neural computation 3(1), 79–87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' JOBSIS, FRANS F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' (1977).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Noninvasive, infrared monitoring of cerebral and myocardial oxygen sufficiency and circulatory parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Science 198(4323), 1264–1267.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' JORDAN, MICHAEL I AND JACOBS, ROBERT A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' (1994).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Hierarchical mixtures of experts and the em algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Neural computation 6(2), 181–214.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' KAKIZAWA, YOSHIHIDE, SHUMWAY, ROBERT H AND TANIGUCHI, MASANOBU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' (1998).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Discrimination and clustering for multivariate time series.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Journal of the American Statistical Association 93(441), 328–340.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' KEENAN, KATE, HIPWELL, ALISON, CHUNG, TAMMY, STEPP, STEPHANIE, STOUTHAMER-LOEBER, MAGDA, LOEBER, ROLF AND MCTIGUE, KATHLEEN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The pittsburgh girls study: overview and initial findings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Journal of Clinical Child & Adolescent Psychology 39(4), 506–521.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' KEOGH, EAMONN J AND PAZZANI, MICHAEL J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' (2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' A simple dimensionality reduction technique for fast similarity search in large time series databases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' In: Pacific-Asia conference on knowledge discovery and data mining.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Springer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' 122–133.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' KIMELDORF, GEORGE S AND WAHBA, GRACE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' (1970).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' A correspondence between bayesian estimation on stochastic processes and smoothing by splines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The Annals of Mathematical Statistics 41(2), 495–502.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' KRAFTY, ROBERT T, HALL, MARTICA AND GUO, WENSHENG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Functional mixed effects spectral analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Biometrika 98(3), 583–598.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' 9 Covariate-guided Bayesian mixture model for multivariate time series KRAFTY, ROBERT T, ROSEN, ORI, STOFFER, DAVID S, BUYSSE, DANIEL J AND HALL, MARTICA H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Conditional spectral analysis of replicated multiple time series with application to nocturnal physiology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Journal of the American Statistical Association 112(520), 1405–1416.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' LI, CEN, BISWAS, GAUTAM, DALE, MIKE AND DALE, PAT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' (2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Building models of ecological dynamics using hmm based temporal data clustering—a preliminary study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' In: International Symposium on Intelligent Data Analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Springer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' 53–62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' LI, ZEDA AND KRAFTY, ROBERT T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Adaptive bayesian time–frequency analysis of multivariate time series.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Journal of the American Statistical Association 114(525), 453–465.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' LIAO, T WARREN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Clustering of time series data—a survey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Pattern recognition 38(11), 1857–1874.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' LIN, JESSICA, KEOGH, EAMONN AND TRUPPEL, WAGNER.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Clustering of streaming time series is meaningless.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' In: Proceedings of the 8th ACM SIGMOD workshop on Research issues in data mining and knowledge discovery.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' 56–65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' MAGRINI, ALESSANDRO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Assessment of agricultural sustainability in european union countries: a group-based multivariate trajectory approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' AStA Advances in Statistical Analysis, 1–31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' MAHARAJ, ELIZABETH ANN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' (1999).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Comparison and classification of stationary multivariate time series.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Pattern Recognition 32(7), 1129–1138.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' MAHARAJ, ELIZABEH ANN, D’URSO, PIERPAOLO AND CAIADO, JORGE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Time Series Clustering and Classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' chapman and hall/CRC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' NAGIN, DANIEL S, JONES, BOBBY L, PASSOS, VALERIA LIMA AND TREMBLAY, RICHARD E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Group-based multi-trajectory modeling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Statistical methods in medical research 27(7), 2015–2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' PAPASTAMOULIS, PANAGIOTIS AND ILIOPOULOS, GEORGE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' An artificial allocations based solution to the label switching problem in bayesian analysis of mixtures of distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Journal of Computational and Graphical Statistics 19(2), 313–331.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' POLSON, NICHOLAS G, SCOTT, JAMES G AND WINDLE, JESSE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Bayesian inference for logistic models using pólya–gamma latent variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Journal of the American statistical Association 108(504), 1339–1349.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' ROSEN, ORI, STOFFER, DAVID S AND WOOD, SALLY.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Local spectral analysis via a bayesian mixture of smoothing splines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Journal of the American Statistical Association 104(485), 249–262.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' ROSEN, ORI, WOOD, SALLY AND STOFFER, DAVID S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Adaptspec: Adaptive spectral estimation for nonstationary time series.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Journal of the American Statistical Association 107(500), 1575–1589.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' SANTOSA, HENDRIK, ZHAI, XUETONG, FISHBURN, FRANK AND HUPPERT, THEODORE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The nirs brain analyzir toolbox.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Algorithms 11(5), 73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' SPECKMAN, PAUL L AND SUN, DONGCHU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Fully bayesian spline smoothing and intrinsic autoregressive priors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Biometrika 90(2), 289–302.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' SPIEGELHALTER, DAVID J, BEST, NICOLA G, CARLIN, BRADLEY P AND VAN DER LINDE, ANGELIKA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' (2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Bayesian measures of model complexity and fit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Journal of the royal statistical society: Series b (statistical methodology) 64(4), 583–639.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' SUN, ZHUOXIN, ROSEN, ORI AND SAMPSON, ALLAN R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Multivariate bernoulli mixture models with application to postmortem tissue studies in schizophrenia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Biometrics 63(3), 901–909.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' TRONICK, EDWARD, ALS, HEIDELISE, ADAMSON, LAUREN, WISE, SUSAN AND BRAZELTON, T BERRY.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' (1978).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The infant’s response to entrapment between contradictory messages in face-to-face interaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Journal of the American Academy of Child psychiatry 17(1), 1–13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' WAHBA, GRACE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' (1978).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Improper priors, spline smoothing and the problem of guarding against model errors in regression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Journal of the Royal Statistical Society: Series B (Methodological) 40(3), 364–372.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' WAHBA, GRACE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' (1980).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Automatic smoothing of the log periodogram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Journal of the American Statistical Associa- tion 75(369), 122–132.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' WAND, MATTHEW P, ORMEROD, JOHN T, PADOAN, SIMONE A AND FRÜHWIRTH, RUDOLF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Mean field variational bayes for elaborate distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Bayesian Analysis 6(4), 847–900.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' WANG, XIAOZHE, WIRTH, ANTHONY AND WANG, LIANG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Structure-based statistical features and multi- variate time series clustering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' In: Seventh IEEE international conference on data mining (ICDM 2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' IEEE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' 351–360.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' WANG, YUEDONG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Smoothing splines: methods and applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' CRC press.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' 10 Covariate-guided Bayesian mixture model for multivariate time series WOOD, SALLY A, JIANG, WENXIN AND TANNER, MARTIN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' (2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Bayesian mixture of splines for spatially adaptive nonparametric regression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Biometrika 89(3), 513–528.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' WOOD, SIMON N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Generalized additive models: an introduction with R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' chapman and hall/CRC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' 11 Covariate-guided Bayesian mixture model for multivariate time series Figure 1: fNIRS probe configuration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' (a) Positioning of 8 sources, 4 detectors and 12 channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' A channel is connected by one source and one detector (blue line).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' (b) Brodmann areas covered by fNIRS probe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Figure 2: An example of processed fNIRS time series from two selected subjects and four selected channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The measurements are the relative concentration of oxy-hemoglobin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' 12 (a) (b) BA-9L BA-44L BA-45L BA-46L BA-9R BA-45R BA-46R Source Detector ChannelChannel1 Channel2 Channel3 Channel4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='75 Subject 1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='50 series 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='00 Time 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='75 Subject 2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='50- 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='00 00 50 75 25 TimeCovariate-guided Bayesian mixture model for multivariate time series Figure 3: Boxplots of the averaged root square error (ARSE), the averaged bias (A-bias) and the variance of bias (V-bias) of estimated trajectories for each component from 100 replicates of 150 two-component trivariate time series of length 50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The proposed method was compared to R package gbmt and TRAJ procedure in SAS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The diamond markers denote the mean statistics of each method and component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Table 1: Root mean square errors (RMSEs) of each logistic parameter for the two-component trivariate model from 100 replicates of N two-component trivariate time series of length n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' RMSEs of the proposed method were compared to TRAJ procedure in SAS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Parameters δ0, δ1, δ2 and δ3 are intercept, first, second and third logistic parameters, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The true values of logistic parameters are 5, −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='5, 1, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='1, respectively n N Method δ0 δ1 δ2 δ3 50 150 Proposed 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='89 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='52 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='29 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='32 TRAJ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='57 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='87 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='36 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='34 70 150 Proposed 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='86 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='29 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='31 TRAJ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='55 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='86 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='36 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='34 50 250 Proposed 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='77 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='40 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='22 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='23 TRAJ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='96 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='23 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='24 70 250 Proposed 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='77 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='41 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='22 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='23 TRAJ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='97 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='51 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='24 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='24 13 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='04 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='150 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='02 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='02 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='125 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='00 RSE A-bias V-bias AR 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='100 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='02 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='075 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='04 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='050 2 2 Component Component Component MethodProposed gbmt TRAJCovariate-guided Bayesian mixture model for multivariate time series Figure 4: Boxplots of the averaged root square error (ARSE), the averaged bias (A-bias) and the variance of bias (V-bias) of estimated trajectories for each component from 100 replicates of 150 four-component bivariate time series of length 50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The proposed method was compared to R package gbmt and TRAJ procedure in SAS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The diamond markers denote the mean statistics of each method and component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' All boxplots are zoomed in for better visualization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Table 2: Root mean square errors (RMSEs) of each logistic parameter for the four-component bivariate model from 100 replicates of 150 four-component bivariate time series of length 50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' RMSEs of the proposed method were compared to TRAJ procedure in SAS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Parameters δ0, δ1, δ2 and δ3 are intercept, first, second and third logistic parameters, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The fourth component was used as the reference component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The true values of logistic parameters are 5, −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='5, 1, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='1 (first component), −4, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='5, −2, −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='2 (second component), 3, −2, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='8, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='2 (third component).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' C1, C2, C3 and C4 denote first, second, third and fourth component, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' n N Method Comparison δ0 δ1 δ2 δ3 50 150 Proposed C1 vs C4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='81 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='53 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='30 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='39 C2 vs C4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='11 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='46 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='42 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='36 C3 vs C4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='89 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='42 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='28 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='34 TRAJ C1 vs C4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='74 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='35 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='41 C2 vs C4 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='81 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='27 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='33 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='49 C3 vs C4 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='07 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='33 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='76 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='32 14 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='08 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='020 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='04 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='015 RSE ias sel AR 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='010 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='04 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='005 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='000 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='08 4 2 3 4 3 4 Component Component Component Method dProposed gbmt TRAJCovariate-guided Bayesian mixture model for multivariate time series Figure 5: Estimated trajectories of the two-component model with four selected channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' I: Interact S: Still-face R: Recovery.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Red curves are posterior mean and two green dashed curves are 95% pointwise credible intervals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' 15 S1D1 S2D2 S5D3 S6D4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='7 S R .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' S .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='. R S R .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='. S .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='. R 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='6 Component1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='5 Itrajectory .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='. 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='4 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='. .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='.-.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='3 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='. Estimated 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='7 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' S R S .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='-.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' R .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='-.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='. S .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' R + + S .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='-.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='. R 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='6 Component2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='4 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='. 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='3 00 00 20 0000 25 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='00 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='25 50 15 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='75 00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Time Component 1:No response Component2:ResponseCovariate-guided Bayesian mixture model for multivariate time series Figure 6: Logistic coefficient estimates and 95% credible intervals for each covariate of the two-component model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' 16 (Intercept) IBQ-NE IBQ-EC Infant age Gestational days Head circumference Sex 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='5 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='0 Coefficient estimateCovariate-guided Bayesian mixture model for multivariate time series 10 Supplemental material Appendix A: Details of the sampling scheme As described in Section 5 of the paper, Gibbs sampling is used to facilitate Bayesian inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' We denote by Θgk = (θ′ gk, τ 2 gk, σ2 gk, δ∗′ g , κ2 ζg)′ the parameters for the gth component and the kth entry, and the parameters in this vector are drawn from the corresponding conditional posterior distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Let ℓ be the current Gibbs sampling iteration;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' detailed Gibbs sampling steps for drawing the parameters at the (ℓ + 1)th iteration are given below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Sampling the basis function coefficients For each component g and time series entry k, based on the augmented likelihood in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='3 and the priors on θgk = (α′ gk, β′ gk)′ described in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' the conditional posterior distribution of (θ(ℓ+1) gk | y,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' τ 2(ℓ) gk ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' σ2(ℓ) gk ) is: p(θ(ℓ+1) gk | y,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='τ 2(ℓ) gk ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' σ2(ℓ) gk ) ∝ p(y | S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' θ(ℓ+1) gk ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' σ2(ℓ) gk ) · p(θ(ℓ+1) gk | τ 2(ℓ) gk ) ∝ N � i=1 � (σ2 gk)−n/2 exp � − 1 2σ2 gk (yik − Sθgk)′(yik − Sθgk) ��zig × |Dgk|−1/2 exp � − 1 2θgkD−1 gk θgk � ∝ exp � − 1 2σ2 gk � N � i=1 zig(yik − Sθgk)′(yik − Sθgk) + θ′ gkσ2 gkD−1 gk θgk �� ∝ exp � − 1 2σ2 gk (θgk − ugk)′(Λgk)−1(θgk − ugk) � ∼ N(ugk,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' σ2 gkΛgk),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' where Λgk = (N (ℓ) g S′S + σ2 gkD−1 gk )−1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' ugk = Λgk �N i=1 zigS′yik,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' N (ℓ) g is the current number of subjects in the gth component,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Dgk = diag(σ2 α12,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' τ 2 gk1m) is the prior covariance matrix for θgk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Hence, for each component g and entry k, we draw θ(ℓ+1) gk from (θ(ℓ+1) gk | y, S, τ 2(ℓ) gk , σ2(ℓ) gk ) ∼ N(ugk, σ2 gkΛgk).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Sampling the error variances Gelman (2006) proposed using the half-t distribution as the prior on scale parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' We follow Wand and others (2011) and express the half-t prior of Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='3 as a scale mixture of inverse Gamma distributions as follows (σ2 gk | aσgk) ∼ IG �νσ 2 , νσ aσgk � , aσgk ∼ IG �1 2, 1 A2σ � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Therefore, the conditional posterior distribution of the latent variable aσgk is p(a(ℓ+1) σgk | σ2(ℓ) gk ) ∝ exp � − 1 aσgk � νσ σ2 gk + 1 A2σ �� × (aσgk)−( 1 2 +1+ νσ 2 ), which is IG � νσ+1 2 , νσ σ2 gk + 1 A2σ � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Denoting by ϵigk the error vector of time series yik for component g, we have ϵigk = yik − Sθgk, where ϵigk ∼ N(0, σ2 gkIn).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The conditional distribution of the error variance is p(σ2(ℓ+1) gk | ϵ(ℓ+1) igk ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' a(ℓ+1) σgk ) ∝ p(ϵ(ℓ+1) igk | σ2(ℓ+1) gk ) · p(a(ℓ+1) σgk | σ2(ℓ+1) gk ) · p(σ2(ℓ+1) gk ) ∝ N � i=1 � (σ2 gk)− n 2 exp � − 1 2σ2 gk ϵ′ igkϵigk ��zig × (σ2 gk)−( νσ 2 +1) exp � − νσ σ2 gkaσgk � ∝ (σ2 gk)−( n 2 N (ℓ) g + νσ 2 +1) exp � − 1 σ2 gk ��N i=1 zigϵ′ igkϵigk 2 + νσ aσgk �� ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' which is IG � nN (ℓ) g +νσ 2 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' �N i=1 zigϵ′ igkϵigk 2 + νσ aσgk � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The sampling scheme proceeds by first sampling (a(ℓ+1) σgk | σ2(ℓ) gk ) and then (σ2(ℓ+1) gk | ϵ(ℓ+1) igk , a(ℓ+1) σgk ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' 17 Covariate-guided Bayesian mixture model for multivariate time series 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Sampling the smoothing parameters The smoothing parameters τ 2 gk are drawn by analogy to the error variances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' We first draw (a(ℓ+1) τgk | τ 2(ℓ) gk ) ∼ IG � ντ +1 2 , ντ τ 2 gk + 1 A2τ � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The conditional posterior distribution of the smoothing parameters is p(τ 2(ℓ+1) gk | β(ℓ+1) gk , a(ℓ+1) τgk ) ∝ p(β(ℓ+1) gk | τ 2(ℓ+1) gk ) · p(a(ℓ+1) τgk | τ 2(ℓ+1) gk ) · p(τ 2(ℓ+1) gk ) ∝ (τ 2 gk)− m+ντ 2 exp � − 1 τ 2 gk � ντ aτgk + β′ gkβgk 2 �� , which is IG � ντ +m 2 , β′ gkβgk 2 + ντ aτgk � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The sampling scheme proceeds by first sampling (a(ℓ+1) τgk | τ 2(ℓ) gk ) and then (τ 2(ℓ+1) gk | β(ℓ+1) gk , a(ℓ+1) τgk ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Sampling the logistic parameters Let δ∗ g = (δT g , ζT g )T be the aggregation of the logistic parameters and all random intercepts for the gth component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Based on the logits of Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='2 and the corresponding priors described in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='4, the conditional posterior distribution of (δ∗(ℓ+1) g | V ∗, z(ℓ) ig , κ2(ℓ) ζg ) is p(δ∗(ℓ+1) g | V ∗, z(ℓ) ig , κ2(ℓ) ζg ) ∝ p(z(ℓ) ig = 1 | V ∗, δ∗(ℓ+1) g ) · p(δ∗(ℓ+1) g | κ2(ℓ) ζg ) = N � i=1 � exp(V ∗′ i δ∗ g) �G h=1 exp(V ∗′ i δ∗ h) �zig p(δ∗(ℓ+1) g | κ2(ℓ) ζg ), where V ∗ = (V ∗ 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' , V ∗ N)′ is a N ×(P +1) matrix with V ∗ i representing all covariates (including intercepts) for subject i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' To sample from the posterior distribution of p(δ∗(ℓ+1) g | V ∗, z(ℓ) ig , κ2(ℓ) ζg ), we adopt the Póyla- Gamma data augmentation strategy of Polson and others (2013) by introducing a latent variable ωig coming from the Pólya-Gamma distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Thus,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' the conditional posterior distributions of the logistic parameters are p(δ∗(ℓ+1) g | V ∗,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' z(ℓ) ig ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' ω(ℓ+1) ig ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' κ2(ℓ) ζg ) ∝ p(z(ℓ) ig = 1 | V ∗,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' ω(ℓ+1) ig ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' δ∗(ℓ+1) g ) · p(ω(ℓ+1) ig | V ∗,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' δ∗(ℓ) g ) p(δ∗(ℓ+1) g | κ2(ℓ) ζg ) ∝ exp � − ωigη2 ig 2 � p(ωig | 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' 0)|Bg|−P/2 exp � − 1 2δ∗′ g B−1 g δ∗ g � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' where ηig = V ∗′ i δ∗ g − Cig and Cig = log � h̸=j exp(V ∗′ i δ∗ h),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' p(ωig | 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' 0) is the Pólya-gamma dis- tribution PG(b,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' c) with b = 1 and c = 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Bg is the prior covariance matrix of Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='4 and Bg = diag(σ2 δg1P +1, κ2 ζg1N).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' By assuming the conjugate prior N(0, Bg) on δ∗ g, the posterior distribu- tion of the Pólya-gamma latent variable is (ω(ℓ+1) ig | V ∗, δ∗(ℓ) g ) ∼ PG(1, ηig).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Thus, the conditional distributions of the logistic parameters (including the random intercepts) are (δ∗(ℓ+1) g | V ∗, z(ℓ) ig , ω(ℓ+1) ig , κ2(ℓ) ζg ) ∼ N(M g, Σg), where Σg = (V ∗′ΩgV ∗ + B−1 g )−1, M g = Σg � V ∗′(ΩgCg + ξg) � , Ωg = diag(ω1g, · · · , ωNg), Cg = (C1g, · · · , CNg)′, and ξg = (ξ1g, · · · , ξNg)′, with ξig = zig − 1 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Thus, δ∗(ℓ+1) g is drawn by first sampling (ω(ℓ+1) ig | V ∗, δ∗(ℓ) g ) and then (δ∗(ℓ+1) g | V ∗, z(ℓ) ig , ω(ℓ+1) ig , κ2(ℓ) ζg ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Sampling the variances of the random intercepts By analogy with sampling the error variances and sthe moothing parameters, we first draw (a(ℓ+1) κg | κ2(ℓ) ζg ) ∼ IG � νκ+1 2 , νκ κ2 ζg + 1 A2κ � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The conditional posterior distributions of the variances of the random intercepts are p(κ2(ℓ+1) ζg | ζ(ℓ+1) g , a(ℓ+1) κg ) ∝ p(ζ(ℓ+1) g | κ2(ℓ+1) ζg ) · p(a(ℓ+1) κg | κ2(ℓ+1) ζg ) · p(κ2(ℓ+1) ζg ) ∝ (κ2 ζg)− N+νκ 2 +1 exp � − 1 κ2 ζg � νκ aκg + ζT g ζg 2 �� , which is IG � νκ+N 2 , ζT g ζg 2 + νκ aκg � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The sampling scheme proceeds by first sampling (a(ℓ+1) κg | κ2(ℓ) ζg ) and then (κ2(ℓ+1) ζg | ζ(ℓ+1) g , a(ℓ+1) κg ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' 18 Covariate-guided Bayesian mixture model for multivariate time series 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Computing the mixing weights After drawing the δ∗ g, the mixing weights π(ℓ+1) ig for each component, given the design matrix V ∗ i , are computed by p(π(ℓ+1) ig | V ∗ i , δ∗(ℓ+1) g ) = exp(V ∗T i δ∗ g) �G h=1 exp(V ∗T i δ∗ h) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Sampling the latent indicators After sampling all parameters and computing the mixing weights, the final Gibbs step is to allocate subjects to different components by drawing the latent indicators zig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' As in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='3, the conditional posterior of these indicators is p(z(ℓ+1) ig = 1 | y, S, Θ(ℓ+1), π(ℓ+1) ig ) = πig �K k=1 fgk(yik | Θgk) �G h=1 πih �K k=1 fhk(yik | Θhk) , and the indicators are drawn from the multinomial distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Appendix B: Additional simulation results Appendix B adds more simulation results in addition to simulation results in the paper itself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' To further demonstrate the performance of the proposed method, we conduct simulation studies under two scenarios: two-component mixture of trivariate time series and four-component mixture of bivariate time series.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The model formula is displayed in Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='1 of the paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' We investigate the performance of our proposed method in terms of estimated trajectories and logistic parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Mean(SD) of the ARSE, A-bias and V-bias for each component of the two-component trivariate model are given in Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' To demonstrate the performance of the proposed method in various settings, we look at combinations of the number of multivariate time series (N = 150, 250) and the length of each time series (n = 50, 70), and compare our proposed method to two existing methods: gbmt package in R (Magrini, 2022) and TRAJ procedure in SAS (Nagin and others, 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The case of n = 50 and N = 150 in Table 3 corresponds to Figure 3 in the main paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The performance of the logistic parameters (RMSEs) with different values of n and N are given in Table 1 of the paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The Mean(SD) of the ARSE, A-bias and V-bias for each component of the N = 150 four-component mixture of bivariate time series of length n = 50 are given in Table 4, which corresponds to Figure 4 in the main paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' RMSEs of the logistic parameters for this setting are listed in Table 2 of the paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Tables 5 - 10 present performance measures of the estimated trajectories and logistic parameters for combinations of different lengths of time series n and numbers of time series N, under the scenario of the four-component bivariate model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' As expected, our proposed method outperforms the two existing methods in terms of the estimated trajectories for each component under different settings (different values of n and N, for both the two-component trivariate and the four-component bivariate scenarios).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The proposed method is able to achieve smaller ARSE and V-bias, while all three methods are able to obtain estimated trajectories with a very small bias.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Notably, for the four-component bivariate scenario, TRAJ gives larger values of mean ARSE, A-bias and V-bias, which result from imprecise estimates of several replicates due to convergence issues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' In terms of the logistic parameters, our proposed method outperforms TRAJ in almost all comparisons, especially for the intercept δ0 and the slope of the first covariate δ1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Our proposed method yields shrinkage estimates for the logistic parameters due to using a Bayesian method, while the multinomial logistic regression used in TRAJ gives inflated parameter estimates in case of perfect separations and unbalanced designs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Appendix C: Additional real-data results Appendix C describes more real-data results in addition to those in Section 7 of the main paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Our motivating study is described in Section 2 of the paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Figure 7 shows the estimated trajectories of the three-component model for another set of four channels (S1D3, S3D2, S5D4, and S7D4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Based on the selection criterion DIC introduced in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='2 of the main paper, the three-component model was selected as the best model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' We named the second component as the mixture response component because it involves both increased and decreased brain activity or hemoglobin level for the still-face period for different channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' In addition, Figure 8 displays the logistic coefficient estimates and 95% credible intervals corresponding to each covariate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The last component (third component) is always used as the reference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' We reach the same conclusion with positive estimates of IBQ-NE scores and negative estimates of IBQ-EC scores for both components (component 1 vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' 3, component 2 vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' In addition to the four-channel analyses, we also present results from all channels (twelve channels).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Figures 9, 10, 11 present the estimated trajectories of the first, second and third component for the three-component model with all twelve 19 Covariate-guided Bayesian mixture model for multivariate time series Table 3: Mean (standard deviation) of the averaged root square error (ARSE), the averaged bias (A-bias) and the variance of bias (V-bias) of estimated trajectories for each component from 100 replicates of N two-component trivariate time series of length n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The proposed method was compared to R package gbmt and TRAJ procedure in SAS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' C1 and C2 denote first and second components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Means were calculated by averaging over estimates of 100 replicates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Standard deviations are Monte Carlo standard deviations from estimates of 100 replicates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Each value was reported ×102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' n N Method ARSE C1 A-bias C1 V-bias C1 ARSE C2 A-bias C2 V-bias C2 50 150 Proposed 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='35 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='26) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='03 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='83) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='68 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='22) 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='65 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='38) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='10 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='76) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='58 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='22) gbmt 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='67 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='91) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='03 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='83) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='15 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='42) 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='08 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='72) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='10 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='76) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='83 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='33) TRAJ 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='06 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='48) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='03 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='83) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='22 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='33) 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='59 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='52) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='10 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='76) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='12 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='34) 70 150 Proposed 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='16 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='04) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='24 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='38) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='51 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='16) 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='53 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='07) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='11 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='42) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='42 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='14) gbmt 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='91 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='96) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='24 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='38) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='01 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='40) 8.' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='11 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='42) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='80 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='20) 50 250 Proposed 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='81 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='02) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='07 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='33) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='46 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='14) 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='22 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='94) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='02 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='31) 0.' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='40) 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='00 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='53) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='02 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='31) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='65 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='26) TRAJ 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='70 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='18) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='07 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='33) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='76 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='21) 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='20 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='03) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='02 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='31) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='67 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='17) 70 250 Proposed 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='65 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='84) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='08 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='00) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='32 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='10) 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='27 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='82) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='06 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='42) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='27 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='09) gbmt 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='15 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='96) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='08 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='00) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='87 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='38) 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='43 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='60) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='06 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='42) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='56 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='26) TRAJ 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='18 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='94) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='08 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='00) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='52 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='14) 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='80 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='77) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='06 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='42) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='45 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='10) Table 4: Mean (standard deviation) of the averaged root square error (ARSE), the averaged bias (A-bias) and the variance of bias (V-bias) of estimated trajectories for each component from 100 replicates of 150 four-component bivariate time series of length 50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The proposed method was compared to R package gbmt and TRAJ procedure in SAS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' C1, C2, C3 and C4 denote first, second, third and fourth component, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Means were calculated by averaging over estimates of 100 replicates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Standard deviations are Monte Carlo standard deviations from estimates of 100 replicates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Each value was reported ×102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' n N Method ARSE C1 A-bias C1 V-bias C1 ARSE C2 A-bias C2 V-bias C2 50 150 Proposed 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='38 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='04) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='38 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='59) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='18 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='08) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='76 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='87) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='01 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='37) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='13 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='06) gbmt 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='75 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='04) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='38 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='59) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='21 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='09) 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='79 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='17) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='01 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='65) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='22 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='11) TRAJ 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='87 (15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='59) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='62 (9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='91) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='39 (9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='24) 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='41 (13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='42) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='08 (9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='74) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='41 (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='37) n N Method ARSE C3 A-bias C3 V-bias C3 ARSE C4 A-bias C4 V-bias C4 50 150 Proposed 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='69 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='14) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='11 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='83) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='20 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='12) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='88 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='15) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='09 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='56) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='14 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='08) gbmt 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='08 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='12) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='12 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='83) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='24 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='12) 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='70 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='32) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='09 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='78) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='21 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='12) TRAJ 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='55 (14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='82) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='58 (10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='31) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='24 (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='35) 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='36 (17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='01) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='12 (9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='92) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='99 (10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='70) 20 Covariate-guided Bayesian mixture model for multivariate time series Table 5: Mean (standard deviation) of the averaged root square error (ARSE), the averaged bias (A-bias) and the variance of bias (V-bias) of estimated trajectories for each component from 100 replicates of 150 four-component bivariate time series of length 70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The proposed method was compared to R package gbmt and TRAJ procedure in SAS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' C1, C2, C3 and C4 denote first, second, third and fourth component, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Means were calculated by averaging over estimates of 100 replicates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Standard deviations are Monte Carlo standard deviations from estimates of 100 replicates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Each value was reported ×102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' n N Method ARSE C1 A-bias C1 V-bias C1 ARSE C2 A-bias C2 V-bias C2 70 150 Proposed 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='82 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='95) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='44 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='30) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='14 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='07) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='22 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='85) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='07 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='95) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='10 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='06) gbmt 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='05 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='97) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='44 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='30) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='16 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='08) 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='11 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='12) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='08 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='15) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='17 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='10) TRAJ 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='51 (17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='04) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='30 (9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='34) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='86 (10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='73) 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='00 (10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='11) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='25 (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='21) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='64 (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='02) n N Method ARSE C3 A-bias C3 V-bias C3 ARSE C4 A-bias C4 V-bias C4 70 150 Proposed 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='12 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='90) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='29 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='69) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='15 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='06) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='52 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='85) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='24 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='22) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='12 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='06) gbmt 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='38 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='01) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='29 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='69) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='17 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='07) 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='13 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='99) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='27 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='40) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='16 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='09) TRAJ 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='03 (17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='04) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='30 (10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='49) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='86 (10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='73) 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='77 (13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='78) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='39 (8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='49) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='57 (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='45) Table 6: Root mean square errors (RMSEs) of each logistic parameter for the four-component bivariate model from 100 replicates of 150 four-component bivariate time series of length 70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' RMSEs of the proposed method were compared to TRAJ procedure in SAS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Parameters δ0, δ1, δ2 and δ3 are intercept, first, second and third logistic parameters, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The fourth component was used as the reference component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The true values of logistic parameters are 5, −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='5, 1, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='1 (first component), −4, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='5, −2, −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='2 (second component), 3, −2, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='8, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='2 (third component).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' C1, C2, C3 and C4 denote first, second, third and fourth component, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' n N Method Comparison δ0 δ1 δ2 δ3 70 150 Proposed C1 vs C4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='81 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='51 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='29 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='41 C2 vs C4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='42 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='73 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='58 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='36 C3 vs C4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='58 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='37 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='31 TRAJ C1 vs C4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='13 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='66 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='31 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='45 C2 vs C4 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='12 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='66 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='99 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='55 C3 vs C4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='74 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='48 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='35 Table 7: Mean (standard deviation) of the averaged root square error (ARSE), the averaged bias (A-bias) and the variance of bias (V-bias) of estimated trajectories for each component from 100 replicates of 250 four-component bivariate time series of length 50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The proposed method was compared to R package gbmt and TRAJ procedure in SAS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' C1, C2, C3 and C4 denote first, second, third and fourth component, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Means were calculated by averaging over estimates of 100 replicates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Standard deviations are Monte Carlo standard deviations from estimates of 100 replicates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Each value was reported ×102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' n N Method ARSE C1 A-bias C1 V-bias C1 ARSE C2 A-bias C2 V-bias C2 50 250 Proposed 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='42 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='78) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='18 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='19) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='11 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='05) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='86 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='61) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='14 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='98) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='08 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='04) gbmt 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='57 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='85) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='18 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='19) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='12 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='06) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='68 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='79) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='15 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='20) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='13 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='06) TRAJ 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='66 (15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='03) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='53 (10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='63) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='50 (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='30) 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='90 (9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='38) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='47 (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='81) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='05 (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='16) n N Method ARSE C3 A-bias C3 V-bias C3 ARSE C4 A-bias C4 V-bias C4 50 250 Proposed 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='93 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='92) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='06 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='48) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='14 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='07) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='28 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='76) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='10 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='19) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='10 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='05) gbmt 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='16 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='95) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='06 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='49) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='16 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='07) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='83 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='83) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='13 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='36) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='14 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='06) TRAJ 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='80 (9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='92) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='49 (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='78) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='83 (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='70) 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='17 (12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='54) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='17 (8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='83) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='84 (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='20) 21 Covariate-guided Bayesian mixture model for multivariate time series Table 8: Root mean square errors (RMSEs) of each logistic parameter for the four-component bivariate model from 100 replicates of 250 four-component bivariate time series of length 50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' RMSEs of the proposed method were compared to TRAJ procedure in SAS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Parameters δ0, δ1, δ2 and δ3 are intercept, first, second and third logistic parameters, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The fourth component was used as the reference component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The true values of logistic parameters are 5, −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='5, 1, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='1 (first component), −4, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='5, −2, −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='2 (second component), 3, −2, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='8, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='2 (third component).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' C1, C2, C3 and C4 denote first, second, third and fourth component, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' n N Method Comparison δ0 δ1 δ2 δ3 50 250 Proposed C1 vs C4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='63 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='41 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='26 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='29 C2 vs C4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='46 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='40 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='27 C3 vs C4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='63 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='33 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='23 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='24 TRAJ C1 vs C4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='91 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='56 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='30 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='28 C2 vs C4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='40 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='86 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='61 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='35 C3 vs C4 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='24 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='40 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='85 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='27 Table 9: Mean (standard deviation) of the averaged root square error (ARSE), the averaged bias (A-bias) and the variance of bias (V-bias) of estimated trajectories for each component from 100 replicates of 250 four-component bivariate time series of length 70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The proposed method was compared to R package gbmt and TRAJ procedure in SAS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' C1, C2, C3 and C4 denote first, second, third and fourth component, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Means were calculated by averaging over estimates of 100 replicates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Standard deviations are Monte Carlo standard deviations from estimates of 100 replicates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Each value was reported ×102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' n N Method ARSE C1 A-bias C1 V-bias C1 ARSE C2 A-bias C2 V-bias C2 70 250 Proposed 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='94 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='60) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='04 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='06) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='08 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='04) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='61 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='57) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='01 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='87) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='06 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='03) gbmt 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='10 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='63) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='04 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='06) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='09 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='04) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='18 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='70) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='01 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='05) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='10 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='05) TRAJ 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='52 (17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='70) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='58 (11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='09) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='71 (8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='80) 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='51 (14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='85) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='19 (9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='98) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='54 (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='10) n N Method ARSE C3 A-bias C3 V-bias C3 ARSE C4 A-bias C4 V-bias C4 70 250 Proposed 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='30 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='76) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='02 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='21) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='10 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='05) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='85 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='73) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='07 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='97) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='08 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='04) gbmt 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='51 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='79) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='01 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='21) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='12 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='06) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='26 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='80) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='09 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='06) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='10 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='05) TRAJ 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='07 (15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='21) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='48 (10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='52) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='90 (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='11) 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='68 (12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='93) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='65 (8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='11) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='16 (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='66) Table 10: Root mean square errors (RMSEs) of each logistic parameter for the four-component bivariate model from 100 replicates of 250 four-component bivariate time series of length 70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' RMSEs of the proposed method were compared to TRAJ procedure in SAS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Parameters δ0, δ1, δ2 and δ3 are intercept, first, second and third logistic parameters, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The fourth component was used as the reference component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The true values of logistic parameters are 5, −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='5, 1, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='1 (first component), −4, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='5, −2, −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='2 (second component), 3, −2, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='8, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='2 (third component).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' C1, C2, C3 and C4 denote first, second, third and fourth component, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' n N Method Comparison δ0 δ1 δ2 δ3 70 250 Proposed C1 vs C4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='64 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='40 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='26 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='28 C2 vs C4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='92 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='42 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='41 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='28 C3 vs C4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='63 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='31 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='23 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='23 TRAJ C1 vs C4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='82 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='27 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='28 C2 vs C4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='47 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='86 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='61 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='36 C3 vs C4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='60 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='96 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='57 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='25 22 Covariate-guided Bayesian mixture model for multivariate time series channels, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' The three-component model was selected as the best model for the twelve-channel analysis based on the adjusted DIC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' We named the three components no response, mixture response, and response component, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Figure 12 displays the logistic coefficient estimates and 95 % credible intervals corresponding to each covariate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' 23 Covariate-guided Bayesian mixture model for multivariate time series Figure 7: Estimated trajectories of the three-component model with four selected channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' I: Interact S: Still-face R: Recovery.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Red curves are posterior means and the two green dashed curves are 95% pointwise credible intervals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' 24 S1D3 S3D2 S5D4 S7D4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='7 S R S R S R S R 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='6 Component 1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='4 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='. 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='3 I trajectory 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='7 S R S R S R S R 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='6 Component2 Estimated 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='4 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='7 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='. S R S R S R S R .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='6 Component3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='4 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='. 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='25 S20 2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='50 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='50 100 00 15 00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='5 O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' O 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='25 O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Time Component1:Noresponse Component 3: ResponseCovariate-guided Bayesian mixture model for multivariate time series Figure 8: Logistic coefficient estimates and 95% credible intervals corresponding to each covariate of the three- component model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' 25 (Intercept) IBQ-NE IBQ-EC model Infant age Component 1 Component 2 Gestational days HeadCircumference Sex 0 4 Coefficient estimateCovariate-guided Bayesian mixture model for multivariate time series Figure 9: Estimated trajectories of the first component for the three-component model with all twelve channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' I: Interact S: Still-face R: Recovery.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Red curves are posterior mean and two green dashed curves are 95% pointwise credible intervals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' 26 S1D1 S1D2 S1D3 S2D2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='7 S R S R S R S .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='. R 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='3 jectory S3D2 S4D2 S5D1 S5D3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='7 R S R traj 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='6 Estimated 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='4 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='3 S5D4 S6D4 S7D4 S8D4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='7 S R S R S R : S R 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='3 00 0 5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' 0 Time Component1:NoresponseCovariate-guided Bayesian mixture model for multivariate time series Figure 10: Estimated trajectories of the second component for the three-component model with all twelve channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' I: Interact S: Still-face R: Recovery.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Red curves are posterior mean and two green dashed curves are 95% pointwise credible intervals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' 27 S1D1 S1D2 S1D3 S2D2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='7 Rn R AR 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='3 trajectory S3D2 S4D2 S5D1 S5D3 0.' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' Red curves are posterior mean and two green dashed curves are 95% pointwise credible intervals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' 28 S1D1 S1D2 S1D3 S2D2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='7 S R 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content='4 0.' metadata={'source': 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credible intervals for each covariate of the three-component model for all twelve channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} +page_content=' 29 (Intercept) IBQ-NE IBQ-EC model Infant age Component 1 Component 2 Gestational days HeadCircumference Sex 4 0 4 Coefficient estimate' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQfavxL/content/2301.01373v1.pdf'} diff --git a/gtAzT4oBgHgl3EQf4P6f/vector_store/index.faiss b/gtAzT4oBgHgl3EQf4P6f/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..44540db61449e0d0c3ea336cd845d39bbf8dd567 --- /dev/null +++ b/gtAzT4oBgHgl3EQf4P6f/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:d674bab4d4079ce8fb3b087247178f3b9bad0c0d5ceb0729e46942bb3c7a4172 +size 2293805 diff --git a/gtAzT4oBgHgl3EQf4P6f/vector_store/index.pkl 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M. Constraints +on Nuclear Symmetry Energy +Parameters. Preprints 2023, 1, 0. +https://doi.org/ +Academic Editor: Armen Sedrakian +Publisher’s Note: MDPI stays neutral +with regard to jurisdictional claims in +published maps and institutional affil- +iations. +Copyright: +© 2022 by the author. +Licensee MDPI, Basel, Switzerland. +This article is an open access article +distributed +under +the +terms +and +conditions of the Creative Commons +Attribution (CC BY) license (https:// +creativecommons.org/licenses/by/ +4.0/). +Article +Constraints on Nuclear Symmetry Energy Parameters +James M. Lattimer +Department of Physics & Astronomy, Stony Brook University, Stony Brook, NY 11794-3800, USA; +james.lattimer@stonybrook.edu +Abstract: A review is made of constraints on the nuclear symmetry energy parameters arising from nuclear +binding energy measurements, theoretical chiral effective field predictions of neutron matter properties, +the unitary gas conjecture, and measurements of neutron skin thicknesses and dipole polarizabilities. +While most studies have been confined to the parameters SV and L, the important roles played by, and +constraints on Ksym, or, equivalently, the neutron matter incompressibility KN, are discussed. Strong +correlations among SV, L, and KN are found from both nuclear binding energies and neutron matter theory. +However, these correlations somewhat differ in the two cases, and those from neutron matter theory have +smaller uncertainties. To 68% confidence, it is found from neutron matter theory that SV = 32.0 ± 1.1 +MeV, L = 51.9 ± 7.9 MeV and KN = 152.2 ± 38.1 MeV. Theoretical predictions for neutron skin thickness +and dipole polarizability measurements of the neutron-rich nuclei 48Ca, 120Sn, and 208Pb are compared to +recent experimental measurements, most notably the CREX and PREX neutron skin experiments from +Jefferson Laboratory. By themselves, PREX I+II measurements of 208Pb and CREX measurement of 48Ca +suggest L = 121 ± 47 MeV and L = −5 ± 40 MeV, respectively, to 68% confidence. However, we show +that nuclear interactions optimally satisfying both measurements imply L = 53 ± 13 MeV, nearly the +range suggested by either nuclear mass measurements or neutron matter theory, and is also consistent +with nuclear dipole polarizability measurements. This small parameter range implies R1.4 = 11.6 ± 1.0 +km and Λ1.4 = 228+148 +−90 , which are consistent with NICER X-ray and LIGO/Virgo gravitational wave +observations of neutron stars. +Keywords: nuclear symmetry energy; neutron stars; neutron skins; neutron star radii +1. Introduction +The nuclear symmetry energy, and its density dependence, as characterized by the tra- +ditional symmetry energy parameters SV and L, has been the focus of much recent activity +because it is the most direct link between nuclear physics and nuclear astrophysics [1–3]. Both +the expected neutrino and gravitational wave signals from gravitational collapse supernovae +within our Galaxy are sensitive to the symmetry energy [4–6]. The symmetry energy near the +baryon density at saturation, ns = 0.155 ± 0.005 fm−3, determines the radius [7] of a neutron +star (NS), which strongly influence the expected gravitational signals from their mergers [8,9]. +The symmetry energy also affects the NS crust’s thickness and thermal relaxation time, poten- +tially observable in cooling and accreting [10] NSs and in giant magnetar flares [11–13]. The +composition of matter at densities above ns, and the existence of neutrino processes which +can rapidly cool NSs, depend on the density dependence of the symmetry energy [14], as do +predicted properties of neutron-rich nuclei and reaction rates involved in the astrophysical +r-process [15]. +Experimental attempts to constrain the nuclear symmetry energy parameters include +measurements of nuclear masses, neutron skin thicknesses, nuclear dipole polarizabilities, +giant and pygmy dipole resonance energies, flows in heavy-ion collisions, and isobaric analog +states. These constraints are influenced by varying degrees of model dependence. In addition, +recent advances in neutron matter theory, especially that of systematic expansions involving +chiral effective field theory (χEFT) [16], also constrain the symmetry energy parameters. +arXiv:2301.03666v1 [nucl-th] 9 Jan 2023 + +BY2 of 29 +Of considerable interest are the recent parity-violating electron scattering neutron skin +experiments of 208Pb (PREX-I and PREX-II) [17] and 48Ca [18]. These measure the mean +square difference of the neutron and proton radii using a technique which is argued to be the +most direct and least model-dependent experiment to date [19]. PREX I+II combined yields +r208 +np = 0.283 ± 0.071 fm [17], which implies [20] 68% confidence ranges of SV = 38.29 ± 4.66 +MeV and L = 109.56 ± 36.41 MeV. Both values, and the measured value of r208 +np itself, are +considerably larger than from expectations from neutron matter and nuclear binding energies, +and also from previous measurements, although overlapping with them at about the 90% +confidence level. This indicates a tension with the current understanding of the equation +of state (EOS). For example, these results imply a tidal deformability that lies above the 90% +confidence upper limit established for a 1.4M⊙ NS by the LIGO/Virgo observation of the binary +NS (BNS) merger GW170817 [21,22]. In contrast, the measurement of the neutron skin of 48Ca +using the same technique [18] are somewhat smaller than the average of earlier experimental +measurements and expectations from nuclear binding energies and neutron matter theory. +Ref. [23] performed a Bayesian analysis of the PREX and CREX results. They found that +the two experimental results are incompatible with each other at 68% confidence level, but +compatible at 90% confidence level. Combining the data, they inferred SV = 30.2+4.1 +−3.0 MeV and +L = 15.3+46.8 +−41.5 MeV at 90% confidence level. They find the combined results predict r48 +np close +to the CREX result, but predict r208 +np considerably smaller than the PREX result. Ref. [24] also +performed a combined analysis, and conclude that a simultaneous accurate description of the +skins of 48Ca and 208Pb cannot be achieved with their models that accommodate mass, charge +radii and experimental dipole polarizabilities. +In this paper we take a different perspective by discovering the properties of nuclear +interactions fit to binding energy and charge radii of large numbers of nuclei that best satisfy +both PREX and CREX measurements. We agree with the assessments of both Ref. [23,24] that no +conventional nuclear interaction can fit both measurements to 68% confidence level. However, +our optimum fit results in ranges of SV and L that not only have central values larger than +those estimated by Ref. [23] but also smaller uncertainties. Our results also agree with results +from neutron matter theory while those from Ref. [23] do not. We find similar results when +historical measurements of the neutron skins of both nuclei are utilized, instead, suggesting +that systematic uncertainties in the measurements are not dominant. +We begin by summarizing nuclear binding energy and theoretical neutron matter con- +straints on the nuclear symmetry energy parameters SV, L and KN. We show that estimates of +symmetry energy parameters from chiral Lagrangian expansions of nuclear matter are more +reliably estimated from neutron matter calculations than from both neutron and symmetric +matter calculations. We explore systematic uncertainties in parameter estimation stemming +from the choice of nuclear interaction model, and note apparent inconsistencies associated with +relatively stiff relativistic mean field (RMF) interactions. We show that nuclear models fit to nu- +clear binding energies that optimally satisfy both CREX and PREX neutron skin measurements +confine symmetry parameter values to narrow ranges that are consistent with expectations +from neutron matter theory. We also show that they are also consistent with theoretical esti- +mates based on dipole polarizability experiments. We also compare our estimates of symmetry +parameters from those estimated from astrophysical observations of neutron stars, especially +from gravitational wave observations of GW170817 and Neutron Star Interior Composition +ExploreR (NICER) X-ray observations of PSR J0030+0451 [25,26] and PSR J0740+6620 [27,28]. +2. The Nuclear Symmetry Energy +The nuclear symmetry energy S(n) is defined here to be the difference between the +energies of pure neutron matter (PNM), EN, and isospin symmetric nuclear matter (SNM), + +3 of 29 +E1/2, at the baryon density n. Related quantities are the density-dependent coefficients, Sn(n), +of an expansion of the bulk energy per baryon, E(n, x), in powers of the neutron excess 1 − 2x: +E(n, x) = E1/2(n) + S2(n)(1 − 2x)2 + S3(n)(1 − 2x)3 + . . . +(1) +A common approximation is to retain only the quadratic term in Equation (1) at every density, +even for small proton fractions x, so that S(n) ≃ S2(n). Chiral Lagrangian expansions for +PNM, nuclear matter with admixtures of protons, and SNM, indicate that this approximation +appears valid [29] for all values of x. For matter with densities below ns, such as that in +nuclei, experimental evidence for higher-than-quadratic contributions is lacking, but this +could be partly due to the near-symmetric character of nuclei. It is customary to introduce +the volume symmetry energy SV = S2(ns), symmetry slope L = 3ns(dS2/dn)ns, symmetry +incompressibility Ksym = 9n2 +s(d2S2/dn2)ns, and symmetry skewness Qsym = 27n3 +s(d3S2/dn3)ns +parameters, the coefficients of a Taylor expansion in density around ns: +S2 = SV + L +3 (u − 1) + Ksym +18 (u − 1)2 + Qsym +162 (u − 1)3 + · · · , +(2) +where u = n/ns. If only the quadratic term in Equation (1) is retained, we note that S = S2. As +a result, the energy per baryon EN and the pressure PN of PNM at ns become +EN(ns) = E(ns, 0) = SV − B; +PN(ns) = P(ns, 0) = Lns/3, +(3) +where B ≡ −E1/2(ns) = 16 ± 1 MeV is the bulk binding energy parameter of SNM. +We also introduce the incompressibility and skewness parameters for SNM, K1/2 and +Q1/2, and for PNM, KN and QN, respectively, so that +E1/2 = E(u, 1/2) += +−B + K1/2 +18 (u − 1)2 + Q1/2 +162 (u − 1)3 + · · · , +EN = E(u, 0) += +L +3 (u − 1) + KN +18 (u − 1)2 + QN +162(u − 1)3 + · · · . +(4) +The corresponding parameters for the symmetry energy are Ksym = KN − K1/2 and Qsym = +QN − Q1/2. K1/2 ≃ 230 ± 20 MeV has been deduced from giant monopole resonances [30,31], +but there is little direct experimental evidence for Q1/2, KN or QN. +In this section, we explore correlations involving the symmetry parameters that arise, +experimentally, from fitting nuclear binding energies, and, theoretically, from recent neutron +matter theory predictions. Neither of these methods can alone predict values of SV or L to +high precision. However, since these correlations are motivated by different considerations, +combining them can yield additional restrictions. +2.1. Nuclear Mass Fitting +It is straightforward to understand why a strong correlation between SV and L from fitting +nuclear masses exists by using the simple nuclear liquid drop model, which consists of five +main terms, +ELD(A, I) = [−B + SV I2]A + [ES − SSI2]A2/3 + ECoul. +(5) +Here I = 1 − 2Z/A and the individual terms represent the volume, surface, and Coulomb +energies, respectively. Additionally, one should consider shell and pairing energies. The terms +proportional to I2 represent the symmetry energy of a nucleus: +SLD(A, I) ≃ SV AI2(1 − SsA−1/3/SV). +(6) + +4 of 29 +If the Coulomb energy is ignored, the experimental symmetry energy Sexp(A, I) can be found +by taking half the difference of the measured energies Eexp(A, I) of nuclei having the same +mass but values of Z and N each differing by 2 units. This procedure also effectively eliminates +shell and pairing effects. +The optimum values of the parameters SV and SS can be found by minimizing +χ2 = +N +∑ +i +[Sexp(Ai, Ii) − SLD(Ai, Ii)]2 +N σ2 +(7) +with respect to themselves. N is the number of measured nuclei, and σ ∼ 1 MeV is a fiducial +uncertainty. The result is a confidence ellipse centered at SV and SS with uncertainties, angle +with respect to the SS axis, and correlation coefficient +σV = +� +χ−1 +VV, +σS = +� +χ−1 +SS , +α = 1 +2 tan−1 +2χVS +χSS − χVV +, +r = +χVS +√χVVχSS +, +(8) +respectively, where χ−1 is the matrix inverse of χij = ∂2χ2/∂Si∂Sj. The slope of the confidence +ellipse is dSS/dSV = cot α ≃ σS/σV when α is small. Since SLD is linear in SV and SS, the +symmetric matrix χ2 depends only on the measured Ai and Ii, not on SV or Ss, +[χVV, χSV, χSS] = +2 +N σ2 ∑ +i +I4 +i +� +A2 +i , −A5/3 +i +, A4/3 +i +� +≃ 1 +σ2 [61.6, −10.7, 1.87]. +(9) +Numerical values were obtained by using the set of 2336 nuclei from Ref. [32] with N ≥ 40 or +Z ≥ 40. As a result, one finds σV = 2.3σ, σS = 13.2σ, α ≃ 9.8◦ and r = 0.997, which represents +a high degree of correlation. +To convert this correlation into one involving SV and L, it can be noted that SS originates +from an integration of the density-dependent symmetry energy through the nuclear density +profile. In the plane-parallel approximation, it can be shown [1] that +SS = ESSV +2 +� 1 +0 +√u(SV/S(u) − 1)(E(u, 1/2) + B)−1/2du +� 1 +0 +√u(E(u, 1/2) + B)1/2du +(10) +The simple approximations S(u) ≃ SV + L(u − 1)/3 and E(u, 1/2) ≃ −B + K1/2(u − 1)2 lead +to +SS +SV +≃ 135ES +2K1/2 +� +1 − +�1 +a − 1 +�1/2 +tan−1 +��1 +a − 1 +�−1/2�� +. +(11) +where a = L/(3SV). When a ≃ 2/3 and 135ES/(2K1/2) ≃ 5, one finds that SS/SV ≃ 1.62 and +d(SS/Sv)/da ≃ 3.85. As a result, SS increases rapidly with L, and the steep SS − SV correlation +translates into a steep L − SV correlation, dL/dSv ≃ 6, with a similar correlation coefficient. +The liquid droplet model [33], in which the nuclear symmetry energy enters as +SLD(A, I) = AI2SV(1 + SSA−1/3/SV)−1, +(12) +provides a much improved fit, and also shows a significant correlation between SV and L. + +5 of 29 +Figure 1. SV and L data from individual Skyrme (black filled circles, Ref. [34]), relativistic mean field +(RMF, black open circles, Ref. [36]) forces, both interaction types (Tagami 2022, red triangles, Ref. [37]), +and all tabulated interactions (combined); corresponding 68.3% confidence ellipses are shown. The green +hatched confidence ellipse is taken from the UNEDF collaboration [38] using σ = 1.2 MeV (see text). The +bounds provided by the Unitary Gas Conjecture (UGC, [35]) and the Unitary Gas Pressure Conjecture are +shown as dotted curves. +This correlation naturally appears when comparing large numbers of non-relativistic +Skyrme-like and RMF nuclear interactions which were fitted to nuclear binding energies and, +in some cases, additional properties, such as charge radii. Of the 240 Skyrme-like interactions +studied by Ref. [34], 45 can be rejected [35] since they have some saturation properties (including +K1/2) outside the empirical window or other anomalous behavior. Similarly, of the 256 RMF +interactions studied by Ref. [36], 100 can be rejected [35]. The compilation of Ref. [37] contains +an additional 206 interactions of both types, of which 169 survive the conditions imposed by +Ref. [35], but an additional 58 of these are duplicates from Refs. [34,36]. The properties of +confidence ellipses for these three groups of interactions are shown in Table 1. +The UNEDF collaboration [38] determined an SV − L correlation in a more precise fashion +using a universal energy density functional fit to binding energies and charge radii of selected +closed-shell nuclei. The confidence ellipse size depends on the arbitrary value of a fiducial +uncertainty parameter σ. The value σ ≃ 1.2 MeV yields an approximately equal uncertainty +to that of the Skyrme forces in the compilation of Ref. [34], as seen in Figure 1. This is not +surprising given the fact that the universal energy density functional of Ref. [38] is non- +relativistic. However, the correlation is much tighter than those found from the compilation of +Refs. [34,36,37] possibly because the latter forces were not subjected to the same strict calibration +involving charge radii. Note that the slope and best-fit parameter values SV0 and L0 do not +depend on the parameter σ. Table 1 gives the confidence ellipse specifics. + +6 of 29 +Table 1. Symmetry energy parameter correlations. +Method/SV − L +SV0 +(MeV) +L0 (MeV) +σSV +(MeV) +σL (MeV) +r +UNEDF [38] +30.5 +45.1 +1.9 +24.0 +0.970 +Skyrme [34] +30.9 +41.5 +2.25 +27.2 +0.812 +RMF [36] +33.1 +85.8 +2.12 +17.4 +0.625 +Tagami [37] +32.0 +57.7 +2.37 +25.2 +0.702 +Combined [34,36,37] +32.1 +62.2 +2.45 +30.6 +0.783 +Combined + UGC/UGPC +32.5 +57.7 +2.09 +20.7 +0.920 +χEFT (SNM+PNM) [39] +31.7 +59.8 +1.1 +4.2 +0.715 +χEFT (SNM+PNM) +31.7 +60.4 +2.4 +8.1 +0.913 +χEFT (PNM) +32.0 +51.9 +1.1 +7.9 +0.978 +neutron skin (CREX+PREX) +32.2 +52.9 +1.7 +13.2 +0.820 +neutron skin (other) +31.0 +42.1 +1.2 +8.2 +0.729 +Method/KN − L +KN0 +(MeV) +L0 (MeV) +σKN +(MeV) +σL (MeV) +r +Skyrme [34] +73.3 +41.6 +98.9 +27.2 +0.952 +RMF [36] +234.0 +85.8 +63.6 +17.4 +0.666 +Tagami 2022 [37] +161.9 +57.9 +99.5 +25.6 +0.757 +Combined [34,36,37] +147.7 +60.4 +113.7 +30.6 +0.899 +Combined [34,36,37] +UGC/UGPC +137.3 +57.7 +74.8 +20.7 +0.745 +χEFT (SNM+PNM) +172.1 +60.4 +27.4 +8.1 +0.558 +χEFT (PNM) +152.3 +51.9 +35.1 +7.9 +0.993 +neutron skin (CREX+PREX) +141.6 +52.9 +73.2 +13.2 +0.530 +neutron skin (other) +104.8 +42.1 +75.4 +8.2 +0.590 +Method/QN − L +QN0 +(MeV) +L0 (MeV) +σQN +(MeV) +σL (MeV) +r +Skyrme [34] +75.3 +41.6 +178.5 +27.2 +-0.843 +RMF [36] +-211.9 +85.8 +421.4 +17.4 +-0.017 +Combined [34,36] +-53.4 +61.2 +341.2 +32.1 +-0.498 +Combined [34,36] + UGC/UGPC +7.86 +58.2 +297.1 +21.6 +-0.378 +χEFT (SNM+PNM) +-123.3 +60.4 +381.3 +8.1 +-0.686 +χEFT (PNM) +112.8 +51.9 +90.7 +7.9 +0.398 +It is also possible to consider correlations involving incompressibilities and skewnesses, It +will be seen to be more straightforward to consider KN = K1/2 + Ksym and QN = Q1/2 + Qsym +rather than Ksym and Qsym. Figure 2 displays these correlations for the interactions compiled +by Refs. [34,36,37]. Generally, it is seen that KN and L are more highly correlated than SV and L +for model interactions, especially for Skyrme-like interactions. Although QN and L are highly +correlated for Skyrme-like interactions, they are much less correlated for RMF interactions. +It is clear there are systematic differences between the behaviors of Skyrme and RMF +interactions. In particular, Skyrme forces tend to display higher degrees of parameter cor- +relations than do RMF forces. In addition, mean values of the parameters SV, L and KN are +larger, and QN is smaller, for RMF compared to Skyrme forces. Importantly, these trends +raise predicted values of neutron skin thicknesses of neutron-rich nuclei, and, further, raise +values of PN for n > ns which increases estimated values of neutron star radii as shown in +section 5. For the compilations of Refs. [34,36], there are 2 1/2 times as many surviving Skyrme +interactions as RMF interactions, but for the compilation of Ref. [37], the two types are more +equally represented. These relative populations are reflected in their combined correlation. + +7 of 29 +Figure 2. The same as Figure 1 but for correlations between KN and L (left panel) and Qn and L (right +panel). The Unitary Gas Pressure Conjecture restricts allowable regions to the right of the dotted lines +labelled UGPC. +Figure 3. Correlations among symmetric energy parameters of forces in compilations of Refs. [34,36]. The +left and right panels show the B − ns and L − ns correlations, respectively. Individual interactions are +shown by filled circles. 68.3% and 95% confidence ellipses for Skyrme (RMF) interactions are shown by +black (red) solid and dashed ellipses, respectively; green ellipses show the confidence ellipses for the +combined force models. 68.3% and 95.5% confidence regions determined from χEFT calculations of SNM +plus PNM (see Section 2.2) are shown by the orange solid and dotted curves, respectively. + +8 of 29 +Figure 4. The same as Figure 3 except the left and right panels show the L − K1/2 and L − Q1/2 correlations, +respectively. +Other systematic differences exist for symmetric matter parameters as well. For com- +parison, we display, using the databases of Refs. [34,36], correlations among the symmetric +energy parameters ns, B, K1/2, and Q1/2, or between these symmetric energy parameters and L, +in Figures 3 and 4. The parameters cluster in what defines the empirical saturation window, +but display themselves display relatively weak correlations. The UNEDF Collaboration [38] +also confirmed the lack of significant correlations among B, ns and K1/2 and between those +parameters and L or SV. +2.2. Neutron Matter Theory +A major recent advance in the understanding of nuclear matter has been made possible +through the development of chiral effective field theory (χEFT) [40,41] which provides the only +known framework allowing a systematic expansion of nuclear forces at low energies [42–45] +based on the symmetries of quantum chromodynamics, the fundamental theory of the strong +interaction. In particular, χEFT allows one to derive systematic estimates of uncertainties of +thermodynamic quantities [46–49] for zero-temperature matter for densities up to ∼ 2ns with +two- and three-nucleon interactions at the next-to-next-to-next-to-leading order (N3LO). The +energy and pressure of SNM are presented, for example by Ref. [39], as central values and their +standard deviations as a function of density. Corresponding values of the energy and pressure +of PNM are also given. +Ref. [39] found that the energies and pressures, and the their uncertainties, for PNM and +SNM are each significantly correlated, and also significantly correlated with each other. From +these calculations, Ref. [39] thereby determined the correlation between SV and L tabulated in +Table 1. It is significantly flatter than from mass fitting, but has very consistent mean values. +These results can be generally reproduced directly using the SNM and PNM results +and assuming a high degree of correlation between them. The SNM calculations predict +a distribution of saturation densities ns (defined by the relation P1/2(ns) = 0, as well as +distributions of binding energy (B = −E1/2(ns)), incompressibility (K1/2) and skewness (Q1/2) +parameters. These distributions are displayed in Figures 3 and 4. +Combining these results with PNM calculations and their distributions of neutron matter +energy (EN(ns)) and pressures (PN(ns)) at the saturation density then yields distributions of SV + +9 of 29 +Figure 5. Black correlation ellipses for SV − L (left panel) and KN − L (right panel) use model interaction +data [34,36,37], with (solid) and without (dashed) application of Unitary Gas Constraints [35] boundaries +(dotted). The blue confidence ellipse shows UNEDF [38] results assuming σ = 1.2 MeV. The red (brown) +confidence ellipses are from chiral EFT studies [39] using PNM results with empirical saturation properties +(combined PNM+SNM results). The red-dashed quadrilateral are limits determined from elliptic flows in +heavy-ion collisions [50]. +and L from SV = EN(ns) − B and L = 3PN(ns)/ns, shown in orange in Figure 5 and tabulated +in Table 1. This procedure gives a similar slope and mean parameter values as Ref. [39], but +systematically larger standard deviations. The differences may be due to our underestimate +of correlations in and between SNM and PNM calculations. The analysis can be extended to +higher-order neutron matter parameters. The case of KN is displayed in orange in Figure 5. +In contrast to mass fitting, the uncertainties of B and ns from SNM χEFT calculations are +extremely large and are also strongly correlated as seen in Figure 3. Most notably, the confidence +ellipse does not pass near the empirical saturation window defined by Skyrme or RMF fits to +nuclear properties. Other symmetric energy parameters also have large uncertainties and show +correlations (Figure 4). Furthermore, the values of Q1/2 are inconsistent with those found from +nuclear mass fits. +The failure of χEFT calculations of SNM to saturate inside the empirical saturation window, +together with inconsistent values of Q1/2, indicates that PNM calculations are much more +reliable than SNM calculations at present. This is not surprising, considering that the latter +emerges from a delicate cancellation sensitive to the short- and intermediate-range three-body +interactions at next-to-next-to-leading order, in contrast to PNM where these interactions are +Pauli-blocked [51]. +Therefore, we alternatively infer symmetry energy parameters using only χEFT PNM +results for the energy and pressure, including their standard deviations, but coupled with +ns and B values randomly chosen from within the empirical saturation window shown in +Figure 3. This alternate χEFT SV − L correlation and those involving KN and L are shown in +Figure 5. Interestingly, the correlations so determined have confidence regions with central +values consistent with those from mass fitting but with noticeably smaller uncertainties, greater +degrees of significance, and also only slightly different slopes. Furthermore, ranges of SV, L, KN +and QN values are compatible with those observed from mass fits, neutron skin and dipole +polarizability measurements, as well as astrophysical studies, as shown below. + +10 of 29 +2.3. The Unitary Gas Conjecture +Ref. [35] proposed a constraint on the symmetry parameters arising from the conjecture +that the energy of pure neutron matter was greater, at all densities, than that of a unitary gas. +A unitary gas is an idealized theoretical collection of fermions interacting only via pairwise +s-wave interactions with an infinite scattering length and a vanishing effective range. The +average particle separation in such a gas is the only length scale, so the energy of the unitary +gas, EUG, is proportional to the Fermi energy, +EUG = 3¯h2k2 +F +10mN +ξ0 ≃ 12.7 +� n +ns +�2/3 += EUG,0u2/3, +(13) +where kF = (3π2ns)2/3 is the Fermi wave number at the saturation density, mN is the neutron +mass, the Bertsch parameter, which is experimentally measured [52,53] to be ξ0 ≃ 0.37, and +EUG,0 ≃ 12.6 MeV. In reality, pure neutron matter at low densities has finite scattering length +and range, but both properties lead to larger energies than for a unitary gas. In addition, +three-body forces in neutron matter are known to be repulsive, further increasing its energy. +The Unitary Gas Conjecture (UGC) states that EN ≥ EUG at all densities. If it is minimally +satisfied EN(ut) = EUG(ut) at some arbitrary density ut, in order for it to remain satisfied at +higher and lower densities requires [35] +�dEN +du +� +ut += +�dEUG +du +� +ut +. +(14) +These conditions automatically impose constraints on the parameters SV and L if the symmetry +energy is expanded as in Equation (2). For example, it sets a minimum value SV,min = B + EUG,0 +where L = 2EUG,0. Further using the correlations shown in Figure 2 to eliminate KN and QN, +and using mean values for ξ0, ns and B, the resulting constraint on SV and L is displayed in +Figure 1 and in subsequent figures. This bound is relatively insensitive to assumed values +of KN and QN [35]. It is notable that the UGC is obeyed by nearly all χEFT results when EN +and empirical values for ns and B are used (PNM method), but only by about half of χEFT +results using both EN and E1/2 (SNM+PNM method). Similarly, most Skyrme interactions +obey the UGC while most RMF forces do not. Even though the exact UGC boundary depends +on uncertainties in ξ0, ns, B and the KN − L and QN − L correlations, it serves as a valuable +consistency check. It supports our previous argument that χEFT studies of symmetric matter +are not presently accurate enough to provide significant constraints, and, further, that RMF +forces do not seem to be as well-suited to fitting nuclear properties as are Skyrme forces. +Because the UGC establishes a lower limit to the energy of pure neutron matter, it effec- +tively sets a lower limit to both the radius and tidal deformability of a neutron star as a function +of its mass [54], being more restrictive than causality in this regard. +Although the UGC cannot impose corresponding bounds in the KN − L or QN − L planes, +it is possible to propose a corollary Unitary Gas Pressure Conjecture (UGPC), which states that +the neutron matter pressure is always greater than the unitary gas pressure for densities larger +than ns. Comparisons shown by Ref. [35] show that this is the case for recent neutron matter +calculations and true for PNM chiral EFT studies even considering 90% lower confidence +bounds. For u < 1, however, it is possible for the unitary gas pressure to be larger than the +neutron matter pressure. Using the 90% upper confidence bound suggested by Figure 2 for +QN as a function of L, but ignoring the correlation between KN and L, the UGPC imposes the +bound in the KN − L plane shown in Figure 2. All RMF forces obey the UGPC. However, about +30% of the formerly permitted Skyrme forces, those having L < 2EUG,0 or KN < −2EUG,0, do +not satisfy the UGPC. + +11 of 29 +One can tighten the constraints imposed from mass fitting by selecting only those forces +whose values of SV and L obey the UGC and the UGPC. The parameters of the revised +correlation ellipses for Skyrme and RMF forces are given in Table 1 and also shown in Figure 5. +3. Neutron Skin Thickness Constraints +It has long been known that the neutron skin thicknesses of neutron-rich nuclei, such +as 48Ca and 208Pb, are highly dependent upon the symmetry parameter L and more weakly +dependent upon SV. For example, the liquid droplet model predicts that the difference between +the mean neutron and proton radii is [33] +tnp = 2roI +3 +SS +SV +[1 + SSA−1/3/SV]−1 +(15) +if Coulomb effects are ignored, where ro = (4πns/3)−1/3 and I = (N − Z)/(N + Z). The +SS/SV term indicates that the radius difference primarily depends on L, and therefore the +symmetry energy slope dS/dn and the neutron matter pressure at ns. However, the appearance +of the last term in Equation (15) implies that a stronger correlation of tnp exists with the +symmetry energy slope dS/dn at a smaller density than ns, namely about 2ns/3 [55,56] which +can be viewed as a sort of average nuclear density. This mimics the situation concerning +nuclear binding energies. Ref. [55] showed, in particular, that the neutron skin thickness of +208Pb, that is, the root-mean-square neutron-proton radius difference r208 +np , is linearly correlated +with the neutron matter pressure (which is proportional to n2dS/dn) most strongly at the +density n1 = 0.10 fm−3: +r208 +np ≃ +(dS/dn)0.1 +882 ± 32 MeV fm−2 +(16) +We will define the symmetry energy slope as +˜L(n) ≡ 3ndS +dn +(17) +so that ˜L(ns) = L. Equation (16) is then equivalent to rnp ∝ ˜L1 ≡ ˜L(n1), an estimate later +generalized by several authors as +r208 +np = ˜a + ˜b˜L1, +(18) +with ˜a and ˜b coefficients given in Table 2. +Table 2. Coefficients for the relation r208 +np = ˜a/fm + ˜b˜L1/MeV and inferred values of ˜L1 from the error- +weighted mean experimental value r208 +np = 0.166 ± 0.017 fm. Also given are two estimated values of ˜L1 +from neutron skin measurements of Sn isotopes. †0.01 fm uncertainty introduced for consistency. +Reference +˜a +˜b +˜L1 (MeV) +[55] +0.0 +0.00378 ± 0.00014 +43.9 ± 4.8 +[57] +0.00994 ± 0.01000 +0.0036 +43.4 ± 5.5 +[58] +0.0101 ± 0.01† +0.00377 +41.4 ± 5.2 +[1] +0.0148 ± 0.0100 +0.00414 +36.5 ± 4.8 +[20] +0.0590 ± 0.0028 +0.00313 +34.2 ± 10.5 +[59] +Sn isotopes +42.9 ± 4.1 +[58] +Sn isotopes +43.7 ± 5.3 +Error-weighted mean +41.7 ± 2.0 + +12 of 29 +Figure 6. Correlations between ˜L(u1) (Ltilde) and L for χEFT PNM (blue) and Skyrme (black) and RMF +(red) interactions from Ref. [34,36], respectively. Green ellipses display the combined Skyrme and RMF +correlations. Correlation coefficients (r) are shown. +We note that ˜L evaluated at a subsaturation density can be related to other symmetry +energy parameters through its Taylor expansion: +˜L(u) = u +� +L + Ksym +3 +(u − 1) + Qsym +18 (u − 1)2 + · · · +� +. +(19) +Given the strong correlations between Ksym and L, and moderate correlations between Qsym +and L, displayed for the Skyrme [34] and RMF [36] forces (both shown in Figure 4), as well as +for χEFT for PNM using B and ns from the empirical saturation window, it is not surprising +that a strong correlation exists also between ˜L(u1) and L (Figure 6). When the Ksym − Qsym − L +correlations are combined in Equation (19), they give a 1σ confidence ellipse centered at +L = 50.09 MeV and ˜L = 41.86 MeV, with standard deviations σL = 6.81 MeV and σ˜L = 2.55 +MeV and correlation 0.843. The result ˜L = 41.7 ± 1.9 MeV from the average Pb and Sn neutron +skin thicknesses shown in Table 2) has nearly the same value and uncertainty as those from +mass fitting and neutron matter theory shown in Figure 6. Their mean value of about 40 MeV +is supported by the results of Refs. [58,59] who argued that a linear rnp − ˜L correlation also +exists for neutron-rich Sn isotopes and derived similar values of ˜L near the density 2ns/3 from +experimental data (Table 2). Collectively, these Pb and Sn studies yield an average value +˜L1 ≃ 42 MeV. The implied value L = 49.9 ± 5.0 MeV is therefore also in remarkable agreement. +The pseudo-linear correlation between ˜L and L implies good linear correlations should +exist between rnp with L for both Pb and Sn nuclei. Theoretical modeling, both from mean-field +analyses and the dispersive optical model, supports an extension to 48Ca. Linear relations are +indeed validated by examining recent compilations [18,20,37,60–62] of neutron skin thicknesses +for 208Pb and 48Ca using a multitude of both non-relativistic and relativistic interactions. The +compilation from Ref. [37] is especially notable in containing results from 206 Skyrme-like and +RMF forces, and the other compilations contribute more than 200 additional values. The model +estimates from these compilations are displayed in Figure 7 and slopes, intercepts and standard +deviations of the linear fits from each reference, as well as their overall means, are provided in + +13 of 29 +Table 3. The mean values of the skin thicknesses from all models shown are nearly the same, +r208 +np = 0.19 ± 0.05 fm and r48 +np = 0.18 ± 0.03 fm, but the two correlations have different slopes. +Both are within ±1σ of the respective mean experimental measurements, see Tables 4 and 5, +indicating an overall consistency exists between theory and experiment even though most +of the models displayed were not explicitly fit to neutron skin values but rather to binding +energy data. In other words, there is no reason to expect that either conventional interactions +or modeling lead to large systematic uncertainties with respect to calculations of neutron skin +thicknesses. +Table 3. Slopes, intercepts, and standard deviations of linear fits rnp/fm = a ± ∆a + bL/MeV. +Reference +a +b +208Pb +[37] +0.0963 ± 0.0041 +0.001566 +[18] +0.1028 ± 0.0115 +0.001617 +[60] +0.0964 ± 0.0039 +0.001563 +[20] +0.0865 ± 0.0124 +0.001837 +[61] +0.0967 ± 0.001447 +0.00145 +[62] +0.0986 ± 0.0137 +0.001537 +Mean +0.0996 ± 0.0096 +0.001518 +48Ca +[37] +0.1250 ± 0.0028 +0.000873 +[18] +0.1261 ± 0.0056 +0.000990 +[60] +0.1290 ± 0.0037 +0.000791 +Mean +0.1255 ± 0.0052 +0.000882 +Figure 7. Neutron skin thicknesses of 48Ca (red) and 208Pb (black) from interactions compiled in Ref. [37] +(filled circles) and Refs. [18,60,63,64] (open circles). Means (1 standard deviations) of linear correlations +are shown as solid (dashed) lines. The horizontal shaded bands indicate the 1 standard deviation ranges +of the averaged experimental results. The dotted black (red) lines indicate the 1 standard deviation range +of r208 +np (r48 +np) from PREX I+II [17] (CREX [18]). + +14 of 29 +Nevertheless, it is worth mentioning that two recent more sophisticated theoretical predic- +tions give divergent views. Relatively small values of neutron skins are implied by coupled +cluster ab-initio calculations which predict r48 +np = 0.135 ± 0.015 fm [65] and r208 +np = 0.17 ± 0.03 +fm [66], which are close to the respective experimental means (Table 4). On the other hand, +the nonlocal dispersive optical model predicts that finite-size effects play an important role in +enhancing the neutron skin, giving r208 +np = 0.25 ± 0.05 fm [67] and r48 +np = 0.249 ± 0.023 fm [68], +both of which are considerably larger than the respective experimental means. +The strong linear correlations existing between model calculations of the neutron skins of +these two nuclei with L obviously implies a strong linear correlation exists between the skin +thicknesses themselves. Neutron skin data from Ref. [37] alone follows the linear relation +r48 +np = (0.0716 ± 0.0006) fm + 0.5554r208 +np +(20) +with a very small uncertainty. Including 179 skin calculations using additional Skyrme and +RMF forces by Refs. [18,60,63,64], the mean linear relation becomes +r48 +np = (0.0730 ± 0.0048) fm + 0.56157r208 +np , +(21) +which is virtually identical except for having a larger standard deviation reflecting a greater +variation in underlying forces (and possibly less strict constraints regarding fitting nuclear +masses and charge radii). The ±1σ confidence bounds on the overall linear correlation are +shown as straight dashed lines in Figure 9. We note that these references contain a number +of the same interactions. These duplicate calculations show variations of as much as 0.01 fm, +which should be included as a systematic modeling uncertainty. However, this uncertainty is +small enough that it does not affect the results significantly. We also note that Ref. [69] has +argued that an accurate determination of r208 +np is insufficient to constrain r48 +np because of the +significant difference in the surface-to-volume ratio of these two nuclei, a conclusion, however, +not supported by our results. +3.1. Neutron Skin Measurements and Correlations +The nuclides 48Ca and 208Pb are especially important because they are the only stable +neutron-rich, closed-shell, nuclei. Measurements of their neutron skin thicknesses are summa- +rized in Tables 4 and 5, as well as Figure 8. The error-weighted mean of all tabulated experimen- +tal measurements is r208 +np = 0.166 ± 0.017 fm, which is consistent with the average theoretical +estimate r208 +np = 0.170 ± 0.008 fm. The mean of historical measurements not including PREX +is r208 +np = 0.159 ± 0.017 fm. For 48Ca, the mean of all measurements is r48 +np = 0.137 ± 0.015 fm, +about 2σ smaller than the average theoretical estimate r48 +np = 0.17 ± 0.03 fm. The average of +historical measurements not including CREX is r48 +np = 0.140 ± 0.017 fm. + +15 of 29 +Figure 8. Neutron skin measurements [17,18,70–81] with 68% confidence intervals and citations. Hori- +zontal dashed lines denote ±1 standard deviations from the weighted means of experiments other than +CREX or PREX I+II. +Table 4. 208Pb neutron skin measurements and theoretical predictions with 1σ uncertainties +208Pb Experiment +Reference +r208 +np (fm) +Coherent π0γ production +[77] +0.15+0.03 +−0.04 +Pionic atoms +[73] +0.15 ± 0.08 +Pion scattering +[73] +0.11 ± 0.06 +¯p annihilation +[78,79] +0.18 ± 0.06 +Elastic polarized p scattering +[70] +0.16 ± 0.05 +Elastic polarized p scattering +[80] +0.211+0.054 +−0.063 +Elastic p scattering +[81] +0.197 ± 0.042 +Elastic p scattering +[72] +0.119 ± 0.045 +Parity-violating e− scattering (PREX I+II) +[17] +0.283 ± 0.071 +208Pb experimental weighted mean +0.166 ± 0.017 +Pygmy dipole resonances +[82] +0.180 ± 0.035 +rSn +np +[83] +0.175 ± 0.020 +Anti-analog giant dipole resonance +[84] +0.216 ± 0.048 +Symmetry energy 208Pb +[85] +0.158 ± 0.014 +Dispersive optical model +[86] +0.18+0.25 +−0.12 +Dispersive optical model +[67] +0.25 ± 0.05 +Coupled cluster expansion +[66] +0.17 ± 0.03 +r48 +np +[63,64], this paper +0.128 ± 0.040 +α208 +D +[62], this paper +0.154 ± 0.019 +α208 +D +[20,64], this paper +0.188 ± 0.017 +208Pb theoretical weighted mean +0.170 ± 0.008 + +16 of 29 +Table 5. 48Ca neutron skin measurements and theoretical predictions with 1σ uncertainties. ∗Uncertainty +scaled upwards as per Ref. [87]. +48Ca Experiment +Reference +r48 +np (fm) +Elastic polarized p scattering +[70] +0.229 ± 0.050 +Elastic p scattering +[76] +0.10 ± 0.03 +Elastic p scattering +[72] +0.098 ± 0.043 +Elastic p scattering +[71] +0.168+0.025 +−0.028 +Pionic atoms +[73] +0.13 ± 0.06 +Pion scattering +[74] +0.11 ± 0.04 +α scattering +[75] +0.171 ± 0.050 +Parity-violating e− scattering (CREX) +[18] +0.121 ± 0.035 +48Ca experimental weighted mean +0.137 ± 0.015∗ +Coupled-cluster expansion +[65] +0.135 ± 0.015 +Dispersive optical model +[68] +0.249 ± 0.023 +r208 +np +[63], this paper +0.173 ± 0.018 +48Ca theoretical weighted mean +0.17 ± 0.03∗ +3.2. Parity-Violating Electron Scattering Measurements +A lot of attention has been paid to the recent PREX [17] and CREX [18] measurements of the +neutron skins of 208Pb and 48Ca, respectively, using parity-violating electron scattering, which +is claimed to have less modeling systematic uncertainty than other experimental methods [19]. +Interestingly, the PREX measurement is more than 1 standard deviation higher than the mean +value of previous 208Pb experiments, while the CREX measurement is smaller than the mean +of previous 48 Ca experiments, but by less than 1 standard deviation. Fitting the neutron skin +thickness from parity-violating scattering of either nuclide alone would give vastly different +values for L, about 110 MeV for Pb [20] and 0 MeV for Ca, as can be seen by reference to +Figure 7. Even using the mean values of all the experimental results would produce disparate +values of L, about 40 MeV and 10 MeV, respectively, although they would lie within a standard +deviation of each other. It is important to note that the weighted mean experimental value of +r208 +np decreases by only about 0.007 fm and that of r48 +np increases by only about 0.003 fm when +the PREX and CREX results are excluded. Without compelling reasons to favor measurements +of either nuclide, our approach is to instead attempt to simultaneously satisfy experimental +information for both nuclides. +We follow two strategies for satisfaction of joint Ca-Pb measurements. First, one could +take the approach that the PREX and CREX experiments qualitatively have fewer systematic +uncertainties than other approaches, and only use those measurements. Alternatively, an +agnostic approach would be to instead consider the weighted means of all measurements. + +17 of 29 +Figure 9. Neutron skin thicknesses of 48Ca and 208Pb from interactions compiled in Ref. [37] (filled circles) +and Refs. [18,60,63,64] (triangles). Colors indicate L values where known; black triangles indicate points +where L values are unspecified. Standard deviations of a linear correlation Equation (21) are shown as +dashed lines. The red (blue) confidence ellipses are from PREX I+II [17] and CREX [18] (mean of all +experiments); solid (dashed) ellipses are 68% (90%) confidence. +As can be seen in Figure 9, the PREX I+II value for r208 +np is too large and the CREX value for +r48 +np is too small to permit any of the reference interactions from the compilation of Refs. [18, +37,60,63,64] from satisfying both of them to within 68% confidence. The situation is different +when considering the mean experimental results for 208Pb and 48Ca, with 4% of the reference +interactions simultaneously satisfying them to 68% confidence. +A much larger number of interactions satisfy skin thickness measurements for both nuclei +when considering 90% confidence regions. About 40% of the interactions from Ref. [37] can +simultaneously satisfy the UGC, UGPC, PREX I+II and CREX results, and these have 0 MeV +< L < 72 MeV. Similarly, about 24% of these interactions simultaneously lie within the 90% +confidence region of the averages of all experiments, and also satisfy the UGC and UGPC, and +these have 0 MeV < L < 58 MeV. +The associated permitted region in SV − L space can be ascertained by weighting those +interactions [37] satisfying both unitary gas constraints, and which also have tabulated SV, L, r48 +np +and r208 +np values, by their probabilities given by a two-dimensional Gaussian defined by the skin +measurements and their uncertainties. Results are shown in Figure 10 and tabulated in Table 1 +for both approaches. Interestingly, using CREX+PREX measurements to define the r48 +np − r208 +np +probabilities gives a confidence ellipse in substantial agreement with the PNM χEFT result. +Using the mean of other skin measurements gives somewhat smaller mean values of SV and L. + +18 of 29 +Figure 10. Symmetry parameters SV − L (left panel) and KN − L (right panel) jointly satisfying parity- +violating experiments to within (exceeding) 90% confidence are shown as red and black filled (black open) +circles; filled black circles violate Unitary Gas constraints (dotted boundary). Red (blue) confidence ellipses +are for models satisfying Unitary Gas constraints weighted by their two-dimensional Gaussian probability +defined by the parity-violating (red) and average (blue) experimental r48 +np and r208 +np measurements and +uncertainties. The black confidence ellipse shows PNM χEFT results. +It is important to note that this internal consistency among neutron skin measurements, +mass fitting and neutron matter theory, using either approach, is not particularly sensitive to +whether relativistic or non-relativistic interactions are considered, suggesting it is relatively +free of associated systematic uncertainties. Partly, this is due to the moderate values of L that +are favored, eliminating most RMF interactions in compilations. +We compare to Ref. [88], who combined data from isobaric analog states and the mean +of experimental Pb neutron skin measurements (taken to be to r208 +np = 0.159 ± 0.041 fm) to +infer L ≃ 50 ± 12 to 68% confidence. Also, Ref. [61] used experimental values for Pb to inferr +19 <∼ L/MeV <∼ 77. However, neither of these sources considered the neutron skin of 48Ca. +We note an inference of SV = 30.2+4.1 +−3.0 MeV and L = 15.346.8 +−41.5 MeV using a combined +analysis of PREX and CREX measurements was recently obtained by Ref. [23]. Their method +differs from the present analysis in that they optimized parameters for a Skyrme-like interaction +using weak and charge form factors from PREX and CREX rather than inferred skin thicknesses, +which are subject to additional theoretical uncertainty, as well as binding, breathing mode and +neutron-proton Fermi energies, and charge and diffraction radii. Their estimates are compatible +with the present results but have larger uncertainties despite the fact that they are not subject +to the addicional theoretical uncertainty relating form factors to skin thicknesses. +Another study by Ref. [24] which also considered dipole polarizabilities concluded that no +single interaction could satisfy both PREX and CREX interactions to 68% confidence, agreeing +with this paper and Ref. [23], but did not attempt to infer a ’best-fit’ interaction. +An analogous analysis for KN is shown in Figure 10. The confidence regions for both +approaches are compatible with that of PNM χEFT, although the results using PREX+CREX +measurements have nearly the same centroid. +4. Other Nuclear Methods +4.1. Correlations from Nuclear Dipole Polarizabilities +Nuclear measurements involving the giant dipole resonance enable additional constraints +on the symmetry energy and can shed light on the somewhat disparate results of recent skin +thickness measurements. Measured dipole polarizabilities for the neutron-rich nuclides 48Ca, + +19 of 29 +Table 6. Dipole polarizabilities with 1σ uncertainties. †αD values corrected as per Ref. [90]. +Nuclide +Reference +αD (fm3) +208Pb +[91] +19.6 ± 0.6† +120Sn +[92] +8.59 ± 0.37† +48Ca +[93] +2.07 ± 0.22 +120Sn and 248Pb are given in Table 6. Support for the experimental values comes from theoretical +calculations of αD by Ref. [89], who found the linear relations: +α48 +D +≃ +(0.10 ± 0.01)α208 +D + 0.36 ± 0.07 MeV fm3, +α208 +D +≃ +(2.2 ± 0.1)α120 +D + 0.1 ± 0.5 fm3, +(22) +with correlation coefficients of 0.82 and 0.96, respectively. These relations predict the values +α48 +D = 2.32 ± 0.21 fm3, slightly larger than the experimental value, from the measured value of +α208 +D , and α208 +D +≃ 19.0 ± 1.2 fm3, slightly smaller than the experimental value, from the measured +value of α120 +D , but both within one standard deviation. +Ref. [94] determined that the central energy of the giant dipole resonance of 208Pb and +the symmetry energy has its greatest correlation at the density n1 = 0.1 fm−3, and from the +measured value of α208 +D +thereby deduced the symmetry energy at that density to be S(u1) = +24.1 ± 0.8 MeV, which is in agreement with S(u1) = 25.7 ± 1.4 MeV deduced from the masses of +closed shell nuclei [55]. Similarly, in a study using 62 non-relativistic and relativistic interactions +fitted to ground-state properties of finite nuclei, Ref. [95] deduced that the electric dipole +polarizability of 208Pb has its greatest correlation with the symmetry energy at the density +n2 = 0.05 fm−3, and found the symmetry energy at that density to be S(u2) = 16.54 ± 1.00 +MeV (after correcting the measured dipole polarizability as per Ref. [90]). Using the expansion +Equation (2), employing empirical correlations to eliminate Ksym and Qsym, and including +uncertainties in ns, these results imply the two linear relations +L = 10.9SV − 288 ± 16 MeV, +L = 8.1SV − 207 ± 12 MeV, +(23) +respectively. These are in essential agreement with the correlation derived from nuclear +mass measurements. The dipole polarizability correlations are also consistent with the relevant +confidence regions established from χEFT as well as from neutron skin thickness measurements. +Ref. [90] showed the existence of a theoretical correlation between the neutron skin +thickness and the electric dipole polarizability, justified by the nuclear droplet model. For 48Ca, +120Sn and 208Pb, these are [89] +α48 +D SV += +(355 ± 44)(r48 +np/fm) + 12 ± 19 MeV fm3, +α120 +D SV += +(1234 ± 93) (r120 +np /fm) + 115 ± 36 MeV fm3, +α208 +D SV += +(1922 ± 73) (r208 +np /fm) + 301 ± 32 MeV fm3. +(24) +We found similar correlations for 208Pb using calculations of Ref. [62] and Ref. [96], respectively: +α208 +D SV += +2195 (r208 +np /fm) + 258 ± 16 MeV fm3, +α208 +D SV += +2125 (r208 +np /fm) + 226 ± 12 MeV fm3. +(25) +Combining relations in Equation (24) with experimental values for the dipole polarizabili- +ties (Table 6) gives the relation +r48 +np ≃ (0.056 ± 0.056) fm + (0.572 ± 0.097)r208 +np +(26) + +20 of 29 +which compares favorably with Equation (21), albeit with larger uncertainties, emphasizing +the consistency of polarizability and skin experimental results with theory. The same result is +achieved using Equation (25) instead. Equations (24) and (25) also suggest that measurements +of rnp and αD for 48Ca, 120Sn or 208Pb provide constraints on SV independently of L. The mean +experimental data for 48Ca, 120Sn (r120 +np values are given in Table 7) and 208Pb yield SV = 29.3 ± +10.4 MeV, 32.1 ± 5.2 MeV, and 31.6 ± 2.6 MeV, respectively, using Equation (24). Equation (25) +alternatively yields SV = 31.8 ± 2.3 MeV and 29.5 ± 2.1 MeV for 208Pb. Collectively, one finds +SV = 30.9 ± 1.3 MeV, which, once again, is consistent with mass fitting, χEFT and the mean +neutron skin results. None of these ranges for SV are consistent with the PREX measurement +by itself. +Table 7. 120Sn neutron skin measurements with 1σ uncertainties +120Sn +Reference +r120 +np (fm) +Elastic p scattering +[97] +0.147 ± 0.033 +Spin-dipole resonance (3He-t) +[98] +0.18 ± 0.07 +¯p annihilation +[99] +0.12 ± 0.02 +120Sn experimental weighted mean +0.130 ± 0.017 +4.2. Correlations from Heavy Ion Collisions +Two general problems with extracting symmetry energy parameters from heavy-ion colli- +sions are: (1) matter in these collisions is close to symmetric, with the symmetry energy being +perhaps 10% of the total and therefore difficult to ascertain; and (2) the matter has excitation +energies of 50-several hundred MeV per baryon (corresponding to T ∼ 20 − −50 Mev). This +paper has therefore concentrated on probes connected with cold finite nuclei where densities +are near ns and a Taylor expansion is appropriate. Here, some results from analyses of heavy +ion experiments are summarized. +It has been proposed [100] to use empirical pressures deduced in cold SNM from hadronic +transport model analyses of heavy-ion collisions [101,102]. Data come from studying kaon +production [103,104], which provides constraints in the density range from 1.3ns to 2.2ns, +and nuclear collective flow [105–108], which provides constraints from 2.0ns to 3.7ns. Pres- +sures from kaon production (collective flows) have estimated uncertainties of about ±22 − +−25%(±19% − −32%), so such constraints have appreciable errors even before systematic +uncertainties, such as from extrapolating from moderate excitation energies to zero temper- +ature, are taken into account. In addition, these estimates are based upon Taylor expansions +of the symmetric matter energy like Equation (4), but including a fourth-order (kurtosis Z) +term. This introduces additional uncertainty, not only because of questionable validity of +such an expansion at high density, but also because the expansion is arbitrarily truncated at +fourth order. Although interesting correlations betweeen K1/2 and Q1/2 are deduced from this +analysis, application to PNM and therefore extraction of symmetry energy parameters becomes +model dependent. +The symmetry energy might more directly probed in heavy ion collisions through the +π−/π+ multiplicity ratio in central collisions [109–111] and from isospin diffusion or elliptic +flows of neutrons and protons [112–115]; see Ref. [116] for a summary. Both approaches, +however, have given rather conflicting results concerning the stiffness of the symmetry energy, +with L ranging from 0 MeV to ∼ 120 MeV, indicating a large degree of model dependence in +the analyses [50,117,118]. + +21 of 29 +For example, the analysis of Ref. [50], which assumes that the density-dependent symmetry +energy has the simple form +S(u) = C1u2/3 + (SV − C1)uγ, +(27) +where C1 ≃ 12.5 MeV, predicts a 2σ band in SV − L space which is shown as HIC in Figure 5. +For S in Equation (27), a line in the SV − L plane with a slope ∆L/∆SV implies that S is best +determined at density ub = exp(−3∆SV/∆L). In addition, any point in this diagram implies a +γ value +γ = +L − 2C1 +3(SV − C1). +(28) +The diagonal sides of the quadrilateral in Figure 5 therefore imply that 0.28 ≤ γ ≤ 1.04 and +0.35 ≤ ub ≤ 0.58. Therefore, this experiment best probes subsaturation densities smaller +than do mass fits (ub ∼ 0.74), neutron skin thicknesses (ub ∼ 0.66) or neutron matter theory +(ub ∼ 0.66). However, the symmetry parameters are rather poorly constrained (possibly +because the extrapolation to saturation density is larger in the HIC case), with the quadrilateral +having a much larger extent than the regions determined in Figure 10. In addition, large +portions of the quadrilateral violate the UGC. Furthermore, another analysis of the same +data [117] suggests L = 122 ± 57 MeV, indicating overall difficulties with this method. +5. Astrophysical Considerations +Astrophysical observations of neutron stars can yield estimates of radii, moments of inertia, +and tidal deformabilities. We will consider two of the currently most popular observations: the +LIGO/Virgo detection of the neutron star merger GW170817 [21,119] and NICER observations +of the rapidly rotating pulsars PSR J0030+0451 [25,26] and PSR J0740+6620 [27,28]. It will be +seen that the symmetry parameters ranges suggested by nuclear experiment and theory are +consistent with inferences from astrophysical observations of neutron stars. +5.1. Neutron Star Radii +For subsets of forces from Refs. [18,37,60,63,64], the radii of 1.4M⊙ neutron stars (R1.4), L +and r48 +np and r208 +np are available (most of the radius information was kindly provided by B. Tsang). +Although nuclear interaction models, having been fit to nuclei, describe matter with large +proton fractions and n <∼ ns, one should be wary of making predictions about neutron stars +from them. Nevertheless, as shown in Figure 11, there is a clear correlation between L and +R1.4. The correlation between PNSM(n) and R1.4 turns out to be greatest at densities in the +range 1.5 − 2ns [48], low enough that interaction models are still reliable. Note, however, that +these models should not be used to constrain neutron star maximum masses, which are most +sensitive to PNSM for n >∼ 3ns [48]. +One can predict a validity range for R1.4 based on neutron skin measurements in the +same way the SV − L predictions shown in Figure 9 were made. Weighting the predicted R1.4 +of models satisfying both Unitary Gas constraints by their double Gaussian probabilities in +r48 +np − r208 +np space, one finds R1.4 = 11.6 ± 1.0 km (and L = 49.4 ± 13.1 MeV) to 68% confidence +using parity-violating neutron skin measurements (Figure 11). In comparison, the weighted +average of other experiments yields R1.4 = 11.0 ± 0.9 km (and L = 40.7 ± 7.9 MeV). +Bayesian analyses combining measurements of tidal deformability (see Section 5.2) from +GW170817 and radii from pulse-profile modeling of PSR J0030+0451 and PSR J0740+6620 +suggest R1.4 = 12.3+0.5 +−0.3 km to 68% confidence [120]. The 68% and 90% confidence intervals are +shown by green shading in the left panel of Figure 11. These astrophysical inferences are in +essential agreement with our results using PREX and CREX data, and are about 1σ larger then +results obtained using other experimental neutron skin data. + +22 of 29 +Figure 11. The same as Figure 10 except showing R1.4 versus L (left panel) and Λ1.4 versus L (right +panel) for subsets of forces from Refs. [18,37,60,63,64]. Black solid and dashed curves in the left panel +show the R1.4 − L correlation and standard deviations derived as in the text. The shaded green bands +are 68% and 95% confidence intervals from a joint analysis of GW170817 and PSR J0030+0451 and PSR +J0740+6620 by Ref. [120] (left panel) and from GW170817 Bayesian analyses posteriors [21], corrected for +Λ priors chosen so as to reflect uniform R priors (right panel). +It is possible to understand the correlation observed in Figure 11. Since NSM is close to +PNM around n = ns, there should a high degree of correlation between PNSM(ns) and L, and +therefore between R1.4 and L. Indeed, a correlation between R1.4 and PNSM, the neutron star +matter pressure, around ns was empirically established some time ago by Ref. [7] and refined +by Ref. [121], +R1.4 ≃ (9.51 ± 0.49)(PNSM/MeV fm−3)1/4 km. +(29) +It is necessary to convert Equation (29) into one depending directly upon the symmetry param- +eters by taking into account how NSM differs from PNM. NSM has a finite proton (electron) +fraction determined by energy minimization with respect to x at every density, leading to +beta-equilibrium. The total energy per baryon of NSM in the quadratic approximation is +ENSM = EN − 4xS(1 − x) + 3 +4 ¯hcx(3π2nx)1/3, +(30) +where EN is the energy of PNM, S(n) is the density-dependent symmetry energy and x is +the proton fraction. The last term is the electron contribution. Beta equilibrium requires +∂ENSM/∂x = 0, giving +x = +�4S +¯hc +�3 (1 − 2x)3 +3π2n +. +(31) +At ns, one finds +PNSM(ns) = n2 ∂ENSM +∂n +���� +ns += Lns +3 [1 − x + 2x2]. +(32) +At ns, Only the L term in a density expansion of S contributes. For a given value of L, a normal +distribution of SV values based on the PNM χEFT correlation (Figure 5), i.e., +SV = 0.139L + (24.63 ± 0.25) MeV, +(33) + +23 of 29 +can be used to find a corresponding x distribution from Equation (31). Then, Equation (32) +gives the PNSM(ns) distribution and Equation (29) gives the R1.4 distribution, which is shown +with uncertainties in Figure 11 as black lines. The agreement, including uncertainties, with +model interactions is remarkable, in spite of the fact that Equation (29) was established using a +far smaller number of interactions. +5.2. Tidal Deformabilities and Radii +For GW170817, the most accurately-measured quantity is the chirp mass [119] +M = +(m1m2)3/5 +(m1 + m2)1/5 = 1.186 ± 0.001M⊙ +(34) +where m1 > m2 are the masses of the merging stars. Less precisely measured is the radius- +sensitive binary tidal deformability of the system, +˜Λ = 16 +13 +(1 + 12q)Λ1 + (12 + q)q4Λ2 +(1 + q)5 +, +(35) +where q = m2/m1 is the mass ratio and Λ1 and Λ2 are the individual stellar deformabilities. +Typical M(R) trajectores in the relevant mass range 1.1M⊙ < M < 1.6M⊙ for BNS merger +components (judging from galactic BNS [3,122]) have relatively small variations in R for a given +EOS. Given the minimum (maximum) neutron star mass is about 1.1M⊙ (2.1M⊙), 0.7 <∼ q ≤ 1. +Ref. [54] found, using piecewise polytropes, that in the absence of significant phase transitions, +the average radius ¯R satisfies | ¯R − R| < 0.5 km for all EOSs in this mass range, and averaged +over all EOSs and masses, | ¯R − R| has a standard deviation of about 0.1 km. Ref. [54] also +determined, to high accuracy, that the dimensionless tidal deformability of individual stars in +this mass range obeys the semi-universal (EOS-independent) relation +Λ = aβ−6; +Λ1 ≃ q6Λ2. +(36) +with a = 0.009 ± 0.002 and β = GM/Rc2. It therefore follows that +˜ΛM ≃ 16a +13 +� ¯Rc2 +GM +�6 +q8/5 (12 − 11q + 12q2) +(1 + q)26/5 +, +(37) +where the notation ˜ΛM reflects that ˜Λ is measured at a well-defined M. The q-dependence in +Equation (37) is weak: ˜ΛM(q = 0.7)/ ˜ΛM(q = 1.0) = 1.029 and (∂ ˜ΛM/∂q)q=1.0 = 0. Thus, the +fact that q is poorly measured has little consequence, and one finds +¯R ≃ (11.3 ± 0.3) M +M⊙ +� ˜ΛM +800 +�1/6 +km. +(38) +Due to radius correlations, the uncertainty in ¯R is only half the uncertainty of a itself. Thus, +˜ΛM carries significant radius information. To the same accuracy, R1.4 ≃ ¯R. +More directly, one can predict Λ1.4, the dimensionless tidal deformability of a 1.4M⊙ +neutron star, from neutron skin measurements using the same procedure as used for R1.4. +Values of Λ1.4 for the interactions in the right panel of Figure 11 were provided by B. Tsang. +Weighting each by the double Gaussian defined by neutron skin thickness measurements and +uncertainties, it is found, to 68% confidence, Λ1.4 = 228+148 +−90 (L = 49.3 ± 14.0 MeV) using the +PREX+CREX neutron skin measurements, and Λ1.4 = 177+117 +−70 (L = 39.3 ± 7.7 MeV) using the +average of other skin measurements. + +24 of 29 +These ranges are consistent with inferences [21] from LIGO/Virgo observations [22,119] +of the BNS merger GW170817 (shaded green regions in the right panel of Figure 11). For this +comparison, it is useful to convert the observed quantity ˜ΛM to Λ1.4. Use of Equation (36) +gives +ΛM ≃ +� +21/5M/M +�6 ˜ΛM. +(39) +For GW170817, Λ1.4 ≃ 0.849 ˜Λ1.186. Ref. [21] calculated the tidal deformability posteriors of +the two merging stars from a grvitational wave analysis assuming Λ1/Λ2 = q6 and causality. +They assumed uniform Λ and M priors for the two stars. They found Λ1.4 = 245+312 +−81 to 68% +confidence and Λ1.4 = 245+651 +−114 to 90% confidence. However, the results are sensitive to the +assumed Λ priors. Perhaps it is more realistic to assume uniformity in ln Λ rather than Λ +because Λ ∝ (R/M)6 has a large dynamic range. This is tantamount to a uniform radius +prior. In this case, to 68% confidence, Λ1.4 = 234+119 +−72 , and to 90% confidence, Λ1.4 = 234+216 +−101. +Although the predicted means are nearly the same, assuming uniformity in the ln Λ priors +dramatically reduces the upper 68% and 90% confidence bounds, and makes them strikingly +similar to those inferred from neutron skin measurements. +6. Conclusions +Compilations containing several hundred theoretical nuclear interactions of both the non- +relativistic (Skyrme) or relativistic (RMF) type, which have been fitted to nuclear masses and/or +charge radii, show that significant correlations exist among symmetry and neutron energy +parameters SV, L, KN and QN. The average values and correlation slopes depend on whether +the interactions considered are non-relativistic or relativistic: the relativistic interactions in +these compilations tend to have larger values of L and KN, for example. In both cases, the 68% +confidence ellipses for the SV − L, L − KN and QN − L correlations considerably overlap with +those predicted by chiral effective field calculations of pure neutron matter, but have different +slopes. +Theoretical calculations of neutron skin thicknesses of neutron-rich closed shell nuclei +(48Ca and 208Pb) predict strong correlations with L with average uncertainties less than 0.01 +fm. The individual weighted means of experimental measurements of these nuclei can be +used to predict comparable ranges of L, 0-40 MeV for 48Ca and 30-60 MeV for 208Pb, both +consistent with the range determined by jointly fitting masses and neutron matter calculations. +Without a strong reason to prefer skin measurements of one nucleus over another, simultaneous +reconciliation of the weighted means of skin measurements of both nuclei with those from +theoretical calculations of forces in the compilations constrains the symmetry parameters +SV = 30.8 ± 1.5 MeV and L = 40 ± 8 MeV. +Alternatively, one could choose to only employ parity-violating electron scattering results +(PREX and CREX), which have been claimed to have smaller systematic uncertainties than other +techniques. The two experiments separately predict incompatible ranges of L (L = −5 ± 40 +MeV and L = 121 ± 47 MeV, respectively), but accepting both measurements to be equally +valid suggests SV = 32 ± 2 MeV and L = 50 ± 12 MeV. These alternative approaches in treating +neutron skin measurements predict closely overlapping ranges that are consistent with ranges +predicted from mass fits and neutron matter theory, and therefore indicate that the PREX and +CREX experimental results are consistent with those of other techniques. These estimates are +compatible with those calculated by Ref. [23]. +Further support for the resulting focus to small ranges of symmetry parameters comes +from measurements and theoretical studies of nuclear dipole polarizabilities (αD). Theory +predicts that αDSV is linearly correlated to rnp. Measured values of αD and rnp for 48Ca, +120Sn and 208Pb then imply SV = 30.9 ± 1.3 MeV in good agreement with our result. Further +proof that existing measurements of αD and rnp are compatible comes from the linear relation + +25 of 29 +between r48 +np and r208 +np resulting from the theoretical αDSV − rnp correlation; this linear relation +is in remarkable agreement with that predicted by theoretical neutron skin calculations of these +nuclei using both relativistic and non-relativistic interactions. +The inferred small ranges of symmetry parameters combining mass fitting, neutron matter +theory, and skin thickness and dipole polarizability measurements and theory are robust +and do not depend significantly on the type of nuclear interaction considered, despite the +systematic differences in predictions of individual quantities arising from a single method +alone. Potentially, an improvement of our predictions can be achieved by directly comparing +predictions and measurements of the charge and weak form factors of 48 Ca and 208Pb, as +done in Ref. [23]. This would remove the additional uncertainty involved in converting form +factors to neutron and proton radii. However, given the compatibility of results from our +work with Rev. [23], this additional uncertainty does not appear to be significant. In any case, +measurements of form factors or neutron skin thicknesses will have to be performed with much +greater precision than at present to improve upon the symmetry parameter constraints from +chiral Lagrangian chiEFT calculations. +For the first time, we extended predictions from neutron skin measurements to include +neutron star radii and tidal deformabilities without employing any information from astrophys- +ical observations. Our estimated ranges for R1.4 and Λ1.4 are compatible with recent studies +using LIGO/Virgo data from the BNS merger GW170817 and NICER X-ray observations of +PSR J0030+0451 and PSR J0740+6620. +Funding: This work was initiated through the NSF-funded Physics Frontier Center Network for Neutri- +nos, Nuclear Astrophysics, and Symmetries (N3AS) and was supported by the U.S. DOE grant DE-AC02- +87ER40317. +Data Availability Statement: Not applicable. +Acknowledgments: Thanks are due to J. Piekarewicz, W. Nazarewicz and B. Tsang for providing data +and, together with T. Zhao, C. J. Horowitz and K. Kumar, helpful discussions. +Conflicts of Interest: The author declares no conflicts of interest. The funders had no role in the design +of the study, the collection, analyses, or interpretation of data, the writing of the manuscript, or in the +decision to publish the results. +Abbreviations +The following abbreviations are used in this manuscript: +NS +neutron star +BNS +binary neutron stars +EOS +equation of state +PSR +pulsar +SNM +symmetric nuclear matter +PNM +pure neutron matter +χEFT +chiral effective field theory +RMF +relativistic mean field +UGC +Unitary Gas Conjecture +UGPC +Unitary Gas Pressure Conjecture +NICER +Neutron Star Interior Composition ExploreR +References +1. +Steiner, A.W.; Prakash, M.; Lattimer, J.M.; Ellis, P. Isospin asymmetry in nuclei and neutron stars. Phys. Rep. 2005, 411, 325. +2. +Lattimer, J.M.; Prakash, M. Neutron star observations: Prognosis for equation of state constraints. Phys. Rept. 2007 442, 109. +3. +Lattimer, J.M. Neutron Stars and the Nuclear Matter Equation of State. Annu. Rev. Nucl. Part. Sci. 2021 71, 433. +4. +Swesty, F.D.; Lattimer, J.M.; Myra, E.S. The Role of the Equation of State in the “Prompt” Phase of Type II Supernovae. Astrophys. J. +1994, 425, 195. +5. +Roberts, L.F.; Shen, G.; Cirigliano, V.; Pons, J.A.; Reddy, S.; Woosley, S.E. Protoneutron Star Cooling with Convection: The Effect of the +Symmetry Energy. Phys. Rev. Lett. 2012, 108, 061103. +6. +Morozova, V.; Radice, D.; Burrows, A.S.; Vartanyan, D. The gravitational wave signal from core-collapse supernovae. Astrophys. J. +2018, 861, 10. + +26 of 29 +7. +Lattimer, J.M.; Prakash, M. Neutron Star Structure and the Equation of State. Astrophys. J. 2001, 550, 426. +8. +Bauswein, A.; Janka, H.-T. Measuring Neutron-Star Properties via Gravitational Waves from Neutron-Star Mergers. Phys. Rev. Lett. +2012, 108, 011101. +9. +Lackey, B.D.; Kyutoku, K.; Shibata, M.; Brady, P.R.; Friedman, J.L.Extracting equation of state parameters from black hole-neutron star +mergers. I. Nonspinning black holes. Phys. Rev. D 2012, 85, 044061. +10. +Page, D.; Reddy, S. Thermal and transport properties of the neutron star inner crust. In Neutron Star Crust; Bertulani, C.A., Piekarewicz, +J., Eds.; Nova Science Publisheres, New York, NY, USA, 2021. arXiv:1201.5602. +11. +Hurley, K.; Boggs, S.E.; Smith, D.M.; Duncan, R.C.; Lin, R.; Zoglauer, A.; Krucker, S.; Hurford, G.; Hudson, H.; Wigger, C.; et al. An +exceptionally bright flare from SGR 1806-20 and the origins of short-duration γ-ray bursts. Nature 2005, 434, 1098. +12. +Thompson, C.; Duncan, R.C. The giant flare of 1998 August 27 from SGR 1900]14. II. Radiative mechanism and physical constraints +on the source. Astrophys. J. 2001, 561, 980 +13. +Samuelsson, L.; Andersson, N. Neutron star asteroseismology. Axial crust oscillations in the Cowling approximation. MNRAS 2007, +374, 256. +14. +Lattimer, J.M.; Pethick, C.J.; Prakash, M.; Haensel, P. Direct URCA process in neutron stars. Phys. Rev. Lett. 1991, 66, 2701. +15. +Nikolov, N.; Schunck, N.; Nazarewicz, W.; Bender, M.; Pei, J. Surface symmetry energy of nuclear energy density functionals. Phys. +Rev. C 2011, 83, 034305. +16. +Drischler, C.; Holt, J.W.; Wellenhofer, C. Chiral Effective Field Theory and the High-Density Nuclear Equation of State. Annu. Rev. +Nucl. Part. Sci. 2021, 71, 403. +17. +Adhikari, D.; Albataineh, H.; Androic, D.; Aniol, K.; Armstrong, D.S.; Averett, T.; Gayoso, C.A.; Barcus, S.; Bellini, V.; Beminiwattha, +R.S.; et al. Accurate determination of the neutron skin thickness of 208Pb through parity-violation in electron scattering Phys. Rev. Lett. +2021, 126, 172502. +18. +Adhikari, D.; Albatainen, H.; Androic, D.; Anioj, K.A.; Armstrong, D.S.; Averett, T.; Ayerbe Gayoso, C.; Barcus, S.K.; Bellini, V.; +Beminiwattha, R.S.; et al. Precision determination of the neutral weak form factor of 48Ca. Phys. Rev. Lett. 2022, 129, 042501 +19. +Thiel, M.; Sfienti, C.; Piekarewicz, J.; Horowitz, C.J.; Vanderhaeghen, M. Neutron skins of atomic nuclei: per aspera ad astra. J. Phys. G +Nucl. Part. Phys. 2019, 46, 093003 +20. +Reed, B.T.; Fattoyev, F.J.; Horowitz, C.J.; Piekarewicz, J. Implications of PREX-2 on the equation of state of neutron-rich matter. Phys. +Rev. Lett. 2021, 126, 172503. +21. +S. De, Finstad, D.; J, Lattimer, M.; Brown, D.A.; Berger, E.; Biwer, C.M. Tidal deformabilities and radii of neutron stars from the +observation of GW170817. Phys. Rev. Lett. 2018 121, 091102 +22. +Abbott, B.P.; Abbott, R.; Abbott, T.D.; Acernese, F.; Ackley, K.; Adams, C.; Adams, T.; Addesso, P.; Adhikari, R.X.; Adya, V.B.; et al. +Properties of the binary neutron star merger GW170817. Phys. Rev. X 2019 9, 011001 +23. +Zhang, Z.; Chen, L.-W. Bayesian inference of the symmetry energy and the neutron skin in 48Ca and 208Pb from CREX and PREX-2. +arXiv 2022, arXiv:2207.03328. +24. +Reinhard, P.G.; Roca-Maza, X.; Nazarewicz, W. Combined theoretical analysis of the parity-violating asymmetry for 48Ca and 208Pb. +Phys. Rev. Lett. 2022, 129, 232501. +25. +Miller, M.C.; Lamb, F.K.; Dittmann, A.J.; Bogdanov, S.; Arzoumanian, Z.; Gendreau, K.C.; Guillot, S.; Harding, A.K.; Ho, W.C.G.; +Lattimer, J.M.; et al. PSR J0030+0451 Mass and Radius from NICER Data and Implications for the Properties of Neutron Star Matter. +Astrophys. J. Lett. 2019, 887, L24.;JML 20 co-authors +26. +Riley, T.E.; Watts, A.L.; Bogdanov, S.; Ray, P.S.; Ludlam, R.M.; Guillot, S.; Arzoumanian, Z.; Baker, C.L.; Bilous, A.V.; Chakrabarty, D.; +et al. A NICER view of PSR J0030+0451: Millisecond pulsar parameter estimation. Astrophys. J. Lett. 2019, 887, L21. +27. +Miller, M.C.; Lamb, F.K.; Dittmann, A.J.; Bogdanov, S.; Arzoumanian, Z.; Gendreau, K.C.; Guillot, S.; Ho, W.C.G.; Lattimer, J.M.; +Loewenstein, M.; et al. The radius of PSR J0740+6620 from NICER and XMM-Newton data. Astrophys. J. Lett. 2021, 918, L28. +28. +Riley, T.E.; Watts, A.L., Ray, P.S., Bogdanov, S., Guillot, S., Morsink, S.M., Bilous, A.V., Arzoumanian, Z., Choudhury, D., Deneva, J.S.; +et al. A NICER view of the massive pulsar PSR J0740+6620 informed by radio timing and XMM-Newton spectroscopy. Astrophys. J. +Lett. 2021, 918, L27. +29. +Wellenhofer, C.; Holt, J.W.; Kaiser, N. Divergence of the isospin-asymmetry expansion of the nuclear equation of state in many-body +perturbation theory. Phys. Rev. C 2016, 93, 055802. +30. +Agrawal, B.K.; Shlomo, S.; Au, V.K. Nuclear matter incompressibility coefficient in relativistic and nonrelativistic microscopic models. +Phys. Rev. C 2003, 68, 031304. +31. +Todd-Rutel, B.G.; Piekarewicz, J. Neutron-rich nuclei and neutron stars: A new accurately calibrated interaction for the study of +neutron-rich matter. Phys. Rev. Lett. 2005, 95, 122501. +32. +Audi, G.; Wapstra, A. H.; Thibault, C. The Ame2003 atomic mass evaluation: (II). Tables, graphs and references. Nucl. Phys. A 2003, +729, 337. +33. +Myers, W.D.; Swiatecki, W.J. Average nuclear properties Ann. Phys. 1969, 55, 395. + +27 of 29 +34. +Dutra, M.; Loureno, O.; Martins, J.S.S.; Delfino, A.; Stone, J.R.; Stevenson, P.D. Skyrme interaction and nuclear matter constraints. +Phys. Rev. 2012, C85, 035201. +35. +Tews, I.; Lattimer, J.M.; Ohnishi, A.; Kolomeitsev, E.E. Symmetry parameter constraints from a lower bound on neutron-matter energy. +Astrophys. J. 2017, 848, 105. +36. +Dutra, M.; O. Loureno, Avancini, S.S.; Carlson, B.V.; Delfino, A.; Menezes, D.P.; Providencia, C.; Typel, S.; and Stone, J.R.; Relativistic +mean-field hadronic models under nuclear matter constraints. Phys. Rev. 2014, C90, 055203. +37. +Tagami, S.; Wakasa, T.; Takechi, M.; Matsui, J.; Yahiro, M. Neutron skin in 48Ca determined from p+48Ca and 48Ca+12C scattering. +arXiv 2022, arXiv:2201.08541. +38. +Kortelainen, M.; T. Lesinski, J. Moré, W. Nazarewicz, J. Sarich, N. Schunck, NStoitsov, M.V.; and S. Wild, Nuclear energy density +optimization. Phys. Rev. C 2010, 82, 024313. +39. +Drischler, C.; Furnstahl, R.J.; Melendez, J.A.; Phillips, D.R. How well do we know the neutron-matter equation of state at the densities +inside neutron stars? A Bayesian approach with correlated uncertainties. Phys. Rev. Lett. 2020, 125, 202702. +40. +Weinberg, S. Precise relations between the spectra of vector and axial-vector mesons. Phys. Rev. Lett. 1967, 18, 507. +41. +Weinberg, S. Nonlinear realizations of chiral symmetry. Phys. Rev. 1968, 166, 1568. +42. +Epelbaum, E.; Hammer, H.-W.; Meissner, U.-G. Modern theory of nuclear forces. Rev. Mod. Phys. 2009, 81, 1773. +43. +Machleidt, R.; Entem, D. Chiral effective field theory and nuclear forces. Phys. Rep. 2011, 503, 1. +44. +Hammer, H.-W.; König, S.; van Kolck, U. Nuclear effective field theory: Status and perspectives. Rev. Mod. Phys. 2020, 92, 025004. +45. +Tews, I.; Davoudi, Z.; Ekström; Holt, J.D.; Lynn, J.E. New Ideas in Constraining Nuclear Forces. J. Phys. G. 2020, 47, 103001. +46. +Drischler, C.; Hebeler, K.; Schwenk, A. Chiral interactions up to next-to-next-to-next-to-leading order and nuclear saturation. Phys. +Rev. Lett. 2019, 122, 042501. +47. +Leonhardt, M.; Pospiech, M.; Schallmo, B.; Braun, J.; Drischler, C.; Hebeler, K.; Schwenk, A. Symmetric nuclear matter from the strong +interaction. Phys. Rev. Lett. 2020, 125, 142502 +48. +Drischler, C.; Han, S.; Lattimer, J.M.; Prakash, M.; Reddy, S.; Zhao, T. Limiting masses and radii of neutron stars and their implications. +Phys. Rev. C 2021, 103, 045808. +49. +Drischler, C.; Melendez, J.A.; Furnstahl, R.J.; Phillips, D.R. Quantifying uncertainties and correlations in the nuclear-matter equation +of state. Phys. Rev. C 2020, 102, 054315. +50. +Tsang, M.B.; Zhang, Y.X.; Danielewicz, P.; Famiano, M.; Li, Z.-X.; Lynch, W.G.; Steiner, A.W. Constraints on the density dependence of +the symmetry energy. Phys. Rev. Lett. 2009, 102, 122701. +51. +Hebeler, K.; Lattimer, J.M.; Pethick, C.J.; Schwenk, A. Constraints on Neutron Star Radii Based on Chiral Effective Field Theory +Interactions. Phys. Rev. Lett. 2010, 105, 161102 +52. +Ku, M.J.H.; Sommer, A.T.; Cheui, L.W.; Zwierlein, M.W. Revealing the superfluid lambda transition in the universal thermodynamics +of a unitary Fermi gas. Science 2012, 335, 563. +53. +Zürn, G.; Lompe, T.; Wenz, A.N.; Jochim, S.; Julienne, P.S.; Hutson, J.M. Precise characterization of 6Li Feshbach resonances using +trap-sideband-resolved RF spectroscopy of weakly bound molecules. Phys. Rev. Lett. 2013, 110, 135301. +54. +Zhao, T.; Lattimer, J.M. Tidal deformabilities and neutron star mergers. Phys. Rev. D 2018, 98, 063020. +55. +Brown, B.A. Neutron radii in nuclei and the neutron equation of state. Phys. Rev. Lett. 2000, 85, 5296. +56. +Centelles, M.; Roca-Maza, X.; Vinas, X.; Warda, M.; Nuclear symmetry energy probed by neutron skin thickness of nuclei. Phys. Rev. +Lett. 2009, 102, 122502. +57. +Typel, S.; Brown, B.A. Neutron radii and the neutron equation of state in relativistic models. Phys. Rev. C 2001, 64, 027302. +58. +Xu, J.; Xie, W.-J.; Li, B.-A. Bayesian inference of nuclear symmetry energy from measured and imagined neutron skin thickness in +116,118,120,122,124,130,132Sn, 208Pb, and 48Ca. Phys. Rev. C 2020, 102, 044316. +59. +Zhang, Z.; Chen, L.-W. Constraining the symmetry energy at subsaturation densities using isotope binding energy difference and +neutron skin thickness. Phys. Lett. B 2013, 726, 234. +60. +Brown, B.A. Mirror charge radii and the neutron equation of state. Phys. Rev. Lett. 2017, 119, 122502. +61. +Furnstahl, R.J. Neutron radii in mean-field models. Nucl. Phys. 2002, A706, 85. +62. +Reinhard, P.-G.; Roca-Maza, X.; Nazarewicz, W. Information content of the parity-violating asymmetry in 208Pb. Phys. Rev. Lett. 2021, +127 232501. +63. +Horowitz, C.J.; Kumar, K.S.; Michaels, R. Electroweak measurements of neutron densities in CREX and PREX at JLab, USA. Eur. Phys. +J. A 2014, 50, 48. +64. +Piekarewicz, J.; Agrawal, B.K.; Colò, G.; Nazarewicz, W.; Paar, N.; Reinhard, P.-G.; Roca-Maza, X.; Vretenar, D. Electric dipole +polarizability and the neutron skin. Phys. Rev. C 2012, 85 041302. +65. +Hagen, G.; Ekström, A.; Forssén, C.; Jansen, G.R.; Nazarewicz, W.; Papenbrock, T.; Wendt, K.A.; Bacca, S.; Barnea, N.; Carlsson, B.; et +al. Neutron and weak-charge distributions of the 48Ca nucleus Nat. Phys. 2016, 12, 186. +66. +Hu, B.; Jiang, W.; Miyagi, T.; Sun, Z.; Ekström, A.; Forssén, C.; Hagen, G.; Holt, J.D.; Papenbrock, T.; Stroberg, S.R. et al. Ab initio +predictions link the neutron skin of 208Pb to nuclear forces. Nature Phys. 2021, 18, 1196. + +28 of 29 +67. +Atkinson, M.C.; Mahzoon, M.H.; Keim, M.A.; Bordelon, B.A.; Pruitt, C.D.; Charity, R.J.; Dickhoff, W.H. Dispersive optical model +analysis of 208Pb generating a neutron-skin prediction beyond the mean field. Phys. Rev. C 2020, 101, 044303. +68. +Mahzoon, M.H.; Atkinson, M.C.; Charity, R.J.; Dickhoff, W.H. Precision Determination of the Neutral Weak Form Factor of 48Ca. Phys. +Rev. Lett. 2017, 119, 22503. +69. +Reinhard, P.-G.; Piekarewicz, J.; Nazarewicz, W.; Agrawal, B.K.; Paar, N.; Roca-Maza, X. Information content of the weak-charge form +factor. Phys. Rev. C 2013, 88, 034325. +70. +Ray, L.Neutron isotopic density differences deduced from 0.8 GeV polarized proton elastic scattering. Phys. Rev. C 1979, 19, 1855. +71. +Zenhiro, J.; Sakaguchi, H.; Terashima, S.; Uesaka, T.; Hagen, G.; Itoh, M.; Murakami, T.; Nakatsugawa, Y.; Ohnishi, T.; Sagawa, +H.; et al. Direct determination of the neutron skin thicknesses in 40,48Ca from proton elastic scattering at Ep=295 MeV. arXiv 2018, +arXiv:1810.11796. +72. +Clark, B.C.; Kerr, L.J.; Hama, S. Neutron densities from a global analysis of medium-energy proton-nucleus elastic scattering. Phys. +Rev. C 2003, 67, 054605. +73. +Friedman, E. Neutron skins of 208Pb and 48Ca from pionic probes. Nucl. Phys. A 2012, 896, 46. +74. +Gibbs, W.R.; Dedonduer, J.-P. Neutron radii of the calcium isotopes. Phys. Rev. C 1992, 46, 1825. +75. +Gils, H.J.; Rebel, H.; Friedman, E. Isotopic and isotonic differences between α particle optical potentials and nuclear densities of 1f 7 +2 +nuclei. Phys. Rev. C 1984, 29, 1295. +76. +Shlomo, S.; Schaeffer, R. The difference between neutron and proton radii in the Ca isotopes. Phys. Lett. B 1979, 83, 5. +77. +Tarbert, C.M.; Watts, D.P.; Glazier, D.I.; Aguar, P.; Ahrens, J.; Annand, J.R.M.; Arends, H.J.; Beck, R.; Bekrenev, V.; Boillat, B.; et al. +Neutron Skin of 208Pb from Coherent Pion Photoproduction Phys. Rev. Lett. 2014, 112, 242502. +78. +Brown, B.A.; Shen, G.; Hillhouse, G.C.; Meng, J.; Trzcinska, A. Neutron skin deduced from antiprotonic atom data. Phys. Rev. C 2007, +76, 034305. +79. +Brown, B.A.; Shen, G.; Hillhouse, G.C.; Meng, J.J.; Trzcinska, A. Neutron density distributions from antiprotonic 208Pb and 209 Bi +atoms. Phys. Rev. C 2007, 76, 014311. +80. +Zenhiro, J.; Sakaguchi, H.; Murakami, T.; Yosoi, M.; Yasuda, Y.; Terashima, S.; Iwao, Y.; Takeda, H.; Itoh, M.; Yoshida, H.P.; et al. +Neutron density distributions of 204,206,208Pb deduced via proton elastic scattering at Ep=295 MeV Phys. Rev. C 2010, 82, 044611. +81. +Starodubnsky, V.E.; Hintz, N.M. Extraction of neutron densities from elastic proton scattering by 206,207,208Pb at 650 MeV. Phys. Rev. C +1994, 49, 2118. +82. +Klimkiewicz, A.; Paar, N.; Adrich, P.; Fallot, M.; Boretzky, K.; Aumann, T.; Cortina-Gil, D.; Pramanik, U.D.; Elze, T.W., Emling, H.; et +al. Nuclear symmetry energy and neutron skins derived from pygmy dipole resonances. Phys. Rev. C 2007, 76, 051603. +83. +Chen, L.-W.; Ko, C.; Li, B.-A.; Xu, J. Density slope of the nuclear symmetry energy from the neutron skin thickness of heavy nuclei. +Phys. Rev. C 2010, 82, 024321. +84. +Yasuda, J.; Wakasa, T.; Okamoto, M.; Dozono, M.; Hatanaka, K.; Ichimura, M.; Kuroita, S.; Maeda, Y.; Noro, T.; Sakemi, Y.; et al. +Anti-Analog Giant Dipole Resonance and the Neutron Skin in 208Pb. JPS Conf. Proc. 2014, 1, 013036. +85. +Dong, J.; Zuo, W.; Gu, J. Constraints on neutron skin thickness in 208Pb and density-dependent symmetry energy. Phys. Rev. C 2015, +91, 034315. +86. +Pruitt, C.D.; Charity, R.J.; Sobotka, L.G.; Atkinson, M.C.; Dickhoff, W.H. Systematic Matter and Binding-Energy Distributions from a +Dispersive Optical Model Analysis. Phys. Rev. Lett. 2020, 125, 102501. +87. +Zyla, P.A.; Barnett, R.M.; Beringer, J.; Dahl, O.; Dwyer, D.A.; Groom, D.E.; Lin, C.J.; Lugovsky, K.S.; Pianori, E.; Robinson, D.J.; et al. +Review of Particle Physics. Prog. Theor. Exp. Phys. 2020, 2020, 083C01. +88. +Danielewicz, P.; Lee, J. Symmetry energy II: Isobaric analog states. Nucl. Phys. A 2014, 922, 1–70. +89. +Roca-Maza, X.; Viñas, X.; Centelles, M.; Agrawal, B.K.; Colò, G.; Paar, N.; Piekarewicz, J.; Vretenar, D. Neutron skin thickness from the +measured electric dipole polarizability in 68Ni, 120Sn, and 208 Pb. Phys. Rev. C 2015, 92, 064304. +90. +Roca-Maza, X.; Brenna, M.; Colò, G.; Centelles, M.; Viñas, X.; Agrawal, B.K.; Paa, N.; Vretenar, D.; Piekarewicz, J.R Electric dipole +polarizability in 208Pb: Insights from the droplet model. Phys. Rev. C 2013, 88, 024316 +91. +Tamii, A.; Complete Electric Dipole Response and the Neutron Skin in 208 Pb. Phys. Rev. Lett. 2011, 107, 062502. +92. +Hashimoto, T.; Krumbholz, A.M.; Reinhard, P.G.; Tamii, A.; von Neumann-Cosel, P.; Adachi, T.; Aoi, N.; Bertulani, C.A.; Fujita, H.; +Fujita, Y.; et al. Dipole polarizability of 120 Sn and nuclear energy density functionals. Phys. Rev. C 2015, 92, 031305. +93. +Birkhan, J.; Miorelli, M.; Bacca, S.; Bassauer, S.; Bertulani, C.A.; Hagen, G.; Matsubara, H.; von Neumann-Cosel, P.; Papenbrock, T.; +Pietralla, N.; et al. Electric Dipole Polarizability of 48 Ca and Implications for the Neutron Skin. Phys. Rev. Lett. 2017, 118, 252501. +94. +Trippa, L.; Coló, G.; Vigezzi, E. Giant dipole resonance as a quantitative constraint on the symmetry energy. Phys. Rev. C 2008, 77, +061304. +95. +Zhang, Z.; Chen, L.-W. Electric dipole polarizability in 208Pb as a probe of the symmetry energy and neutron matter around ρ0/3. +Phys. Rev. C 2015, 92, 031301. +96. +Piekarewicz, J. Implications of PREX-2 on the electric dipole polarizability of neutron rich nuclei. Phys. Rev. C 2021, 104, 024329. + +29 of 29 +97. +Terashima, S.; Sakaguchi, H.; Takeda, H.; Ishikawa, T.; Itoh, M.; Kawabata, T.; Murakami, T.; Uchida, M.; Yasuda, Y.; Yosoi, M.; et al. +Proton elastic scattering from tin isotopes at 295 MeV and systematic change of neutron density distributions. Phys. Rev. C 2008, 77, +024317. +98. +Karsznahorkay, A.; Fujiwara, M.; van Aarle, P.; Akimune, H.; Daito, I.; Fujimura, H.; Fujita, Y.; Harakeh, M.N.; Inomata, T.; Jänecke, J. +et al. Excitation of Isovector Spin-Dipole Resonances and Neutron Skin of Nuclei. Phys. Rev. Lett. 1999, 82, 3216. +99. +Trzcinska, A.; Jastrze¸bski, J.; Lubi´nski, P.; Hartmann, F.J.; Schmidt, R.; von Egidy, T.; Kłos, B. Neutron Density Distributions Deduced +from Antiprotonic Atoms. Phys. Rev. Lett. 2001, 87, 082501. +100. Xie, W.-J.; Li, B.-A. Bayesian inference of the incompressibility, skewness and kurtosis of nuclear matter from empirical pressures in +relativistic heavy-ion collisions. J. Phys. G Nucl. Part. Phys. 2021, 48, 025110. +101. Fuchs, C. Kaon production in heavy ion reactions at intermediate energies. Prog. Part. Nucl. Phys. 2006, 56, 1. +102. Danielewicz, P.; Lacey, R.; Lynch, W.G. The Equation of State of Nuclear Matter and Neutron Stars Properties. Science 2002, 298, 1592. +103. Laue, F.; Sturm, C.; Böttcher, I.; De¸bowski, M.; Förster, A.; Grosse, E.; Koczo´n, P.; Kohlmeyer, B.; Mang, M.; Naumann, L.; et al. +Medium Effects in Kaon and Antikaon Production in Nuclear Collisions at Subthreshold Beam Energies. Phys. Rev. Lett. 1999, 82, +1640. +104. Ivanov, E.I.; Stienike, D.L.; Ryabchikov, D.I.; Adams, G.S.; Adams, T.; Bar-Yam, Z.; Bishop, J.M.; Bodyagin, V.A.; Brown, D.S.; Cason, +N.M.; et al. Observation of Exotic Meson Production in the Reaction π−p → η′π−p at 18 GeV/c. Phys. Rev. Lett. 2001, 86, 3977–3980. +105. Partlan, M.D.; Albergo, S.; Bieser, F.; Brady, F.P.; Caccia, Z.; Cebra, D.; Chacon, A.D.; Chance, J.; Choi, Y.; Costa, S; et al. Fragment Flow +in Au +Au Collisions. Phys. Rev. Lett. 1995, 75, 2100. +106. Liu, H.; Ajitanand, N.N.; Alexander, J.; Anderson, M.; Best, D.; Brady, F.P.; Case, T.; Caskey, W.; Cebra, D.; Chance, J.; et al. Sideward +Flow in Au+Au Collisions between 2A and 8A GeV. Phys. Rev. Lett. 2000, 84, 5488 +107. Pinkenburg, C.; Ajitanand, N.N.; Alexander, J.M.; Anderson, M.; Best, D.; Brady, F.P.; Case, T.; Caskey, W.; Cebra, D.; Chance, J.L. et al. +Elliptic Flow: Transition from Out-of-Plane to In-Plane Emission in Au+Au Collisions. Phys. Rev. Lett. 1999, 83, 1295. +108. Braun-Munzinger, P.; Stachel, J. Dynamics of ultra-relativistic nuclear collisions with heavy beams: An experimental overview Nucl. +Phys. A 1998, 638, 3c. +109. Xiao, Z.; Li, B.-A.; Chen, L.-W.; Yong, G.-C.; Zhang, M. Circumstantial Evidence for a Soft Nuclear Symmetry Energy at Suprasaturation +Densities. Phys. Rev. Lett. 2009, 102, 062502. +110. Feng, Z.-Q.; Jin, G.-M. Probing high-density behavior of symmetry energy from pion emission in heavy-ion collisions. Phys. Lett. B +2010, 683, 140. +111. Xie, W.-J.; Su, J.; Zhu, L.; Zhang, F.-S. Symmetry energy and pion production in the Boltzmann-Langevin approach. Phys. Lett. B 2013, +718, 1510. +112. Tsang, M.B.; Liu, T.X.; Shi, L.; Danielewicz, P.; Gelbke, C.K.; Liu, X.D.; Lynch, W.G.; Tan, W.P.; Verde, G.; Wagner, A.; et al. Isospin +Diffusion and the Nuclear Symmetry Energy in Heavy Ion Reactions. Phys. Rev. Lett. 2004, 92, 062701. +113. Liu, T.-X.; Lynch, W.G.; Tsang, M.B.; Liu, X.D.; Shomin, R.; Tan, W.P.; Verde, G.; Wagner, A.; Xi, H.F.; Xu, H.S.; et al. Isospin diffusion +observables in heavy-ion reactions. Phys. Rev. C 2007, 76, 034603. +114. Famiano, M.A.; Liu, T.; Lynch, W.G.; Mocko, M.; Rogers, A.M.; Tsang, M.B.; Wallace, M.S.; Charity, R.J.; Komarov, S.; Sarantites, D.G.; +et al. Neutron and proton transverse emission ratio measurements and the density dependence of the asymmetry term of the nuclear +equation of state. Phys. Rev. Lett. 2006, 97, 052701. +115. Cozma, M.D.; Leifels, Y.; Trautmann, W.; Li, Q.; Russotto, P. Toward a model-independent constraint of the high-density dependence +of the symmetry energy. Phys. Rev. C 2013, 88, 044912. +116. Yong, G.-C.; Guo, Y.-F. Probing High-density Symmetry Energy Using Heavy-ion Collisions at Intermediate Energies. Nucl. Phys. Rev. +2020, 37, 136. +117. Cozma, M.D.; Tsang, M.B. In-medium ∆(1232) potential, pion production in heavy-ion collisions and the symmetry energy. Eur. Phys. +J. A 2021, 57, 309. +118. Jhang, G.; Estee, J.; Barney, J.; Cerizza, G.; Kaneko, M.; Lee, J.W.; Lynch, W.G.; Isobe, T.; Kurata-Nishimura, M.; Murakami, T.; et al. +Symmetry energy investigation with pion production from Sn+Sn systems. Phys. Lett. B 2021, 813, 136016. +119. Abbott, B.; Abbott, A.; Abbott, T.D.; Acernese, F.; Ackley, K.; Adams, C.; Adams, T.; Addesso, P.; Adhikari, R.X.; Adya, V.B.; et al. +GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral. Phys. Rev. Lett. 2017, 119, 161101. +120. Raaijmakers, G.; Greif, S.K.; Hebeler, K.; Hinderer, T.; Nissanke, S.; Schwenk, A.; Riley, T.E.; Watts, A.L.; Lattimer, J.M.; Ho, W.C.G. +Constraints on the Dense Matter Equation of State and Neutron Star Properties from NICER’s Mass–Radius Estimate of PSR +J0740+6620 and Multimessenger Observations. Ap. J. Lett. 2021, 918, L29. +121. Lattimer, J.M.; Lim, Y. Constraining the Symmetry Parameters of the Nuclear Interaction. Astrophys. J. 2013, 771, 51. +122. Lattimer, J.M. The Nuclear Equation of State and Neutron Star Masses. Annu. Rev. Nucl. Part. Sci. 2012, 62, 485. + diff --git a/gtE2T4oBgHgl3EQfHQZr/content/tmp_files/load_file.txt b/gtE2T4oBgHgl3EQfHQZr/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..ec675031ff7592839ec9324426bc631e475d9021 --- /dev/null +++ b/gtE2T4oBgHgl3EQfHQZr/content/tmp_files/load_file.txt @@ -0,0 +1,3137 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf,len=3136 +page_content='Citation: Lattimer, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Constraints on Nuclear Symmetry Energy Parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Preprints 2023, 1, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='org/ Academic Editor: Armen Sedrakian Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Copyright: © 2022 by the author.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Licensee MDPI, Basel, Switzerland.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='org/licenses/by/ 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='0/).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Article Constraints on Nuclear Symmetry Energy Parameters James M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lattimer Department of Physics & Astronomy, Stony Brook University, Stony Brook, NY 11794-3800, USA;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' james.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='lattimer@stonybrook.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='edu Abstract: A review is made of constraints on the nuclear symmetry energy parameters arising from nuclear binding energy measurements, theoretical chiral effective field predictions of neutron matter properties, the unitary gas conjecture, and measurements of neutron skin thicknesses and dipole polarizabilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' While most studies have been confined to the parameters SV and L, the important roles played by, and constraints on Ksym, or, equivalently, the neutron matter incompressibility KN, are discussed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Strong correlations among SV, L, and KN are found from both nuclear binding energies and neutron matter theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' However, these correlations somewhat differ in the two cases, and those from neutron matter theory have smaller uncertainties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' To 68% confidence, it is found from neutron matter theory that SV = 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='0 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='1 MeV, L = 51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='9 ± 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='9 MeV and KN = 152.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='2 ± 38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='1 MeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Theoretical predictions for neutron skin thickness and dipole polarizability measurements of the neutron-rich nuclei 48Ca, 120Sn, and 208Pb are compared to recent experimental measurements, most notably the CREX and PREX neutron skin experiments from Jefferson Laboratory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' By themselves, PREX I+II measurements of 208Pb and CREX measurement of 48Ca suggest L = 121 ± 47 MeV and L = −5 ± 40 MeV, respectively, to 68% confidence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' However, we show that nuclear interactions optimally satisfying both measurements imply L = 53 ± 13 MeV, nearly the range suggested by either nuclear mass measurements or neutron matter theory, and is also consistent with nuclear dipole polarizability measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' This small parameter range implies R1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='4 = 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='6 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='0 km and Λ1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='4 = 228+148 −90 , which are consistent with NICER X-ray and LIGO/Virgo gravitational wave observations of neutron stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Keywords: nuclear symmetry energy;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' neutron stars;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' neutron skins;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' neutron star radii 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Introduction The nuclear symmetry energy, and its density dependence, as characterized by the tra- ditional symmetry energy parameters SV and L, has been the focus of much recent activity because it is the most direct link between nuclear physics and nuclear astrophysics [1–3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Both the expected neutrino and gravitational wave signals from gravitational collapse supernovae within our Galaxy are sensitive to the symmetry energy [4–6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The symmetry energy near the baryon density at saturation, ns = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='155 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='005 fm−3, determines the radius [7] of a neutron star (NS), which strongly influence the expected gravitational signals from their mergers [8,9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The symmetry energy also affects the NS crust’s thickness and thermal relaxation time, poten- tially observable in cooling and accreting [10] NSs and in giant magnetar flares [11–13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The composition of matter at densities above ns, and the existence of neutrino processes which can rapidly cool NSs, depend on the density dependence of the symmetry energy [14], as do predicted properties of neutron-rich nuclei and reaction rates involved in the astrophysical r-process [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Experimental attempts to constrain the nuclear symmetry energy parameters include measurements of nuclear masses, neutron skin thicknesses, nuclear dipole polarizabilities, giant and pygmy dipole resonance energies, flows in heavy-ion collisions, and isobaric analog states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' These constraints are influenced by varying degrees of model dependence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' In addition, recent advances in neutron matter theory, especially that of systematic expansions involving chiral effective field theory (χEFT) [16], also constrain the symmetry energy parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='03666v1 [nucl-th] 9 Jan 2023 BY2 of 29 Of considerable interest are the recent parity-violating electron scattering neutron skin experiments of 208Pb (PREX-I and PREX-II) [17] and 48Ca [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' These measure the mean square difference of the neutron and proton radii using a technique which is argued to be the most direct and least model-dependent experiment to date [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' PREX I+II combined yields r208 np = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='283 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='071 fm [17], which implies [20] 68% confidence ranges of SV = 38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='29 ± 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='66 MeV and L = 109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='56 ± 36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='41 MeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Both values, and the measured value of r208 np itself, are considerably larger than from expectations from neutron matter and nuclear binding energies, and also from previous measurements, although overlapping with them at about the 90% confidence level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' This indicates a tension with the current understanding of the equation of state (EOS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' For example, these results imply a tidal deformability that lies above the 90% confidence upper limit established for a 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='4M⊙ NS by the LIGO/Virgo observation of the binary NS (BNS) merger GW170817 [21,22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' In contrast, the measurement of the neutron skin of 48Ca using the same technique [18] are somewhat smaller than the average of earlier experimental measurements and expectations from nuclear binding energies and neutron matter theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [23] performed a Bayesian analysis of the PREX and CREX results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' They found that the two experimental results are incompatible with each other at 68% confidence level, but compatible at 90% confidence level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Combining the data, they inferred SV = 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='2+4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='1 −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='0 MeV and L = 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='3+46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='8 −41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='5 MeV at 90% confidence level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' They find the combined results predict r48 np close to the CREX result, but predict r208 np considerably smaller than the PREX result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [24] also performed a combined analysis, and conclude that a simultaneous accurate description of the skins of 48Ca and 208Pb cannot be achieved with their models that accommodate mass, charge radii and experimental dipole polarizabilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' In this paper we take a different perspective by discovering the properties of nuclear interactions fit to binding energy and charge radii of large numbers of nuclei that best satisfy both PREX and CREX measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' We agree with the assessments of both Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [23,24] that no conventional nuclear interaction can fit both measurements to 68% confidence level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' However, our optimum fit results in ranges of SV and L that not only have central values larger than those estimated by Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [23] but also smaller uncertainties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Our results also agree with results from neutron matter theory while those from Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [23] do not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' We find similar results when historical measurements of the neutron skins of both nuclei are utilized, instead, suggesting that systematic uncertainties in the measurements are not dominant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' We begin by summarizing nuclear binding energy and theoretical neutron matter con- straints on the nuclear symmetry energy parameters SV, L and KN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' We show that estimates of symmetry energy parameters from chiral Lagrangian expansions of nuclear matter are more reliably estimated from neutron matter calculations than from both neutron and symmetric matter calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' We explore systematic uncertainties in parameter estimation stemming from the choice of nuclear interaction model, and note apparent inconsistencies associated with relatively stiff relativistic mean field (RMF) interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' We show that nuclear models fit to nu- clear binding energies that optimally satisfy both CREX and PREX neutron skin measurements confine symmetry parameter values to narrow ranges that are consistent with expectations from neutron matter theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' We also show that they are also consistent with theoretical esti- mates based on dipole polarizability experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' We also compare our estimates of symmetry parameters from those estimated from astrophysical observations of neutron stars, especially from gravitational wave observations of GW170817 and Neutron Star Interior Composition ExploreR (NICER) X-ray observations of PSR J0030+0451 [25,26] and PSR J0740+6620 [27,28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The Nuclear Symmetry Energy The nuclear symmetry energy S(n) is defined here to be the difference between the energies of pure neutron matter (PNM), EN, and isospin symmetric nuclear matter (SNM), 3 of 29 E1/2, at the baryon density n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Related quantities are the density-dependent coefficients, Sn(n), of an expansion of the bulk energy per baryon, E(n, x), in powers of the neutron excess 1 − 2x: E(n, x) = E1/2(n) + S2(n)(1 − 2x)2 + S3(n)(1 − 2x)3 + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' (1) A common approximation is to retain only the quadratic term in Equation (1) at every density, even for small proton fractions x, so that S(n) ≃ S2(n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Chiral Lagrangian expansions for PNM, nuclear matter with admixtures of protons, and SNM, indicate that this approximation appears valid [29] for all values of x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' For matter with densities below ns, such as that in nuclei, experimental evidence for higher-than-quadratic contributions is lacking, but this could be partly due to the near-symmetric character of nuclei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' It is customary to introduce the volume symmetry energy SV = S2(ns), symmetry slope L = 3ns(dS2/dn)ns, symmetry incompressibility Ksym = 9n2 s(d2S2/dn2)ns, and symmetry skewness Qsym = 27n3 s(d3S2/dn3)ns parameters, the coefficients of a Taylor expansion in density around ns: S2 = SV + L 3 (u − 1) + Ksym 18 (u − 1)2 + Qsym 162 (u − 1)3 + · · · , (2) where u = n/ns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' If only the quadratic term in Equation (1) is retained, we note that S = S2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' As a result, the energy per baryon EN and the pressure PN of PNM at ns become EN(ns) = E(ns, 0) = SV − B;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' PN(ns) = P(ns, 0) = Lns/3, (3) where B ≡ −E1/2(ns) = 16 ± 1 MeV is the bulk binding energy parameter of SNM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' We also introduce the incompressibility and skewness parameters for SNM, K1/2 and Q1/2, and for PNM, KN and QN, respectively, so that E1/2 = E(u, 1/2) = −B + K1/2 18 (u − 1)2 + Q1/2 162 (u − 1)3 + · · · , EN = E(u, 0) = L 3 (u − 1) + KN 18 (u − 1)2 + QN 162(u − 1)3 + · · · .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' (4) The corresponding parameters for the symmetry energy are Ksym = KN − K1/2 and Qsym = QN − Q1/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' K1/2 ≃ 230 ± 20 MeV has been deduced from giant monopole resonances [30,31], but there is little direct experimental evidence for Q1/2, KN or QN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' In this section, we explore correlations involving the symmetry parameters that arise, experimentally, from fitting nuclear binding energies, and, theoretically, from recent neutron matter theory predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Neither of these methods can alone predict values of SV or L to high precision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' However, since these correlations are motivated by different considerations, combining them can yield additional restrictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Nuclear Mass Fitting It is straightforward to understand why a strong correlation between SV and L from fitting nuclear masses exists by using the simple nuclear liquid drop model, which consists of five main terms, ELD(A, I) = [−B + SV I2]A + [ES − SSI2]A2/3 + ECoul.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' (5) Here I = 1 − 2Z/A and the individual terms represent the volume, surface, and Coulomb energies, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Additionally, one should consider shell and pairing energies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The terms proportional to I2 represent the symmetry energy of a nucleus: SLD(A, I) ≃ SV AI2(1 − SsA−1/3/SV).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' (6) 4 of 29 If the Coulomb energy is ignored, the experimental symmetry energy Sexp(A, I) can be found by taking half the difference of the measured energies Eexp(A, I) of nuclei having the same mass but values of Z and N each differing by 2 units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' This procedure also effectively eliminates shell and pairing effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The optimum values of the parameters SV and SS can be found by minimizing χ2 = N ∑ i [Sexp(Ai, Ii) − SLD(Ai, Ii)]2 N σ2 (7) with respect to themselves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' N is the number of measured nuclei, and σ ∼ 1 MeV is a fiducial uncertainty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The result is a confidence ellipse centered at SV and SS with uncertainties, angle with respect to the SS axis, and correlation coefficient σV = � χ−1 VV, σS = � χ−1 SS , α = 1 2 tan−1 2χVS χSS − χVV , r = χVS √χVVχSS , (8) respectively, where χ−1 is the matrix inverse of χij = ∂2χ2/∂Si∂Sj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The slope of the confidence ellipse is dSS/dSV = cot α ≃ σS/σV when α is small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Since SLD is linear in SV and SS, the symmetric matrix χ2 depends only on the measured Ai and Ii, not on SV or Ss, [χVV, χSV, χSS] = 2 N σ2 ∑ i I4 i � A2 i , −A5/3 i , A4/3 i � ≃ 1 σ2 [61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='6, −10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='7, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='87].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' (9) Numerical values were obtained by using the set of 2336 nuclei from Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [32] with N ≥ 40 or Z ≥ 40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' As a result, one finds σV = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='3σ, σS = 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='2σ, α ≃ 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='8◦ and r = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='997, which represents a high degree of correlation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' To convert this correlation into one involving SV and L, it can be noted that SS originates from an integration of the density-dependent symmetry energy through the nuclear density profile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' In the plane-parallel approximation, it can be shown [1] that SS = ESSV 2 � 1 0 √u(SV/S(u) − 1)(E(u, 1/2) + B)−1/2du � 1 0 √u(E(u, 1/2) + B)1/2du (10) The simple approximations S(u) ≃ SV + L(u − 1)/3 and E(u, 1/2) ≃ −B + K1/2(u − 1)2 lead to SS SV ≃ 135ES 2K1/2 � 1 − �1 a − 1 �1/2 tan−1 ��1 a − 1 �−1/2�� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' (11) where a = L/(3SV).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' When a ≃ 2/3 and 135ES/(2K1/2) ≃ 5, one finds that SS/SV ≃ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='62 and d(SS/Sv)/da ≃ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' As a result, SS increases rapidly with L, and the steep SS − SV correlation translates into a steep L − SV correlation, dL/dSv ≃ 6, with a similar correlation coefficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The liquid droplet model [33], in which the nuclear symmetry energy enters as SLD(A, I) = AI2SV(1 + SSA−1/3/SV)−1, (12) provides a much improved fit, and also shows a significant correlation between SV and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 5 of 29 Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' SV and L data from individual Skyrme (black filled circles, Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [34]), relativistic mean field (RMF, black open circles, Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [36]) forces, both interaction types (Tagami 2022, red triangles, Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [37]), and all tabulated interactions (combined);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' corresponding 68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='3% confidence ellipses are shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The green hatched confidence ellipse is taken from the UNEDF collaboration [38] using σ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='2 MeV (see text).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The bounds provided by the Unitary Gas Conjecture (UGC, [35]) and the Unitary Gas Pressure Conjecture are shown as dotted curves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' This correlation naturally appears when comparing large numbers of non-relativistic Skyrme-like and RMF nuclear interactions which were fitted to nuclear binding energies and, in some cases, additional properties, such as charge radii.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Of the 240 Skyrme-like interactions studied by Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [34], 45 can be rejected [35] since they have some saturation properties (including K1/2) outside the empirical window or other anomalous behavior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Similarly, of the 256 RMF interactions studied by Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [36], 100 can be rejected [35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The compilation of Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [37] contains an additional 206 interactions of both types, of which 169 survive the conditions imposed by Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [35], but an additional 58 of these are duplicates from Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [34,36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The properties of confidence ellipses for these three groups of interactions are shown in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The UNEDF collaboration [38] determined an SV − L correlation in a more precise fashion using a universal energy density functional fit to binding energies and charge radii of selected closed-shell nuclei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The confidence ellipse size depends on the arbitrary value of a fiducial uncertainty parameter σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The value σ ≃ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='2 MeV yields an approximately equal uncertainty to that of the Skyrme forces in the compilation of Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [34], as seen in Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' This is not surprising given the fact that the universal energy density functional of Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [38] is non- relativistic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' However, the correlation is much tighter than those found from the compilation of Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [34,36,37] possibly because the latter forces were not subjected to the same strict calibration involving charge radii.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Note that the slope and best-fit parameter values SV0 and L0 do not depend on the parameter σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Table 1 gives the confidence ellipse specifics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 6 of 29 Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Symmetry energy parameter correlations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Method/SV − L SV0 (MeV) L0 (MeV) σSV (MeV) σL (MeV) r UNEDF [38] 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='5 45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='9 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='970 Skyrme [34] 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='9 41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='5 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='25 27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='812 RMF [36] 33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='1 85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='8 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='12 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='625 Tagami [37] 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='0 57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='7 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='37 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='702 Combined [34,36,37] 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='1 62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='45 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='783 Combined + UGC/UGPC 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='5 57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='7 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='09 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='920 χEFT (SNM+PNM) [39] 31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='7 59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='1 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='715 χEFT (SNM+PNM) 31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='7 60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='4 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='4 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='913 χEFT (PNM) 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='0 51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='9 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='1 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='9 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='978 neutron skin (CREX+PREX) 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='2 52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='9 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='7 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='820 neutron skin (other) 31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='0 42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='2 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='729 Method/KN − L KN0 (MeV) L0 (MeV) σKN (MeV) σL (MeV) r Skyrme [34] 73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='3 41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='6 98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='9 27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='952 RMF [36] 234.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='0 85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='8 63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='6 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='666 Tagami 2022 [37] 161.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='9 57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='9 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='5 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='757 Combined [34,36,37] 147.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='7 60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='4 113.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='7 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='899 Combined [34,36,37] +UGC/UGPC 137.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='3 57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='7 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='8 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='745 χEFT (SNM+PNM) 172.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='1 60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='4 27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='4 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='558 χEFT (PNM) 152.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='3 51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='9 35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='1 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='9 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='993 neutron skin (CREX+PREX) 141.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='6 52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='9 73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='2 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='530 neutron skin (other) 104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='8 42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='1 75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='4 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='590 Method/QN − L QN0 (MeV) L0 (MeV) σQN (MeV) σL (MeV) r Skyrme [34] 75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='3 41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='6 178.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='5 27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='843 RMF [36] 211.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='9 85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='8 421.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='4 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='017 Combined [34,36] 53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='4 61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='2 341.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='2 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='498 Combined [34,36] + UGC/UGPC 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='86 58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='2 297.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='1 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='378 χEFT (SNM+PNM) 123.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='3 60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='4 381.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='3 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='686 χEFT (PNM) 112.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='8 51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='9 90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='7 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='9 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='398 It is also possible to consider correlations involving incompressibilities and skewnesses, It will be seen to be more straightforward to consider KN = K1/2 + Ksym and QN = Q1/2 + Qsym rather than Ksym and Qsym.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Figure 2 displays these correlations for the interactions compiled by Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [34,36,37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Generally, it is seen that KN and L are more highly correlated than SV and L for model interactions, especially for Skyrme-like interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Although QN and L are highly correlated for Skyrme-like interactions, they are much less correlated for RMF interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' It is clear there are systematic differences between the behaviors of Skyrme and RMF interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' In particular, Skyrme forces tend to display higher degrees of parameter cor- relations than do RMF forces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' In addition, mean values of the parameters SV, L and KN are larger, and QN is smaller, for RMF compared to Skyrme forces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Importantly, these trends raise predicted values of neutron skin thicknesses of neutron-rich nuclei, and, further, raise values of PN for n > ns which increases estimated values of neutron star radii as shown in section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' For the compilations of Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [34,36], there are 2 1/2 times as many surviving Skyrme interactions as RMF interactions, but for the compilation of Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [37], the two types are more equally represented.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' These relative populations are reflected in their combined correlation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 7 of 29 Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The same as Figure 1 but for correlations between KN and L (left panel) and Qn and L (right panel).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The Unitary Gas Pressure Conjecture restricts allowable regions to the right of the dotted lines labelled UGPC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Correlations among symmetric energy parameters of forces in compilations of Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [34,36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The left and right panels show the B − ns and L − ns correlations, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Individual interactions are shown by filled circles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='3% and 95% confidence ellipses for Skyrme (RMF) interactions are shown by black (red) solid and dashed ellipses, respectively;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' green ellipses show the confidence ellipses for the combined force models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='3% and 95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='5% confidence regions determined from χEFT calculations of SNM plus PNM (see Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='2) are shown by the orange solid and dotted curves, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 8 of 29 Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The same as Figure 3 except the left and right panels show the L − K1/2 and L − Q1/2 correlations, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Other systematic differences exist for symmetric matter parameters as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' For com- parison, we display, using the databases of Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [34,36], correlations among the symmetric energy parameters ns, B, K1/2, and Q1/2, or between these symmetric energy parameters and L, in Figures 3 and 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The parameters cluster in what defines the empirical saturation window, but display themselves display relatively weak correlations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The UNEDF Collaboration [38] also confirmed the lack of significant correlations among B, ns and K1/2 and between those parameters and L or SV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Neutron Matter Theory A major recent advance in the understanding of nuclear matter has been made possible through the development of chiral effective field theory (χEFT) [40,41] which provides the only known framework allowing a systematic expansion of nuclear forces at low energies [42–45] based on the symmetries of quantum chromodynamics, the fundamental theory of the strong interaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' In particular, χEFT allows one to derive systematic estimates of uncertainties of thermodynamic quantities [46–49] for zero-temperature matter for densities up to ∼ 2ns with two- and three-nucleon interactions at the next-to-next-to-next-to-leading order (N3LO).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The energy and pressure of SNM are presented, for example by Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [39], as central values and their standard deviations as a function of density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Corresponding values of the energy and pressure of PNM are also given.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [39] found that the energies and pressures, and the their uncertainties, for PNM and SNM are each significantly correlated, and also significantly correlated with each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' From these calculations, Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [39] thereby determined the correlation between SV and L tabulated in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' It is significantly flatter than from mass fitting, but has very consistent mean values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' These results can be generally reproduced directly using the SNM and PNM results and assuming a high degree of correlation between them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The SNM calculations predict a distribution of saturation densities ns (defined by the relation P1/2(ns) = 0, as well as distributions of binding energy (B = −E1/2(ns)), incompressibility (K1/2) and skewness (Q1/2) parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' These distributions are displayed in Figures 3 and 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Combining these results with PNM calculations and their distributions of neutron matter energy (EN(ns)) and pressures (PN(ns)) at the saturation density then yields distributions of SV 9 of 29 Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Black correlation ellipses for SV − L (left panel) and KN − L (right panel) use model interaction data [34,36,37], with (solid) and without (dashed) application of Unitary Gas Constraints [35] boundaries (dotted).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The blue confidence ellipse shows UNEDF [38] results assuming σ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='2 MeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The red (brown) confidence ellipses are from chiral EFT studies [39] using PNM results with empirical saturation properties (combined PNM+SNM results).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The red-dashed quadrilateral are limits determined from elliptic flows in heavy-ion collisions [50].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' and L from SV = EN(ns) − B and L = 3PN(ns)/ns, shown in orange in Figure 5 and tabulated in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' This procedure gives a similar slope and mean parameter values as Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [39], but systematically larger standard deviations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The differences may be due to our underestimate of correlations in and between SNM and PNM calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The analysis can be extended to higher-order neutron matter parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The case of KN is displayed in orange in Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' In contrast to mass fitting, the uncertainties of B and ns from SNM χEFT calculations are extremely large and are also strongly correlated as seen in Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Most notably, the confidence ellipse does not pass near the empirical saturation window defined by Skyrme or RMF fits to nuclear properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Other symmetric energy parameters also have large uncertainties and show correlations (Figure 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Furthermore, the values of Q1/2 are inconsistent with those found from nuclear mass fits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The failure of χEFT calculations of SNM to saturate inside the empirical saturation window, together with inconsistent values of Q1/2, indicates that PNM calculations are much more reliable than SNM calculations at present.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' This is not surprising, considering that the latter emerges from a delicate cancellation sensitive to the short- and intermediate-range three-body interactions at next-to-next-to-leading order, in contrast to PNM where these interactions are Pauli-blocked [51].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Therefore, we alternatively infer symmetry energy parameters using only χEFT PNM results for the energy and pressure, including their standard deviations, but coupled with ns and B values randomly chosen from within the empirical saturation window shown in Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' This alternate χEFT SV − L correlation and those involving KN and L are shown in Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Interestingly, the correlations so determined have confidence regions with central values consistent with those from mass fitting but with noticeably smaller uncertainties, greater degrees of significance, and also only slightly different slopes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Furthermore, ranges of SV, L, KN and QN values are compatible with those observed from mass fits, neutron skin and dipole polarizability measurements, as well as astrophysical studies, as shown below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 10 of 29 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The Unitary Gas Conjecture Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [35] proposed a constraint on the symmetry parameters arising from the conjecture that the energy of pure neutron matter was greater, at all densities, than that of a unitary gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' A unitary gas is an idealized theoretical collection of fermions interacting only via pairwise s-wave interactions with an infinite scattering length and a vanishing effective range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The average particle separation in such a gas is the only length scale, so the energy of the unitary gas, EUG, is proportional to the Fermi energy, EUG = 3¯h2k2 F 10mN ξ0 ≃ 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='7 � n ns �2/3 = EUG,0u2/3, (13) where kF = (3π2ns)2/3 is the Fermi wave number at the saturation density, mN is the neutron mass, the Bertsch parameter, which is experimentally measured [52,53] to be ξ0 ≃ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='37, and EUG,0 ≃ 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='6 MeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' In reality, pure neutron matter at low densities has finite scattering length and range, but both properties lead to larger energies than for a unitary gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' In addition, three-body forces in neutron matter are known to be repulsive, further increasing its energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The Unitary Gas Conjecture (UGC) states that EN ≥ EUG at all densities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' If it is minimally satisfied EN(ut) = EUG(ut) at some arbitrary density ut, in order for it to remain satisfied at higher and lower densities requires [35] �dEN du � ut = �dEUG du � ut .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' (14) These conditions automatically impose constraints on the parameters SV and L if the symmetry energy is expanded as in Equation (2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' For example, it sets a minimum value SV,min = B + EUG,0 where L = 2EUG,0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Further using the correlations shown in Figure 2 to eliminate KN and QN, and using mean values for ξ0, ns and B, the resulting constraint on SV and L is displayed in Figure 1 and in subsequent figures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' This bound is relatively insensitive to assumed values of KN and QN [35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' It is notable that the UGC is obeyed by nearly all χEFT results when EN and empirical values for ns and B are used (PNM method), but only by about half of χEFT results using both EN and E1/2 (SNM+PNM method).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Similarly, most Skyrme interactions obey the UGC while most RMF forces do not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Even though the exact UGC boundary depends on uncertainties in ξ0, ns, B and the KN − L and QN − L correlations, it serves as a valuable consistency check.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' It supports our previous argument that χEFT studies of symmetric matter are not presently accurate enough to provide significant constraints, and, further, that RMF forces do not seem to be as well-suited to fitting nuclear properties as are Skyrme forces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Because the UGC establishes a lower limit to the energy of pure neutron matter, it effec- tively sets a lower limit to both the radius and tidal deformability of a neutron star as a function of its mass [54], being more restrictive than causality in this regard.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Although the UGC cannot impose corresponding bounds in the KN − L or QN − L planes, it is possible to propose a corollary Unitary Gas Pressure Conjecture (UGPC), which states that the neutron matter pressure is always greater than the unitary gas pressure for densities larger than ns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Comparisons shown by Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [35] show that this is the case for recent neutron matter calculations and true for PNM chiral EFT studies even considering 90% lower confidence bounds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' For u < 1, however, it is possible for the unitary gas pressure to be larger than the neutron matter pressure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Using the 90% upper confidence bound suggested by Figure 2 for QN as a function of L, but ignoring the correlation between KN and L, the UGPC imposes the bound in the KN − L plane shown in Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' All RMF forces obey the UGPC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' However, about 30% of the formerly permitted Skyrme forces, those having L < 2EUG,0 or KN < −2EUG,0, do not satisfy the UGPC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 11 of 29 One can tighten the constraints imposed from mass fitting by selecting only those forces whose values of SV and L obey the UGC and the UGPC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The parameters of the revised correlation ellipses for Skyrme and RMF forces are given in Table 1 and also shown in Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Neutron Skin Thickness Constraints It has long been known that the neutron skin thicknesses of neutron-rich nuclei, such as 48Ca and 208Pb, are highly dependent upon the symmetry parameter L and more weakly dependent upon SV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' For example, the liquid droplet model predicts that the difference between the mean neutron and proton radii is [33] tnp = 2roI 3 SS SV [1 + SSA−1/3/SV]−1 (15) if Coulomb effects are ignored, where ro = (4πns/3)−1/3 and I = (N − Z)/(N + Z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The SS/SV term indicates that the radius difference primarily depends on L, and therefore the symmetry energy slope dS/dn and the neutron matter pressure at ns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' However, the appearance of the last term in Equation (15) implies that a stronger correlation of tnp exists with the symmetry energy slope dS/dn at a smaller density than ns, namely about 2ns/3 [55,56] which can be viewed as a sort of average nuclear density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' This mimics the situation concerning nuclear binding energies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [55] showed, in particular, that the neutron skin thickness of 208Pb, that is, the root-mean-square neutron-proton radius difference r208 np , is linearly correlated with the neutron matter pressure (which is proportional to n2dS/dn) most strongly at the density n1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='10 fm−3: r208 np ≃ (dS/dn)0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='1 882 ± 32 MeV fm−2 (16) We will define the symmetry energy slope as ˜L(n) ≡ 3ndS dn (17) so that ˜L(ns) = L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Equation (16) is then equivalent to rnp ∝ ˜L1 ≡ ˜L(n1), an estimate later generalized by several authors as r208 np = ˜a + ˜b˜L1, (18) with ˜a and ˜b coefficients given in Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Coefficients for the relation r208 np = ˜a/fm + ˜b˜L1/MeV and inferred values of ˜L1 from the error- weighted mean experimental value r208 np = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='166 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='017 fm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Also given are two estimated values of ˜L1 from neutron skin measurements of Sn isotopes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' †0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='01 fm uncertainty introduced for consistency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Reference ˜a ˜b ˜L1 (MeV) [55] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='00378 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='00014 43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='9 ± 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='8 [57] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='00994 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='01000 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='0036 43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='4 ± 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='5 [58] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='0101 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='01† 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='00377 41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='4 ± 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='2 [1] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='0148 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='0100 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='00414 36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='5 ± 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='8 [20] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='0590 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='0028 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='00313 34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='2 ± 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='5 [59] Sn isotopes 42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='9 ± 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='1 [58] Sn isotopes 43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='7 ± 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='3 Error-weighted mean 41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='7 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='0 12 of 29 Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Correlations between ˜L(u1) (Ltilde) and L for χEFT PNM (blue) and Skyrme (black) and RMF (red) interactions from Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [34,36], respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Green ellipses display the combined Skyrme and RMF correlations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Correlation coefficients (r) are shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' We note that ˜L evaluated at a subsaturation density can be related to other symmetry energy parameters through its Taylor expansion: ˜L(u) = u � L + Ksym 3 (u − 1) + Qsym 18 (u − 1)2 + · · · � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' (19) Given the strong correlations between Ksym and L, and moderate correlations between Qsym and L, displayed for the Skyrme [34] and RMF [36] forces (both shown in Figure 4), as well as for χEFT for PNM using B and ns from the empirical saturation window, it is not surprising that a strong correlation exists also between ˜L(u1) and L (Figure 6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' When the Ksym − Qsym − L correlations are combined in Equation (19), they give a 1σ confidence ellipse centered at L = 50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='09 MeV and ˜L = 41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='86 MeV, with standard deviations σL = 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='81 MeV and σ˜L = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='55 MeV and correlation 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='843.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The result ˜L = 41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='7 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='9 MeV from the average Pb and Sn neutron skin thicknesses shown in Table 2) has nearly the same value and uncertainty as those from mass fitting and neutron matter theory shown in Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Their mean value of about 40 MeV is supported by the results of Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [58,59] who argued that a linear rnp − ˜L correlation also exists for neutron-rich Sn isotopes and derived similar values of ˜L near the density 2ns/3 from experimental data (Table 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Collectively, these Pb and Sn studies yield an average value ˜L1 ≃ 42 MeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The implied value L = 49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='9 ± 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='0 MeV is therefore also in remarkable agreement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The pseudo-linear correlation between ˜L and L implies good linear correlations should exist between rnp with L for both Pb and Sn nuclei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Theoretical modeling, both from mean-field analyses and the dispersive optical model, supports an extension to 48Ca.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Linear relations are indeed validated by examining recent compilations [18,20,37,60–62] of neutron skin thicknesses for 208Pb and 48Ca using a multitude of both non-relativistic and relativistic interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The compilation from Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [37] is especially notable in containing results from 206 Skyrme-like and RMF forces, and the other compilations contribute more than 200 additional values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The model estimates from these compilations are displayed in Figure 7 and slopes, intercepts and standard deviations of the linear fits from each reference, as well as their overall means, are provided in 13 of 29 Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The mean values of the skin thicknesses from all models shown are nearly the same, r208 np = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='19 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='05 fm and r48 np = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='18 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='03 fm, but the two correlations have different slopes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Both are within ±1σ of the respective mean experimental measurements, see Tables 4 and 5, indicating an overall consistency exists between theory and experiment even though most of the models displayed were not explicitly fit to neutron skin values but rather to binding energy data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' In other words, there is no reason to expect that either conventional interactions or modeling lead to large systematic uncertainties with respect to calculations of neutron skin thicknesses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Slopes, intercepts, and standard deviations of linear fits rnp/fm = a ± ∆a + bL/MeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Reference a b 208Pb [37] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='0963 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='0041 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='001566 [18] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='1028 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='0115 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='001617 [60] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='0964 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='0039 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='001563 [20] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='0865 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='0124 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='001837 [61] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='0967 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='001447 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='00145 [62] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='0986 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='0137 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='001537 Mean 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='0996 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='0096 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='001518 48Ca [37] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='1250 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='0028 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='000873 [18] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='1261 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='0056 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='000990 [60] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='1290 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='0037 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='000791 Mean 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='1255 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='0052 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='000882 Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Neutron skin thicknesses of 48Ca (red) and 208Pb (black) from interactions compiled in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [37] (filled circles) and Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [18,60,63,64] (open circles).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Means (1 standard deviations) of linear correlations are shown as solid (dashed) lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The horizontal shaded bands indicate the 1 standard deviation ranges of the averaged experimental results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The dotted black (red) lines indicate the 1 standard deviation range of r208 np (r48 np) from PREX I+II [17] (CREX [18]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 14 of 29 Nevertheless, it is worth mentioning that two recent more sophisticated theoretical predic- tions give divergent views.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Relatively small values of neutron skins are implied by coupled cluster ab-initio calculations which predict r48 np = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='135 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='015 fm [65] and r208 np = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='17 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='03 fm [66], which are close to the respective experimental means (Table 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' On the other hand, the nonlocal dispersive optical model predicts that finite-size effects play an important role in enhancing the neutron skin, giving r208 np = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='25 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='05 fm [67] and r48 np = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='249 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='023 fm [68], both of which are considerably larger than the respective experimental means.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The strong linear correlations existing between model calculations of the neutron skins of these two nuclei with L obviously implies a strong linear correlation exists between the skin thicknesses themselves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Neutron skin data from Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [37] alone follows the linear relation r48 np = (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='0716 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='0006) fm + 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='5554r208 np (20) with a very small uncertainty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Including 179 skin calculations using additional Skyrme and RMF forces by Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [18,60,63,64], the mean linear relation becomes r48 np = (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='0730 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='0048) fm + 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='56157r208 np , (21) which is virtually identical except for having a larger standard deviation reflecting a greater variation in underlying forces (and possibly less strict constraints regarding fitting nuclear masses and charge radii).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The ±1σ confidence bounds on the overall linear correlation are shown as straight dashed lines in Figure 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' We note that these references contain a number of the same interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' These duplicate calculations show variations of as much as 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='01 fm, which should be included as a systematic modeling uncertainty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' However, this uncertainty is small enough that it does not affect the results significantly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' We also note that Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [69] has argued that an accurate determination of r208 np is insufficient to constrain r48 np because of the significant difference in the surface-to-volume ratio of these two nuclei, a conclusion, however, not supported by our results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Neutron Skin Measurements and Correlations The nuclides 48Ca and 208Pb are especially important because they are the only stable neutron-rich, closed-shell, nuclei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Measurements of their neutron skin thicknesses are summa- rized in Tables 4 and 5, as well as Figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The error-weighted mean of all tabulated experimen- tal measurements is r208 np = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='166 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='017 fm, which is consistent with the average theoretical estimate r208 np = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='170 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='008 fm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The mean of historical measurements not including PREX is r208 np = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='159 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='017 fm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' For 48Ca, the mean of all measurements is r48 np = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='137 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='015 fm, about 2σ smaller than the average theoretical estimate r48 np = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='17 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='03 fm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The average of historical measurements not including CREX is r48 np = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='140 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='017 fm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 15 of 29 Figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Neutron skin measurements [17,18,70–81] with 68% confidence intervals and citations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Hori- zontal dashed lines denote ±1 standard deviations from the weighted means of experiments other than CREX or PREX I+II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 208Pb neutron skin measurements and theoretical predictions with 1σ uncertainties 208Pb Experiment Reference r208 np (fm) Coherent π0γ production [77] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='15+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='03 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='04 Pionic atoms [73] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='15 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='08 Pion scattering [73] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='11 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='06 ¯p annihilation [78,79] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='18 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='06 Elastic polarized p scattering [70] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='16 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='05 Elastic polarized p scattering [80] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='211+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='054 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='063 Elastic p scattering [81] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='197 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='042 Elastic p scattering [72] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='119 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='045 Parity-violating e− scattering (PREX I+II) [17] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='283 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='071 208Pb experimental weighted mean 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='166 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='017 Pygmy dipole resonances [82] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='180 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='035 rSn np [83] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='175 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='020 Anti-analog giant dipole resonance [84] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='216 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='048 Symmetry energy 208Pb [85] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='158 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='014 Dispersive optical model [86] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='18+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='25 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='12 Dispersive optical model [67] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='25 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='05 Coupled cluster expansion [66] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='17 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='03 r48 np [63,64], this paper 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='128 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='040 α208 D [62], this paper 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='154 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='019 α208 D [20,64], this paper 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='188 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='017 208Pb theoretical weighted mean 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='170 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='008 16 of 29 Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 48Ca neutron skin measurements and theoretical predictions with 1σ uncertainties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ∗Uncertainty scaled upwards as per Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [87].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 48Ca Experiment Reference r48 np (fm) Elastic polarized p scattering [70] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='229 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='050 Elastic p scattering [76] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='10 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='03 Elastic p scattering [72] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='098 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='043 Elastic p scattering [71] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='168+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='025 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='028 Pionic atoms [73] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='13 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='06 Pion scattering [74] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='11 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='04 α scattering [75] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='171 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='050 Parity-violating e− scattering (CREX) [18] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='121 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='035 48Ca experimental weighted mean 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='137 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='015∗ Coupled-cluster expansion [65] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='135 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='015 Dispersive optical model [68] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='249 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='023 r208 np [63], this paper 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='173 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='018 48Ca theoretical weighted mean 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='17 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='03∗ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Parity-Violating Electron Scattering Measurements A lot of attention has been paid to the recent PREX [17] and CREX [18] measurements of the neutron skins of 208Pb and 48Ca, respectively, using parity-violating electron scattering, which is claimed to have less modeling systematic uncertainty than other experimental methods [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Interestingly, the PREX measurement is more than 1 standard deviation higher than the mean value of previous 208Pb experiments, while the CREX measurement is smaller than the mean of previous 48 Ca experiments, but by less than 1 standard deviation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Fitting the neutron skin thickness from parity-violating scattering of either nuclide alone would give vastly different values for L, about 110 MeV for Pb [20] and 0 MeV for Ca, as can be seen by reference to Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Even using the mean values of all the experimental results would produce disparate values of L, about 40 MeV and 10 MeV, respectively, although they would lie within a standard deviation of each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' It is important to note that the weighted mean experimental value of r208 np decreases by only about 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='007 fm and that of r48 np increases by only about 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='003 fm when the PREX and CREX results are excluded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Without compelling reasons to favor measurements of either nuclide, our approach is to instead attempt to simultaneously satisfy experimental information for both nuclides.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' We follow two strategies for satisfaction of joint Ca-Pb measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' First, one could take the approach that the PREX and CREX experiments qualitatively have fewer systematic uncertainties than other approaches, and only use those measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Alternatively, an agnostic approach would be to instead consider the weighted means of all measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 17 of 29 Figure 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Neutron skin thicknesses of 48Ca and 208Pb from interactions compiled in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [37] (filled circles) and Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [18,60,63,64] (triangles).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Colors indicate L values where known;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' black triangles indicate points where L values are unspecified.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Standard deviations of a linear correlation Equation (21) are shown as dashed lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The red (blue) confidence ellipses are from PREX I+II [17] and CREX [18] (mean of all experiments);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' solid (dashed) ellipses are 68% (90%) confidence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' As can be seen in Figure 9, the PREX I+II value for r208 np is too large and the CREX value for r48 np is too small to permit any of the reference interactions from the compilation of Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [18, 37,60,63,64] from satisfying both of them to within 68% confidence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The situation is different when considering the mean experimental results for 208Pb and 48Ca, with 4% of the reference interactions simultaneously satisfying them to 68% confidence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' A much larger number of interactions satisfy skin thickness measurements for both nuclei when considering 90% confidence regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' About 40% of the interactions from Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [37] can simultaneously satisfy the UGC, UGPC, PREX I+II and CREX results, and these have 0 MeV < L < 72 MeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Similarly, about 24% of these interactions simultaneously lie within the 90% confidence region of the averages of all experiments, and also satisfy the UGC and UGPC, and these have 0 MeV < L < 58 MeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The associated permitted region in SV − L space can be ascertained by weighting those interactions [37] satisfying both unitary gas constraints, and which also have tabulated SV, L, r48 np and r208 np values, by their probabilities given by a two-dimensional Gaussian defined by the skin measurements and their uncertainties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Results are shown in Figure 10 and tabulated in Table 1 for both approaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Interestingly, using CREX+PREX measurements to define the r48 np − r208 np probabilities gives a confidence ellipse in substantial agreement with the PNM χEFT result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Using the mean of other skin measurements gives somewhat smaller mean values of SV and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 18 of 29 Figure 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Symmetry parameters SV − L (left panel) and KN − L (right panel) jointly satisfying parity- violating experiments to within (exceeding) 90% confidence are shown as red and black filled (black open) circles;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' filled black circles violate Unitary Gas constraints (dotted boundary).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Red (blue) confidence ellipses are for models satisfying Unitary Gas constraints weighted by their two-dimensional Gaussian probability defined by the parity-violating (red) and average (blue) experimental r48 np and r208 np measurements and uncertainties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The black confidence ellipse shows PNM χEFT results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' It is important to note that this internal consistency among neutron skin measurements, mass fitting and neutron matter theory, using either approach, is not particularly sensitive to whether relativistic or non-relativistic interactions are considered, suggesting it is relatively free of associated systematic uncertainties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Partly, this is due to the moderate values of L that are favored, eliminating most RMF interactions in compilations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' We compare to Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [88], who combined data from isobaric analog states and the mean of experimental Pb neutron skin measurements (taken to be to r208 np = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='159 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='041 fm) to infer L ≃ 50 ± 12 to 68% confidence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Also, Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [61] used experimental values for Pb to inferr 19 <∼ L/MeV <∼ 77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' However, neither of these sources considered the neutron skin of 48Ca.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' We note an inference of SV = 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='2+4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='1 −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='0 MeV and L = 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='346.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='8 −41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='5 MeV using a combined analysis of PREX and CREX measurements was recently obtained by Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Their method differs from the present analysis in that they optimized parameters for a Skyrme-like interaction using weak and charge form factors from PREX and CREX rather than inferred skin thicknesses, which are subject to additional theoretical uncertainty, as well as binding, breathing mode and neutron-proton Fermi energies, and charge and diffraction radii.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Their estimates are compatible with the present results but have larger uncertainties despite the fact that they are not subject to the addicional theoretical uncertainty relating form factors to skin thicknesses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Another study by Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [24] which also considered dipole polarizabilities concluded that no single interaction could satisfy both PREX and CREX interactions to 68% confidence, agreeing with this paper and Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [23], but did not attempt to infer a ’best-fit’ interaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' An analogous analysis for KN is shown in Figure 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The confidence regions for both approaches are compatible with that of PNM χEFT, although the results using PREX+CREX measurements have nearly the same centroid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Other Nuclear Methods 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Correlations from Nuclear Dipole Polarizabilities Nuclear measurements involving the giant dipole resonance enable additional constraints on the symmetry energy and can shed light on the somewhat disparate results of recent skin thickness measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Measured dipole polarizabilities for the neutron-rich nuclides 48Ca, 19 of 29 Table 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Dipole polarizabilities with 1σ uncertainties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' †αD values corrected as per Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [90].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Nuclide Reference αD (fm3) 208Pb [91] 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='6 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='6† 120Sn [92] 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='59 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='37† 48Ca [93] 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='07 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='22 120Sn and 248Pb are given in Table 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Support for the experimental values comes from theoretical calculations of αD by Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [89], who found the linear relations: α48 D ≃ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='10 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='01)α208 D + 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='36 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='07 MeV fm3, α208 D ≃ (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='2 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='1)α120 D + 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='1 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='5 fm3, (22) with correlation coefficients of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='82 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='96, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' These relations predict the values α48 D = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='32 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='21 fm3, slightly larger than the experimental value, from the measured value of α208 D , and α208 D ≃ 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='0 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='2 fm3, slightly smaller than the experimental value, from the measured value of α120 D , but both within one standard deviation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [94] determined that the central energy of the giant dipole resonance of 208Pb and the symmetry energy has its greatest correlation at the density n1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='1 fm−3, and from the measured value of α208 D thereby deduced the symmetry energy at that density to be S(u1) = 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='1 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='8 MeV, which is in agreement with S(u1) = 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='7 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='4 MeV deduced from the masses of closed shell nuclei [55].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Similarly, in a study using 62 non-relativistic and relativistic interactions fitted to ground-state properties of finite nuclei, Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [95] deduced that the electric dipole polarizability of 208Pb has its greatest correlation with the symmetry energy at the density n2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='05 fm−3, and found the symmetry energy at that density to be S(u2) = 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='54 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='00 MeV (after correcting the measured dipole polarizability as per Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [90]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Using the expansion Equation (2), employing empirical correlations to eliminate Ksym and Qsym, and including uncertainties in ns, these results imply the two linear relations L = 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='9SV − 288 ± 16 MeV, L = 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='1SV − 207 ± 12 MeV, (23) respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' These are in essential agreement with the correlation derived from nuclear mass measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The dipole polarizability correlations are also consistent with the relevant confidence regions established from χEFT as well as from neutron skin thickness measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [90] showed the existence of a theoretical correlation between the neutron skin thickness and the electric dipole polarizability, justified by the nuclear droplet model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' For 48Ca, 120Sn and 208Pb, these are [89] α48 D SV = (355 ± 44)(r48 np/fm) + 12 ± 19 MeV fm3, α120 D SV = (1234 ± 93) (r120 np /fm) + 115 ± 36 MeV fm3, α208 D SV = (1922 ± 73) (r208 np /fm) + 301 ± 32 MeV fm3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' (24) We found similar correlations for 208Pb using calculations of Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [62] and Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [96], respectively: α208 D SV = 2195 (r208 np /fm) + 258 ± 16 MeV fm3, α208 D SV = 2125 (r208 np /fm) + 226 ± 12 MeV fm3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' (25) Combining relations in Equation (24) with experimental values for the dipole polarizabili- ties (Table 6) gives the relation r48 np ≃ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='056 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='056) fm + (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='572 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='097)r208 np (26) 20 of 29 which compares favorably with Equation (21), albeit with larger uncertainties, emphasizing the consistency of polarizability and skin experimental results with theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The same result is achieved using Equation (25) instead.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Equations (24) and (25) also suggest that measurements of rnp and αD for 48Ca, 120Sn or 208Pb provide constraints on SV independently of L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The mean experimental data for 48Ca, 120Sn (r120 np values are given in Table 7) and 208Pb yield SV = 29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='3 ± 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='4 MeV, 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='1 ± 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='2 MeV, and 31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='6 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='6 MeV, respectively, using Equation (24).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Equation (25) alternatively yields SV = 31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='8 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='3 MeV and 29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='5 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='1 MeV for 208Pb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Collectively, one finds SV = 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='9 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='3 MeV, which, once again, is consistent with mass fitting, χEFT and the mean neutron skin results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' None of these ranges for SV are consistent with the PREX measurement by itself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Table 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 120Sn neutron skin measurements with 1σ uncertainties 120Sn Reference r120 np (fm) Elastic p scattering [97] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='147 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='033 Spin-dipole resonance (3He-t) [98] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='18 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='07 ¯p annihilation [99] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='12 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='02 120Sn experimental weighted mean 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='130 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='017 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Correlations from Heavy Ion Collisions Two general problems with extracting symmetry energy parameters from heavy-ion colli- sions are: (1) matter in these collisions is close to symmetric, with the symmetry energy being perhaps 10% of the total and therefore difficult to ascertain;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' and (2) the matter has excitation energies of 50-several hundred MeV per baryon (corresponding to T ∼ 20 − −50 Mev).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' This paper has therefore concentrated on probes connected with cold finite nuclei where densities are near ns and a Taylor expansion is appropriate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Here, some results from analyses of heavy ion experiments are summarized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' It has been proposed [100] to use empirical pressures deduced in cold SNM from hadronic transport model analyses of heavy-ion collisions [101,102].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Data come from studying kaon production [103,104], which provides constraints in the density range from 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='3ns to 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='2ns, and nuclear collective flow [105–108], which provides constraints from 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='0ns to 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='7ns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Pres- sures from kaon production (collective flows) have estimated uncertainties of about ±22 − −25%(±19% − −32%), so such constraints have appreciable errors even before systematic uncertainties, such as from extrapolating from moderate excitation energies to zero temper- ature, are taken into account.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' In addition, these estimates are based upon Taylor expansions of the symmetric matter energy like Equation (4), but including a fourth-order (kurtosis Z) term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' This introduces additional uncertainty, not only because of questionable validity of such an expansion at high density, but also because the expansion is arbitrarily truncated at fourth order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Although interesting correlations betweeen K1/2 and Q1/2 are deduced from this analysis, application to PNM and therefore extraction of symmetry energy parameters becomes model dependent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The symmetry energy might more directly probed in heavy ion collisions through the π−/π+ multiplicity ratio in central collisions [109–111] and from isospin diffusion or elliptic flows of neutrons and protons [112–115];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' see Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [116] for a summary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Both approaches, however, have given rather conflicting results concerning the stiffness of the symmetry energy, with L ranging from 0 MeV to ∼ 120 MeV, indicating a large degree of model dependence in the analyses [50,117,118].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 21 of 29 For example, the analysis of Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [50], which assumes that the density-dependent symmetry energy has the simple form S(u) = C1u2/3 + (SV − C1)uγ, (27) where C1 ≃ 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='5 MeV, predicts a 2σ band in SV − L space which is shown as HIC in Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' For S in Equation (27), a line in the SV − L plane with a slope ∆L/∆SV implies that S is best determined at density ub = exp(−3∆SV/∆L).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' In addition, any point in this diagram implies a γ value γ = L − 2C1 3(SV − C1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' (28) The diagonal sides of the quadrilateral in Figure 5 therefore imply that 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='28 ≤ γ ≤ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='04 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='35 ≤ ub ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Therefore, this experiment best probes subsaturation densities smaller than do mass fits (ub ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='74), neutron skin thicknesses (ub ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='66) or neutron matter theory (ub ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='66).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' However, the symmetry parameters are rather poorly constrained (possibly because the extrapolation to saturation density is larger in the HIC case), with the quadrilateral having a much larger extent than the regions determined in Figure 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' In addition, large portions of the quadrilateral violate the UGC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Furthermore, another analysis of the same data [117] suggests L = 122 ± 57 MeV, indicating overall difficulties with this method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Astrophysical Considerations Astrophysical observations of neutron stars can yield estimates of radii, moments of inertia, and tidal deformabilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' We will consider two of the currently most popular observations: the LIGO/Virgo detection of the neutron star merger GW170817 [21,119] and NICER observations of the rapidly rotating pulsars PSR J0030+0451 [25,26] and PSR J0740+6620 [27,28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' It will be seen that the symmetry parameters ranges suggested by nuclear experiment and theory are consistent with inferences from astrophysical observations of neutron stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Neutron Star Radii For subsets of forces from Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [18,37,60,63,64], the radii of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='4M⊙ neutron stars (R1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='4), L and r48 np and r208 np are available (most of the radius information was kindly provided by B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Tsang).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Although nuclear interaction models, having been fit to nuclei, describe matter with large proton fractions and n <∼ ns, one should be wary of making predictions about neutron stars from them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Nevertheless, as shown in Figure 11, there is a clear correlation between L and R1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The correlation between PNSM(n) and R1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='4 turns out to be greatest at densities in the range 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='5 − 2ns [48], low enough that interaction models are still reliable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Note, however, that these models should not be used to constrain neutron star maximum masses, which are most sensitive to PNSM for n >∼ 3ns [48].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' One can predict a validity range for R1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='4 based on neutron skin measurements in the same way the SV − L predictions shown in Figure 9 were made.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Weighting the predicted R1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='4 of models satisfying both Unitary Gas constraints by their double Gaussian probabilities in r48 np − r208 np space, one finds R1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='4 = 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='6 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='0 km (and L = 49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='4 ± 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='1 MeV) to 68% confidence using parity-violating neutron skin measurements (Figure 11).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' In comparison, the weighted average of other experiments yields R1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='4 = 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='0 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='9 km (and L = 40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='7 ± 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='9 MeV).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Bayesian analyses combining measurements of tidal deformability (see Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='2) from GW170817 and radii from pulse-profile modeling of PSR J0030+0451 and PSR J0740+6620 suggest R1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='4 = 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='3+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='5 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='3 km to 68% confidence [120].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The 68% and 90% confidence intervals are shown by green shading in the left panel of Figure 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' These astrophysical inferences are in essential agreement with our results using PREX and CREX data, and are about 1σ larger then results obtained using other experimental neutron skin data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 22 of 29 Figure 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The same as Figure 10 except showing R1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='4 versus L (left panel) and Λ1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='4 versus L (right panel) for subsets of forces from Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [18,37,60,63,64].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Black solid and dashed curves in the left panel show the R1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='4 − L correlation and standard deviations derived as in the text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The shaded green bands are 68% and 95% confidence intervals from a joint analysis of GW170817 and PSR J0030+0451 and PSR J0740+6620 by Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [120] (left panel) and from GW170817 Bayesian analyses posteriors [21], corrected for Λ priors chosen so as to reflect uniform R priors (right panel).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' It is possible to understand the correlation observed in Figure 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Since NSM is close to PNM around n = ns, there should a high degree of correlation between PNSM(ns) and L, and therefore between R1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='4 and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Indeed, a correlation between R1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='4 and PNSM, the neutron star matter pressure, around ns was empirically established some time ago by Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [7] and refined by Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [121], R1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='4 ≃ (9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='51 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='49)(PNSM/MeV fm−3)1/4 km.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' (29) It is necessary to convert Equation (29) into one depending directly upon the symmetry param- eters by taking into account how NSM differs from PNM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' NSM has a finite proton (electron) fraction determined by energy minimization with respect to x at every density, leading to beta-equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The total energy per baryon of NSM in the quadratic approximation is ENSM = EN − 4xS(1 − x) + 3 4 ¯hcx(3π2nx)1/3, (30) where EN is the energy of PNM, S(n) is the density-dependent symmetry energy and x is the proton fraction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The last term is the electron contribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Beta equilibrium requires ∂ENSM/∂x = 0, giving x = �4S ¯hc �3 (1 − 2x)3 3π2n .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' (31) At ns, one finds PNSM(ns) = n2 ∂ENSM ∂n ���� ns = Lns 3 [1 − x + 2x2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' (32) At ns, Only the L term in a density expansion of S contributes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' For a given value of L, a normal distribution of SV values based on the PNM χEFT correlation (Figure 5), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=', SV = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='139L + (24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='63 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='25) MeV, (33) 23 of 29 can be used to find a corresponding x distribution from Equation (31).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Then, Equation (32) gives the PNSM(ns) distribution and Equation (29) gives the R1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='4 distribution, which is shown with uncertainties in Figure 11 as black lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The agreement, including uncertainties, with model interactions is remarkable, in spite of the fact that Equation (29) was established using a far smaller number of interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Tidal Deformabilities and Radii For GW170817, the most accurately-measured quantity is the chirp mass [119] M = (m1m2)3/5 (m1 + m2)1/5 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='186 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='001M⊙ (34) where m1 > m2 are the masses of the merging stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Less precisely measured is the radius- sensitive binary tidal deformability of the system, ˜Λ = 16 13 (1 + 12q)Λ1 + (12 + q)q4Λ2 (1 + q)5 , (35) where q = m2/m1 is the mass ratio and Λ1 and Λ2 are the individual stellar deformabilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Typical M(R) trajectores in the relevant mass range 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='1M⊙ < M < 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='6M⊙ for BNS merger components (judging from galactic BNS [3,122]) have relatively small variations in R for a given EOS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Given the minimum (maximum) neutron star mass is about 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='1M⊙ (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='1M⊙), 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='7 <∼ q ≤ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [54] found, using piecewise polytropes, that in the absence of significant phase transitions, the average radius ¯R satisfies | ¯R − R| < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='5 km for all EOSs in this mass range, and averaged over all EOSs and masses, | ¯R − R| has a standard deviation of about 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='1 km.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [54] also determined, to high accuracy, that the dimensionless tidal deformability of individual stars in this mass range obeys the semi-universal (EOS-independent) relation Λ = aβ−6;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Λ1 ≃ q6Λ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' (36) with a = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='009 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='002 and β = GM/Rc2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' It therefore follows that ˜ΛM ≃ 16a 13 � ¯Rc2 GM �6 q8/5 (12 − 11q + 12q2) (1 + q)26/5 , (37) where the notation ˜ΛM reflects that ˜Λ is measured at a well-defined M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The q-dependence in Equation (37) is weak: ˜ΛM(q = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='7)/ ˜ΛM(q = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='0) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='029 and (∂ ˜ΛM/∂q)q=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Thus, the fact that q is poorly measured has little consequence, and one finds ¯R ≃ (11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='3 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='3) M M⊙ � ˜ΛM 800 �1/6 km.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' (38) Due to radius correlations, the uncertainty in ¯R is only half the uncertainty of a itself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Thus, ˜ΛM carries significant radius information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' To the same accuracy, R1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='4 ≃ ¯R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' More directly, one can predict Λ1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='4, the dimensionless tidal deformability of a 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='4M⊙ neutron star, from neutron skin measurements using the same procedure as used for R1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Values of Λ1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='4 for the interactions in the right panel of Figure 11 were provided by B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Tsang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Weighting each by the double Gaussian defined by neutron skin thickness measurements and uncertainties, it is found, to 68% confidence, Λ1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='4 = 228+148 −90 (L = 49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='3 ± 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='0 MeV) using the PREX+CREX neutron skin measurements, and Λ1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='4 = 177+117 −70 (L = 39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='3 ± 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='7 MeV) using the average of other skin measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 24 of 29 These ranges are consistent with inferences [21] from LIGO/Virgo observations [22,119] of the BNS merger GW170817 (shaded green regions in the right panel of Figure 11).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' For this comparison, it is useful to convert the observed quantity ˜ΛM to Λ1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Use of Equation (36) gives ΛM ≃ � 21/5M/M �6 ˜ΛM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' (39) For GW170817, Λ1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='4 ≃ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='849 ˜Λ1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='186.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [21] calculated the tidal deformability posteriors of the two merging stars from a grvitational wave analysis assuming Λ1/Λ2 = q6 and causality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' They assumed uniform Λ and M priors for the two stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' They found Λ1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='4 = 245+312 −81 to 68% confidence and Λ1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='4 = 245+651 −114 to 90% confidence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' However, the results are sensitive to the assumed Λ priors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Perhaps it is more realistic to assume uniformity in ln Λ rather than Λ because Λ ∝ (R/M)6 has a large dynamic range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' This is tantamount to a uniform radius prior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' In this case, to 68% confidence, Λ1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='4 = 234+119 −72 , and to 90% confidence, Λ1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='4 = 234+216 −101.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Although the predicted means are nearly the same, assuming uniformity in the ln Λ priors dramatically reduces the upper 68% and 90% confidence bounds, and makes them strikingly similar to those inferred from neutron skin measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Conclusions Compilations containing several hundred theoretical nuclear interactions of both the non- relativistic (Skyrme) or relativistic (RMF) type, which have been fitted to nuclear masses and/or charge radii, show that significant correlations exist among symmetry and neutron energy parameters SV, L, KN and QN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The average values and correlation slopes depend on whether the interactions considered are non-relativistic or relativistic: the relativistic interactions in these compilations tend to have larger values of L and KN, for example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' In both cases, the 68% confidence ellipses for the SV − L, L − KN and QN − L correlations considerably overlap with those predicted by chiral effective field calculations of pure neutron matter, but have different slopes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Theoretical calculations of neutron skin thicknesses of neutron-rich closed shell nuclei (48Ca and 208Pb) predict strong correlations with L with average uncertainties less than 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='01 fm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The individual weighted means of experimental measurements of these nuclei can be used to predict comparable ranges of L, 0-40 MeV for 48Ca and 30-60 MeV for 208Pb, both consistent with the range determined by jointly fitting masses and neutron matter calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Without a strong reason to prefer skin measurements of one nucleus over another, simultaneous reconciliation of the weighted means of skin measurements of both nuclei with those from theoretical calculations of forces in the compilations constrains the symmetry parameters SV = 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='8 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='5 MeV and L = 40 ± 8 MeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Alternatively, one could choose to only employ parity-violating electron scattering results (PREX and CREX), which have been claimed to have smaller systematic uncertainties than other techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The two experiments separately predict incompatible ranges of L (L = −5 ± 40 MeV and L = 121 ± 47 MeV, respectively), but accepting both measurements to be equally valid suggests SV = 32 ± 2 MeV and L = 50 ± 12 MeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' These alternative approaches in treating neutron skin measurements predict closely overlapping ranges that are consistent with ranges predicted from mass fits and neutron matter theory, and therefore indicate that the PREX and CREX experimental results are consistent with those of other techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' These estimates are compatible with those calculated by Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Further support for the resulting focus to small ranges of symmetry parameters comes from measurements and theoretical studies of nuclear dipole polarizabilities (αD).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Theory predicts that αDSV is linearly correlated to rnp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Measured values of αD and rnp for 48Ca, 120Sn and 208Pb then imply SV = 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='9 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='3 MeV in good agreement with our result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Further proof that existing measurements of αD and rnp are compatible comes from the linear relation 25 of 29 between r48 np and r208 np resulting from the theoretical αDSV − rnp correlation;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' this linear relation is in remarkable agreement with that predicted by theoretical neutron skin calculations of these nuclei using both relativistic and non-relativistic interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The inferred small ranges of symmetry parameters combining mass fitting, neutron matter theory, and skin thickness and dipole polarizability measurements and theory are robust and do not depend significantly on the type of nuclear interaction considered, despite the systematic differences in predictions of individual quantities arising from a single method alone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Potentially, an improvement of our predictions can be achieved by directly comparing predictions and measurements of the charge and weak form factors of 48 Ca and 208Pb, as done in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' This would remove the additional uncertainty involved in converting form factors to neutron and proton radii.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' However, given the compatibility of results from our work with Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' [23], this additional uncertainty does not appear to be significant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' In any case, measurements of form factors or neutron skin thicknesses will have to be performed with much greater precision than at present to improve upon the symmetry parameter constraints from chiral Lagrangian chiEFT calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' For the first time, we extended predictions from neutron skin measurements to include neutron star radii and tidal deformabilities without employing any information from astrophys- ical observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Our estimated ranges for R1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='4 and Λ1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='4 are compatible with recent studies using LIGO/Virgo data from the BNS merger GW170817 and NICER X-ray observations of PSR J0030+0451 and PSR J0740+6620.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Funding: This work was initiated through the NSF-funded Physics Frontier Center Network for Neutri- nos, Nuclear Astrophysics, and Symmetries (N3AS) and was supported by the U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' DOE grant DE-AC02- 87ER40317.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Data Availability Statement: Not applicable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Acknowledgments: Thanks are due to J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Piekarewicz, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Nazarewicz and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Tsang for providing data and, together with T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Zhao, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Horowitz and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Kumar, helpful discussions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Conflicts of Interest: The author declares no conflicts of interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The funders had no role in the design of the study, the collection, analyses, or interpretation of data, the writing of the manuscript, or in the decision to publish the results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Abbreviations The following abbreviations are used in this manuscript: NS neutron star BNS binary neutron stars EOS equation of state PSR pulsar SNM symmetric nuclear matter PNM pure neutron matter χEFT chiral effective field theory RMF relativistic mean field UGC Unitary Gas Conjecture UGPC Unitary Gas Pressure Conjecture NICER Neutron Star Interior Composition ExploreR References 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Steiner, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Prakash, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lattimer, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Ellis, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Isospin asymmetry in nuclei and neutron stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2005, 411, 325.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lattimer, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Prakash, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Neutron star observations: Prognosis for equation of state constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2007 442, 109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lattimer, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Neutron Stars and the Nuclear Matter Equation of State.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Annu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Part.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2021 71, 433.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Swesty, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lattimer, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Myra, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The Role of the Equation of State in the “Prompt” Phase of Type II Supernovae.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 1994, 425, 195.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Roberts, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Shen, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Cirigliano, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Pons, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Reddy, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Woosley, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Protoneutron Star Cooling with Convection: The Effect of the Symmetry Energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2012, 108, 061103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Morozova, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Radice, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Burrows, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Vartanyan, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The gravitational wave signal from core-collapse supernovae.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2018, 861, 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 26 of 29 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lattimer, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Prakash, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Neutron Star Structure and the Equation of State.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2001, 550, 426.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Bauswein, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Janka, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='-T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Measuring Neutron-Star Properties via Gravitational Waves from Neutron-Star Mergers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2012, 108, 011101.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lackey, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Kyutoku, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Shibata, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Brady, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Friedman, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='Extracting equation of state parameters from black hole-neutron star mergers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Nonspinning black holes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' D 2012, 85, 044061.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Page, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Reddy, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Thermal and transport properties of the neutron star inner crust.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' In Neutron Star Crust;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Bertulani, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=', Piekarewicz, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=', Eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Nova Science Publisheres, New York, NY, USA, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' arXiv:1201.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='5602.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Hurley, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Boggs, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Smith, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Duncan, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lin, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Zoglauer, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Krucker, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Hurford, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Hudson, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Wigger, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' An exceptionally bright flare from SGR 1806-20 and the origins of short-duration γ-ray bursts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Nature 2005, 434, 1098.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Thompson, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Duncan, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The giant flare of 1998 August 27 from SGR 1900]14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Radiative mechanism and physical constraints on the source.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2001, 561, 980 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Samuelsson, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Andersson, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Neutron star asteroseismology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Axial crust oscillations in the Cowling approximation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' MNRAS 2007, 374, 256.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lattimer, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Pethick, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Prakash, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Haensel, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Direct URCA process in neutron stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 1991, 66, 2701.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Nikolov, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Schunck, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Nazarewicz, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Bender, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Pei, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Surface symmetry energy of nuclear energy density functionals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' C 2011, 83, 034305.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Drischler, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Holt, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Wellenhofer, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Chiral Effective Field Theory and the High-Density Nuclear Equation of State.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Annu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Part.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2021, 71, 403.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Adhikari, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Albataineh, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Androic, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Aniol, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Armstrong, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Averett, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Gayoso, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Barcus, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Bellini, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Beminiwattha, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Accurate determination of the neutron skin thickness of 208Pb through parity-violation in electron scattering Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2021, 126, 172502.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Adhikari, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Albatainen, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Androic, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Anioj, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Armstrong, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Averett, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Ayerbe Gayoso, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Barcus, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Bellini, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Beminiwattha, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Precision determination of the neutral weak form factor of 48Ca.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2022, 129, 042501 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Thiel, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Sfienti, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Piekarewicz, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Horowitz, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Vanderhaeghen, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Neutron skins of atomic nuclei: per aspera ad astra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' G Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Part.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2019, 46, 093003 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Reed, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Fattoyev, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Horowitz, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Piekarewicz, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Implications of PREX-2 on the equation of state of neutron-rich matter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2021, 126, 172503.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' De, Finstad, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' J, Lattimer, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Brown, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Berger, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Biwer, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Tidal deformabilities and radii of neutron stars from the observation of GW170817.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2018 121, 091102 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Abbott, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Abbott, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Abbott, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Acernese, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Ackley, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Adams, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Adams, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Addesso, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Adhikari, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Adya, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Properties of the binary neutron star merger GW170817.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' X 2019 9, 011001 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Zhang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Chen, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='-W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Bayesian inference of the symmetry energy and the neutron skin in 48Ca and 208Pb from CREX and PREX-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' arXiv 2022, arXiv:2207.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='03328.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Reinhard, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Roca-Maza, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Nazarewicz, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Combined theoretical analysis of the parity-violating asymmetry for 48Ca and 208Pb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2022, 129, 232501.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Miller, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lamb, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Dittmann, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Bogdanov, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Arzoumanian, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Gendreau, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Guillot, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Harding, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Ho, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lattimer, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' PSR J0030+0451 Mass and Radius from NICER Data and Implications for the Properties of Neutron Star Matter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2019, 887, L24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='JML 20 co-authors 26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Riley, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Watts, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Bogdanov, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Ray, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Ludlam, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Guillot, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Arzoumanian, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Baker, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Bilous, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Chakrabarty, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' A NICER view of PSR J0030+0451: Millisecond pulsar parameter estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2019, 887, L21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Miller, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lamb, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Dittmann, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Bogdanov, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Arzoumanian, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Gendreau, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Guillot, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Ho, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lattimer, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Loewenstein, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The radius of PSR J0740+6620 from NICER and XMM-Newton data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2021, 918, L28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Riley, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Watts, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=', Ray, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=', Bogdanov, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=', Guillot, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=', Morsink, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=', Bilous, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=', Arzoumanian, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=', Choudhury, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=', Deneva, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' A NICER view of the massive pulsar PSR J0740+6620 informed by radio timing and XMM-Newton spectroscopy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2021, 918, L27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Wellenhofer, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Holt, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Kaiser, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Divergence of the isospin-asymmetry expansion of the nuclear equation of state in many-body perturbation theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' C 2016, 93, 055802.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Agrawal, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Shlomo, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Au, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Nuclear matter incompressibility coefficient in relativistic and nonrelativistic microscopic models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' C 2003, 68, 031304.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Todd-Rutel, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Piekarewicz, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Neutron-rich nuclei and neutron stars: A new accurately calibrated interaction for the study of neutron-rich matter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2005, 95, 122501.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Audi, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Wapstra, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Thibault, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The Ame2003 atomic mass evaluation: (II).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Tables, graphs and references.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' A 2003, 729, 337.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Myers, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Swiatecki, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Average nuclear properties Ann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 1969, 55, 395.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 27 of 29 34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Dutra, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Loureno, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Martins, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Delfino, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Stone, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Stevenson, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Skyrme interaction and nuclear matter constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2012, C85, 035201.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Tews, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lattimer, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Ohnishi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Kolomeitsev, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Symmetry parameter constraints from a lower bound on neutron-matter energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2017, 848, 105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Dutra, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Loureno, Avancini, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Carlson, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Delfino, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Menezes, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Providencia, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Typel, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' and Stone, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Relativistic mean-field hadronic models under nuclear matter constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2014, C90, 055203.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Tagami, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Wakasa, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Takechi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Matsui, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Yahiro, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Neutron skin in 48Ca determined from p+48Ca and 48Ca+12C scattering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' arXiv 2022, arXiv:2201.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='08541.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Kortelainen, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lesinski, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Moré, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Nazarewicz, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Sarich, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Schunck, NStoitsov, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Wild, Nuclear energy density optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' C 2010, 82, 024313.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Drischler, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Furnstahl, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Melendez, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phillips, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' How well do we know the neutron-matter equation of state at the densities inside neutron stars?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' A Bayesian approach with correlated uncertainties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2020, 125, 202702.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Weinberg, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Precise relations between the spectra of vector and axial-vector mesons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 1967, 18, 507.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Weinberg, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Nonlinear realizations of chiral symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 1968, 166, 1568.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Epelbaum, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Hammer, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='-W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Meissner, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='-G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Modern theory of nuclear forces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2009, 81, 1773.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Machleidt, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Entem, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Chiral effective field theory and nuclear forces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2011, 503, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Hammer, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='-W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' König, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' van Kolck, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Nuclear effective field theory: Status and perspectives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2020, 92, 025004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Tews, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Davoudi, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Ekström;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Holt, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lynn, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' New Ideas in Constraining Nuclear Forces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2020, 47, 103001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Drischler, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Hebeler, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Schwenk, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Chiral interactions up to next-to-next-to-next-to-leading order and nuclear saturation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2019, 122, 042501.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Leonhardt, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Pospiech, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Schallmo, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Braun, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Drischler, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Hebeler, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Schwenk, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Symmetric nuclear matter from the strong interaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2020, 125, 142502 48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Drischler, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Han, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lattimer, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Prakash, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Reddy, 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phillips, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Quantifying uncertainties and correlations in the nuclear-matter equation of state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Danielewicz, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Famiano, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Li, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='-X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lynch, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Steiner, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Constraints on the density dependence of the symmetry energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2009, 102, 122701.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Hebeler, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lattimer, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Pethick, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Schwenk, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Constraints on Neutron Star Radii Based on Chiral Effective Field Theory Interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2010, 105, 161102 52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Ku, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Sommer, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Cheui, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Zwierlein, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Revealing the superfluid lambda transition in the universal thermodynamics of a unitary Fermi gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Science 2012, 335, 563.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Zürn, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lompe, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Wenz, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Jochim, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Julienne, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Hutson, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Precise characterization of 6Li Feshbach resonances using trap-sideband-resolved RF spectroscopy of weakly bound molecules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2013, 110, 135301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Zhao, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lattimer, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Tidal deformabilities and neutron star mergers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' D 2018, 98, 063020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Brown, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Neutron radii in nuclei and the neutron equation of state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2000, 85, 5296.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Centelles, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Roca-Maza, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Vinas, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Warda, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Nuclear symmetry energy probed by neutron skin thickness of nuclei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2009, 102, 122502.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Typel, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Brown, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Neutron radii and the neutron equation of state in relativistic models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' C 2001, 64, 027302.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Xu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Xie, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Li, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='-A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Bayesian inference of nuclear symmetry energy from measured and imagined neutron skin thickness in 116,118,120,122,124,130,132Sn, 208Pb, and 48Ca.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' C 2020, 102, 044316.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Zhang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Chen, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='-W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Constraining the symmetry energy at subsaturation densities using isotope binding energy difference and neutron skin thickness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' B 2013, 726, 234.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Brown, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Mirror charge radii and the neutron equation of state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2017, 119, 122502.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Furnstahl, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Neutron radii in mean-field models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2002, A706, 85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Reinhard, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='-G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Roca-Maza, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Nazarewicz, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Information content of the parity-violating asymmetry in 208Pb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2021, 127 232501.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Horowitz, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Kumar, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Michaels, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Electroweak measurements of neutron densities in CREX and PREX at JLab, USA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' A 2014, 50, 48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Piekarewicz, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Agrawal, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Colò, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Nazarewicz, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Paar, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Reinhard, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='-G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Roca-Maza, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Vretenar, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Electric dipole polarizability and the neutron skin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' C 2012, 85 041302.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Hagen, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Ekström, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Forssén, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Jansen, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Nazarewicz, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Papenbrock, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Wendt, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Bacca, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Barnea, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Carlsson, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Neutron and weak-charge distributions of the 48Ca nucleus Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2016, 12, 186.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Hu, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Jiang, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Miyagi, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Sun, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Ekström, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Forssén, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Hagen, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Holt, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Papenbrock, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Stroberg, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Ab initio predictions link the neutron skin of 208Pb to nuclear forces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Nature Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2021, 18, 1196.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 28 of 29 67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Atkinson, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Mahzoon, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Keim, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Bordelon, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Pruitt, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Charity, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Dickhoff, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Dispersive optical model analysis of 208Pb generating a neutron-skin prediction beyond the mean field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' C 2020, 101, 044303.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Mahzoon, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Atkinson, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Charity, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Dickhoff, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Precision Determination of the Neutral Weak Form Factor of 48Ca.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2017, 119, 22503.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Reinhard, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='-G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Piekarewicz, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Nazarewicz, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Agrawal, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Paar, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Roca-Maza, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Information content of the weak-charge form factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' C 2013, 88, 034325.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Ray, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='Neutron isotopic density differences deduced from 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='8 GeV polarized proton elastic scattering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' C 1979, 19, 1855.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Zenhiro, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Sakaguchi, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Terashima, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Uesaka, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Hagen, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Itoh, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Murakami, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Nakatsugawa, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Ohnishi, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Sagawa, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Direct determination of the neutron skin thicknesses in 40,48Ca from proton elastic scattering at Ep=295 MeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' arXiv 2018, arXiv:1810.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='11796.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Clark, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Kerr, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Hama, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Neutron densities from a global analysis of medium-energy proton-nucleus elastic scattering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' C 2003, 67, 054605.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Friedman, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Neutron skins of 208Pb and 48Ca from pionic probes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' A 2012, 896, 46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Gibbs, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Dedonduer, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='-P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Neutron radii of the calcium isotopes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' C 1992, 46, 1825.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Gils, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rebel, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Friedman, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Isotopic and isotonic differences between α particle optical potentials and nuclear densities of 1f 7 2 nuclei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' C 1984, 29, 1295.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Shlomo, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Schaeffer, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The difference between neutron and proton radii in the Ca isotopes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' B 1979, 83, 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Tarbert, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Watts, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Glazier, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Aguar, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Ahrens, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Annand, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Arends, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Beck, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Bekrenev, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Boillat, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Neutron Skin of 208Pb from Coherent Pion Photoproduction Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2014, 112, 242502.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Brown, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Shen, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Hillhouse, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Meng, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Trzcinska, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Neutron skin deduced from antiprotonic atom data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' C 2007, 76, 034305.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Brown, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Shen, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Hillhouse, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Meng, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Trzcinska, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Neutron density distributions from antiprotonic 208Pb and 209 Bi atoms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' C 2007, 76, 014311.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Zenhiro, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Sakaguchi, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Murakami, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Yosoi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Yasuda, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Terashima, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Iwao, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Takeda, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Itoh, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Yoshida, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Neutron density distributions of 204,206,208Pb deduced via proton elastic scattering at Ep=295 MeV Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' C 2010, 82, 044611.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Starodubnsky, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Hintz, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Extraction of neutron densities from elastic proton scattering by 206,207,208Pb at 650 MeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' C 1994, 49, 2118.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Klimkiewicz, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Paar, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Adrich, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Fallot, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Boretzky, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Aumann, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Cortina-Gil, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Pramanik, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Elze, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=', Emling, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Nuclear symmetry energy and neutron skins derived from pygmy dipole resonances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' C 2007, 76, 051603.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Chen, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='-W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Ko, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Li, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='-A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Xu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Density slope of the nuclear symmetry energy from the neutron skin thickness of heavy nuclei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' C 2010, 82, 024321.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Yasuda, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Wakasa, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Okamoto, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Dozono, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Hatanaka, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Ichimura, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Kuroita, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Maeda, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Noro, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Sakemi, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Anti-Analog Giant Dipole Resonance and the Neutron Skin in 208Pb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' JPS Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2014, 1, 013036.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Dong, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Zuo, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Gu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Constraints on neutron skin thickness in 208Pb and density-dependent symmetry energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' C 2015, 91, 034315.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Pruitt, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Charity, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Sobotka, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Atkinson, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Dickhoff, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Systematic Matter and Binding-Energy Distributions from a Dispersive Optical Model Analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2020, 125, 102501.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Zyla, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Barnett, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Beringer, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Dahl, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Dwyer, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Groom, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lin, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lugovsky, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Pianori, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Robinson, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Review of Particle Physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Prog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Theor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Exp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2020, 2020, 083C01.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Danielewicz, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lee, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Symmetry energy II: Isobaric analog states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' A 2014, 922, 1–70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Roca-Maza, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Viñas, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Centelles, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Agrawal, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Colò, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Paar, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Piekarewicz, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Vretenar, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Neutron skin thickness from the measured electric dipole polarizability in 68Ni, 120Sn, and 208 Pb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' C 2015, 92, 064304.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Roca-Maza, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Brenna, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Colò, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Centelles, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Viñas, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Agrawal, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Paa, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Vretenar, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Piekarewicz, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='R Electric dipole polarizability in 208Pb: Insights from the droplet model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' C 2013, 88, 024316 91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Tamii, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Complete Electric Dipole Response and the Neutron Skin in 208 Pb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2011, 107, 062502.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Hashimoto, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Krumbholz, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Reinhard, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Tamii, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' von Neumann-Cosel, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Adachi, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Aoi, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Bertulani, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Fujita, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Fujita, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Dipole polarizability of 120 Sn and nuclear energy density functionals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' C 2015, 92, 031305.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Birkhan, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Miorelli, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Bacca, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Bassauer, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Bertulani, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Hagen, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Matsubara, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' von Neumann-Cosel, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Papenbrock, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Pietralla, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Electric Dipole Polarizability of 48 Ca and Implications for the Neutron Skin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2017, 118, 252501.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Trippa, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Coló, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Vigezzi, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Giant dipole resonance as a quantitative constraint on the symmetry energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' C 2008, 77, 061304.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Zhang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Chen, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='-W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Electric dipole polarizability in 208Pb as a probe of the symmetry energy and neutron matter around ρ0/3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' C 2015, 92, 031301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Piekarewicz, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Implications of PREX-2 on the electric dipole polarizability of neutron rich nuclei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' C 2021, 104, 024329.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 29 of 29 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Terashima, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Sakaguchi, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Takeda, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Ishikawa, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Itoh, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Kawabata, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Murakami, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Uchida, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Yasuda, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Yosoi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Proton elastic scattering from tin isotopes at 295 MeV and systematic change of neutron density distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' C 2008, 77, 024317.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Karsznahorkay, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Fujiwara, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' van Aarle, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Akimune, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Daito, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Fujimura, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Fujita, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Harakeh, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Inomata, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Jänecke, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Excitation of Isovector Spin-Dipole Resonances and Neutron Skin of Nuclei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 1999, 82, 3216.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Trzcinska, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Jastrze¸bski, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lubi´nski, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Hartmann, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Schmidt, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' von Egidy, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Kłos, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Neutron Density Distributions Deduced from Antiprotonic Atoms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2001, 87, 082501.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Xie, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Li, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='-A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Bayesian inference of the incompressibility, skewness and kurtosis of nuclear matter from empirical pressures in relativistic heavy-ion collisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' G Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Part.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2021, 48, 025110.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 101.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Fuchs, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Kaon production in heavy ion reactions at intermediate energies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Prog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Part.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2006, 56, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Danielewicz, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lacey, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lynch, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The Equation of State of Nuclear Matter and Neutron Stars Properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Science 2002, 298, 1592.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Laue, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Sturm, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Böttcher, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' De¸bowski, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Förster, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Grosse, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Koczo´n, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Kohlmeyer, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Mang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Naumann, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Medium Effects in Kaon and Antikaon Production in Nuclear Collisions at Subthreshold Beam Energies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 1999, 82, 1640.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Ivanov, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Stienike, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Ryabchikov, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Adams, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Adams, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Bar-Yam, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Bishop, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Bodyagin, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Brown, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Cason, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Observation of Exotic Meson Production in the Reaction π−p → η′π−p at 18 GeV/c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2001, 86, 3977–3980.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Partlan, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Albergo, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Bieser, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Brady, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Caccia, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Cebra, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Chacon, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Chance, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Choi, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Costa, S;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Fragment Flow in Au +Au Collisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 1995, 75, 2100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Liu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Ajitanand, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Alexander, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Anderson, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Best, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Brady, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Case, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Caskey, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Cebra, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Chance, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Sideward Flow in Au+Au Collisions between 2A and 8A GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2000, 84, 5488 107.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Pinkenburg, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Ajitanand, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Alexander, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Anderson, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Best, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Brady, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Case, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Caskey, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Cebra, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Chance, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Elliptic Flow: Transition from Out-of-Plane to In-Plane Emission in Au+Au Collisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 1999, 83, 1295.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 108.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Braun-Munzinger, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Stachel, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Dynamics of ultra-relativistic nuclear collisions with heavy beams: An experimental overview Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' A 1998, 638, 3c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Xiao, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Li, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='-A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Chen, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='-W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Yong, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Zhang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Circumstantial Evidence for a Soft Nuclear Symmetry Energy at Suprasaturation Densities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2009, 102, 062502.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 110.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Feng, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='-Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Jin, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='-M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Probing high-density behavior of symmetry energy from pion emission in heavy-ion collisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' B 2010, 683, 140.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 111.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Xie, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Su, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Zhu, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Zhang, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Symmetry energy and pion production in the Boltzmann-Langevin approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' B 2013, 718, 1510.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 112.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Tsang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Liu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Shi, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Danielewicz, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Gelbke, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Liu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lynch, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Tan, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Verde, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Wagner, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Isospin Diffusion and the Nuclear Symmetry Energy in Heavy Ion Reactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2004, 92, 062701.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 113.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Liu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='-X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lynch, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Tsang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Liu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Shomin, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Tan, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Verde, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Wagner, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Xi, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Xu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Isospin diffusion observables in heavy-ion reactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' C 2007, 76, 034603.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 114.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Famiano, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Liu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lynch, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Mocko, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rogers, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Tsang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Wallace, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Charity, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Komarov, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Sarantites, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Neutron and proton transverse emission ratio measurements and the density dependence of the asymmetry term of the nuclear equation of state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2006, 97, 052701.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 115.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Cozma, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Leifels, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Trautmann, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Li, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Russotto, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Toward a model-independent constraint of the high-density dependence of the symmetry energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' C 2013, 88, 044912.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 116.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Yong, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Guo, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='-F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Probing High-density Symmetry Energy Using Heavy-ion Collisions at Intermediate Energies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2020, 37, 136.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 117.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Cozma, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Tsang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' In-medium ∆(1232) potential, pion production in heavy-ion collisions and the symmetry energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' A 2021, 57, 309.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 118.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Jhang, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Estee, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Barney, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Cerizza, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Kaneko, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lee, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lynch, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Isobe, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Kurata-Nishimura, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Murakami, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Symmetry energy investigation with pion production from Sn+Sn systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' B 2021, 813, 136016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 119.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Abbott, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Abbott, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Abbott, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Acernese, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Ackley, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Adams, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Adams, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Addesso, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Adhikari, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Adya, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2017, 119, 161101.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 120.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Raaijmakers, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Greif, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Hebeler, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Hinderer, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Nissanke, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Schwenk, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Riley, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Watts, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lattimer, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Ho, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Constraints on the Dense Matter Equation of State and Neutron Star Properties from NICER’s Mass–Radius Estimate of PSR J0740+6620 and Multimessenger Observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Ap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2021, 918, L29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 121.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lattimer, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lim, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Constraining the Symmetry Parameters of the Nuclear Interaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2013, 771, 51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 122.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Lattimer, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' The Nuclear Equation of State and Neutron Star Masses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Annu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Part.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} +page_content=' 2012, 62, 485.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtE2T4oBgHgl3EQfHQZr/content/2301.03666v1.pdf'} diff --git a/gtFMT4oBgHgl3EQf2zH5/content/tmp_files/2301.12446v1.pdf.txt b/gtFMT4oBgHgl3EQf2zH5/content/tmp_files/2301.12446v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..9e401a27abc5da92e09cd44190a730402c053999 --- /dev/null +++ b/gtFMT4oBgHgl3EQf2zH5/content/tmp_files/2301.12446v1.pdf.txt @@ -0,0 +1,1640 @@ +The escape transition in a self-avoiding walk model of linear polymers +EJ Janse van Rensburg1 +1Department of Mathematics and Statistics, York University, Toronto, Ontario M3J 1P3, Canada +E-mail: ‡rensburg@yorku.ca +31 January 2023 +Abstract. +A linear polymer grafted to a hard wall and underneath an AFM tip can be modelled in a lattice +as a grafted lattice polymer (or self-avoiding walk) compressed underneath a piston approaching the wall. +As the piston approaches the wall the increasingly confined polymer escapes from the confined region to +explore conformations beside the piston. This conformational change is believed to be a phase transition in +the thermodynamic limit, and has been argued to be first order, based on numerical results in reference [12]. +In this paper a lattice self-avoiding walk model of the escape transition is constructed. It is proven that +this model has a critical point in the thermodynamic limit corresponding to the escape transition of grafted +linear polymers being compressed by a piston. This result relies on the analysis of ballistic self-avoiding +walks in slits and slabs in the square and cubic lattices. Additionally, numerical estimates of the location of +the escape transition critical point is reported based on Monte Carlo simulations of self-avoiding walks in +slits and in slabs. +Keywords: Escape transition, linear polymer, self-avoiding walk, ballistic walk, slits and slabs +1. Introduction +The properties of polymers grafted to hard walls or interfaces, or in confined geometries, are of significant +interest in polymer physics [5]. These properties underlie important applications of polymers, including the +stabilization of colloids [6, 20, 22, 36], the in vivo adsorption and delivery of drugs using polymer coatings +on medical devises, such as stents [2, 17, 30], the behaviour of biopolymers at cell membranes [9], or the +interaction of grafted polymers and small particles [31], amongst many other examples. +Confinement and manipulation of single polymer molecules have become possible using atomic force +microscopy (AFM). Confining a polymer which is grafted to hard wall by an approaching tip of the atomic +force microscope reduces the conformational degrees of freedom of the polymer, and it may undergo an +“escape” transition where part of it escapes from underneath the tip to explore conformations in the region +beside the tip [8]. +A lattice model of a grafted linear polymer being compressed by the AFM tip is shown in figure 1. A +lattice self-avoiding walk is grafted at the origin in the hard wall (or “anvil”), and explores its conformations +in a space Σw above the anvil and below or outside the AFM tip (the “piston”). If the piston is far above +the anvil, then Σw is large, and the walk explores it conformations primarily below the piston. As the piston +approaches the anvil, the conformational degrees of freedom of the walk is reduced, and the walk eventually +escapes from the space below the piston. In this case the walk is stretch to the boundary of the piston, and +its remaining part (or “tail”) explores conformations primary outside the piston (rather than below it). +The model in figure 1 is a lattice version of models examined in a series of excellent papers [8,12,21,24] +exploring the scaling and transition in linear and star polymers compressed by a piston. Additional numerical +results on star polymers can be found in references [26, 27]. These studies are of bead-spring models [21], +lattice models [12], and molecular dynamics simulations [24]. While an escape transition is not established +rigorously in these models, there are ample numerical evidence in these models of such a transition. In +references [8,21] a theoretical approach using phenomenological arguments based on a “blob” analysis (see, +for example, [5]) of the confined polymer is pursued. The analysis in reference [8] proceeds by considering +arXiv:2301.12446v1 [cond-mat.soft] 29 Jan 2023 + +the free energy as a function of the separation between the anvil and the piston, while reference [21] proceeds +by considering the escape transition as a function of the force f exerted on the piston by the polymer (this +force is conjugate to the separation of the anvil and piston). In these references the phenomenological blob +analysis and numerical simulations using a bead-spring and other models show convincing evidence of an +escape transition in two dimensions. However, the order of the transition is still unresolved [12]. +1.1. Lattice models and main results +Let cn be the number of self-avoiding walks from the origin in the d-dimensional hypercubic lattice. Then +the growth constant µd of the self-avoiding walk is defined by +log µd = lim +n→∞ +1 +n log cn. +(1) +The growth constant has been estimated to high accurancy in the square and cubic lattices, namely +µd = +� +2.63815853032790(3), +if d = 2 (square lattice) [13]; +4.684039931(27), +if d = 3 (cubic lattice) [4] . +(2) +If the walk is confined by boundaries in the lattice, then the value of the growth constant may change, and +this is in particular the case if the walk is confined by a piston when it is grafted to a piston. In figure 1 +a square lattice model of a piston of radius R compressing a self-avoiding walk against an anvil is shown. +As the piston approaches the anvil, the polymer is confined to a region Σw, which consists of the space +underneath and beside the piston and above the anvil. The thermodynamic limit in this model is taken by +fixing the ratio of the piston radius R to the length of the walk n, and then to take n → ∞ with R/n fixed. +In the lattice geometry this is achieved by putting R = ⌊λn⌋, as illustrated in figure 2. In this paper it is +shown that, in the thermodynamic limit, there exists a phase transition in this model, in both the square +and cubic lattices. +In the lattice model in figure 1 the origin is located on the anvil centered underneath the piston. In +the square lattice the piston is a rectangle with vertical bisector running through the origin. In the cubic +lattice, the piston may be assumed to have a square or circular horisontal projection onto the anvil, and its +vertical symmetry axis runs through the origin. The linear polymer is a self-avoiding walk of length n from +the origin (or grafted at the origin), and confined to explore conformations in Σw. +• 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+Piston +Anvil +Σw +.................................................................................................... +................................ ................................................................................................................................................................................. +.................................................................................................................................................................................................. ................................ +R +n +.............................................................................................................................................................................................................. +Figure 1: A lattice model of a linear polymer grafted to a surface (the “anvil”) and being squeezed by a piston approaching +the anvil. If the polymer is long, then part of it may escape from the confining space underneath the piston into the +bulk region beside the piston. +The vertical distance between the anvil and the piston is w, and the radius of the piston is the length of +the shortest self-avoiding walk from the origin to a vertex underneath the edge of the piston. If a piston has +radius ⌊λn⌋, then the number of self-avoiding walks of length n from the origin in Σw is denoted by wn(λ). +The free energy of this model, per unit length, is given by +ρn(λ) = 1 +n log wn(λ). +(3) +2 + +The limit of ρn(λ) as n → ∞ is the limiting free energy of the model, and should be compared to log µd in +equation (1). In this paper we show that for a range of values of λ the limit in equation (3) exits. The main +result is theorem 1. +Theorem 1. Define λ0 = 1/(w+1) in the square lattice, and λ0 = 0 in the cubic lattice. Then there exists +a λ1 ∈ [λ0, 1) such that the limiting free energy of a walk from the origin in Σw is given by +ρ(w)(λ) = lim +n→∞ +1 +n log wn(λ) +for every λ ∈ [λ1, 1] in the square lattice, or in the cubic lattice. +In figure 2 the region underneath the piston and above the anvil is denoted by Sw(λ). Notice that +Sw(λ) does not extend beyond the edge of the piston, and so is a finite part of the square lattice (that is, +Sw(λ) ⊂ Σw). Sw(λ) is similarly defined in the cubic lattice, underneath the piston, and above the anvil, +and it also does not extend beyond the boundary of the piston in any direction. In the square lattice Sw(λ) +is a slitof length 2⌊λn⌋, and in the cubic lattice it is a slab of radius ⌊λn⌋. +•••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• +•••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• +···················································································································································································································································································································· +• +• +······························································································································ +w +·············································································································································································································································································································································································································· ······················ +⌊λn⌋ +n +Sw(λ) +········································································································································ +················································ +················································ +Figure 2: Schematic of a walk of length n being squeezed by a piston of radius ⌊λn⌋ with λ > 1. In this case the walk +is confined to the slit or slab Sw(λ) underneath the piston and above the anvil. Notice that Sw(λ) does not extend +beyond the edge of the piston. +The radius of the piston is ⌊λn⌋, so that if λ > 1, then a walk of length n is entirely confined to Sw(λ). +This is shown schematically in figure 2. In the limit as n → ∞, Sw(λ) becomes a slit or a slab of infinite +extent denoted by Sw(∞) ≡ Sw, and the walk is confined to it, even as the limit n → ∞ is taken. +Let c(w) +n +be the number of self-avoiding walks from the origin in Sw(∞) of height w ≥ 0. It is known +that the limit +lim +n→∞ +1 +n log c(w) +n += log µ(d) +w +(4) +exists in the square and cubic lattices [32]. In the case that λ ≥ 1, wn(λ) = c(w) +n +for all n ≥ 0, since the +piston is wide enough to confine all the conformations of a walk of length n to Sw(λ). This shows that +ρ(λ) = log µ(d) +w , +if λ ≥ 1. +(5) +Moreover, ρ(w)(λ) → log µd as w → ∞ and λ ≥ 1. +On the other hand, if 0 ≤ λ < 1, then the walk may be partially inside Sw(λ) and then escape into +the bulk regime outside Sw(λ), as illustrated schematically in figure 3. If the walk escapes into the bulk as +shown, then it has a first part of length ⌊δn⌋ from the origin to its first vertex underneath the edge of the +piston before it steps outside Sw(λ). The remaining part of the walk has length n−⌊δn⌋ and explores its +conformations in Σw (that is, it may reenter Sw(λ)). Notice that λ ≤ δ < 1 in figure 3. In section 3 we show +that exists a λc such that ρ(w)(λ) = log µ(d) +w +if λ > λc, and ρ(w)(λ) > log µ(d) +w +if λ < λc. That is, ρ(w)(λ) has +a non-analytic point at λc ∈ [0, 1), and that this critical point corresponds to the escape transition of the +walk. +This paper is organised as follows. In section 2 models of ballistic walks in slits and slabs in the square +and cubic lattice are examined. Existance of a thermodynamic limit is proven in these cases using unfolded +loops and walks in a slit or in a slab. These results are then used in section 3 to examine the full model of +3 + +••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• +•••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• +··································································································································································································································································································································································································································································································································································· +• +• +• +······························································································································ +w +····································································································································································································· ······················ +⌊λn⌋ +⌊δn⌋ +n − ⌊δn⌋ +Sw(λ) +Σw +x +············································································································································ +················································ +················································ +Figure 3: Schematic of a walk of length n escaping from Sw(λ) underneath the piston. In this case the piston has radius +⌊λn⌋, and λ < 1. The walk exits the slit or slab Sw(λ) for the first time at x and its part from the origin to x has length +⌊δn⌋ and is confined to Sw(λ). The remaining part of length n − ⌊δn⌋ starts at x and may reenter and reexist Sw(λ). +Clearly, λ ≤ δ ≤ 1. +walks underneath the piston and the escape transition. Existence of a critical point λc is established, and a +lower bound on it is proven, namely +λc ≥ log(µd/µ(d) +w ) +log µd +. +(6) +In addition to these results, numerical simulations of walks in a slit or slab using the PERM algorithm [7] +in its flat histogram [25] version, and with a parallel implementation [1], were done to determine the free +energy of ballistic walks in a slit or a slab. Combining these results with the expressions for the free energy +of walks underneath a piston gives numerical approximations of λc, as shown in table 2. +2. Ballistic self-avoiding walks in slits and slabs +Denote the coordinates of vertices v ∈ Zd in the hypercubic lattice by (x1(v), x2(v), · · · , xd(v)) and recall +that Sw ≡ Sw(∞) so that +Sw = {v ∈ Zd | 0 ≤ xd(v) ≤ w}. +(7) +The height of Sw is w. As before, the number of self-avoiding walks of length n from the origin in Sw is +denoted by c(w) +n +and the growth constant µ(d) +w +of these walks is given in equation (4). +Generally log µ(d) +w +< log µ(d) +w+1 [28,29] and limw→∞ log µ(d) +w += log µd where µd is the growth constant of +the self-avoiding walk in d dimensions (see reference [34] for more results and references [3, 16, 33–35] for +additional results and in particular lemma 8.18 and theorem 8.19 in reference [14]). In the square lattice +log µ(2) +0 += 0 and log µ(2) +1 +> 0 while in the cubic lattice log µ(3) +0 += log µ2. +If w → ∞, then µ(d) +w → µd, the growth constant of self-avoiding walks, as noted above. In addition, +1 = µ(2) +0 +< µ(2) +w < µ(2) +w+1 < µ2, +(8) +1 < µ2 < µ(3) +w < µ(3) +w+1 < µ3 +(9) +In addition, µ2 = µ(3) +0 . +The number c(w) +n +of self-avoiding walks from the origin in Sw, of length n, is a lower bound on +the number of walks in Sw(λ). +Thus, wn(λ) ≥ c(w) +n , since every walk in Sw is also a walk in Sw(λ). +Thus, lim infn→∞ 1 +n log wn(ϵ) ≥ limn→∞ 1 +n log c(w) +n . +If λ ≥ 1, then wn(λ) = c(w) +n +with the result that +limn→∞ 1 +n log wn(ϵ) = limn→∞ 1 +n log c(w) +n . Using equation (4) this gives theorem 2. +Theorem 2. For all λ ≥ 0, +lim inf +n→∞ +1 +n log wn(λ) ≥ lim +n→∞ +1 +n log c(w) +n += log µ(d) +w . +If λ ≥ 1, ρ(w)(λ) = limn→∞ 1 +n log wn(λ) = log µ(d) +w . +4 + +2.1. Ballistic walks in Sw +A self-avoiding walk ω = (ω0, ω1, . . . , ωn) of length n in Sw with |x1(ω0) − x1(ωn)| = s is a ballistic walk of +span s. That is, the span of the ballistic walk is the absolute difference between the x1-coordinates of its +first and last vertices, and an example is illustrated in the left panel of figure 4. +A ballistic walk ω of span s is unfolded if x1(ω0) < x1(ωi) ≤ x1(ωn). That is, the walk steps from its +unique left-most vertex ω0 in the x1-direction to ω1, and finally terminates in a right-most vertex ωn. An +unfolded walk is illustrated in the right panel in figure 4. The walk is also a loop of span s (figure 4(right)), +which are unfolded walks from the origin in Sw with last vertex of height xd(ωn) = 0. Define +c(w) +n (s) += # {ballistic walks from the origin in Sw of length n and span s} +c(†,w) +n +(s) = # {unfolded ballistic walks from the origin in Sw of length n and span s} +ℓ(w) +n (s) += # {ballistic loops from the origin in Sw of length n and span s} . +Sw +Sw +• +• +• +• +••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• 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+....................................................................................................................................... +...................... +....................................................................................................................................... ...................... +s +............................................................................................................................................................................. +...................... +............................................................................................................................................................................. ...................... +s +Figure 4: Ballistic walks ω = (ω0, ω1, . . . , ωn) from the origin in Sw. (Left) This walk has span s = |x1(ω0) − x1(ωn)|. +(Right) An unfolded self-avoiding walk of span s. In this walk x1(ω0) < x1(ωi) ≤ x1(ωn) for all 1 ≤ i ≤ n so that the +origin is the unique left-most vertex, the first step from the origin is in the x1-direction, and the last vertex ωn is a +right-most vertex. Since the heights of the first and last vertices in ω is zero, this unfolded walk is also a loop. +2.1.1. Ballistic loops in Sw +A loop of length n and span s in Sw can be concatenated with a loop of length +m and span t in Sw by placing the first vertex of the second loop on the last vertex of the first loop. The +result is another loop of length n+m and span s+t in Sw. Since there are ℓ(w) +n (s) choices for the first loop, +and ℓ(m) +m (t) choices for the second loop, +ℓ(w) +n (s) ℓ(w) +m (t) ≤ ℓ(w) +n+m(s+t). +(10) +Notice that ℓ(w) +n (s) > 0 if ⌈n/(w+1)⌉ ≤ s ≤ n in the square lattice (the lower bound follows by packing a +loop densely into a slit of height w). In three dimensions, ℓ(w) +n (s) > 0 if 0 ≤ s ≤ n. Define +λ0 = +� +1/(w+1), +if d = 2; +0, +if d = 3. +(11) +Then the following theorem follows. +Theorem 3. The limit log Lw(λ) = +lim +n→∞ +1 +n log ℓ(w) +n (⌊λn⌋) exists and is a concave function of λ for +λ ∈ (λ0, 1). Moreover, +sup +λ∈(0,1) +log Lw(λ) = log µ(d) +w . +Proof. Existence of the limit and concavity follows from equation (10) and by lemma 1 and theorem 2 in +reference [15]. +Since ℓ(w) +n (n) = 2 in both the square lattice and the cubic lattice it follows that log Lw(1) = 0. It is also +the case that log Lw(λ) is left-continuous at λ = 1. +Lemma 1. +lim +λ→1− log Lw(λ) = log Lw(1) = 0. Thus, log Lw(λ) is left-continuous at λ = 1, and therefore +left-continuous on (λ0, 1]. +5 + +Proof. Observe that ℓ(w) +n (s) ≥ 1 for s ≤ n. Thus, for λ ∈ (λ0, 1], log Lw(λ) = lim +n→∞ +1 +n log ℓ(w) +n (⌊λn⌋) ≥ 0. +On the other hand, ℓ(w) +n (s) is bounded above by the number of random walks of length n and with span +s. Selecting s steps of a random walk to be East (to the right), and then over-counting by allowing the +remaining n−s steps to be in an arbitrary directions, +ℓ(w) +n (s) ≤ +�n +s +� +(2d)n−s. +Put s = ⌊λn⌋, take the power 1/n of the above, and let n → ∞. This gives +log Lw(λ) ≤ lim +n→∞ log +�� n +⌊λn⌋ +�1/n +(2d)1−⌊λn⌋/n +� += log +� +(2d)1−λ +λλ (1 − λ)1−λ +� +. +Take λ → 1− to complete the proof. +An additional and useful result is given by theorems 4 and 5 in reference [15]. +Theorem 4. Suppose that (kn) is a sequence such that limn→∞(kn/n) = λ ∈ (λ0, 1]. Then the limit +lim +n→∞ +1 +n log ℓ(w) +n (kn) = log Lw(λ) +exists. +Next, define the functions ℓn(≤s) = �s +t=0 ℓn(t) and ℓn(≥s) = �n +t=s ℓn(t). By reference [15] the following +limits exist. +Theorem 5. The following limits exist for λ ∈ (λ0, 1) +log Lw(≤λ) = lim +n→∞ +1 +n log ℓn(≤⌊λn⌋), and log Lw(≥λ) = lim +n→∞ +1 +n log ℓn(≥⌊λn⌋). +log Lw(≤λ) and log Lw(≥λ) are concave functions on (λ0, 1), and log Lw(λ) = min(log Lw(≤λ), log Lw(≥λ)) +and max(log Lw(≤λ), log Lw(≥λ)) = log µ(d) +w . In addition, log Lw(≤λ) is non-decreasing while log Lw(≥λ) +is non-increasing. +Proof. The proof of this theorem follows from theorem 6 in reference [15]. +The minimum span s(min) +n +of a loop of length n in Sw for w > 0 in the square lattice is at least ⌊n/(w+1)⌋ +and at most ⌈n/(w+1)⌉ + 1. In the cubic lattice s(min) +n += 1 for all n ≥ 1 and w > 0. Define +log Lw(λ0) def += +lim +λ→λ+ +0 +log Lw(λ) ≥ lim sup +n→∞ +1 +n log ℓ(w) +n (s(min) +n +). +(12) +This defines log Lw(λ) to be a concave function on [λ0, 1] in the square and cubic lattices. In the square +lattice, λ0 = 1/(w+1) and log Lw(λ0) = 0 if w ∈ {0, 1} and log Lw(λ0) > 0 if w ≥ 2. Notice that if w = 0 +then log Lw(λ0) = 0 of λ0 = 1 and it is not defined otherwise, and if w = 1, then 1/2 ≤ λ0 ≤ 1. +In the cubic lattice log Lw(0) = log µ(2) +w where µ(2) +w is the square lattice growth contant of walks in a slit +of width w. That is, log Lw(0) = 0 if w = 0 and log Lw(0) > 0 if w ≥ 1. Collecting these gives +log Lw(λ0) def += +lim +λ→λ+ +0 +log Lw(λ) +� +� +� +� +� +� +� +� +� +� +� +� += 0, +if w ≤ 1; +> 0, +if w ≥ 2; +if d = 2; +� += 0, +if w = 0; +> 0, +if w ≥ 1; +if d = 3. +(13) +A pattern theorem [11,18,19] for walks and loops in Sw in either the square or cubic lattice was proven +in reference [28] for w ≥ 0 (see section 8.3 in reference [14]). +6 + +Lemma 2. In the square lattice there exists a λ1 > λ0 such that for all λ ∈ [λ0, λ1), +log Lw(λ) = lim +n→∞ +1 +n log ℓ(w) +n (⌊λn⌋) < lim +n→∞ +1 +n log ℓ(w) +n += log µ(d) +w +provided that w ≥ 1. +Proof. Let P be a pattern consisting of two consecutive steps in the x1-direction. That is, P = (ν0, ν1, ν2) +with x1(ν0) + 1 = x1(ν1) = x1(ν2) − 1 and xj(ν0) = xj(ν1) = xj(ν2) for 2 ≤ j ≤ d. In addition, let P require +all vertices v ∈ Sw with x1(v) = x1(ν1) to be unoccupied by the walk. P occurs at the i-th vertex ωi in a +walk ω if P can be translated such that ν1 = ωi so that νj = ωi+j−1 for j = 0, 1, 2 while all vertices v ∈ Sw +with x1(v) = x1(ωi) and v ̸= ωi is not in ω (that is, v ̸∈ ω). +If P occurs k times in a walk ω of length n, then the span s of ω is at least k + ⌊n/(w+1)⌋. Conversely, +if the span of a walk is s = k + ⌊n/(w+1)⌋, then the number of occurances of P is at most k. Denote by +ℓ(w) +n +the number of loops of length n from the origin in Sw, and by ℓ(w) +n (#P≤k) the number of loops from +the origin in Sw in which the pattern P occurs at most k times. +Since ℓ(w) +n (s) containes the pattern P at most s−⌊n/(w+1)⌋ times, it follows that for λ > 1/(w+1) = λ0, +ℓ(w) +n (⌊λn⌋) ≤ ℓ(w) +n (#P≤⌊λn⌋−⌊λ0n⌋) ≤ ℓ(w) +n . +Take the logarithms of these inequalities, divide by n and take the limit superior as n → ∞. This shows +that +log Lw(λ) ≤ lim sup +n→∞ +1 +n log ℓ(w) +n (#P≤⌊λn⌋−⌊λ0n⌋) ≤ log µ(2) +w . +By the pattern theorem for loops in Sw there exists a λ∗ > λ0 such that for all λ ∈ [λ0, λ∗], +lim sup +n→∞ +1 +n log ℓ(w) +n (#P≤⌊λn⌋−⌊λ0n⌋) < log µ(2) +w , +in particular also since ℓ(w) +n (#P≤k) is a non-decreasing function of k. This shows that for all λ ∈ [λ0, λ∗], +log Lw(λ) ≤ log µ(2) +w . This completes the proof. +Underlying lemma 2 is the fact that a square lattice self-avoiding walk in Sw is ballistic. That is, in the +case of a loop of length n, the span s = O(n). Presumably this is not the case in Sw in the cubic lattice +where one expects s = o(n). Since loops of length n and span ⌊λn⌋ are ballistic, it should be the case that +log Lw(λ) is a non-increasing function of λ ∈ [λ0, 1] (and in the cubic lattice could be a strictly decreasing +function of λ ∈ [λ0, 1]). This is stated as a conjecture. +Conjecture 1. In the cubic lattice log Lw(λ) (for w ≥ 0) is a strictly decreasing function of λ ∈ [λ0, 1]. In +addition, +sup +0<λ≤1 +log Lw(λ) = lim +λ→0+ log Lw(λ) = log µ(3) +w . +By equation (12) and theorem 3 the function log Lw(λ) is a concave function on [λ0, 1]. By lemmas 1 +and 2 there exist λ1 ∈ (λ0, 1) such that, in the square lattice, log Lw(λ) < log Lw(λ1) = log µ(d) +w . In the +cubic lattice, λ1 ∈ [0, 1), and similarly log Lw(λ1) = log µ(d) +w . By conjecture 1 it may be the case that λ1 = 0 +in the cubic lattice. +In other words, log Lw(λ) is strictly increasing in [λ0, λ1) in the square lattice. Since log Lw(λ) is concave +on [λ0, 1], it follows that it has a maximum at an λ2 ∈ [λ1, 1] where λ2 > λ0 in the square lattice if w ≥ 1 +and λ2 ≥ 0 if w ≥ 0 in the cubic lattice. +Corollary 1. For w ≥ 0 in the square or cubic lattices, there exists critical values λ1, λ2 ∈ [λ0, 1) given by +λ1 = inf{λ | log Lw(λ) = log µ(d) +w } +and +λ2 = sup{λ | log Lw(λ) = log µ(d) +w }, +such that λ1 ≤ λ2 and in the square lattice λ0 < λ1. In addition, log Lw(λ) < log Lw(λ1) = log µ(d) +w +if +λ ∈ [λ0, λ1), log Lw(λ) = log µ(d) +w +if λ ∈ [λ1, λ2], and log Lw(λ) < log Lw(λ2) = log µ(d) +w +if λ ∈ (λ2, 1]. +7 + +Proof. By theorem 3, lemma 1 and equation (12), sup0<λ<1 log Lw(λ) = log µ(d) +w +and log Lw(λ) is a concave +function on [λ0, 1]. +If w = 0 in the square lattice, then trivially λ1 = λ2 = 1. +If w > 0 in the square lattice, or w ≥ 0 in the cubic lattice, then define λ1 and λ2 as above. Then +λ0 < λ1 ≤ λ2 < 1 in the square lattice if w > 0, and 0 ≤ λ1 ≤ λ2 < 1 in the cubic lattice. +Thus, +log Lw(λ) < log Lw(λ1) = log µ(d) +w +if λ ∈ [λ0, λ1), by theorem 3 and lemma 2. +By theorem 3 and lemma 1 it is necessarily the case that λ2 < 1 if w > 0 in the square lattice, or w ≥ 0 +in the cubic lattice. By the definition of λ2, log Lw(λ) < log Lw(λ2) = log µ(d) +w +if λ ∈ (λ2, 1]. +In view of corollary 1 the following conjectures: +Conjecture 2. In corollary 1, λ1 = λ2. +This is consistent with conjecture 3. +Conjecture 3. For w > 0 in the square lattice, or w ≥ 0 in the cubic lattice, the function log Lw(λ) is a +strictly concave function on [λ0, 1]. +By theorem 2 and corollary 1, log Lw(≤λ) is strictly increasing for λ ∈ (λ0, λ1) if λ0 < λ1. It follows +that limλ→λ+ +0 log Lw(≤λ) = limλ→λ+ +0 log Lw(λ) = log Lw(λ+ +0 ) in both the square lattice (if w > 0) and in the +cubic lattice (if w ≥ 0). +Defining log Lw(≤λ0) = log Lw(λ0) and log Lw(≤1) = log µ(d) +w , and similarly for log Lw(≥λ), the +domains of these functions are extended to [λ0, 1]. Moreover, by theorems 3 and 2, and since ℓ(w) +n (≤s) + +ℓ(w) +n (≥s) ≥ ℓ(w) +n , it follows that for each λ ∈ [λ0, 1], +max +λ∈[λ0,1](log Lw(≤λ), log Lw(≥λ)) = log µ(d) +w . +(14) +......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................... +............................................................................................................................................................................................................................................................................................................... +O +............................................................................................................................................................................................................................................................................................................... +1 +log Lw(λ) +log µ(w) +d +λ +.............. +.............. +λ1 +λ2 +λ0 +• +• +• +• +• +• +........................................................................................................................................................................................................................................................................................................................................... +.................................. +.................................. +.......................................................................................................................................... +...................................................................................................................................................................................................................... +.............................................................................................................................................................................................................................................................................................. +Figure 5: A schematic plot of log Lw(λ). +The function is concave and has a maximum value log µ(w) +d +(theorem 3). +As λ → 1− it approaches zero (lemma 1). In the square lattice λ0 = 1/(w+1) and in the cubic lattice λ0 = 0. By +corollary 1 there exists λ1 ≤ λ2 < 1 such that log Lw(λ) = log µ(d) +w +when λ ∈ [λ1, λ2]. In the square lattice λ0 < λ1 (by +lemma 2). By corollary 2 log Lw(≤λ) = log Lw(λ) if λ ∈ [λ0, λ2] while log Lw(≤λ) = log µ(d) +w +if λ ∈ [λ1, 1]. Similarly, +log Lw(≥λ) = log Lw(λ) if λ ∈ [λ1, 1] while log Lw(≥λ) = log µ(d) +w +if λ ∈ [λ0, λ2]. By conjectures 1 and 2 it may be +the case that λ2 = λ1 = λ0 = 0 in the cubic lattice. By conjecture 3 the graph may be strictly concave, in which case +λ1 = λ2 and it has a maximum at exactly one point. +Corollary 2. If w > 0 in the square lattice, or w ≥ 0 in the cubic lattice, there exists a critical value +λ2 ∈ [λ0, 1), such that for each λ ∈ (λ2, 1], log Lw(≤λ) = log µ(d) +w +and log Lw(λ) = log Lw(≥λ) < log µ(d) +w . +Proof. Since log Lw(λ) = min(log Lw(≤λ), log Lw(≥λ)) and log Lw(≤λ) is non-decreasing while log Lw(≥λ) +is non-increasing (and these functions are continuous on [λ0, 1]), it follows by theorem 3 that +lim +λ→1− log Lw(≥λ) = 0. +8 + +By corollary (1) there exists an λ2 ∈ [λ0, 1) such that for each λ ∈ [λ2, 1], log Lw(≤λ) = log µw and +Lw(≥λ) < log µw. +Corollary 3. If w ≥ 1 in the square lattice, or w ≥ 0 in the cubic lattice, then for λ ∈ [0, λ1], +log Lw(λ) = log Lw(≤λ). Similarly, for λ ∈ [λ2, 1], log Lw(λ) = log Lw(≥λ). In addition, if λ ∈ [λ1, λ2], +then log Lw(λ) = log Lw(≤λ) = log Lw(≥λ) = log µ(d) +w . Moreover +lim +λ→1− log L(λ) = +lim +λ→1− log L(≥λ) = 0 so +that λ1 ≤ λ2 < 1. +2.1.2. Unfolded ballistic walks in a slit or a slab: +Denote the number of unfolded walks from the origin, of +length n in Sw, with span s, by c(†,w) +n +(s). Clearly, ℓ(w) +n (s) ≤ c(†,w) +n +(s), since each loop is also an unfolded +walk. This shows that for λ ∈ [λ0, 1], +log Lw(λ) ≤ lim inf +n→∞ +1 +n log c(†,w) +n +(⌊λn⌋). +(15) +Sw +Sw +• +• +• +• +• +••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• +••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• +••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• +••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• +................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. +........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................ +............................................................................................................................................................... +...................... +............................................................................................................................................................... ...................... +s +............................................................................................................................................................... +...................... +.................................................................................................................................................... ...................... +s+1 +Figure 6: An unfolded walk (left) of span s in a slit Sw of width w. This walk can be turned into a loop (right) of span +s+1 by appending at most w+1 steps on the right to reattach the endpoint to the bottom boundary of Sw. +On the other hand, each unfolded walk of length n can be turned into an unfolded loop by adding +no more than w+1 steps at the end of the walk (see figure 6) to reconnect its endpoint with the bottom +boundary of Sw. This shows that +c(†,w) +n +(s) ≤ +w+1 +� +j=1 +ℓ(w) +n+j(s+1). +(16) +This gives the following lemma. +Lemma 3. If λ ∈ [λ0, 1], then the limit lim +n→∞ +1 +n log c(†,w) +n +(⌊λn⌋) = log Lw(λ) exists. +Proof. Add w+1−j horisontal steps to each loop counted by the right hand side of equation (16). Then all +the loops have length n+w+1, and spans in {s+1, s+2, . . . , s+w+2}. That is +c(†,w) +n +(s) ≤ +w+1 +� +j=1 +ℓ(w) +n+w+1(s+w+2−j). +(∗) +By theorem 4, for each fixed j, lim +n→∞ +1 +n log ℓ(w) +n+w+1(⌊λn⌋+w+2−j) = log Lw(λ). Thus, taking logs of equation +(*) and putting s = ⌊λn⌋, dividing by n, and then letting n → ∞, +lim sup +n→∞ +1 +n log c(†,w) +n +(⌊λn⌋) ≤ lim +n→∞ +1 +n log +w+1 +� +j=1 +ℓ(w) +n+w+1(⌊λn⌋+w+2−j) = log Lw(λ). +By equation (15) this proves existence of the limit. This completes the proof. +Consider next c†,w +n (≤t) and c†,w +n (≥t) defined by +c(†,w) +n +(≤t) = +t +� +s=0 +c(†,w) +n +(s), +and +c(†,w) +n +(≥t) = +n +� +s=t +c(†,w) +n +(s). +(17) +9 + +Lemma 4. The following limits exist for λ ∈ [λ0, 1]: +lim +n→∞ +1 +n log c(†,w) +n +(≤⌊λn⌋) = log Lw(≤λ), and +lim +n→∞ +1 +n log c(†,w) +n +(≥⌊λn⌋) = log Lw(≥λ). +Proof. By appending w+1−j edges to the endpoint of the loops on the right hand side of equation (16), +c(†,w) +n +(≤s) ≤ +w+1 +� +j=1 +ℓ(w) +n+j(≤s+1) ≤ +w+1 +� +j=1 +ℓ(w) +n+w+1(≤s+w+2−j) ≤ (w+1) ℓ(w) +n+w+1(≤s+w+2) +Consider the term on the right hand side above if s = ⌊λn⌋. This is +ℓ(w) +n+w+1(≤⌊λn⌋+w+2) = +⌊λn⌋+w+2 +� +k=0 +ℓ(w) +n+w+1(k) ≤ (⌊λn⌋+w+2) ℓ(w) +n+w+1(γn) +where k = γn ∈ [0, ⌊ϵn⌋+w+2] maximizes the terms in the summation for each value of n. Take logarithms, +divide by n, and then take n → ∞. +The sequence of points (γn/(n+w+1) has an accumulation point +γ ∈ [0, λ] and by theorem 4, this gives +lim sup +n→∞ +1 +n log c(†,w) +n +(≤⌊λn⌋+w+2) +≤ lim sup +n→∞ +1 +n log ℓ(w) +n+w+1(≤⌊λn⌋+w+2) ≤ log Lw(γ) ≤ log Lw(≤λ) +since γ ≤ λ. +On the other hand, ℓ(w) +n (≤s) ≤ c(†,w) +n +(≤s), so that +log Lw(≤λ) = lim +n→∞ +1 +n log ℓ(w) +n (≤⌊λn⌋) ≤ lim inf +n→∞ +1 +n log c(†,w) +n +(≤⌊λn⌋). +This completes the proof for c(†,w) +n +(≤⌊λn⌋). +The proof for c(†,w) +n +(≥⌊λn⌋) is similar. +2.1.3. Ballistic walks in slits and slabs: +Now consider a self-avoiding walk in Sw, with its span (the distance +between its endpoints) in the x1-direction equal to s (as illustrated in the left panel in figure 4). Let the +number of such walks, from the origin, of length n with span between endpoints equal to s, be c(w) +n (s). +If d = 2 and w = 0, then c(0) +0 (0) = 1 and c(0) +n (n) = 2 if n > 0, otherwise it is zero. This shows that +lim +n→∞ +1 +n log c(0) +n (⌊λn⌋) = 0 +if λ = 1, +(18) +and otherwise this limit is equal to −∞. +Thus, assume that w ≥ 1 if d = 2. +By unfolding walks of length n [11] and of span s = ⌊λn⌋ in the x1-direction one obtains +ℓ(w) +n (⌊λn⌋) ≤ c(w) +n (⌊λn⌋) ≤ eo(n) +n +� +s=⌊λn⌋ +c(†,w) +n +(s) = eo(n) c(†,w) +n +(≥⌊λn⌋), +(19) +since unfolding a walk will increase its span. Applying the construction in figure 5 to the right hand side of +this equation, +ℓ(w) +n (⌊λn⌋) ≤ c(w) +n (⌊λn⌋) ≤ (w+1) eo(n) ℓ(w) +n+w+1(≥⌊λn⌋). +(20) +Taking logarithms, dividing by n and letting n → ∞ give, by theorems 3 and 5, +log Lw(λ) ≤ lim inf +n→∞ +1 +n log c(w) +n (⌊λn⌋) ≤ lim sup +n→∞ +1 +n log c(w) +n (⌊λn⌋) ≤ log Lw(≥λ). +(21) +By corollary 1, there exists λ1, λ2 ∈ [λ0, 1) such that λ1 ≤ λ2 and if λ ∈ [λ1, 1] then log Lw(λ) = log Lw(≥λ). +Putting λ0 = λ1 = 1 when d = 2 and w = 0 this gives, with equation (18), theorem 6. +10 + +Theorem 6. Let λ ∈ [λ1, 1]. Then the limit log Cw(λ) = lim +n→∞ +1 +n log c(w) +n (⌊λn⌋) = log Lw(λ) exists. +In the event that λ ∈ [λ0, λ1) define +log Cw(λ) = lim sup +n→∞ +1 +n log c(w) +n (⌊λn⌋) +(22) +The pattern theorem for walks and loops in Sw [28] for w ≥ 1 shows that, in the square lattice, +log Cw(λ) = lim sup +n→∞ +1 +n log c(w) +n (⌊λn⌋) < log µ(2) +w , +if |λ − λ0| is small. +(23) +The proof of this is similar to the proof of lemma 2. In view of this a corollary of theorem 6 and corollary 3 +is the following. +Corollary 4. If w ≥ 1 in the square lattice then there exists a λ′ +1 such that λ0 < λ′ +1 ≤ λ1 ≤ λ2 < 1. In +addition +log Cw(λ) +� +� +� +� +� +� +� +� +� +� +� +< log µ(2) +w , +if λ ∈ [λ0, λ′ +1); += log µ(2) +w , +if λ ∈ [λ′ +1, λ2]; +< log µ(2) +w , +if λ ∈ (λ2, 1); += 0, +if λ = 1. +Proof. The proof proceeds by showing that there exists a λ′ +1 ∈ (λ0, λ1] such that log Cw(λ) < log µ(2) +w +if +λ ∈ [0, λ′ +1]. +Since ℓ(2) +w (⌊λn⌋) ≤ c(w) +n (⌊λn⌋) it follows that log Lw(λ) ≤ Cw(λ). Since log Lw(λ) = log µ(2) +w +in the +square lattice for λ ∈ [λ1, λ2] and log Cw(λ) < log µ(2) +w +for λ − λ0 is small positive, there exists a λ′ +1 ≤ λ1 as +claimed. +The remaining relations are consequences of corollaries 1 and 3. +We conjecture that log Cw(λ) exists as a limit for all w ≥ 0, and that log Cw(λ) = log Lw(λ) on [λ0, 1] +in the square lattice. +In the cubic lattice log Cw(λ) is bounded by the following corollary. +Corollary 5. In the cubic lattice λ0 = 0 ≤ λ1 ≤ λ2 < 1. Then +log Cw(λ) +� +� +� +� +� += log µ(3) +w , +if λ ∈ [λ1, λ2]; +< log µ(3) +w , +if λ ∈ (λ2, 1); += 0, +if λ = 1. +Proof. This follows from corollaries 1 and 3. +In the cubic lattice, we conjecture that λ1 = λ2 = 0 (that is, log Cw(0) = log µ(3) +w and log Cw(λ) < log µ(3) +w +if λ ∈ (0, 1]. +Finally, in view of conjecture 1 the following for ballistic cubic lattice walks in Sw. +A walk ω = +{ω0, ω1, . . . , ωn} with ω0 at the origin and ωn = (0, 1, 0) has span 0 and may be turned into a polygon by +adding an edge to join its endpoints. This gives a polygon rooted at the origin and the vertex (0, 1, 0) of +length n+1 in Lw. Conversely, a polygon rooted in the edge joining the origin to (0, 1, 0) can be turned into +a self-avoiding walk of span 0. Denote the number of such rooted polygons of length n+1 in Sw by p(w) +n+1. It +follows that +c(w) +n (0) ≥ p(w) +n+1. +(24) +By reference [29] it follows that +log µ(3) +w = lim +n→∞ +1 +n+1 log pn+1 ≤ lim inf +n→∞ +1 +n log c(w) +n (0) ≤ lim sup +n→∞ +1 +n log c(w) +n (0) ≤ log µ(3) +w . +(25) +11 + +Figure 7: Finite size approximations to log Cw(λ) for 10 ≤ n ≤ 200 in the square lattice and for w = 4. Larger values +of n correspond to darker points in the plot. As n increases, the points accumulate close to the limiting curve which +is a concave curve approaching 0 and λ → 1−. The maximum in the data corresponding to n = 200 is approximately +located at λ ≈ 0.526. +Since λ0 = 0 in the cubic lattice, this shows that +lim +n→∞ +1 +n log c(w) +n (⌊λ0n⌋) = log Cw(λ0) = log µ(3) +w . +(26) +By corollary 5 this shows that log Cw(λ0) = log Cw(λ) = log µ(3) +w +for λ ∈ [λ1, λ2]. It is not known that +log Cw(λ) is monotone for λ ∈ [0, 1]. However, the above is consistent with λ0 = λ1 = λ2 = 0 in which case +log Cw(λ) exists and is strictly decreasing in [0, 1]. +2.1.4. +Numerical results: Numerical estimates of log Cw(λ) can be obtained by sampling self-avoiding +walks in slits and slabs. This was done using the PERM algorithm [7], in its flatPERM [25] and parallel +implementation [1], to sample self-avoiding walks from the origin in a slit or slab to length 200 in the square +lattice, and 400 in the cubic lattice, while keeping track of the span of the walk (the span as defined in figure +4). Data were collected for slits of width 1 ≤ w ≤ 5 in the square lattice and 0 ≤ w ≤ 5 in the cubic lattice. +In particular, the algorithm gives numerical approximations to c(w) +n (s), namely the number of walks from +the origin in Sw and of length n and span s. The details of the calculations are shown in table 1. In figure +7 we plot the square lattice finite approximation +log Cw(λ) ≈ 1 +n log c(w) +n (⌊λn⌋) +(27) +determined from our data for 10 ≤ n ≤ 200 for w = 4. The curve appears to have a single maximum, which +is an estimate of λ2 in figure 5. It is also consistent with λ′ +1 = λ1 = λ2. The cubic lattice approximations +are similarly plotted in figure 8. In this case, the data appear to converge to a non-increasing limiting curve +consistent with λ0 = λ1 = λ2 = 2. Finite size estimates of λ2 are listed in table 1. +In table 1 the details and results of the simulations are shown. Estimates for µ(d) +w +are shown, as well as +estimates for λ2 (the location of the maximum in log Cw(λ)). If d = 2 and w = 0, then µ(2) +0 += 1. If w = 1 +instead, then µ(2) +1 += 2/( +√ +5 − 1) (Sloane online sequences of integers A038577; see reference [23]). +In order to estimate µ(w) +w +for larger values of w, assume that +c(w) +n += Aw nγw−1 (µ(d) +w )n (1 + o(1)). +(28) +12 + +0.9 +0.6 +log Cw +0.3 +0 +0 +0.2 +0.4 +0.6 +0.8 +入Figure 8: Finite size approximations to log Cw(λ) for 10 ≤ n ≤ 400 in the cubic lattice and for w = 4. Larger values +of n correspond to darker points in the plot. As n increases, the points accumulate close to the limiting curve which +is a concave curve approaching 0 and λ → 1−. The maximum in the data corresponding to n = 400 is approximately +located at λ ≈ 0.05. +Table 1: Numerical estimates of µ(d) +w +and λ2 +w +Iterations +nmax +µ(d) +w +λ2 +0 +square lattice +– +– +1 (exact) +– +1 +4 × 106 +200 +(1+ +√ +5)/2 ∗ +0.723(2) +2 +4 × 106 +200 +1.9144(3) +0.624(1) +3 +4 × 106 +200 +2.0873(1) +0.567(2) +4 +8 × 106 +200 +2.1990(2) +0.526(2) +5 +1 × 107 +200 +2.2770(9) +0.499(2) +0 +cubic lattice +5 × 106 +400 +2.63815(2) † +0.07(5) +1 +6 × 106 +400 +3.55333(4) +0.06(4) +2 +8 × 106 +400 +3.9456(2) +0.05(3) +3 +1 × 107 +400 +4.1577(4) +0.04(3) +4 +1 × 107 +400 +4.2869(4) +0.05(4) +5 +1 × 107 +400 +4.3719(4) +0.04(3) +* Sloane A038577, [23], Numerical estimate: 1.6185(4) +† µ2 = 2.63815853032790(3) [13] +Expanding and simplifying the log of c(w) +n+1/c(w) +n +give +log(c(w) +n+1/c(w) +n ) = (γw − 1) log(1+1/n) + log µ(d) +w + o(1). +(29) +Plotting the left hand side as a function of 1/n ≈ log(1 + 1/n) gave graphs such as in figure 9 (for w = 2). +Fitting a quadratic curve to the data points with n ≥ 40 gives our best estimate of µ(d) +w . This is shown +in table 1. The estimate of λ2 (see figure 5) is obtained by determining the maximum in the finite size +approximation +log Cw(λ) ≈ 1 +n log cn(⌊λn⌋). +(30) +In the square lattice these estimates were extrapolated in the same way as in figure 9 gives, for example, +13 + +1.5 +1 +log Cw +0.5 +0 +0 +0.2 +0.4 +0.6 +0.8 +入Figure 9: Finite size approximations to µ(d) +w +for 10 ≤ n ≤ 200 in the square lattice and for w = 2. The initial partiy +effects die down as n increases, and the estimate stabilize well towards the y-axis. Extrapolating this gives an estimate +of µ(d) +w . +λ2 = 0.723(5) when w = 1, and λ2 = 0.624(2) if w = 2. In the cubic lattice more care was needed. The +estimates were distributed along a curve when plotted against 1/n, and it proved difficult to extrapolate it. +Experimentation shows that the data lines up along a straight line segment when plotted against (log n)/√n. +Extrapolating this gives the estimates in table 1. The results give estimates close to zero, consistent with a +conjecture that λ2 = 0 in the cubic lattice. +3. A self-avoiding walk underneath a piston +Now turn to the full model in figure 1. A walk from the origin located on the anvil and centered underneath +the piston is pushed into a slit (in two dimensions) or a slab (in three dimensions) Sw(λ) and may escape +from underneath the piston at its edge. +The (finite size) free energy ρn(λ) = (log wn(λ))/n is defined in equation (3), where (as in section 1.1), +wn(λ) is the number of self-avoiding walks from the origin of length n avoiding the piston and the anvil. +The limiting free energy is defined in theorem 1. If λ ≥ 1, then ρ(λ) = log µ(d) +w +and the limit exists (equation +(5)) since the walk is entirely contained in the slit or slab above the anvil and underneath the piston. More +generally ρ(λ) ≥ log µ(d) +w +if λ ≤ 1. +In general the walk is partitioned as illustrated in figure 3, where a walk of length n has its first section +of length ⌊δn⌋ confined to the slit or slab Sw(λ), until it first exits this region to become a walk of length +n − ⌊δn⌋ into the bulk (this part of the walk may reenter and reexit the slit or slab Sw(λ). +3.1. The free energy ρ(λ) +Lower and upper bounds on wn(ϵ) will be obtained by either fixing x in figure 3 at height zero, or otherwise +cutting the walk at x into a walk of span ⌊λn⌋ underneath the piston, and replacing its remaining part by +an arbitrary self-avoiding walk. +3.1.1. Lower bound: +Denote the number of walks in a 90o wedge W, starting in the vertex of W (square +lattice), or in the spine (cubic) of W, of length n, by c +..................... +n. Then it is known that limn→∞ 1 +n log c +..................... +n = log µd [10]. +If the vertex x in figure 3 has height zero, then a lower bound is obtained by splitting the walk into a +loop of span ⌊λn⌋ from the origin to x in Sw(λ) underneath the piston. The remaining part of the walk, of +14 + +1.98 +.94 +1.9 +0 +0.03 +0.06 +0.09 +log +nlength n − ⌊λn⌋, is confined to the 90o wedge W formed by the edge of the piston and the anvil. This walk +starts in the vertex x located in the spine of the wedge. Since this arrangement undercounts wn(λ) (and +wn(λ) ≥ c(w) +n , it follows that +wn(λ) ≥ ℓ(w) +⌊δn⌋(⌊λn⌋) × c +..................... +n−⌊δn⌋. +(31) +Take logarithms, divide by n and let n → ∞ to see that, by theorems 2 and 4, +lim inf +n→∞ +1 +n log wn(λ) ≥ max{log µ(d) +w , δ log Lw(λ/δ) + (1 − δ) log µd}. +(32) +The right hand side can be optimized by taking the supremum over δ: +lim inf +n→∞ +1 +n log wn(λ) ≥ max{log µ(d) +w , +sup +λ<δ<1 +(δ log Lw(λ/δ) + (1 − δ) log µd)}. +(33) +3.1.2. Upper bound: +The situation is slightly different in two and in three dimensions, so consider these in +turn. +Two dimensions: Cut the walk into two segments at the vertex x. Replace the first segment of the walk +with a walk of length ⌊ϵn⌋ ∈ (⌊λn⌋, n) and span ⌊λn⌋ in a slit of width w. The remaining segment of the +walk is replaced by an arbitrary self-avoiding walk of lenth n − ⌊ϵn⌋ from x. This gives an upper bound on +the number of walks from the origin underneath the piston with the first ⌊ϵn⌋ steps to x inside the slit: +c(w) +⌊ϵn⌋(⌊λn⌋) × cn−⌊ϵn⌋. +(34) +For each value of n, there exists a ϵ ∈ [λ, 1] maximizing this product. Denote this value by ϵ∗ (a function of +n). Define kn = ⌊ϵ∗n⌋. Then, for each n, define +vn(λ) = c(w) +kn (⌊λn⌋) × cn−kn. +(35) +Next, consider equation (35), take logarithms, divide by n, and take the limit superior on the right hand +side as n → ∞. Then n → ∞ on the right hand side along a subsequence (ni), and since (kn/n) is bounded, +it has an accumulation point δ ∈ [λ, 1] along a subsequence (nij) so that (knij/nij) → δ as j → ∞. Put +mj = nij and rj = knij. Then (mj) is a subsequence of (ni) and (rj) is a subsequence of (kni), such that +(rj/mj) → δ as j → ∞. +That is, (mj) ⊆ (ni) and (rj) ⊆ (kni). +Taking the limit superior of the right hand side of equation (35) along the subsequence (mj) then gives +1 +n log vn(λ) ≤ lim sup +n→∞ +1 +n log +� +c(w) +kn (⌊λn⌋) × cn−kn +� += lim +j→∞ +1 +mj log +� +c(w) +rj (⌊λmj⌋) × cmj−rj +� +. +(36) +Since (rj/mj) → δ as j → ∞, the result is that +1 +n log vn(λ) ≤ κ log Cw(λ/δ) + (1−δ) log µ2. +(37) +Taking the supremum over δ on the right hand side, and then the limit superior of the left hand side as +n → ∞ gives +lim sup +n→∞ +1 +n log vn(λ) ≤ sup +λ≤δ≤1 +(κ log Cw(λ/δ) + (1−δ) log µ2) . +(38) +It is also the case that +wn(λ) ≤ max{c(w) +n , vn(λ)} +(39) +for each n. Thus, by equation (38), +lim sup +n→∞ +1 +n log wn(λ) ≤ max{log µ(2) +w , sup +λ<δ<1 +(δ log Cw(λ/δ) + (1 − δ) log µ2)}. +(40) +Three dimensions: This is analysed similarly to the two dimensional case, but with the complication +that the location of x in figure 3 also depends on the shape of the piston. In particular, projecting the piston +onto the anvil, the image of x is located in the boundary of the projected piston. The shortest self-avoiding +15 + +walk from the origin to such a vertex x is α⌊λn⌋ + m where α ≥ 1 and m ∈ [0, w − 1]. For example, if the +piston is square, then 1 ≤ α ≤ 2, and if it is circular, then 1 ≤ α ≤ +√ +2. Notice that λ α ≤ 1. +In general, for given λ and δ in figure 3, α is also a function of n, so write α = α(n). As n → ∞, α(n) +varies, so define α∗ = lim infn→∞ α(n) ≥ 1. Then λ α∗ ≤ 1. +Proceeding as in the two dimensional case gives equation (38) but with κ ∈ [ϵ α∗, 1]. Since α∗ ≥ 1, +extend the range of δ in the supremum to (λ, 1) to recover equation (40). +By theorem 6, and equations (33) and (40), existence of the free energy is obtained for λ ∈ [λ1, 1]: +Theorem 7. If λ ∈ [λ1, 1], then +ρ(λ) = lim +n→∞ +1 +n log wn(λ) = max{log µ(d) +w , +sup +λ<δ<1 +(δ log Lw(λ/δ) + (1 − δ) log µd)}. +This also completes the proof of theorem 1. We conjecture that theorem 7 is valid for all λ ∈ [λ0, 1]. +By theorem 7 the following bounds can be obtained on ρ(λ): +max(log µ(d) +w , (1 − λ) log µd) ≤ ρ(λ) ≤ log µd + λ log(µ(d) +w /µd). +(41) +These bounds follow since 0 ≤ log Cw(λ/δ) ≤ log µ(d) +w +for all λ ∈ [0, 1] and δ ∈ [λ, 1]. +3.2. The critical point λc +By theorem 7 +ρ(λ) = max{log µ(d) +w , sup +λ<δ<1 +(δ log Lw(λ/δ) + (1 − δ) log µd)}, +for λ ∈ [λ1, 1]. +(42) +Since ρ(λ) is a constant for large λ, and a function of λ for small λ, it is a non-analytic function of λ and is +singular at least at one point λc defined by +λc = inf{λ | ρ(λ) = log µ(d) +w }. +(43) +By noting that 0 ≤ log Cw(λ/δ) ≤ log µ(d) +w , a bound on the location of λc can be determined. Replacing +log Cw(λ.δ) = 0 shows that if δ is small enough that (1 − δ) log µd > log µ(d) +w , then ρ(λ) > log µ(d) +w . This can +only occur if δ (and thus λ) is small enough, giving an lower bound on λc: +λc ≥ λ∗ = log(µd/µ(d) +w ) +log µd +. +(44) +If λ > λc, then the self-avoiding walk does not escape from the region Sw(λ) underneath the piston, and if +λ < λ∗, then the self-avoiding walk escapes from Sw(λ). Notice that it is not obvious that λc ≥ λ1. +If d = 2 and w = 0, then µ(2) +0 += 1 so that λc = 1. This shows that for all λ < 1 the walk escapes, +as one expects in this case. If w = 1 instead, then µ(2) +1 += (1 + +√ +5)/2 (Sloane online sequences of integers +A038577; see also reference [23]), so that, using the estimate of µ2 in equation (2), and the data in table 1, +λc ≥ λ∗ = 0.50394 . . .. This is the lower bound in table 2 for w = 1 in the square lattice. The remaining +bounds λ∗ are obtained by using the data in table 1. In the cubic lattice, the estimate of the growth constant +is given in equation (2), and with the data in table 1 gives the estimate of λ∗ in table 2. +To estimate the value of λc numerically, consider equation (42) and define, for λ ∈ [0, 1] and λ ≤ δ ≤ 1, +Q(λ, δ) = δ log Lw(λ/δ) + (1 − δ) log µd − log µ(d) +w . +(45) +For large λ, the walk is confined under the piston, so that its free energy is equal to log µ(d) +w . That is, for all +δ ∈ [λ, 1], Q(λ, δ) ≤ 0. On the other hand, if λ is small, then the walk escapes. In this case there must exist +a δ ∈ [λ, 1] such that Q(λ, δ) > 0. +Using the finite size approximation, one may consider +Qn(λ, δ) = δ( 1 +n log c(w) +n (⌊λn/δ⌋) + (1 − δ) log µd) − log µ(d) +w +(46) +16 + +Table 2: Numerical estimates of λc +w +dimension +λ∗ (lower bound)† +λc (best estimate) +0 +square lattice +1 +1.0 +1 +0.5039 . . . +0.758(3) +2 +0.3305 . . . +0.663(5) +3 +0.2415 . . . +0.612(2) +4 +0.1876 . . . +0.569(8) +5 +0.1517 . . . +0.540(8) +0 +cubic lattice +0.3717 . . . +0.522(2) +1 +0.1789 . . . +0.360(2) +2 +0.1111 . . . +0.292(3) +3 +0.0772 . . . +0.251(3) +4 +0.0574 . . . +0.222(4) +5 +0.0447 . . . +0.201(4) +† Equation (44). +Figure 10: Finite size approximations to λc for 10 ≤ n ≤ 200 in the square lattice and for w = 1. The initial partiy effects +die down as n increases. Extrapolating the curve to the y-axis using a quadratic curve gives the estimate λc ≈ 0.759. +and find the largest value of λ (say λn) such that there exists a δ ∈ [λn, 1] such that Qn(λn, δ) > 0. Then λn +is an approximation of λc. Increasing n gives a sequence (λn) which can be extrapolated to n = ∞ to obtain +a limiting estimate. In the case that w = 0 in the square lattice, this trivially gives λn = 1, consistent with +the critical point at λc = 1. +In the case that w > 0 in the square lattice, the data collected in section 2.1.4 can be used to estimate +λn, and then extrapolate it to λc. If w = 1 in the square lattice then by equation (46) estimates of λn can +be obtained and plotted as a function of 1/n. This plot curves as n increases, but plotting against 1/√n +straightens the curve somewhat (figure 10). Extrapolating this using a quadratic curve gives λn → λc ≈ 0.758 +as n → ∞. This estimate is shown in table 2. The error bar is obtained by using a linear extrapolation and +comparing results. The absolute difference between the estimates is taken as a confidence interval. +Graphs of the finite size free energy can similarly be obtained from the numerical data. The finite size +numerical approximation is obtained from Qn(λ, δ) (equation (46)) by +ρ(λ) ≈ max +� +max +λ≤δ≤1 (Qn(λ, δ)) , log µ(2) +w +� +. +(47) +17 + +0.76 +0.74 +0.72 +0 +0.1 +0.2 +1 +nFigure 11: Finite size approximations of the free energy ρ(λ) for w = 2 in the square lattice. The critical point is well +defined at λc ≈ 0.663 (see table 2. If λ < λc, then the radius of the piston is small and the walk escapes so that ρ(λ) is +not constant. If λ > λc, then the radius of the piston is large, and the walk is retracted underneath the piston so that +it is not a function of λ. These plots are for n = 10, 20, . . . , 200 and they lie very close to each other. The sharp corner +at the critical point suggests a strong first order transition. +In figure 11 our data is plotted for w = 2 in the square lattice for n = 10, 20, . . . , 200. The graphs are very +close to each other and show two regimes, namely a retracted phase whent he walk is confined to the slit +for large λ and the free energy is independent of λ, and escaped phase where the walk escapes and the free +energy is a function of λ. For λ < λc the free energy is dependent on λ, and for λ > λc by log µ(2) +w . The +sharp transition at the critical point is consistent with a strong first order transition as the polymer escapes +from underneath the piston. +4. Conclusions +Our numerical analysis show a very clear phase transition separating a retracted and an escaped phase in +the model. +The data indicate a strong first order transition at a critical point λc which was estimated +numerically and listed in table 2. +The existence of a critical point was proven in section 3, relying on the results for ballistic walks in +slits and slabs in section 2. Our analysis of these ballistic walks proved existence of a limiting free energy in +the model in figure 1 for a range of values of λ as stated in theorem 1. However, there remains an interval +[λ0, λ1) (corollary 4 and corollary 5) where existence of the free energy was not proven. We conjectured in +both cases that λ′ +1 = λ1 = λ0, so that the free energy exists for all λ ∈ [λ0, 1], but this remains to be proven. +Our main results are summarized in theorem 1 and in theorem 7 give an explicit expression for the free +energy ρ(λ) in terms of the growth constant Lw(λ) of ballistic loops in a slit or in a slab in the square and +cubic lattices respective. However, the lower bound in equation (44) proved to be quite weak, as seen in +table 2. +Acknowledgement +EJJvR acknowledges financial support from NSERC (Canada) in the form of a Discovery Grant RGPIN- +2019-06303 and is grateful to SG Whittington for discussions about this model. Data generated for this +study are available on reasonable request. +18 + +0.9 +p(α) +0.7 +0.5 +0 +0.3 +0.6 +0.9 +入References +[1] S Campbell and EJ Janse van Rensburg. Parallel PERM. J Phys A: Math Theo, 53:265005, 2020. +[2] JM Chan, PM Valencia, L Zhang, R Langer, and OC Farokhzad. Polymeric nanoparticles for drug delivery. In Cancer +Nanotech, pages 163–175. Springer, 2010. +[3] M-N Chee and SG Whittington. The growth constant of uniform star polymers in a slab geometry. J Phys A: Math Gen, +20:4915–4921, 1987. +[4] N Clisby. Calculation of the connective constant for self-avoiding walks via the pivot algorithm. J Phys A: Math Theo, +46:245001, 2013. +[5] P-G de Gennes. Scaling Concepts in Polymer Physics. Cornell, 1979. +[6] S Friberg. Polymeric stabilization of colloidal dispersions. donald h. napper. academic press, new york, 1984. pp. xvi & +plus; 428. J Dispersion Sci & Tech, 6(4):497–497, 1985. +[7] P Grassberger. Pruned-enriched Rosenbluth method: Simulations of θ polymers of chain length up to 1000000. Phys Rev +E, 56:3682–3693, 1997. +[8] MC Gufford, DRM Williams, and Sevick EM. End-tethered polymer chains under afm tips: Compression and escape in +theta solvents. Langmuir, 13(21):5691–5696, 1997. +[9] AR Hall and M Geoghegan. Polymers and biopolymers at interfaces. Rep Prog Phys, 81(3):036601, 2018. +[10] JM Hammersley and Whittington SG. Self-avoiding walks in wedges. J Phys A: Math Gen, 18:101–111, 1985. +[11] JM Hammersley and DJA Welsh. Further results on the rate of convergence to the connective constant of the hypercubical +lattice. Quart J Math, 13:108–110, 1962. +[12] H-P Hsu, K Binder, LI Klushin, and AM Skvortsov. What is the order of the two-dimensional polymer escape transition? +Phys Rev E, 76(2):021108, 2007. +[13] JL Jacobsen, CR Scullard, and AJ Guttmann. On the growth constant for square-lattice self-avoiding walks. J Phys A: +Math Theo, 49:494004, 2016. +[14] EJ Janse van Rensburg. The Statistical Mechanics of Interacting Walks, Polygons, Animals and Vesicles, 2nd ed. Oxford +University Press, 2015. +[15] EJ Janse van Rensburg. Supermultiplicative relations in models of interacting self-avoiding walks and polygons. J Phys +A: Math Theor, 54(10):105003, 2021. +[16] EJ Janse van Rensburg, E Orlandini, and SG Whittington. +Self-avoiding walks in a slab: Rigorous results. +J Phys A: +Math Gen, 39:13869–13902, 2006. +[17] N Jawahar and SN Meyyanathan. Polymeric nanoparticles for drug delivery and targeting: A comprehensive review. Int +J Health & Allied Sci, 1(4):217, 2012. +[18] H Kesten. On the number of self-avoiding walks. J Math Phys, 4:960–969, 1963. +[19] H Kesten. On the number of self-avoiding walks II. J Math Phys, 5:1128–1137, 1964. +[20] S Levine, MM Thomlinson, and K Robinson. +Modes of polymer adsorption with excluded volume on parallel colloidal +plates and their interaction. Faraday Disc Chem Soc, 65:202–214, 1978. +[21] A Milchev, V Yamakov, and K Binder. +Escape transition of a compressed polymer mushroom under good solvent +conditions. Europhys Lett, 47(6):675, 1999. +[22] G N¨agele, B D’Aguanno, and AZ Akcasu. Preface of Proceedings of the Workshop on Colloid Physics held at the University +of Konstanz, Germany from 30 November to 2 December 1995. Elsevier, 1997. +[23] N Nikolov. Self-avoiding walks on Z × {0, 1}. J Stat Plan Inf, 142:376–377, 01 2012. +[24] J Paturej, A Milchev, SA Egorov, and K Binder. The escape transition of a compressed star polymer: Self-consistent field +predictions tested by simulation. Macromol, 46(19):8009–8016, 2013. +[25] T Prellberg and J Krawczyk. +Flat histogram version of the pruned and enriched Rosenbluth method. +Phys Rev Lett, +92:120602, 2004. +[26] D Raˇcko and P Cifra. Arm retraction and escape transition in semi-flexible star polymer under cylindrical confinement. +J Mol Modeling, 21(7):1–10, 2015. +[27] EM Sevick. Compression and escape of a star polymer. Macromol, 33(15):5743–5746, 2000. +[28] CE Soteros. +Knots in graphs in subsets of Z3. +In SG Whittington, DW Sumners and T Lodge, editor, Topology and +Geometry in Polymer Science, pages 101–133. Springer, 1998. +[29] CE Soteros and SG Whittington. Polygons and stars in a slit geometry. J Phys A: Math Gen, 21:L857–L861, 1988. +[30] A Srivastava, T Yadav, S Sharma, A Nayak, A Kumari, and N Mishra. +Polymers in drug delivery. +J Biosci Med, +4(1):69–84, 2015. +[31] G Subramanian, DRM Williams, and PA Pincus. +Interaction between finite-sized particles and end grafted polymers. +Macromol, 29(11):4045–4050, 1996. +[32] SG Whittington. Self-avoiding walks with geometrical constraints. J Stat Phys, 30:449–456, 1983. +[33] SG Whittington. +Self-avoiding walks in restricted geometries. +In RC Lacher, editor, Proceedings of the International +Course and Conference in Interfaces between Mathematics, Chemistry and Computer Science, volume 54, pages 297– +306, 1987. +[34] SG Whittington and CE Soteros. Polymers in slabs, slits, and pores. Israel J Chem, 31:127–133, 1991. +[35] SG Whittington and CE Soteros. +Uniform branched polymers in confined geometries. +Macromol Rep, 29(S2):195–199, +1992. +[36] TA Witten and PA Pincus. Colloid stabilization of long grafted polymers. Macromolecules, 19:2509–2513, 1986. +19 + diff --git a/gtFMT4oBgHgl3EQf2zH5/content/tmp_files/load_file.txt b/gtFMT4oBgHgl3EQf2zH5/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..78660d2d2ca13cb13d03df6cade68d12f688004f --- /dev/null +++ b/gtFMT4oBgHgl3EQf2zH5/content/tmp_files/load_file.txt @@ -0,0 +1,6385 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf,len=6384 +page_content='The escape transition in a self-avoiding walk model of linear polymers EJ Janse van Rensburg1 1Department of Mathematics and Statistics, York University, Toronto, Ontario M3J 1P3, Canada E-mail: ‡rensburg@yorku.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='ca 31 January 2023 Abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' A linear polymer grafted to a hard wall and underneath an AFM tip can be modelled in a lattice as a grafted lattice polymer (or self-avoiding walk) compressed underneath a piston approaching the wall.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' As the piston approaches the wall the increasingly confined polymer escapes from the confined region to explore conformations beside the piston.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' This conformational change is believed to be a phase transition in the thermodynamic limit, and has been argued to be first order, based on numerical results in reference [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' In this paper a lattice self-avoiding walk model of the escape transition is constructed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' It is proven that this model has a critical point in the thermodynamic limit corresponding to the escape transition of grafted linear polymers being compressed by a piston.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' This result relies on the analysis of ballistic self-avoiding walks in slits and slabs in the square and cubic lattices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Additionally, numerical estimates of the location of the escape transition critical point is reported based on Monte Carlo simulations of self-avoiding walks in slits and in slabs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Keywords: Escape transition, linear polymer, self-avoiding walk, ballistic walk, slits and slabs 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Introduction The properties of polymers grafted to hard walls or interfaces, or in confined geometries, are of significant interest in polymer physics [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' These properties underlie important applications of polymers, including the stabilization of colloids [6, 20, 22, 36], the in vivo adsorption and delivery of drugs using polymer coatings on medical devises, such as stents [2, 17, 30], the behaviour of biopolymers at cell membranes [9], or the interaction of grafted polymers and small particles [31], amongst many other examples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Confinement and manipulation of single polymer molecules have become possible using atomic force microscopy (AFM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Confining a polymer which is grafted to hard wall by an approaching tip of the atomic force microscope reduces the conformational degrees of freedom of the polymer, and it may undergo an “escape” transition where part of it escapes from underneath the tip to explore conformations in the region beside the tip [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' A lattice model of a grafted linear polymer being compressed by the AFM tip is shown in figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' A lattice self-avoiding walk is grafted at the origin in the hard wall (or “anvil”), and explores its conformations in a space Σw above the anvil and below or outside the AFM tip (the “piston”).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' If the piston is far above the anvil, then Σw is large, and the walk explores it conformations primarily below the piston.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' As the piston approaches the anvil, the conformational degrees of freedom of the walk is reduced, and the walk eventually escapes from the space below the piston.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' In this case the walk is stretch to the boundary of the piston, and its remaining part (or “tail”) explores conformations primary outside the piston (rather than below it).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' The model in figure 1 is a lattice version of models examined in a series of excellent papers [8,12,21,24] exploring the scaling and transition in linear and star polymers compressed by a piston.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Additional numerical results on star polymers can be found in references [26, 27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' These studies are of bead-spring models [21], lattice models [12], and molecular dynamics simulations [24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' While an escape transition is not established rigorously in these models, there are ample numerical evidence in these models of such a transition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' In references [8,21] a theoretical approach using phenomenological arguments based on a “blob” analysis (see, for example, [5]) of the confined polymer is pursued.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' The analysis in reference [8] proceeds by considering arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='12446v1 [cond-mat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='soft] 29 Jan 2023 the free energy as a function of the separation between the anvil and the piston, while reference [21] proceeds by considering the escape transition as a function of the force f exerted on the piston by the polymer (this force is conjugate to the separation of the anvil and piston).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' In these references the phenomenological blob analysis and numerical simulations using a bead-spring and other models show convincing evidence of an escape transition in two dimensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' However, the order of the transition is still unresolved [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Lattice models and main results Let cn be the number of self-avoiding walks from the origin in the d-dimensional hypercubic lattice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Then the growth constant µd of the self-avoiding walk is defined by log µd = lim n→∞ 1 n log cn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' (1) The growth constant has been estimated to high accurancy in the square and cubic lattices, namely µd = � 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='63815853032790(3), if d = 2 (square lattice) [13];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='684039931(27), if d = 3 (cubic lattice) [4] .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' (2) If the walk is confined by boundaries in the lattice, then the value of the growth constant may change, and this is in particular the case if the walk is confined by a piston when it is grafted to a piston.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' In figure 1 a square lattice model of a piston of radius R compressing a self-avoiding walk against an anvil is shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' As the piston approaches the anvil, the polymer is confined to a region Σw, which consists of the space underneath and beside the piston and above the anvil.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' The thermodynamic limit in this model is taken by fixing the ratio of the piston radius R to the length of the walk n, and then to take n → ∞ with R/n fixed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' In the lattice geometry this is achieved by putting R = ⌊λn⌋, as illustrated in figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' In this paper it is shown that, in the thermodynamic limit, there exists a phase transition in this model, in both the square and cubic lattices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' In the lattice model in figure 1 the origin is located on the anvil centered underneath the piston.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' In the square lattice the piston is a rectangle with vertical bisector running through the origin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' In the cubic lattice, the piston may be assumed to have a square or circular horisontal projection onto the anvil, and its vertical symmetry axis runs through the origin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' The linear polymer is a self-avoiding walk of length n from the origin (or grafted at the origin), and confined to explore conformations in Σw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='. Figure 1: A lattice model of a linear polymer grafted to a surface (the “anvil”) and being squeezed by a piston approaching the anvil.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' If the polymer is long, then part of it may escape from the confining space underneath the piston into the bulk region beside the piston.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' The vertical distance between the anvil and the piston is w, and the radius of the piston is the length of the shortest self-avoiding walk from the origin to a vertex underneath the edge of the piston.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' If a piston has radius ⌊λn⌋, then the number of self-avoiding walks of length n from the origin in Σw is denoted by wn(λ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' The free energy of this model, per unit length, is given by ρn(λ) = 1 n log wn(λ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' (3) 2 The limit of ρn(λ) as n → ∞ is the limiting free energy of the model, and should be compared to log µd in equation (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' In this paper we show that for a range of values of λ the limit in equation (3) exits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' The main result is theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Define λ0 = 1/(w+1) in the square lattice, and λ0 = 0 in the cubic lattice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Then there exists a λ1 ∈ [λ0, 1) such that the limiting free energy of a walk from the origin in Σw is given by ρ(w)(λ) = lim n→∞ 1 n log wn(λ) for every λ ∈ [λ1, 1] in the square lattice, or in the cubic lattice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' In figure 2 the region underneath the piston and above the anvil is denoted by Sw(λ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Notice that Sw(λ) does not extend beyond the edge of the piston, and so is a finite part of the square lattice (that is, Sw(λ) ⊂ Σw).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Sw(λ) is similarly defined in the cubic lattice, underneath the piston, and above the anvil, and it also does not extend beyond the boundary of the piston in any direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' In the square lattice Sw(λ) is a slitof length 2⌊λn⌋, and in the cubic lattice it is a slab of radius ⌊λn⌋.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} 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metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='···················································································································································································································································································································· ······························································································································ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='w ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='·············································································································································································································································································································································································································· ······················ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='⌊λn⌋ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='n ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='Sw(λ) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='········································································································································ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='················································ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='················································ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='Figure 2: Schematic of a walk of length n being squeezed by a piston of radius ⌊λn⌋ with λ > 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' In this case the walk is confined to the slit or slab Sw(λ) underneath the piston and above the anvil.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Notice that Sw(λ) does not extend beyond the edge of the piston.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' The radius of the piston is ⌊λn⌋, so that if λ > 1, then a walk of length n is entirely confined to Sw(λ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' This is shown schematically in figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' In the limit as n → ∞, Sw(λ) becomes a slit or a slab of infinite extent denoted by Sw(∞) ≡ Sw, and the walk is confined to it, even as the limit n → ∞ is taken.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Let c(w) n be the number of self-avoiding walks from the origin in Sw(∞) of height w ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' It is known that the limit lim n→∞ 1 n log c(w) n = log µ(d) w (4) exists in the square and cubic lattices [32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' In the case that λ ≥ 1, wn(λ) = c(w) n for all n ≥ 0, since the piston is wide enough to confine all the conformations of a walk of length n to Sw(λ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' This shows that ρ(λ) = log µ(d) w , if λ ≥ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' (5) Moreover, ρ(w)(λ) → log µd as w → ∞ and λ ≥ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' On the other hand, if 0 ≤ λ < 1, then the walk may be partially inside Sw(λ) and then escape into the bulk regime outside Sw(λ), as illustrated schematically in figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' If the walk escapes into the bulk as shown, then it has a first part of length ⌊δn⌋ from the origin to its first vertex underneath the edge of the piston before it steps outside Sw(λ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' The remaining part of the walk has length n−⌊δn⌋ and explores its conformations in Σw (that is, it may reenter Sw(λ)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Notice that λ ≤ δ < 1 in figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' In section 3 we show that exists a λc such that ρ(w)(λ) = log µ(d) w if λ > λc, and ρ(w)(λ) > log µ(d) w if λ < λc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' That is, ρ(w)(λ) has a non-analytic point at λc ∈ [0, 1), and that this critical point corresponds to the escape transition of the walk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' This paper is organised as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' In section 2 models of ballistic walks in slits and slabs in the square and cubic lattice are examined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Existance of a thermodynamic limit is proven in these cases using unfolded loops and walks in a slit or in a slab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' These results are then used in section 3 to examine the full model of ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='····································································································································································································· ······················ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='⌊λn⌋ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='⌊δn⌋ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='n − ⌊δn⌋ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='Sw(λ) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='Σw ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='x ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='············································································································································ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='················································ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='················································ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='Figure 3: Schematic of a walk of length n escaping from Sw(λ) underneath the piston.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' In this case the piston has radius ⌊λn⌋, and λ < 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' The walk exits the slit or slab Sw(λ) for the first time at x and its part from the origin to x has length ⌊δn⌋ and is confined to Sw(λ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' The remaining part of length n − ⌊δn⌋ starts at x and may reenter and reexist Sw(λ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Clearly, λ ≤ δ ≤ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' walks underneath the piston and the escape transition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Existence of a critical point λc is established, and a lower bound on it is proven, namely λc ≥ log(µd/µ(d) w ) log µd .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' (6) In addition to these results, numerical simulations of walks in a slit or slab using the PERM algorithm [7] in its flat histogram [25] version, and with a parallel implementation [1], were done to determine the free energy of ballistic walks in a slit or a slab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Combining these results with the expressions for the free energy of walks underneath a piston gives numerical approximations of λc, as shown in table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Ballistic self-avoiding walks in slits and slabs Denote the coordinates of vertices v ∈ Zd in the hypercubic lattice by (x1(v), x2(v), · · · , xd(v)) and recall that Sw ≡ Sw(∞) so that Sw = {v ∈ Zd | 0 ≤ xd(v) ≤ w}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' (7) The height of Sw is w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' As before, the number of self-avoiding walks of length n from the origin in Sw is denoted by c(w) n and the growth constant µ(d) w of these walks is given in equation (4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Generally log µ(d) w < log µ(d) w+1 [28,29] and limw→∞ log µ(d) w = log µd where µd is the growth constant of the self-avoiding walk in d dimensions (see reference [34] for more results and references [3, 16, 33–35] for additional results and in particular lemma 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='18 and theorem 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='19 in reference [14]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' In the square lattice log µ(2) 0 = 0 and log µ(2) 1 > 0 while in the cubic lattice log µ(3) 0 = log µ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' If w → ∞, then µ(d) w → µd, the growth constant of self-avoiding walks, as noted above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' In addition, 1 = µ(2) 0 < µ(2) w < µ(2) w+1 < µ2, (8) 1 < µ2 < µ(3) w < µ(3) w+1 < µ3 (9) In addition, µ2 = µ(3) 0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' The number c(w) n of self-avoiding walks from the origin in Sw, of length n, is a lower bound on the number of walks in Sw(λ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Thus, wn(λ) ≥ c(w) n , since every walk in Sw is also a walk in Sw(λ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Thus, lim infn→∞ 1 n log wn(ϵ) ≥ limn→∞ 1 n log c(w) n .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' If λ ≥ 1, then wn(λ) = c(w) n with the result that limn→∞ 1 n log wn(ϵ) = limn→∞ 1 n log c(w) n .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Using equation (4) this gives theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' For all λ ≥ 0, lim inf n→∞ 1 n log wn(λ) ≥ lim n→∞ 1 n log c(w) n = log µ(d) w .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' If λ ≥ 1, ρ(w)(λ) = limn→∞ 1 n log wn(λ) = log µ(d) w .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' 4 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Ballistic walks in Sw A self-avoiding walk ω = (ω0, ω1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' , ωn) of length n in Sw with |x1(ω0) − x1(ωn)| = s is a ballistic walk of span s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' That is, the span of the ballistic walk is the absolute difference between the x1-coordinates of its first and last vertices, and an example is illustrated in the left panel of figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' A ballistic walk ω of span s is unfolded if x1(ω0) < x1(ωi) ≤ x1(ωn).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' That is, the walk steps from its unique left-most vertex ω0 in the x1-direction to ω1, and finally terminates in a right-most vertex ωn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' An unfolded walk is illustrated in the right panel in figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' The walk is also a loop of span s (figure 4(right)), which are unfolded walks from the origin in Sw with last vertex of height xd(ωn) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Define c(w) n (s) = # {ballistic walks from the origin in Sw of length n and span s} c(†,w) n (s) = # {unfolded ballistic walks from the origin in Sw of length n and span s} ℓ(w) n (s) = # {ballistic loops from the origin in Sw of length n and span s} .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' ' 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='. s Figure 4: Ballistic walks ω = (ω0, ω1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' , ωn) from the origin in Sw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' (Left) This walk has span s = |x1(ω0) − x1(ωn)|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' (Right) An unfolded self-avoiding walk of span s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' In this walk x1(ω0) < x1(ωi) ≤ x1(ωn) for all 1 ≤ i ≤ n so that the origin is the unique left-most vertex, the first step from the origin is in the x1-direction, and the last vertex ωn is a right-most vertex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Since the heights of the first and last vertices in ω is zero, this unfolded walk is also a loop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Ballistic loops in Sw A loop of length n and span s in Sw can be concatenated with a loop of length m and span t in Sw by placing the first vertex of the second loop on the last vertex of the first loop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' The result is another loop of length n+m and span s+t in Sw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Since there are ℓ(w) n (s) choices for the first loop, and ℓ(m) m (t) choices for the second loop, ℓ(w) n (s) ℓ(w) m (t) ≤ ℓ(w) n+m(s+t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' (10) Notice that ℓ(w) n (s) > 0 if ⌈n/(w+1)⌉ ≤ s ≤ n in the square lattice (the lower bound follows by packing a loop densely into a slit of height w).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' In three dimensions, ℓ(w) n (s) > 0 if 0 ≤ s ≤ n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Define λ0 = � 1/(w+1), if d = 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' 0, if d = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' (11) Then the following theorem follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' The limit log Lw(λ) = lim n→∞ 1 n log ℓ(w) n (⌊λn⌋) exists and is a concave function of λ for λ ∈ (λ0, 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Moreover, sup λ∈(0,1) log Lw(λ) = log µ(d) w .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Existence of the limit and concavity follows from equation (10) and by lemma 1 and theorem 2 in reference [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Since ℓ(w) n (n) = 2 in both the square lattice and the cubic lattice it follows that log Lw(1) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' It is also the case that log Lw(λ) is left-continuous at λ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' lim λ→1− log Lw(λ) = log Lw(1) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Thus, log Lw(λ) is left-continuous at λ = 1, and therefore left-continuous on (λ0, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' 5 Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Observe that ℓ(w) n (s) ≥ 1 for s ≤ n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Thus, for λ ∈ (λ0, 1], log Lw(λ) = lim n→∞ 1 n log ℓ(w) n (⌊λn⌋) ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' On the other hand, ℓ(w) n (s) is bounded above by the number of random walks of length n and with span s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Selecting s steps of a random walk to be East (to the right), and then over-counting by allowing the remaining n−s steps to be in an arbitrary directions, ℓ(w) n (s) ≤ �n s � (2d)n−s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Put s = ⌊λn⌋, take the power 1/n of the above, and let n → ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' This gives log Lw(λ) ≤ lim n→∞ log �� n ⌊λn⌋ �1/n (2d)1−⌊λn⌋/n � = log � (2d)1−λ λλ (1 − λ)1−λ � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Take λ → 1− to complete the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' An additional and useful result is given by theorems 4 and 5 in reference [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Suppose that (kn) is a sequence such that limn→∞(kn/n) = λ ∈ (λ0, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Then the limit lim n→∞ 1 n log ℓ(w) n (kn) = log Lw(λ) exists.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Next, define the functions ℓn(≤s) = �s t=0 ℓn(t) and ℓn(≥s) = �n t=s ℓn(t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' By reference [15] the following limits exist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' The following limits exist for λ ∈ (λ0, 1) log Lw(≤λ) = lim n→∞ 1 n log ℓn(≤⌊λn⌋), and log Lw(≥λ) = lim n→∞ 1 n log ℓn(≥⌊λn⌋).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' log Lw(≤λ) and log Lw(≥λ) are concave functions on (λ0, 1), and log Lw(λ) = min(log Lw(≤λ), log Lw(≥λ)) and max(log Lw(≤λ), log Lw(≥λ)) = log µ(d) w .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' In addition, log Lw(≤λ) is non-decreasing while log Lw(≥λ) is non-increasing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' The proof of this theorem follows from theorem 6 in reference [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' The minimum span s(min) n of a loop of length n in Sw for w > 0 in the square lattice is at least ⌊n/(w+1)⌋ and at most ⌈n/(w+1)⌉ + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' In the cubic lattice s(min) n = 1 for all n ≥ 1 and w > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Define log Lw(λ0) def = lim λ→λ+ 0 log Lw(λ) ≥ lim sup n→∞ 1 n log ℓ(w) n (s(min) n ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' (12) This defines log Lw(λ) to be a concave function on [λ0, 1] in the square and cubic lattices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' In the square lattice, λ0 = 1/(w+1) and log Lw(λ0) = 0 if w ∈ {0, 1} and log Lw(λ0) > 0 if w ≥ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Notice that if w = 0 then log Lw(λ0) = 0 of λ0 = 1 and it is not defined otherwise, and if w = 1, then 1/2 ≤ λ0 ≤ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' In the cubic lattice log Lw(0) = log µ(2) w where µ(2) w is the square lattice growth contant of walks in a slit of width w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' That is, log Lw(0) = 0 if w = 0 and log Lw(0) > 0 if w ≥ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Collecting these gives log Lw(λ0) def = lim λ→λ+ 0 log Lw(λ) � � � � � � � � � � � � = 0, if w ≤ 1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' > 0, if w ≥ 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' if d = 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' � = 0, if w = 0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' > 0, if w ≥ 1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' if d = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' (13) A pattern theorem [11,18,19] for walks and loops in Sw in either the square or cubic lattice was proven in reference [28] for w ≥ 0 (see section 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='3 in reference [14]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' 6 Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' In the square lattice there exists a λ1 > λ0 such that for all λ ∈ [λ0, λ1), log Lw(λ) = lim n→∞ 1 n log ℓ(w) n (⌊λn⌋) < lim n→∞ 1 n log ℓ(w) n = log µ(d) w provided that w ≥ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Let P be a pattern consisting of two consecutive steps in the x1-direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' That is, P = (ν0, ν1, ν2) with x1(ν0) + 1 = x1(ν1) = x1(ν2) − 1 and xj(ν0) = xj(ν1) = xj(ν2) for 2 ≤ j ≤ d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' In addition, let P require all vertices v ∈ Sw with x1(v) = x1(ν1) to be unoccupied by the walk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' P occurs at the i-th vertex ωi in a walk ω if P can be translated such that ν1 = ωi so that νj = ωi+j−1 for j = 0, 1, 2 while all vertices v ∈ Sw with x1(v) = x1(ωi) and v ̸= ωi is not in ω (that is, v ̸∈ ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' If P occurs k times in a walk ω of length n, then the span s of ω is at least k + ⌊n/(w+1)⌋.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Conversely, if the span of a walk is s = k + ⌊n/(w+1)⌋, then the number of occurances of P is at most k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Denote by ℓ(w) n the number of loops of length n from the origin in Sw, and by ℓ(w) n (#P≤k) the number of loops from the origin in Sw in which the pattern P occurs at most k times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Since ℓ(w) n (s) containes the pattern P at most s−⌊n/(w+1)⌋ times, it follows that for λ > 1/(w+1) = λ0, ℓ(w) n (⌊λn⌋) ≤ ℓ(w) n (#P≤⌊λn⌋−⌊λ0n⌋) ≤ ℓ(w) n .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Take the logarithms of these inequalities, divide by n and take the limit superior as n → ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' This shows that log Lw(λ) ≤ lim sup n→∞ 1 n log ℓ(w) n (#P≤⌊λn⌋−⌊λ0n⌋) ≤ log µ(2) w .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' By the pattern theorem for loops in Sw there exists a λ∗ > λ0 such that for all λ ∈ [λ0, λ∗], lim sup n→∞ 1 n log ℓ(w) n (#P≤⌊λn⌋−⌊λ0n⌋) < log µ(2) w , in particular also since ℓ(w) n (#P≤k) is a non-decreasing function of k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' This shows that for all λ ∈ [λ0, λ∗], log Lw(λ) ≤ log µ(2) w .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' This completes the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Underlying lemma 2 is the fact that a square lattice self-avoiding walk in Sw is ballistic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' That is, in the case of a loop of length n, the span s = O(n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Presumably this is not the case in Sw in the cubic lattice where one expects s = o(n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Since loops of length n and span ⌊λn⌋ are ballistic, it should be the case that log Lw(λ) is a non-increasing function of λ ∈ [λ0, 1] (and in the cubic lattice could be a strictly decreasing function of λ ∈ [λ0, 1]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' This is stated as a conjecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Conjecture 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' In the cubic lattice log Lw(λ) (for w ≥ 0) is a strictly decreasing function of λ ∈ [λ0, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' In addition, sup 0<λ≤1 log Lw(λ) = lim λ→0+ log Lw(λ) = log µ(3) w .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' By equation (12) and theorem 3 the function log Lw(λ) is a concave function on [λ0, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' By lemmas 1 and 2 there exist λ1 ∈ (λ0, 1) such that, in the square lattice, log Lw(λ) < log Lw(λ1) = log µ(d) w .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' In the cubic lattice, λ1 ∈ [0, 1), and similarly log Lw(λ1) = log µ(d) w .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' By conjecture 1 it may be the case that λ1 = 0 in the cubic lattice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' In other words, log Lw(λ) is strictly increasing in [λ0, λ1) in the square lattice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Since log Lw(λ) is concave on [λ0, 1], it follows that it has a maximum at an λ2 ∈ [λ1, 1] where λ2 > λ0 in the square lattice if w ≥ 1 and λ2 ≥ 0 if w ≥ 0 in the cubic lattice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Corollary 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' For w ≥ 0 in the square or cubic lattices, there exists critical values λ1, λ2 ∈ [λ0, 1) given by λ1 = inf{λ | log Lw(λ) = log µ(d) w } and λ2 = sup{λ | log Lw(λ) = log µ(d) w }, such that λ1 ≤ λ2 and in the square lattice λ0 < λ1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' In addition, log Lw(λ) < log Lw(λ1) = log µ(d) w if λ ∈ [λ0, λ1), log Lw(λ) = log µ(d) w if λ ∈ [λ1, λ2], and log Lw(λ) < log Lw(λ2) = log µ(d) w if λ ∈ (λ2, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' 7 Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' By theorem 3, lemma 1 and equation (12), sup0<λ<1 log Lw(λ) = log µ(d) w and log Lw(λ) is a concave function on [λ0, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' If w = 0 in the square lattice, then trivially λ1 = λ2 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' If w > 0 in the square lattice, or w ≥ 0 in the cubic lattice, then define λ1 and λ2 as above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Then λ0 < λ1 ≤ λ2 < 1 in the square lattice if w > 0, and 0 ≤ λ1 ≤ λ2 < 1 in the cubic lattice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Thus, log Lw(λ) < log Lw(λ1) = log µ(d) w if λ ∈ [λ0, λ1), by theorem 3 and lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' By theorem 3 and lemma 1 it is necessarily the case that λ2 < 1 if w > 0 in the square lattice, or w ≥ 0 in the cubic lattice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' By the definition of λ2, log Lw(λ) < log Lw(λ2) = log µ(d) w if λ ∈ (λ2, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' In view of corollary 1 the following conjectures: Conjecture 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' In corollary 1, λ1 = λ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' This is consistent with conjecture 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Conjecture 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' For w > 0 in the square lattice, or w ≥ 0 in the cubic lattice, the function log Lw(λ) is a strictly concave function on [λ0, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' By theorem 2 and corollary 1, log Lw(≤λ) is strictly increasing for λ ∈ (λ0, λ1) if λ0 < λ1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' It follows that limλ→λ+ 0 log Lw(≤λ) = limλ→λ+ 0 log Lw(λ) = log Lw(λ+ 0 ) in both the square lattice (if w > 0) and in the cubic lattice (if w ≥ 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Defining log Lw(≤λ0) = log Lw(λ0) and log Lw(≤1) = log µ(d) w , and similarly for log Lw(≥λ), the domains of these functions are extended to [λ0, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Moreover, by theorems 3 and 2, and since ℓ(w) n (≤s) + ℓ(w) n (≥s) ≥ ℓ(w) n , it follows that for each λ ∈ [λ0, 1], max λ∈[λ0,1](log Lw(≤λ), log Lw(≥λ)) = log µ(d) w .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' (14) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='. Figure 5: A schematic plot of log Lw(λ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' The function is concave and has a maximum value log µ(w) d (theorem 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' As λ → 1− it approaches zero (lemma 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' In the square lattice λ0 = 1/(w+1) and in the cubic lattice λ0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' By corollary 1 there exists λ1 ≤ λ2 < 1 such that log Lw(λ) = log µ(d) w when λ ∈ [λ1, λ2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' In the square lattice λ0 < λ1 (by lemma 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' By corollary 2 log Lw(≤λ) = log Lw(λ) if λ ∈ [λ0, λ2] while log Lw(≤λ) = log µ(d) w if λ ∈ [λ1, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Similarly, log Lw(≥λ) = log Lw(λ) if λ ∈ [λ1, 1] while log Lw(≥λ) = log µ(d) w if λ ∈ [λ0, λ2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' By conjectures 1 and 2 it may be the case that λ2 = λ1 = λ0 = 0 in the cubic lattice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' By conjecture 3 the graph may be strictly concave, in which case λ1 = λ2 and it has a maximum at exactly one point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' If w > 0 in the square lattice, or w ≥ 0 in the cubic lattice, there exists a critical value λ2 ∈ [λ0, 1), such that for each λ ∈ (λ2, 1], log Lw(≤λ) = log µ(d) w and log Lw(λ) = log Lw(≥λ) < log µ(d) w .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Since log Lw(λ) = min(log Lw(≤λ), log Lw(≥λ)) and log Lw(≤λ) is non-decreasing while log Lw(≥λ) is non-increasing (and these functions are continuous on [λ0, 1]), it follows by theorem 3 that lim λ→1− log Lw(≥λ) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' 8 By corollary (1) there exists an λ2 ∈ [λ0, 1) such that for each λ ∈ [λ2, 1], log Lw(≤λ) = log µw and Lw(≥λ) < log µw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' If w ≥ 1 in the square lattice, or w ≥ 0 in the cubic lattice, then for λ ∈ [0, λ1], log Lw(λ) = log Lw(≤λ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Similarly, for λ ∈ [λ2, 1], log Lw(λ) = log Lw(≥λ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' In addition, if λ ∈ [λ1, λ2], then log Lw(λ) = log Lw(≤λ) = log Lw(≥λ) = log µ(d) w .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Moreover lim λ→1− log L(λ) = lim λ→1− log L(≥λ) = 0 so that λ1 ≤ λ2 < 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Unfolded ballistic walks in a slit or a slab: Denote the number of unfolded walks from the origin, of length n in Sw, with span s, by c(†,w) n (s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Clearly, ℓ(w) n (s) ≤ c(†,w) n (s), since each loop is also an unfolded walk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' This shows that for λ ∈ [λ0, 1], log Lw(λ) ≤ lim inf n→∞ 1 n log c(†,w) n (⌊λn⌋).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='(15) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='Sw ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='Sw ' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='. .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='. s+1 Figure 6: An unfolded walk (left) of span s in a slit Sw of width w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' This walk can be turned into a loop (right) of span s+1 by appending at most w+1 steps on the right to reattach the endpoint to the bottom boundary of Sw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' On the other hand, each unfolded walk of length n can be turned into an unfolded loop by adding no more than w+1 steps at the end of the walk (see figure 6) to reconnect its endpoint with the bottom boundary of Sw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' This shows that c(†,w) n (s) ≤ w+1 � j=1 ℓ(w) n+j(s+1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' (16) This gives the following lemma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' If λ ∈ [λ0, 1], then the limit lim n→∞ 1 n log c(†,w) n (⌊λn⌋) = log Lw(λ) exists.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Add w+1−j horisontal steps to each loop counted by the right hand side of equation (16).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Then all the loops have length n+w+1, and spans in {s+1, s+2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' , s+w+2}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' That is c(†,w) n (s) ≤ w+1 � j=1 ℓ(w) n+w+1(s+w+2−j).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' (∗) By theorem 4, for each fixed j, lim n→∞ 1 n log ℓ(w) n+w+1(⌊λn⌋+w+2−j) = log Lw(λ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Thus, taking logs of equation (*) and putting s = ⌊λn⌋, dividing by n, and then letting n → ∞, lim sup n→∞ 1 n log c(†,w) n (⌊λn⌋) ≤ lim n→∞ 1 n log w+1 � j=1 ℓ(w) n+w+1(⌊λn⌋+w+2−j) = log Lw(λ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' By equation (15) this proves existence of the limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' This completes the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Consider next c†,w n (≤t) and c†,w n (≥t) defined by c(†,w) n (≤t) = t � s=0 c(†,w) n (s), and c(†,w) n (≥t) = n � s=t c(†,w) n (s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' (17) 9 Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' The following limits exist for λ ∈ [λ0, 1]: lim n→∞ 1 n log c(†,w) n (≤⌊λn⌋) = log Lw(≤λ), and lim n→∞ 1 n log c(†,w) n (≥⌊λn⌋) = log Lw(≥λ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' By appending w+1−j edges to the endpoint of the loops on the right hand side of equation (16), c(†,w) n (≤s) ≤ w+1 � j=1 ℓ(w) n+j(≤s+1) ≤ w+1 � j=1 ℓ(w) n+w+1(≤s+w+2−j) ≤ (w+1) ℓ(w) n+w+1(≤s+w+2) Consider the term on the right hand side above if s = ⌊λn⌋.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' This is ℓ(w) n+w+1(≤⌊λn⌋+w+2) = ⌊λn⌋+w+2 � k=0 ℓ(w) n+w+1(k) ≤ (⌊λn⌋+w+2) ℓ(w) n+w+1(γn) where k = γn ∈ [0, ⌊ϵn⌋+w+2] maximizes the terms in the summation for each value of n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Take logarithms, divide by n, and then take n → ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' The sequence of points (γn/(n+w+1) has an accumulation point γ ∈ [0, λ] and by theorem 4, this gives lim sup n→∞ 1 n log c(†,w) n (≤⌊λn⌋+w+2) ≤ lim sup n→∞ 1 n log ℓ(w) n+w+1(≤⌊λn⌋+w+2) ≤ log Lw(γ) ≤ log Lw(≤λ) since γ ≤ λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' On the other hand, ℓ(w) n (≤s) ≤ c(†,w) n (≤s), so that log Lw(≤λ) = lim n→∞ 1 n log ℓ(w) n (≤⌊λn⌋) ≤ lim inf n→∞ 1 n log c(†,w) n (≤⌊λn⌋).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' This completes the proof for c(†,w) n (≤⌊λn⌋).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' The proof for c(†,w) n (≥⌊λn⌋) is similar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Ballistic walks in slits and slabs: Now consider a self-avoiding walk in Sw, with its span (the distance between its endpoints) in the x1-direction equal to s (as illustrated in the left panel in figure 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Let the number of such walks, from the origin, of length n with span between endpoints equal to s, be c(w) n (s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' If d = 2 and w = 0, then c(0) 0 (0) = 1 and c(0) n (n) = 2 if n > 0, otherwise it is zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' This shows that lim n→∞ 1 n log c(0) n (⌊λn⌋) = 0 if λ = 1, (18) and otherwise this limit is equal to −∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Thus, assume that w ≥ 1 if d = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' By unfolding walks of length n [11] and of span s = ⌊λn⌋ in the x1-direction one obtains ℓ(w) n (⌊λn⌋) ≤ c(w) n (⌊λn⌋) ≤ eo(n) n � s=⌊λn⌋ c(†,w) n (s) = eo(n) c(†,w) n (≥⌊λn⌋), (19) since unfolding a walk will increase its span.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Applying the construction in figure 5 to the right hand side of this equation, ℓ(w) n (⌊λn⌋) ≤ c(w) n (⌊λn⌋) ≤ (w+1) eo(n) ℓ(w) n+w+1(≥⌊λn⌋).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' (20) Taking logarithms, dividing by n and letting n → ∞ give, by theorems 3 and 5, log Lw(λ) ≤ lim inf n→∞ 1 n log c(w) n (⌊λn⌋) ≤ lim sup n→∞ 1 n log c(w) n (⌊λn⌋) ≤ log Lw(≥λ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' (21) By corollary 1, there exists λ1, λ2 ∈ [λ0, 1) such that λ1 ≤ λ2 and if λ ∈ [λ1, 1] then log Lw(λ) = log Lw(≥λ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Putting λ0 = λ1 = 1 when d = 2 and w = 0 this gives, with equation (18), theorem 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' 10 Theorem 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Let λ ∈ [λ1, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Then the limit log Cw(λ) = lim n→∞ 1 n log c(w) n (⌊λn⌋) = log Lw(λ) exists.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' In the event that λ ∈ [λ0, λ1) define log Cw(λ) = lim sup n→∞ 1 n log c(w) n (⌊λn⌋) (22) The pattern theorem for walks and loops in Sw [28] for w ≥ 1 shows that, in the square lattice, log Cw(λ) = lim sup n→∞ 1 n log c(w) n (⌊λn⌋) < log µ(2) w , if |λ − λ0| is small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' (23) The proof of this is similar to the proof of lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' In view of this a corollary of theorem 6 and corollary 3 is the following.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Corollary 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' If w ≥ 1 in the square lattice then there exists a λ′ 1 such that λ0 < λ′ 1 ≤ λ1 ≤ λ2 < 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' In addition log Cw(λ) � � � � � � � � � � � < log µ(2) w , if λ ∈ [λ0, λ′ 1);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' = log µ(2) w , if λ ∈ [λ′ 1, λ2];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' < log µ(2) w , if λ ∈ (λ2, 1);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' = 0, if λ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' The proof proceeds by showing that there exists a λ′ 1 ∈ (λ0, λ1] such that log Cw(λ) < log µ(2) w if λ ∈ [0, λ′ 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Since ℓ(2) w (⌊λn⌋) ≤ c(w) n (⌊λn⌋) it follows that log Lw(λ) ≤ Cw(λ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Since log Lw(λ) = log µ(2) w in the square lattice for λ ∈ [λ1, λ2] and log Cw(λ) < log µ(2) w for λ − λ0 is small positive, there exists a λ′ 1 ≤ λ1 as claimed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' The remaining relations are consequences of corollaries 1 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' We conjecture that log Cw(λ) exists as a limit for all w ≥ 0, and that log Cw(λ) = log Lw(λ) on [λ0, 1] in the square lattice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' In the cubic lattice log Cw(λ) is bounded by the following corollary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Corollary 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' In the cubic lattice λ0 = 0 ≤ λ1 ≤ λ2 < 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Then log Cw(λ) � � � � � = log µ(3) w , if λ ∈ [λ1, λ2];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' < log µ(3) w , if λ ∈ (λ2, 1);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' = 0, if λ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' This follows from corollaries 1 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' In the cubic lattice, we conjecture that λ1 = λ2 = 0 (that is, log Cw(0) = log µ(3) w and log Cw(λ) < log µ(3) w if λ ∈ (0, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Finally, in view of conjecture 1 the following for ballistic cubic lattice walks in Sw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' A walk ω = {ω0, ω1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' , ωn} with ω0 at the origin and ωn = (0, 1, 0) has span 0 and may be turned into a polygon by adding an edge to join its endpoints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' This gives a polygon rooted at the origin and the vertex (0, 1, 0) of length n+1 in Lw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Conversely, a polygon rooted in the edge joining the origin to (0, 1, 0) can be turned into a self-avoiding walk of span 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Denote the number of such rooted polygons of length n+1 in Sw by p(w) n+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' It follows that c(w) n (0) ≥ p(w) n+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' (24) By reference [29] it follows that log µ(3) w = lim n→∞ 1 n+1 log pn+1 ≤ lim inf n→∞ 1 n log c(w) n (0) ≤ lim sup n→∞ 1 n log c(w) n (0) ≤ log µ(3) w .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' (25) 11 Figure 7: Finite size approximations to log Cw(λ) for 10 ≤ n ≤ 200 in the square lattice and for w = 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Larger values of n correspond to darker points in the plot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' As n increases, the points accumulate close to the limiting curve which is a concave curve approaching 0 and λ → 1−.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' The maximum in the data corresponding to n = 200 is approximately located at λ ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='526.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Since λ0 = 0 in the cubic lattice, this shows that lim n→∞ 1 n log c(w) n (⌊λ0n⌋) = log Cw(λ0) = log µ(3) w .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' (26) By corollary 5 this shows that log Cw(λ0) = log Cw(λ) = log µ(3) w for λ ∈ [λ1, λ2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' It is not known that log Cw(λ) is monotone for λ ∈ [0, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' However, the above is consistent with λ0 = λ1 = λ2 = 0 in which case log Cw(λ) exists and is strictly decreasing in [0, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Numerical results: Numerical estimates of log Cw(λ) can be obtained by sampling self-avoiding walks in slits and slabs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' This was done using the PERM algorithm [7], in its flatPERM [25] and parallel implementation [1], to sample self-avoiding walks from the origin in a slit or slab to length 200 in the square lattice, and 400 in the cubic lattice, while keeping track of the span of the walk (the span as defined in figure 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Data were collected for slits of width 1 ≤ w ≤ 5 in the square lattice and 0 ≤ w ≤ 5 in the cubic lattice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' In particular, the algorithm gives numerical approximations to c(w) n (s), namely the number of walks from the origin in Sw and of length n and span s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' The details of the calculations are shown in table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' In figure 7 we plot the square lattice finite approximation log Cw(λ) ≈ 1 n log c(w) n (⌊λn⌋) (27) determined from our data for 10 ≤ n ≤ 200 for w = 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' The curve appears to have a single maximum, which is an estimate of λ2 in figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' It is also consistent with λ′ 1 = λ1 = λ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' The cubic lattice approximations are similarly plotted in figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' In this case, the data appear to converge to a non-increasing limiting curve consistent with λ0 = λ1 = λ2 = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Finite size estimates of λ2 are listed in table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' In table 1 the details and results of the simulations are shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Estimates for µ(d) w are shown, as well as estimates for λ2 (the location of the maximum in log Cw(λ)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' If d = 2 and w = 0, then µ(2) 0 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' If w = 1 instead, then µ(2) 1 = 2/( √ 5 − 1) (Sloane online sequences of integers A038577;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' see reference [23]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' In order to estimate µ(w) w for larger values of w, assume that c(w) n = Aw nγw−1 (µ(d) w )n (1 + o(1)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' (28) 12 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='9 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='6 log Cw 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='3 0 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='8 入Figure 8: Finite size approximations to log Cw(λ) for 10 ≤ n ≤ 400 in the cubic lattice and for w = 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Larger values of n correspond to darker points in the plot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' As n increases, the points accumulate close to the limiting curve which is a concave curve approaching 0 and λ → 1−.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' The maximum in the data corresponding to n = 400 is approximately located at λ ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Table 1: Numerical estimates of µ(d) w and λ2 w Iterations nmax µ(d) w λ2 0 square lattice – – 1 (exact) – 1 4 × 106 200 (1+ √ 5)/2 ∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='723(2) 2 4 × 106 200 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='9144(3) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='624(1) 3 4 × 106 200 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='0873(1) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='567(2) 4 8 × 106 200 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='1990(2) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='526(2) 5 1 × 107 200 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='2770(9) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='499(2) 0 cubic lattice 5 × 106 400 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='63815(2) † 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='07(5) 1 6 × 106 400 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='55333(4) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='06(4) 2 8 × 106 400 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='9456(2) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='05(3) 3 1 × 107 400 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='1577(4) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='04(3) 4 1 × 107 400 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='2869(4) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='05(4) 5 1 × 107 400 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='3719(4) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='04(3) Sloane A038577, [23], Numerical estimate: 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='6185(4) † µ2 = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='63815853032790(3) [13] Expanding and simplifying the log of c(w) n+1/c(w) n give log(c(w) n+1/c(w) n ) = (γw − 1) log(1+1/n) + log µ(d) w + o(1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' (29) Plotting the left hand side as a function of 1/n ≈ log(1 + 1/n) gave graphs such as in figure 9 (for w = 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Fitting a quadratic curve to the data points with n ≥ 40 gives our best estimate of µ(d) w .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' This is shown in table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' The estimate of λ2 (see figure 5) is obtained by determining the maximum in the finite size approximation log Cw(λ) ≈ 1 n log cn(⌊λn⌋).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' (30) In the square lattice these estimates were extrapolated in the same way as in figure 9 gives, for example, 13 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='5 1 log Cw 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='5 0 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='8 入Figure 9: Finite size approximations to µ(d) w for 10 ≤ n ≤ 200 in the square lattice and for w = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' The initial partiy effects die down as n increases, and the estimate stabilize well towards the y-axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Extrapolating this gives an estimate of µ(d) w .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' λ2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='723(5) when w = 1, and λ2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='624(2) if w = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' In the cubic lattice more care was needed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' The estimates were distributed along a curve when plotted against 1/n, and it proved difficult to extrapolate it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Experimentation shows that the data lines up along a straight line segment when plotted against (log n)/√n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Extrapolating this gives the estimates in table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' The results give estimates close to zero, consistent with a conjecture that λ2 = 0 in the cubic lattice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' A self-avoiding walk underneath a piston Now turn to the full model in figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' A walk from the origin located on the anvil and centered underneath the piston is pushed into a slit (in two dimensions) or a slab (in three dimensions) Sw(λ) and may escape from underneath the piston at its edge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' The (finite size) free energy ρn(λ) = (log wn(λ))/n is defined in equation (3), where (as in section 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='1), wn(λ) is the number of self-avoiding walks from the origin of length n avoiding the piston and the anvil.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' The limiting free energy is defined in theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' If λ ≥ 1, then ρ(λ) = log µ(d) w and the limit exists (equation (5)) since the walk is entirely contained in the slit or slab above the anvil and underneath the piston.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' More generally ρ(λ) ≥ log µ(d) w if λ ≤ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' In general the walk is partitioned as illustrated in figure 3, where a walk of length n has its first section of length ⌊δn⌋ confined to the slit or slab Sw(λ), until it first exits this region to become a walk of length n − ⌊δn⌋ into the bulk (this part of the walk may reenter and reexit the slit or slab Sw(λ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' The free energy ρ(λ) Lower and upper bounds on wn(ϵ) will be obtained by either fixing x in figure 3 at height zero, or otherwise cutting the walk at x into a walk of span ⌊λn⌋ underneath the piston, and replacing its remaining part by an arbitrary self-avoiding walk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Lower bound: Denote the number of walks in a 90o wedge W, starting in the vertex of W (square lattice), or in the spine (cubic) of W, of length n, by c .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Then it is known that limn→∞ 1 n log c .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' n = log µd [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' If the vertex x in figure 3 has height zero, then a lower bound is obtained by splitting the walk into a loop of span ⌊λn⌋ from the origin to x in Sw(λ) underneath the piston.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' The remaining part of the walk, of 14 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='98 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='94 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='9 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='03 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='06 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='09 log nlength n − ⌊λn⌋, is confined to the 90o wedge W formed by the edge of the piston and the anvil.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' This walk starts in the vertex x located in the spine of the wedge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Since this arrangement undercounts wn(λ) (and wn(λ) ≥ c(w) n , it follows that wn(λ) ≥ ℓ(w) ⌊δn⌋(⌊λn⌋) × c .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' n−⌊δn⌋.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' (31) Take logarithms, divide by n and let n → ∞ to see that, by theorems 2 and 4, lim inf n→∞ 1 n log wn(λ) ≥ max{log µ(d) w , δ log Lw(λ/δ) + (1 − δ) log µd}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' (32) The right hand side can be optimized by taking the supremum over δ: lim inf n→∞ 1 n log wn(λ) ≥ max{log µ(d) w , sup λ<δ<1 (δ log Lw(λ/δ) + (1 − δ) log µd)}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' (33) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Upper bound: The situation is slightly different in two and in three dimensions, so consider these in turn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Two dimensions: Cut the walk into two segments at the vertex x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Replace the first segment of the walk with a walk of length ⌊ϵn⌋ ∈ (⌊λn⌋, n) and span ⌊λn⌋ in a slit of width w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' The remaining segment of the walk is replaced by an arbitrary self-avoiding walk of lenth n − ⌊ϵn⌋ from x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' This gives an upper bound on the number of walks from the origin underneath the piston with the first ⌊ϵn⌋ steps to x inside the slit: c(w) ⌊ϵn⌋(⌊λn⌋) × cn−⌊ϵn⌋.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' (34) For each value of n, there exists a ϵ ∈ [λ, 1] maximizing this product.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Denote this value by ϵ∗ (a function of n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Define kn = ⌊ϵ∗n⌋.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Then, for each n, define vn(λ) = c(w) kn (⌊λn⌋) × cn−kn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' (35) Next, consider equation (35), take logarithms, divide by n, and take the limit superior on the right hand side as n → ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Then n → ∞ on the right hand side along a subsequence (ni), and since (kn/n) is bounded, it has an accumulation point δ ∈ [λ, 1] along a subsequence (nij) so that (knij/nij) → δ as j → ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Put mj = nij and rj = knij.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Then (mj) is a subsequence of (ni) and (rj) is a subsequence of (kni), such that (rj/mj) → δ as j → ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' That is, (mj) ⊆ (ni) and (rj) ⊆ (kni).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Taking the limit superior of the right hand side of equation (35) along the subsequence (mj) then gives 1 n log vn(λ) ≤ lim sup n→∞ 1 n log � c(w) kn (⌊λn⌋) × cn−kn � = lim j→∞ 1 mj log � c(w) rj (⌊λmj⌋) × cmj−rj � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' (36) Since (rj/mj) → δ as j → ∞, the result is that 1 n log vn(λ) ≤ κ log Cw(λ/δ) + (1−δ) log µ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' (37) Taking the supremum over δ on the right hand side, and then the limit superior of the left hand side as n → ∞ gives lim sup n→∞ 1 n log vn(λ) ≤ sup λ≤δ≤1 (κ log Cw(λ/δ) + (1−δ) log µ2) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' (38) It is also the case that wn(λ) ≤ max{c(w) n , vn(λ)} (39) for each n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Thus, by equation (38), lim sup n→∞ 1 n log wn(λ) ≤ max{log µ(2) w , sup λ<δ<1 (δ log Cw(λ/δ) + (1 − δ) log µ2)}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' (40) Three dimensions: This is analysed similarly to the two dimensional case, but with the complication that the location of x in figure 3 also depends on the shape of the piston.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' In particular, projecting the piston onto the anvil, the image of x is located in the boundary of the projected piston.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' The shortest self-avoiding 15 walk from the origin to such a vertex x is α⌊λn⌋ + m where α ≥ 1 and m ∈ [0, w − 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' For example, if the piston is square, then 1 ≤ α ≤ 2, and if it is circular, then 1 ≤ α ≤ √ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Notice that λ α ≤ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' In general, for given λ and δ in figure 3, α is also a function of n, so write α = α(n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' As n → ∞, α(n) varies, so define α∗ = lim infn→∞ α(n) ≥ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Then λ α∗ ≤ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Proceeding as in the two dimensional case gives equation (38) but with κ ∈ [ϵ α∗, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Since α∗ ≥ 1, extend the range of δ in the supremum to (λ, 1) to recover equation (40).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' By theorem 6, and equations (33) and (40), existence of the free energy is obtained for λ ∈ [λ1, 1]: Theorem 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' If λ ∈ [λ1, 1], then ρ(λ) = lim n→∞ 1 n log wn(λ) = max{log µ(d) w , sup λ<δ<1 (δ log Lw(λ/δ) + (1 − δ) log µd)}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' This also completes the proof of theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' We conjecture that theorem 7 is valid for all λ ∈ [λ0, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' By theorem 7 the following bounds can be obtained on ρ(λ): max(log µ(d) w , (1 − λ) log µd) ≤ ρ(λ) ≤ log µd + λ log(µ(d) w /µd).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' (41) These bounds follow since 0 ≤ log Cw(λ/δ) ≤ log µ(d) w for all λ ∈ [0, 1] and δ ∈ [λ, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' The critical point λc By theorem 7 ρ(λ) = max{log µ(d) w , sup λ<δ<1 (δ log Lw(λ/δ) + (1 − δ) log µd)}, for λ ∈ [λ1, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' (42) Since ρ(λ) is a constant for large λ, and a function of λ for small λ, it is a non-analytic function of λ and is singular at least at one point λc defined by λc = inf{λ | ρ(λ) = log µ(d) w }.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' (43) By noting that 0 ≤ log Cw(λ/δ) ≤ log µ(d) w , a bound on the location of λc can be determined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Replacing log Cw(λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='δ) = 0 shows that if δ is small enough that (1 − δ) log µd > log µ(d) w , then ρ(λ) > log µ(d) w .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' This can only occur if δ (and thus λ) is small enough, giving an lower bound on λc: λc ≥ λ∗ = log(µd/µ(d) w ) log µd .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' (44) If λ > λc, then the self-avoiding walk does not escape from the region Sw(λ) underneath the piston, and if λ < λ∗, then the self-avoiding walk escapes from Sw(λ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Notice that it is not obvious that λc ≥ λ1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' If d = 2 and w = 0, then µ(2) 0 = 1 so that λc = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' This shows that for all λ < 1 the walk escapes, as one expects in this case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' If w = 1 instead, then µ(2) 1 = (1 + √ 5)/2 (Sloane online sequences of integers A038577;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' see also reference [23]), so that, using the estimate of µ2 in equation (2), and the data in table 1, λc ≥ λ∗ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='50394 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='. This is the lower bound in table 2 for w = 1 in the square lattice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' The remaining bounds λ∗ are obtained by using the data in table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' In the cubic lattice, the estimate of the growth constant is given in equation (2), and with the data in table 1 gives the estimate of λ∗ in table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' To estimate the value of λc numerically, consider equation (42) and define, for λ ∈ [0, 1] and λ ≤ δ ≤ 1, Q(λ, δ) = δ log Lw(λ/δ) + (1 − δ) log µd − log µ(d) w .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' (45) For large λ, the walk is confined under the piston, so that its free energy is equal to log µ(d) w .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' That is, for all δ ∈ [λ, 1], Q(λ, δ) ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' On the other hand, if λ is small, then the walk escapes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' In this case there must exist a δ ∈ [λ, 1] such that Q(λ, δ) > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Using the finite size approximation, one may consider Qn(λ, δ) = δ( 1 n log c(w) n (⌊λn/δ⌋) + (1 − δ) log µd) − log µ(d) w (46) 16 Table 2: Numerical estimates of λc w dimension λ∗ (lower bound)† λc (best estimate) 0 square lattice 1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='0 1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='5039 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='758(3) 2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='3305 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='663(5) 3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='2415 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='612(2) 4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='1876 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='569(8) 5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='1517 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='540(8) 0 cubic lattice 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='3717 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='522(2) 1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='1789 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='360(2) 2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='1111 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='292(3) 3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='0772 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='251(3) 4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='0574 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='222(4) 5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='0447 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='201(4) † Equation (44).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Figure 10: Finite size approximations to λc for 10 ≤ n ≤ 200 in the square lattice and for w = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' The initial partiy effects die down as n increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Extrapolating the curve to the y-axis using a quadratic curve gives the estimate λc ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='759.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' and find the largest value of λ (say λn) such that there exists a δ ∈ [λn, 1] such that Qn(λn, δ) > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Then λn is an approximation of λc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Increasing n gives a sequence (λn) which can be extrapolated to n = ∞ to obtain a limiting estimate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' In the case that w = 0 in the square lattice, this trivially gives λn = 1, consistent with the critical point at λc = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' In the case that w > 0 in the square lattice, the data collected in section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='4 can be used to estimate λn, and then extrapolate it to λc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' If w = 1 in the square lattice then by equation (46) estimates of λn can be obtained and plotted as a function of 1/n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' This plot curves as n increases, but plotting against 1/√n straightens the curve somewhat (figure 10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Extrapolating this using a quadratic curve gives λn → λc ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='758 as n → ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' This estimate is shown in table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' The error bar is obtained by using a linear extrapolation and comparing results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' The absolute difference between the estimates is taken as a confidence interval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Graphs of the finite size free energy can similarly be obtained from the numerical data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' The finite size numerical approximation is obtained from Qn(λ, δ) (equation (46)) by ρ(λ) ≈ max � max λ≤δ≤1 (Qn(λ, δ)) , log µ(2) w � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' (47) 17 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='76 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='74 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='72 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='2 1 nFigure 11: Finite size approximations of the free energy ρ(λ) for w = 2 in the square lattice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' The critical point is well defined at λc ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='663 (see table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' If λ < λc, then the radius of the piston is small and the walk escapes so that ρ(λ) is not constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' If λ > λc, then the radius of the piston is large, and the walk is retracted underneath the piston so that it is not a function of λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' These plots are for n = 10, 20, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' , 200 and they lie very close to each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' The sharp corner at the critical point suggests a strong first order transition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' In figure 11 our data is plotted for w = 2 in the square lattice for n = 10, 20, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' , 200.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' The graphs are very close to each other and show two regimes, namely a retracted phase whent he walk is confined to the slit for large λ and the free energy is independent of λ, and escaped phase where the walk escapes and the free energy is a function of λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' For λ < λc the free energy is dependent on λ, and for λ > λc by log µ(2) w .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' The sharp transition at the critical point is consistent with a strong first order transition as the polymer escapes from underneath the piston.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Conclusions Our numerical analysis show a very clear phase transition separating a retracted and an escaped phase in the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' The data indicate a strong first order transition at a critical point λc which was estimated numerically and listed in table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' The existence of a critical point was proven in section 3, relying on the results for ballistic walks in slits and slabs in section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Our analysis of these ballistic walks proved existence of a limiting free energy in the model in figure 1 for a range of values of λ as stated in theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' However, there remains an interval [λ0, λ1) (corollary 4 and corollary 5) where existence of the free energy was not proven.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' We conjectured in both cases that λ′ 1 = λ1 = λ0, so that the free energy exists for all λ ∈ [λ0, 1], but this remains to be proven.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Our main results are summarized in theorem 1 and in theorem 7 give an explicit expression for the free energy ρ(λ) in terms of the growth constant Lw(λ) of ballistic loops in a slit or in a slab in the square and cubic lattices respective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' However, the lower bound in equation (44) proved to be quite weak, as seen in table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Acknowledgement EJJvR acknowledges financial support from NSERC (Canada) in the form of a Discovery Grant RGPIN- 2019-06303 and is grateful to SG Whittington for discussions about this model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Data generated for this study are available on reasonable request.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' 18 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='9 p(α) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='5 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content='9 入References [1] S Campbell and EJ Janse van Rensburg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Parallel PERM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' J Phys A: Math Theo, 53:265005, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' [2] JM Chan, PM Valencia, L Zhang, R Langer, and OC Farokhzad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Polymeric nanoparticles for drug delivery.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' In Cancer Nanotech, pages 163–175.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Springer, 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' [3] M-N Chee and SG Whittington.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' The growth constant of uniform star polymers in a slab geometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' J Phys A: Math Gen, 20:4915–4921, 1987.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' [4] N Clisby.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Calculation of the connective constant for self-avoiding walks via the pivot algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' J Phys A: Math Theo, 46:245001, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' [5] P-G de Gennes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Scaling Concepts in Polymer Physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Cornell, 1979.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' [6] S Friberg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Polymeric stabilization of colloidal dispersions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' donald h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' napper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' academic press, new york, 1984.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' xvi & plus;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' 428.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' J Dispersion Sci & Tech, 6(4):497–497, 1985.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' [7] P Grassberger.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Pruned-enriched Rosenbluth method: Simulations of θ polymers of chain length up to 1000000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Phys Rev E, 56:3682–3693, 1997.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' [8] MC Gufford, DRM Williams, and Sevick EM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' End-tethered polymer chains under afm tips: Compression and escape in theta solvents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Langmuir, 13(21):5691–5696, 1997.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' [9] AR Hall and M Geoghegan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Polymers and biopolymers at interfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Rep Prog Phys, 81(3):036601, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' [10] JM Hammersley and Whittington SG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Self-avoiding walks in wedges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' J Phys A: Math Gen, 18:101–111, 1985.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' [11] JM Hammersley and DJA Welsh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Further results on the rate of convergence to the connective constant of the hypercubical lattice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Quart J Math, 13:108–110, 1962.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' [12] H-P Hsu, K Binder, LI Klushin, and AM Skvortsov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' What is the order of the two-dimensional polymer escape transition?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Phys Rev E, 76(2):021108, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' [13] JL Jacobsen, CR Scullard, and AJ Guttmann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' On the growth constant for square-lattice self-avoiding walks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' J Phys A: Math Theo, 49:494004, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' [14] EJ Janse van Rensburg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' The Statistical Mechanics of Interacting Walks, Polygons, Animals and Vesicles, 2nd ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Oxford University Press, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' [15] EJ Janse van Rensburg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Supermultiplicative relations in models of interacting self-avoiding walks and polygons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' J Phys A: Math Theor, 54(10):105003, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' [16] EJ Janse van Rensburg, E Orlandini, and SG Whittington.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Self-avoiding walks in a slab: Rigorous results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' J Phys A: Math Gen, 39:13869–13902, 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' [17] N Jawahar and SN Meyyanathan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Polymeric nanoparticles for drug delivery and targeting: A comprehensive review.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Int J Health & Allied Sci, 1(4):217, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' [18] H Kesten.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' On the number of self-avoiding walks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' J Math Phys, 4:960–969, 1963.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' [19] H Kesten.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' On the number of self-avoiding walks II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' J Math Phys, 5:1128–1137, 1964.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' [20] S Levine, MM Thomlinson, and K Robinson.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Modes of polymer adsorption with excluded volume on parallel colloidal plates and their interaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Faraday Disc Chem Soc, 65:202–214, 1978.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' [21] A Milchev, V Yamakov, and K Binder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Escape transition of a compressed polymer mushroom under good solvent conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Europhys Lett, 47(6):675, 1999.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' [22] G N¨agele, B D’Aguanno, and AZ Akcasu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Preface of Proceedings of the Workshop on Colloid Physics held at the University of Konstanz, Germany from 30 November to 2 December 1995.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Elsevier, 1997.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' [23] N Nikolov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Self-avoiding walks on Z × {0, 1}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' J Stat Plan Inf, 142:376–377, 01 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' [24] J Paturej, A Milchev, SA Egorov, and K Binder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' The escape transition of a compressed star polymer: Self-consistent field predictions tested by simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Macromol, 46(19):8009–8016, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' [25] T Prellberg and J Krawczyk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Flat histogram version of the pruned and enriched Rosenbluth method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Phys Rev Lett, 92:120602, 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' [26] D Raˇcko and P Cifra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Arm retraction and escape transition in semi-flexible star polymer under cylindrical confinement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' J Mol Modeling, 21(7):1–10, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' [27] EM Sevick.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Compression and escape of a star polymer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Macromol, 33(15):5743–5746, 2000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' [28] CE Soteros.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Knots in graphs in subsets of Z3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' In SG Whittington, DW Sumners and T Lodge, editor, Topology and Geometry in Polymer Science, pages 101–133.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Springer, 1998.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' [29] CE Soteros and SG Whittington.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Polygons and stars in a slit geometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' J Phys A: Math Gen, 21:L857–L861, 1988.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' [30] A Srivastava, T Yadav, S Sharma, A Nayak, A Kumari, and N Mishra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Polymers in drug delivery.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' J Biosci Med, 4(1):69–84, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' [31] G Subramanian, DRM Williams, and PA Pincus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Interaction between finite-sized particles and end grafted polymers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Macromol, 29(11):4045–4050, 1996.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' [32] SG Whittington.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Self-avoiding walks with geometrical constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' J Stat Phys, 30:449–456, 1983.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' [33] SG Whittington.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Self-avoiding walks in restricted geometries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' In RC Lacher, editor, Proceedings of the International Course and Conference in Interfaces between Mathematics, Chemistry and Computer Science, volume 54, pages 297– 306, 1987.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' [34] SG Whittington and CE Soteros.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Polymers in slabs, slits, and pores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Israel J Chem, 31:127–133, 1991.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' [35] SG Whittington and CE Soteros.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Uniform branched polymers in confined geometries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Macromol Rep, 29(S2):195–199, 1992.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' [36] TA Witten and PA Pincus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Colloid stabilization of long grafted polymers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' Macromolecules, 19:2509–2513, 1986.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} +page_content=' 19' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gtFMT4oBgHgl3EQf2zH5/content/2301.12446v1.pdf'} diff --git a/h9E3T4oBgHgl3EQf4gse/content/tmp_files/2301.04772v1.pdf.txt b/h9E3T4oBgHgl3EQf4gse/content/tmp_files/2301.04772v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..c8e984d906197926a13e9b9d0bf7bdbce02bd918 --- /dev/null +++ b/h9E3T4oBgHgl3EQf4gse/content/tmp_files/2301.04772v1.pdf.txt @@ -0,0 +1,819 @@ +Draft version January 13, 2023 +Typeset using LATEX twocolumn style in AASTeX631 +Climbing the Cliffs: Classifying YSOs in the Cosmic Cliffs using a ML Approach with JWST Data +B. L. Crompvoets +,1, 2 H.Teimoorinia,2, 1 and J. Di Francesco +2, 1 +1Department of Physics and Astronomy, University of Victoria, Victoria, BC, Canada +2NRC Herzberg Astronomy and Astrophysics, 5071 West Saanich Road, Victoria, BC V9E 2E7, Canada +ABSTRACT +The James Webb Space Telescope (JWST) observed a section of the star forming region NGC +3324 during its Early Release Observations. We make use of the Probabilistic Random Forest machine +learning model to identify YSOs within the field of view. We build a matched catalog from photometry +data products available on the Mikulski Space Telescope Archive and retrieve 8632 objects, of which +Spitzer previously detected 458. We use previously classified data from Spitzer to train on a sample of +the Webb data. We retrieve a total of 72 YSO candidates within the data field, 52 of which are only +visible with JWST. +1. INTRODUCTION +On July 11th, 2022, the first observations from the +James Webb Space Telescope (JWST) were released +(Pontoppidan et al. 2022). These data included observa- +tions of four different astrophysical objects, one of which +was the NGC 3324 star-forming region located adjacent +to the Carina Nebula. JWST imaged NGC 3324 with +two instruments: the Near Infra-Red Camera (NIRCam) +to observe the dust collections and look for emission lines +of H2, Poly-Aromatic Hydrocarbons (PAHs) and Pa-α; +and the Mid Infra-Red Instrument (MIRI) which was +Filter +texp(s) +Use +F090W +25768.32 +dust and background stellar field +F187N +46382.88 +ionized gas via the bright Pa-α +F200W +25768.32 +dust and background stellar field +F335M +6442.08 +3.3 µm PAH emission +F444W +6442.08 +dust scattering from large grains +F470N +11595.72 +H2 from embedded jets/outflows +F770W +6771.08 +PAH emission +F1130W +6771.08 +PAH emission +F1280W +6993.12 +12.81 µm [Ne II] line emission +F1800W +5994.08 +cool dust and proplyds +Table 1. JWST filters used by ERO to image NGC 3324, +their exposure times, and their uses as described in Pontop- +pidan et al. (2022). The first block lists NIRCam filters and +the second lists MIRI filters. +Corresponding author: B. L. Crompvoets +bcrompvoets@uvic.ca +able to probe for objects hidden within the dust that +may have been rendered invisible at shorter wavelengths. +The Early Release Observations (ERO, Pontoppidan +et al. 2022) of NGC 3324 focused on a ∼7.′4 × 4.′4 area +with NIRCam, and a ∼6.′4 × 2.′2 area within the NIR- +Cam field with MIRI, relatively small areas in compar- +ison to the entirety of NGC 3324, termed the Cosmic +Cliffs (hereafter CC). The data were collected in six +NIRCam bands and four MIRI bands; see Table 1 for +details on bands used, exposure times, and uses. The +exposure times varied for each filter, and the FULLBOX +10-point dither pattern was used for NIRCam imaging +and 8-point dither for MIRI imaging (Pontoppidan et al. +2022). +The FITS images as well as a source catalog +generated for each filter by the JWST pipeline were +made publicly available through the Mikulski Archive +for Space Telescopes1. For our use, we access the source +catalogs at MAST created using Source Extractor (SEx- +tractor, Bertin & Arnouts 1996) as part of the JWST +pipelines2. These data products were reprocessed since +July 2022 as better JWST flux calibrations became +available; for this paper, the data products for NGC +3324 were last accessed on December 19th, 2022. +Already, the JWST data of NGC 3324 have been +probed to understand the capabilities of JWST to de- +tect jets and outflows. Reiter et al. (2022) looked at the +narrowband 1.87 µm filter and the difference between +the narrowband 4.7 µm and wideband 4.44 µm filters +from JWST. In combination with archival Hubble data, +1 https://doi.org/10.17909/67ft-nb86 +2 https://jwst-pipeline.readthedocs.io/en/stable/jwst/source catalog +arXiv:2301.04772v1 [astro-ph.SR] 12 Jan 2023 + +ID2 +Crompvoets et al. +they used this dataset to identify 31 outflows within the +field of view, including 7 Herbig-Haro objects only visi- +ble in the infrared (IR). Along with their identifications +of outflows, they provided a list of 24 possible progen- +itor Young Stellar Objects (YSOs). These progenitors +were determined as IR-excess sources located along the +estimated line of travel determined by tracing the out- +flows back in time. As not all objects were visible in +the Hubble data, they did not have proper motions for +all outflows, and so straight-line estimation was used +when appropriate. Reiter et al. (2022) also checked to +see if any of their identified YSO candidates had been +previously identified with Spitzer data via comparison +with the Spitzer-IRAC Catalog for YSOs (SPICY, Kuhn +et al. 2021), a catalog developed with the use of machine +learning (ML), and found matches to 6/24 possible pro- +genitors. +1.1. Machine Learning Tools +Within the last several years, ML has emerged as a +useful tool within star formation (e.g. Miettinen 2018; +Cornu & Montillaud 2021; Chiu et al. 2021; Kuhn et al. +2021). +These and other works have used Gradient +Boosting (Miettinen 2018), neural networks (Miettinen +2018; Cornu & Montillaud 2021; Chiu et al. 2021), and +random forest models (Kuhn et al. 2021), among oth- +ers. Each of these ML approaches have their strengths, +and each has successfully separated YSOs from the con- +taminating classes of stars, galaxies, PAHs, and Active +Galactic Nuclei (AGN) to high accuracies. +A common pitfall with ML classification algorithms +occurs with imbalanced data-sets. As YSOs are much +less frequent than regular field stars, this imbalance is a +relevant issue within the star formation field. Random +Forest (RF) models are better at handling imbalanced +datasets, by individually classifying each object based +off of a training set (Breiman 2001). Kuhn et al. (2021), +whose catalog previously included the YSOs within the +CC, utilized a RF trained on an imbalanced mix of +YSOs and contaminant field objects where the number +of YSOs accounted for less than 25% of the full train- +ing set. They used the area under the receiver-operator +curve as their metric to determine the best fit model. As +RF models output the probabilities of objects being in +the positive class, Kuhn et al. (2021) chose that an ob- +ject would be classified as a YSO if it had at least a 50% +probability of being so as determined by their singular +RF network. After YSOs were identified, Kuhn et al. +(2021) further used cuts based on the spectral index to +determine the stages of star formation the YSOs are in, +labelling them as either Class I, Flat-Spectrum, or Class +II YSOs. +A second common issue with ML is that most ML al- +gorithms cannot handle missing data. Kuhn et al. (2021) +worked around this issue by using copulas, i.e., functions +which connect the probability distributions of different +features to each other. When using copulas, the joint +probability distributions of the data are decomposed +into their marginal components, and the copula couples +these probabilities together (Nelsen 2007). Using copu- +las to fill missing data, however, assumes that data are +missing because an object is not in the field of view of the +given filter. Chiu et al. (2021) used a different approach +to missing data that assumes objects in question are +within the field of view of the filter, but no point sources +were detected. Such detection gaps could happen when +an object is heavily obscured in certain filters. The so- +lution provided by Chiu et al. (2021) is to fill the data +in missing bands with 1% of the smallest flux obtained +in that band as a reasonable estimate for the thermal +noise of the detector. This method hence accounts for +the clarity of an object at different wavelengths, which +is important for the determination of class. +An alternative solution to the issue of missing data +is provided by the Probabilistic Random Forest (PRF) +method released by Reis & Baron (2019), which has suc- +cessfully been applied to high-mass YSO identification +in Local Group galaxies (e.g., Kinson et al. 2021, 2022). +The PRF method uses both the values and errors of each +filter to create probability distributions for each data +point, where the expectation value is the data point’s +flux, and the standard deviation is the error on this flux, +assuming a Gaussian distribution. An RF-like algorithm +is hence trained, and when an object is sent through the +network, it is no longer sent along one branch of the tree. +Instead, at every decision node, the probability of the +object being on either side of the node is propagated, +with probability determined by the Gaussian distribu- +tion. For a full prescription, see Reis & Baron (2019). +This method has the benefit of not assuming what the +missing data may be while still accounting for them by +passing any node that relies upon the data with equal +probability to either side. +Reis & Baron (2019) provide a comparison with the +regular RF that shows that when all labels are correct, +the PRF and RF perform at the same accuracy. When +purposefully introducing incorrect target labels, how- +ever, they find that the PRF greatly outperforms the +regular RF. We perform our own check of the perfor- +mance of the PRF vs a regular RF, using both copu- +las and thermal noise to fill the missing data with the +regular RF. To perform a fair comparison, we use data +from the Cores to Disks (c2d, Evans et al. 2014) sur- +vey, which contains data with both completely filled + +Climbing the Cliffs +3 +Figure 1. A comparison of the F1-Scores for the validation +set of the PRF (solid red line), RF filled via copulas (blue +dashed line), and RF filled with thermal noise (purple dashed +line) as a function of the amount of missing data. +and missing values. We first use 10 000 objects with +all bands available, then 9000 objects with all bands +available and an additional 1000 (randomly chosen) ob- +jects with data missing in at least one band to obtain a +case where 90% of data is filled. Similarly, we also ob- +tain data-sets where 80%, 70%, 60%, and 50% of data +are filled. In all cases, the data are real observations, +and no data are artificially removed. We use YSOs as +our positive class and all others as contaminants, where +YSOs make up approximately 1/3 of the sample. Fig- +ure 1.1 shows the performance in all three cases with a +decrease in available data. We find that all three cases +perform within a few percent. In general, filling the data +with noise and using copulas perform equally well. We +use the Python package copulas for our calculations. +This Letter is split into the following sections. Sec- +tion 2 describes how we created the catalog of JWST +data for NGC 3324, as well as a description of the ML +model used. Section 3 provides the results of this ML +model, including the number of candidate YSOs de- +tected and a comparison with those found by both Kuhn +et al. (2021) and Reiter et al. (2022). Finally, Section 4 +discusses the accuracies of our classification, and pro- +vides an analysis of the capabilities of JWST for YSO +detection in comparison to Spitzer. +2. METHODOLOGY +2.1. Catalog Creation +The data retrieved from MAST were available as +the direct outputs from SExtractor (Bertin & Arnouts +1996), which provided both fluxes and magnitudes, as +well as sizes and locations, for all of the point sources de- +tected within a given filter. To match objects between +filters, we find those objects whose equatorial coordi- +nates are within one sigma of the center of the source, +as determined by SExtractor in F470N-F444W. Because +of JWST’s extraordinary resolution, this matching cri- +terion remains a very small solid angle, ensuring each +object is correctly linked across wavelengths. We used +the Astropy (The Astropy Collaboration et al. 2018) +match coordinates sky +task to build our catalog of +objects in all bands. We removed all objects which con- +tained only one data-point after catalog matching was +completed. This approach resulted in a total of 8632 +individual point sources. +We next used the Astropy (The Astropy Collabo- +ration et al. 2018) match coordinates sky +task to +match the Spitzer detections from the GLIMPSE cat- +alog (Preibisch et al. 2014)3 and available SPICY tar- +gets (Kuhn et al. 2021). Again, matches were identified +when objects were within one sigma of the JWST source, +resulting in 458 objects detected by both Spitzer and +JWST, 26 of which were labelled as YSOs with SPICY +(Kuhn et al. 2021). +The MAST SExtractor files provided both vari- +able aperture and isophotal photometry for each point +source. To identify the best type of photometry to use, +we compared the photometry of sources matched in both +the JWST 4.44 µm and Spitzer 4.5 µm bands, whose +transmission curves are very similar. As such, we ex- +pect that flux values in these two bands should be very +similar. We find that the isophotal photometry best ap- +proaches a 1:1 correlation between these two bands, and +thus our final catalog uses only isophotal photometry for +JWST data. +2.2. Applying the Probabilistic Random Forest method +To classify the full JWST dataset, we must first have +predetermined classifications for some portion of the +data. The SPICY catalog (Kuhn et al. 2021) provided +classifications of all YSOs within the GLIMPSE survey, +of which NGC 3324 was included. After retrieving the +GLIMPSE catalog, and matching it to the SPICY tar- +gets, we were able to say that any object not classified as +a YSO by SPICY was then classified as a contaminant +(Kuhn et al. 2021), and so we obtained classifications +for all objects detected in the Spitzer IRAC bands for +the CC. The cross-matched catalogue became the train- +ing set for classifying further JWST data within the CC +field of view. By training on data within this field, the +3 https://doi.org/10.26131/IRSA213 + +1.00 +0.98 +F1-Score +0.96 +0.94 +0.92 +PRF +RF Copula +RF Noise +- +0.90 +100 +90 +80 +70 +60 +50 +% Data Available4 +Crompvoets et al. +possible effects of extinction on the measured fluxes are +eliminated. Furthermore, the absolute flux calibration +is less important that the shape of the spectrum as it +the latter is what the model learns. +The very dusty field of the CC means there are many +objects within it that are not visible at all wavelengths. +We hence choose to use the probabilistic random forest +(PRF) method for our classification. The PRF requires +three input parameters for supervised classification: the +input data, errors on the input data, and the targets +for the input data. We test several different input data +structures: including all ten bands available, removing +only the narrow bands, removing only the MIRI bands, +and finally removing one band at a time to test for im- +provements within the classification. In all cases, our +training set is then made up of 25% YSOs and 75% con- +taminant objects. Our validation set was the entire set +of previously classified objects. +To determine the best configuration of the PRF, we +ran the model 500 times, changing the random seed be- +tween 0 and 1000. There are four possible metrics we +could have chosen from: accuracy, recall, precision, and +F1-Score. Each of these metrics requires some combina- +tion of the numbers of True Positives (TP), False Pos- +itives (FP), True Negatives (TN), and False Negatives +(FN). For our case, TP is the number of objects cor- +rectly classified as YSOs, TN is the number of objects +correctly classified as contaminants, FP is the number +of contaminant objects incorrectly classified as YSOs, +and FN is the number of YSOs incorrectly classified as +contaminants. Accuracy, A = (TP + TN)/(TP + FP + +FN + TN) is a measure of the total number of cor- +rect identifications but can be easily made suspiciously +high as a result of a much larger negative class. +As +such, we do not use it as our metric. +The F1-score, +F1 = 2R×P/(R+P), however, is a metric defined as the +harmonic balance between recall R = TP/(TP + FN) +and precision P = TP/(TP + FP). We use it as our +metric of choice because we wish to obtain a network +with low contamination by much more numerous stars +(high precision) while still maintaining a high recovery +of YSOs (high recall). +Along with providing classifications, the PRF also al- +lows us to determine which bands are most important to +the classification and which bands, if any, are superflu- +ous through the PRF feature importances method. +To determine the order of importance, the most im- +portant band is successively removed from the data in- +put ensemble, and the classification is repeated until no +bands are left. Table 2 lists the bands from most im- +portant to least important, the F1-scores for both the +training and validation sets when only that band is re- +moved, and the number of YSOs found in the full JWST +dataset of 8632 objects. +Band +F1 % (tr) +F1 % (va) +# YSOs +F470N +84 +72 +63a +F444W +82 +68 +107 +F335M +84 +73 +73 +F187N +84 +75 +90 +F090W +94 +75 +95 +F200W +92 +67 +985 +F1280W +82 +72 +72 +F1130W +82 +71 +99 +F770W +87 +75 +97 +F1800W +84 +72 +149 +All bands present +84 +72 +141 +N bands removed +82 +71 +62 +MIRI bands removed +84 +75 +126 +a +The number of YSOs and F1-Scores are for one run only. +Table 2. +The bands are listed from from most to least +important for YSO identification as determined using the +PRF feature importances tool. In each column, the band +in that row is removed, and the metrics are calculated. F1- +Scores are given for the training and validation sets in the +first and second columns, respectively. +F1-Scores have an +error of ∼ 2%. The number of YSOs found in the full JWST +dataset are labelled in the last column. +The number of YSOs identified is seen to vary based +on the classification, despite the F1-Scores remaining +similar. Indeed, when we randomly seed the PRF 1000 +times we find that ∼60% of the time, less than 100 ob- +jects out of 8632 are classified as YSOs. Figure 2 shows +the distribution of the number of objects classified as +YSOs compared to the F1-Scores for each run. Hence, +we take the classifications for all objects over 1000 runs +of the model and take the probability of a given object +being a YSO as the fraction of times that it is identified +as a YSO. As in Kuhn et al. (2021), if a given object has +a probability of greater than 50%, then it is classified as +a YSO. Figure 3 shows various metrics for the valida- +tion set of the YSO classification as a function of the +cut on the probability of a given object being a YSO. +The higher the cut, the fewer objects are classified as +YSOs, leading to a decrease in recall and increase in +precision, though the F1-Score remains relatively even. +At around a cut of 40%, the precision, recall, and F1- +Score are nearly equivalent. There are no YSOs with +100% probability, leading to the sharp decrease in all +metrics at this cut. The figure confirms that 50% is a +reasonable cut for the probability of the object being a +YSO. + +Climbing the Cliffs +5 +Figure 2. A plot comparing the number of YSOs found vs +the F1-Score on the validation sets for 1000 runs of the PRF +using all JWST bands available. +Figure 3. The trends of various metrics with a variation +of the cut in probability that determines if a given object +is a YSO. The number of YSOs returned dependant on this +probability. There are no YSOs with 100% probability. +3. RESULTS +From the JWST photometry of CC, we retrieve a total +of 8632 objects. Only 72 of these objects are found to be +YSOs, with a probability greater than 50%. Of these, +20 were recovered from the 26 SPICY objects, leading +to a recall of 73%, precision of 90%, and an F1-Score of +81%. We also find that of the 23 candidate progenitors +identified in Reiter et al. (2022) only three, previously +identified in SPICY (Kuhn et al. 2021), were found to +be YSOs in our final classification. +While analyzing the feature importances , it is ex- +pected that if all features (filters) are independent, the +importance of each band will remain the same even as +other bands are taken away. In the case where two bands +switch position in the order of feature importance +these bands are correlated. Some correlation is appar- +ent between F770W, F1280W, and F1800W, as these +three bands routinely shifted ordering when determin- +ing the band importance. Similarly, F090W and F200W +were found to be slightly correlated by this method. The +narrow bands F187N and F470N, which trace Pa-α and +H2 emission, respectively, were not found to be espe- +cially important for classification. Removing one or the +other did not greatly impact the classification, nor did +the removal of both filters data. +In general, any one +band can be removed without a great impact on the +F1-Score. +Similarly, MIRI bands were not found to be especially +influential to the classification, although this is likely +due to the unavailability of data for nearly half the +field of view imaged by NIRCam. Furthermore, we were +only able to train on objects with Spitzer IRAC data; +for those objects whose SEDs peak within the mid- to +far-infrared they may not be sampled in the training +set, whose JWST SEDs will follow the Spitzer SEDs. +This potential bias will hopefully be eliminated in fu- +ture work. +We found that, out of the 458 objects classified by +SPICY in the CC, 418 were consistently classified by +both us and SPICY. Unsurprisingly, we found that the +objects not consistently classified between our approach +and that of SPICY tend to have fewer bands available. +In particular, there were two objects which were clas- +sified as YSOs in SPICY but as contaminants in our +work, and they both contain data in only three out of +ten bands. +Indeed, this behaviour may be biased by +the match between Spitzer and JWST data, where the +locations of the Spitzer point sources may have been +closer to a different point source in JWST data, an ef- +fect caused by the lower resolution of Spitzer in com- +parison to JWST. Similarly, objects classified as con- +taminants in SPICY and YSOs in our work tend to be +missing the 4.44 µm and 4.70 µm JWST photometry, +while their proposed Spitzer counterparts contain data +in this range. One of the SPICY YSOs is only captured +in the MIRI data as it is offset from the NIRCam data. +4. DISCUSSION AND CONCLUSION +This work aimed to provide classifications of YSOs +within the ERO JWST data of NGC 3324. There are +∼ 8600 objects within the JWST fields of ∼ 7.4′×4.4′ by +NIRCam and ∼ 6.4′ × 2.2′ by MIRI. Of these objects, + +200 +0 +0.80 +0.78 +0.76 +Os +S +0.74 +of +Score +0.72 +0.70 +L +0.68 +0.66 +0 +250 +500 +750 +1000 +1250 + 1500 +0 +200 +Amount of objects classified as YsOs1.0 +0.8 +S +Metric Score +103 +S +0.6 +JO +lumber +0.4 +102 +F1-Score +Precision +Z +0.2 - +Recall +Number YSOs +0.0 +0.0 +0.1 +0.2 +0.3 +0.4 +0.5 +0.6 +0.7 +0.8 +0.9 +1.0 +Probability YSO Cut6 +Crompvoets et al. +less than 500 were detectable by Spitzer. Those that +were detectable were classified and made available as a +catalog (SPICY) by Kuhn et al. (2021). We match the +SPICY catalog to the GLIMPSE data (Preibisch et al. +2014) so that we have a record of the objects which +are contaminants or YSOs. +The classified population +within the CC fields then made up our training set for +our probabilistic random forest model to classify JWST +data. +With our small training set, it is very possible to have +overfit our model to the available data. We do see that +the training set performs around 10% better, a key sign- +post of overfitting. However we do see a similar trend +between the training and validation sets as we modify +the input data, suggesting that the issue is not as severe. +With even this small amount of classified data, we +were able to separate 72 YSO candidates from the rest +of the JWST data. Table 3 contains a comparison of +the objects labelled by Reiter et al. (2022) and Kuhn +et al. (2021) as well as those objects we newly identify +as YSO candidates. We recover 20/26 SPICY YSOs, i.e. +approximately a 73% recall rate. +The YSOs identified in SPICY are estimated to have a +less than 10% contamination rate (Kuhn et al. 2022). Of +the seven objects identified as contaminants in our algo- +rithm, one of them was mismatched, and one of them is +only available in MIRI data. Of the remaining five, three +have a probability of being a YSO less than 10%. As +such, 3/26 objects give a contamination rate of 11.5%, +which is similar to the 10% contamination rate identi- +fied in Kuhn et al. (2022) over an analysis of 26 YSO +candidates. +At this stage, we obtained a high F1-Score for the +validation set, and we can assume a low contamination +based off of the number of YSOs that we retrieved from +the full dataset of 8632 objects. If even 10% of contami- +nants were misclassified as YSOs, we would have greater +than 800 objects classified as YSOs. As it is, by boot- +strapping the results, we obtained the probability of an +object being a YSO based off the number of times it +was classified by a PRF (whose validation F1-Score was +approximately 81%). We report an object as a YSO if +the probability of being a YSO is greater than the prob- +ability of being a contaminant (50%). We include the +probabilities in our published catalog for future refer- +ence. +Based upon these probabilities, we find that the PRF +method (Reis & Baron 2019) holds promise for accurate +YSO identification from JWST data, especially as we +wait for more data to become available. At this stage, +we are limited by the relatively small amount of previ- +ously classified data available. We cannot yet, for in- +stance, realistically apply the ML model to determine +the stage of star formation. +The PRF, however, was +able to recover previously identified YSOs to 85% F1- +Score and retrieved a reasonable number of YSOs from +the entire set. With more JWST data becoming avail- +able and the use of synthetic JWST data, these metrics +can only improve. +The authors would like to thank Peter Stetson, Chris +Willott, and Nicholas Martis for advice on JWST pho- +tometry. In addition, we thank the staff of the NASA- +funded Mikulski Archive for Space Telescopes (MAST) +for providing the data products used for this paper. JDF +acknowledges the support of an NSERC Discovery Grant +held at the University of Victoria. +REFERENCES +Bertin, E., & Arnouts, S. 1996, A&AS, 117, 393, +doi: 10.1051/aas:1996164 +Breiman, L. 2001, Machine Learning, 45, 5, +doi: 10.1023/A:1010933404324 +Chiu, Y. L., Ho, C. T., Wang, D. W., & Lai, S. P. 2021, +Astronomy and Computing, 36, 100470, +doi: 10.1016/j.ascom.2021.100470 +Cornu, D., & Montillaud, J. 2021, A&A, 647, A116, +doi: 10.1051/0004-6361/202038516 +Evans, N. J., I., Allen, L. E., Blake, G. A., et al. 2014, +VizieR Online Data Catalog, II/332 +Kinson, D. A., Oliveira, J. M., & van Loon, J. T. 2021, +MNRAS, 507, 5106, doi: 10.1093/mnras/stab2386 +—. 2022, MNRAS, 517, 140, doi: 10.1093/mnras/stac2692 +Kuhn, M. A., de Souza, R. S., Krone-Martins, A., et al. +2021, ApJS, 254, 33, doi: 10.3847/1538-4365/abe465 +Kuhn, M. A., Saber, R., Povich, M. S., et al. 2022, AJ, 165, +3, doi: 10.3847/1538-3881/ac9314 +Miettinen, O. 2018, Ap&SS, 363, 197, +doi: 10.1007/s10509-018-3418-7 +Nelsen, R. B. 2007, An introduction to copulas (Springer +Science & Business Media) +Pontoppidan, K. M., Barrientes, J., Blome, C., et al. 2022, +ApJL, 936, L14, doi: 10.17909/67ft-nb86 + +Climbing the Cliffs +7 +Preibisch, T., Zeidler, P., Ratzka, T., Roccatagliata, V., & +Petr-Gotzens, M. G. 2014, A&A, 572, A116, +doi: 10.1051/0004-6361/201424045 +Reis, I., & Baron, D. 2019, PRF: Probabilistic Random +Forest, Astrophysics Source Code Library, record +ascl:1903.009. http://ascl.net/1903.009 +Reiter, M., Morse, J. A., Smith, N., et al. 2022, MNRAS, +doi: 10.1093/mnras/stac2820 +The Astropy Collaboration, Price-Whelan, A. M., Sip˝ocz, +B. M., et al. 2018, AJ, 156, 123, +doi: 10.3847/1538-3881/aabc4f + +8 +Crompvoets et al. +JWST Number +Kuhn et al. (2021) +This work +J103635.2-584029 +CI - SPICY 7409 +J103648.7-583803 +CII - SPICY 7428 +YSO +J103652.5-583725 +CI - SPICY 7435 +YSO +J103656.6-583659 +CII - SPICY 7444 +YSO +J103657.4-583637 +CII - SPICY 7447 +YSO +J103658.4-583619 +FS - SPICY 7448 +YSO +J103658.9-583742 +CII - SPICY 7452 +J103659.1-583524 +FS - SPICY 7454 +YSO +J103700.1-583528 +FS - SPICY 7461 +YSO +J103700.4-583829 +CII - SPICY 7462 +YSO +J103700.7-583545 +CII - SPICY 7464 +YSO +J103700.8-583622 +FS - SPICY 7465 +YSO +J103702.5-583403 +CI - SPICY 7469 +YSO +J103705.7-583418 +FS - SPICY 7473 +YSO +J103706.4-583517 +CII - SPICY 7475 +YSO +J103706.7-583419 +CII - SPICY 7476 +YSO +J103706.9-583655 +CII - SPICY 7477 +YSO +J103708.4-583654 +CII - SPICY 7479 +YSO +J103711.3-583445 +CII - SPICY 7481 +YSO +J103711.7-583424 +CII - SPICY 7482 +J103642.3-583804 +- +J103648.0-583819 +- +J103647.3-583810 +CI - SPICY 7423 +YSO +J103646.7-583805 +- +J103651.5-583754 +- +J103650.5-583752 +- +J103651.4-583748 +- +J103653.8-583748 +- +J103651.5-583710 +- +J103654.2-583626 +- +J103654.4-583618 +- +J103654.0-583720 +CI - SPICY 7441 +J103653.6-583520 +- +J103653.1-583737 +- +J103653.3-583754 +UN - SPICY 7438 +YSO +J103652.7-583805 +J103653.1-583708 +- +J103651.6-583658 +- +J103652.3-583809 +CI - SPICY 7434 +J103653.9-583629 +FS - SPICY 7440 +J103701.5-583751 +- +J103702.1-583658 +CII - SPICY 7467 +YSO +J103653.9-583632 +- +Table 3. The top half of this table shows the YSOs identi- +fied with Kuhn et al. (2021) and whether or not they were +classified as YSOs with our model. Classes are included as +CI = Class I, CII = Class II, FS = Flat Spectrum, and UN = +Uncertain for those objects found within Kuhn et al. (2021). +The bottom half of this table shows the objects identified +by Reiter et al. (2022) as potential progenitors for jets and +the comparable YSO candidates within this work and Kuhn +et al. (2021). + diff --git a/h9E3T4oBgHgl3EQf4gse/content/tmp_files/load_file.txt b/h9E3T4oBgHgl3EQf4gse/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..b61004c2ac7444592c42f3ae3c0b304484d39f0f --- /dev/null +++ b/h9E3T4oBgHgl3EQf4gse/content/tmp_files/load_file.txt @@ -0,0 +1,455 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf,len=454 +page_content='Draft version January 13, 2023 Typeset using LATEX twocolumn style in AASTeX631 Climbing the Cliffs: Classifying YSOs in the Cosmic Cliffs using a ML Approach with JWST Data B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Crompvoets ,1, 2 H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='Teimoorinia,2, 1 and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Di Francesco 2, 1 1Department of Physics and Astronomy, University of Victoria, Victoria, BC, Canada 2NRC Herzberg Astronomy and Astrophysics, 5071 West Saanich Road, Victoria, BC V9E 2E7, Canada ABSTRACT The James Webb Space Telescope (JWST) observed a section of the star forming region NGC 3324 during its Early Release Observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' We make use of the Probabilistic Random Forest machine learning model to identify YSOs within the field of view.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' We build a matched catalog from photometry data products available on the Mikulski Space Telescope Archive and retrieve 8632 objects, of which Spitzer previously detected 458.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' We use previously classified data from Spitzer to train on a sample of the Webb data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' We retrieve a total of 72 YSO candidates within the data field, 52 of which are only visible with JWST.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' INTRODUCTION On July 11th, 2022, the first observations from the James Webb Space Telescope (JWST) were released (Pontoppidan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' These data included observa- tions of four different astrophysical objects, one of which was the NGC 3324 star-forming region located adjacent to the Carina Nebula.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' JWST imaged NGC 3324 with two instruments: the Near Infra-Red Camera (NIRCam) to observe the dust collections and look for emission lines of H2, Poly-Aromatic Hydrocarbons (PAHs) and Pa-α;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' and the Mid Infra-Red Instrument (MIRI) which was Filter texp(s) Use F090W 25768.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='32 dust and background stellar field F187N 46382.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='88 ionized gas via the bright Pa-α F200W 25768.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='32 dust and background stellar field F335M 6442.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='08 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='3 µm PAH emission F444W 6442.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='08 dust scattering from large grains F470N 11595.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='72 H2 from embedded jets/outflows F770W 6771.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='08 PAH emission F1130W 6771.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='08 PAH emission F1280W 6993.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='12 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='81 µm [Ne II] line emission F1800W 5994.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='08 cool dust and proplyds Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' JWST filters used by ERO to image NGC 3324, their exposure times, and their uses as described in Pontop- pidan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' The first block lists NIRCam filters and the second lists MIRI filters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Corresponding author: B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Crompvoets bcrompvoets@uvic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='ca able to probe for objects hidden within the dust that may have been rendered invisible at shorter wavelengths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' The Early Release Observations (ERO, Pontoppidan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' 2022) of NGC 3324 focused on a ∼7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='′4 × 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='′4 area with NIRCam, and a ∼6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='′4 × 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='′2 area within the NIR- Cam field with MIRI, relatively small areas in compar- ison to the entirety of NGC 3324, termed the Cosmic Cliffs (hereafter CC).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' The data were collected in six NIRCam bands and four MIRI bands;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' see Table 1 for details on bands used, exposure times, and uses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' The exposure times varied for each filter, and the FULLBOX 10-point dither pattern was used for NIRCam imaging and 8-point dither for MIRI imaging (Pontoppidan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' The FITS images as well as a source catalog generated for each filter by the JWST pipeline were made publicly available through the Mikulski Archive for Space Telescopes1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' For our use, we access the source catalogs at MAST created using Source Extractor (SEx- tractor, Bertin & Arnouts 1996) as part of the JWST pipelines2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' These data products were reprocessed since July 2022 as better JWST flux calibrations became available;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' for this paper, the data products for NGC 3324 were last accessed on December 19th, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Already, the JWST data of NGC 3324 have been probed to understand the capabilities of JWST to de- tect jets and outflows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Reiter et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' (2022) looked at the narrowband 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='87 µm filter and the difference between the narrowband 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='7 µm and wideband 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='44 µm filters from JWST.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' In combination with archival Hubble data, 1 https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='17909/67ft-nb86 2 https://jwst-pipeline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='readthedocs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='io/en/stable/jwst/source catalog arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='04772v1 [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='SR] 12 Jan 2023 ID2 Crompvoets et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' they used this dataset to identify 31 outflows within the field of view, including 7 Herbig-Haro objects only visi- ble in the infrared (IR).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Along with their identifications of outflows, they provided a list of 24 possible progen- itor Young Stellar Objects (YSOs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' These progenitors were determined as IR-excess sources located along the estimated line of travel determined by tracing the out- flows back in time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' As not all objects were visible in the Hubble data, they did not have proper motions for all outflows, and so straight-line estimation was used when appropriate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Reiter et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' (2022) also checked to see if any of their identified YSO candidates had been previously identified with Spitzer data via comparison with the Spitzer-IRAC Catalog for YSOs (SPICY, Kuhn et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' 2021), a catalog developed with the use of machine learning (ML), and found matches to 6/24 possible pro- genitors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Machine Learning Tools Within the last several years, ML has emerged as a useful tool within star formation (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Miettinen 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Cornu & Montillaud 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Chiu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Kuhn et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' These and other works have used Gradient Boosting (Miettinen 2018), neural networks (Miettinen 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Cornu & Montillaud 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Chiu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' 2021), and random forest models (Kuhn et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' 2021), among oth- ers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Each of these ML approaches have their strengths, and each has successfully separated YSOs from the con- taminating classes of stars, galaxies, PAHs, and Active Galactic Nuclei (AGN) to high accuracies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' A common pitfall with ML classification algorithms occurs with imbalanced data-sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' As YSOs are much less frequent than regular field stars, this imbalance is a relevant issue within the star formation field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Random Forest (RF) models are better at handling imbalanced datasets, by individually classifying each object based off of a training set (Breiman 2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Kuhn et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' (2021), whose catalog previously included the YSOs within the CC, utilized a RF trained on an imbalanced mix of YSOs and contaminant field objects where the number of YSOs accounted for less than 25% of the full train- ing set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' They used the area under the receiver-operator curve as their metric to determine the best fit model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' As RF models output the probabilities of objects being in the positive class, Kuhn et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' (2021) chose that an ob- ject would be classified as a YSO if it had at least a 50% probability of being so as determined by their singular RF network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' After YSOs were identified, Kuhn et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' (2021) further used cuts based on the spectral index to determine the stages of star formation the YSOs are in, labelling them as either Class I, Flat-Spectrum, or Class II YSOs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' A second common issue with ML is that most ML al- gorithms cannot handle missing data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Kuhn et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' (2021) worked around this issue by using copulas, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=', functions which connect the probability distributions of different features to each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' When using copulas, the joint probability distributions of the data are decomposed into their marginal components, and the copula couples these probabilities together (Nelsen 2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Using copu- las to fill missing data, however, assumes that data are missing because an object is not in the field of view of the given filter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Chiu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' (2021) used a different approach to missing data that assumes objects in question are within the field of view of the filter, but no point sources were detected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Such detection gaps could happen when an object is heavily obscured in certain filters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' The so- lution provided by Chiu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' (2021) is to fill the data in missing bands with 1% of the smallest flux obtained in that band as a reasonable estimate for the thermal noise of the detector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' This method hence accounts for the clarity of an object at different wavelengths, which is important for the determination of class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' An alternative solution to the issue of missing data is provided by the Probabilistic Random Forest (PRF) method released by Reis & Baron (2019), which has suc- cessfully been applied to high-mass YSO identification in Local Group galaxies (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=', Kinson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' 2021, 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' The PRF method uses both the values and errors of each filter to create probability distributions for each data point, where the expectation value is the data point’s flux, and the standard deviation is the error on this flux, assuming a Gaussian distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' An RF-like algorithm is hence trained, and when an object is sent through the network, it is no longer sent along one branch of the tree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Instead, at every decision node, the probability of the object being on either side of the node is propagated, with probability determined by the Gaussian distribu- tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' For a full prescription, see Reis & Baron (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' This method has the benefit of not assuming what the missing data may be while still accounting for them by passing any node that relies upon the data with equal probability to either side.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Reis & Baron (2019) provide a comparison with the regular RF that shows that when all labels are correct, the PRF and RF perform at the same accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' When purposefully introducing incorrect target labels, how- ever, they find that the PRF greatly outperforms the regular RF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' We perform our own check of the perfor- mance of the PRF vs a regular RF, using both copu- las and thermal noise to fill the missing data with the regular RF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' To perform a fair comparison, we use data from the Cores to Disks (c2d, Evans et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' 2014) sur- vey, which contains data with both completely filled Climbing the Cliffs 3 Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' A comparison of the F1-Scores for the validation set of the PRF (solid red line), RF filled via copulas (blue dashed line), and RF filled with thermal noise (purple dashed line) as a function of the amount of missing data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' and missing values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' We first use 10 000 objects with all bands available, then 9000 objects with all bands available and an additional 1000 (randomly chosen) ob- jects with data missing in at least one band to obtain a case where 90% of data is filled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Similarly, we also ob- tain data-sets where 80%, 70%, 60%, and 50% of data are filled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' In all cases, the data are real observations, and no data are artificially removed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' We use YSOs as our positive class and all others as contaminants, where YSOs make up approximately 1/3 of the sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Fig- ure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='1 shows the performance in all three cases with a decrease in available data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' We find that all three cases perform within a few percent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' In general, filling the data with noise and using copulas perform equally well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' We use the Python package copulas for our calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' This Letter is split into the following sections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Sec- tion 2 describes how we created the catalog of JWST data for NGC 3324, as well as a description of the ML model used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Section 3 provides the results of this ML model, including the number of candidate YSOs de- tected and a comparison with those found by both Kuhn et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' (2021) and Reiter et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Finally, Section 4 discusses the accuracies of our classification, and pro- vides an analysis of the capabilities of JWST for YSO detection in comparison to Spitzer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' METHODOLOGY 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Catalog Creation The data retrieved from MAST were available as the direct outputs from SExtractor (Bertin & Arnouts 1996), which provided both fluxes and magnitudes, as well as sizes and locations, for all of the point sources de- tected within a given filter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' To match objects between filters, we find those objects whose equatorial coordi- nates are within one sigma of the center of the source, as determined by SExtractor in F470N-F444W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Because of JWST’s extraordinary resolution, this matching cri- terion remains a very small solid angle, ensuring each object is correctly linked across wavelengths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' We used the Astropy (The Astropy Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' 2018) match coordinates sky task to build our catalog of objects in all bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' We removed all objects which con- tained only one data-point after catalog matching was completed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' This approach resulted in a total of 8632 individual point sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' We next used the Astropy (The Astropy Collabo- ration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' 2018) match coordinates sky task to match the Spitzer detections from the GLIMPSE cat- alog (Preibisch et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' 2014)3 and available SPICY tar- gets (Kuhn et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Again, matches were identified when objects were within one sigma of the JWST source, resulting in 458 objects detected by both Spitzer and JWST, 26 of which were labelled as YSOs with SPICY (Kuhn et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' The MAST SExtractor files provided both vari- able aperture and isophotal photometry for each point source.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' To identify the best type of photometry to use, we compared the photometry of sources matched in both the JWST 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='44 µm and Spitzer 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='5 µm bands, whose transmission curves are very similar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' As such, we ex- pect that flux values in these two bands should be very similar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' We find that the isophotal photometry best ap- proaches a 1:1 correlation between these two bands, and thus our final catalog uses only isophotal photometry for JWST data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Applying the Probabilistic Random Forest method To classify the full JWST dataset, we must first have predetermined classifications for some portion of the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' The SPICY catalog (Kuhn et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' 2021) provided classifications of all YSOs within the GLIMPSE survey, of which NGC 3324 was included.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' After retrieving the GLIMPSE catalog, and matching it to the SPICY tar- gets, we were able to say that any object not classified as a YSO by SPICY was then classified as a contaminant (Kuhn et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' 2021), and so we obtained classifications for all objects detected in the Spitzer IRAC bands for the CC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' The cross-matched catalogue became the train- ing set for classifying further JWST data within the CC field of view.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' By training on data within this field, the 3 https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='26131/IRSA213 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='98 F1-Score 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='96 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='94 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='92 PRF RF Copula RF Noise 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='90 100 90 80 70 60 50 % Data Available4 Crompvoets et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' possible effects of extinction on the measured fluxes are eliminated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Furthermore, the absolute flux calibration is less important that the shape of the spectrum as it the latter is what the model learns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' The very dusty field of the CC means there are many objects within it that are not visible at all wavelengths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' We hence choose to use the probabilistic random forest (PRF) method for our classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' The PRF requires three input parameters for supervised classification: the input data, errors on the input data, and the targets for the input data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' We test several different input data structures: including all ten bands available, removing only the narrow bands, removing only the MIRI bands, and finally removing one band at a time to test for im- provements within the classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' In all cases, our training set is then made up of 25% YSOs and 75% con- taminant objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Our validation set was the entire set of previously classified objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' To determine the best configuration of the PRF, we ran the model 500 times, changing the random seed be- tween 0 and 1000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' There are four possible metrics we could have chosen from: accuracy, recall, precision, and F1-Score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Each of these metrics requires some combina- tion of the numbers of True Positives (TP), False Pos- itives (FP), True Negatives (TN), and False Negatives (FN).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' For our case, TP is the number of objects cor- rectly classified as YSOs, TN is the number of objects correctly classified as contaminants, FP is the number of contaminant objects incorrectly classified as YSOs, and FN is the number of YSOs incorrectly classified as contaminants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Accuracy, A = (TP + TN)/(TP + FP + FN + TN) is a measure of the total number of cor- rect identifications but can be easily made suspiciously high as a result of a much larger negative class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' As such, we do not use it as our metric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' The F1-score, F1 = 2R×P/(R+P), however, is a metric defined as the harmonic balance between recall R = TP/(TP + FN) and precision P = TP/(TP + FP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' We use it as our metric of choice because we wish to obtain a network with low contamination by much more numerous stars (high precision) while still maintaining a high recovery of YSOs (high recall).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Along with providing classifications, the PRF also al- lows us to determine which bands are most important to the classification and which bands, if any, are superflu- ous through the PRF feature importances method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' To determine the order of importance, the most im- portant band is successively removed from the data in- put ensemble, and the classification is repeated until no bands are left.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Table 2 lists the bands from most im- portant to least important, the F1-scores for both the training and validation sets when only that band is re- moved, and the number of YSOs found in the full JWST dataset of 8632 objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Band F1 % (tr) F1 % (va) # YSOs F470N 84 72 63a F444W 82 68 107 F335M 84 73 73 F187N 84 75 90 F090W 94 75 95 F200W 92 67 985 F1280W 82 72 72 F1130W 82 71 99 F770W 87 75 97 F1800W 84 72 149 All bands present 84 72 141 N bands removed 82 71 62 MIRI bands removed 84 75 126 a The number of YSOs and F1-Scores are for one run only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' The bands are listed from from most to least important for YSO identification as determined using the PRF feature importances tool.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' In each column, the band in that row is removed, and the metrics are calculated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' F1- Scores are given for the training and validation sets in the first and second columns, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' F1-Scores have an error of ∼ 2%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' The number of YSOs found in the full JWST dataset are labelled in the last column.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' The number of YSOs identified is seen to vary based on the classification, despite the F1-Scores remaining similar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Indeed, when we randomly seed the PRF 1000 times we find that ∼60% of the time, less than 100 ob- jects out of 8632 are classified as YSOs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Figure 2 shows the distribution of the number of objects classified as YSOs compared to the F1-Scores for each run.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Hence, we take the classifications for all objects over 1000 runs of the model and take the probability of a given object being a YSO as the fraction of times that it is identified as a YSO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' As in Kuhn et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' (2021), if a given object has a probability of greater than 50%, then it is classified as a YSO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Figure 3 shows various metrics for the valida- tion set of the YSO classification as a function of the cut on the probability of a given object being a YSO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' The higher the cut, the fewer objects are classified as YSOs, leading to a decrease in recall and increase in precision, though the F1-Score remains relatively even.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' At around a cut of 40%, the precision, recall, and F1- Score are nearly equivalent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' There are no YSOs with 100% probability, leading to the sharp decrease in all metrics at this cut.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' The figure confirms that 50% is a reasonable cut for the probability of the object being a YSO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Climbing the Cliffs 5 Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' A plot comparing the number of YSOs found vs the F1-Score on the validation sets for 1000 runs of the PRF using all JWST bands available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' The trends of various metrics with a variation of the cut in probability that determines if a given object is a YSO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' The number of YSOs returned dependant on this probability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' There are no YSOs with 100% probability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' RESULTS From the JWST photometry of CC, we retrieve a total of 8632 objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Only 72 of these objects are found to be YSOs, with a probability greater than 50%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Of these, 20 were recovered from the 26 SPICY objects, leading to a recall of 73%, precision of 90%, and an F1-Score of 81%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' We also find that of the 23 candidate progenitors identified in Reiter et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' (2022) only three, previously identified in SPICY (Kuhn et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' 2021), were found to be YSOs in our final classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' While analyzing the feature importances , it is ex- pected that if all features (filters) are independent, the importance of each band will remain the same even as other bands are taken away.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' In the case where two bands switch position in the order of feature importance these bands are correlated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Some correlation is appar- ent between F770W, F1280W, and F1800W, as these three bands routinely shifted ordering when determin- ing the band importance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Similarly, F090W and F200W were found to be slightly correlated by this method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' The narrow bands F187N and F470N, which trace Pa-α and H2 emission, respectively, were not found to be espe- cially important for classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Removing one or the other did not greatly impact the classification, nor did the removal of both filters data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' In general, any one band can be removed without a great impact on the F1-Score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Similarly, MIRI bands were not found to be especially influential to the classification, although this is likely due to the unavailability of data for nearly half the field of view imaged by NIRCam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Furthermore, we were only able to train on objects with Spitzer IRAC data;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' for those objects whose SEDs peak within the mid- to far-infrared they may not be sampled in the training set, whose JWST SEDs will follow the Spitzer SEDs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' This potential bias will hopefully be eliminated in fu- ture work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' We found that, out of the 458 objects classified by SPICY in the CC, 418 were consistently classified by both us and SPICY.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Unsurprisingly, we found that the objects not consistently classified between our approach and that of SPICY tend to have fewer bands available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' In particular, there were two objects which were clas- sified as YSOs in SPICY but as contaminants in our work, and they both contain data in only three out of ten bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Indeed, this behaviour may be biased by the match between Spitzer and JWST data, where the locations of the Spitzer point sources may have been closer to a different point source in JWST data, an ef- fect caused by the lower resolution of Spitzer in com- parison to JWST.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Similarly, objects classified as con- taminants in SPICY and YSOs in our work tend to be missing the 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='44 µm and 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='70 µm JWST photometry, while their proposed Spitzer counterparts contain data in this range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' One of the SPICY YSOs is only captured in the MIRI data as it is offset from the NIRCam data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' DISCUSSION AND CONCLUSION This work aimed to provide classifications of YSOs within the ERO JWST data of NGC 3324.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' There are ∼ 8600 objects within the JWST fields of ∼ 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='4′×4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='4′ by NIRCam and ∼ 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='4′ × 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='2′ by MIRI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Of these objects, 200 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='80 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='78 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='76 Os S 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='74 of Score 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='72 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='70 L 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='68 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='66 0 250 500 750 1000 1250 1500 0 200 Amount of objects classified as YsOs1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='8 S Metric Score 103 S 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='6 JO lumber 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='4 102 F1-Score Precision Z 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='2 - Recall Number YSOs 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='9 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='0 Probability YSO Cut6 Crompvoets et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' less than 500 were detectable by Spitzer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Those that were detectable were classified and made available as a catalog (SPICY) by Kuhn et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' We match the SPICY catalog to the GLIMPSE data (Preibisch et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' 2014) so that we have a record of the objects which are contaminants or YSOs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' The classified population within the CC fields then made up our training set for our probabilistic random forest model to classify JWST data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' With our small training set, it is very possible to have overfit our model to the available data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' We do see that the training set performs around 10% better, a key sign- post of overfitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' However we do see a similar trend between the training and validation sets as we modify the input data, suggesting that the issue is not as severe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' With even this small amount of classified data, we were able to separate 72 YSO candidates from the rest of the JWST data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Table 3 contains a comparison of the objects labelled by Reiter et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' (2022) and Kuhn et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' (2021) as well as those objects we newly identify as YSO candidates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' We recover 20/26 SPICY YSOs, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' approximately a 73% recall rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' The YSOs identified in SPICY are estimated to have a less than 10% contamination rate (Kuhn et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Of the seven objects identified as contaminants in our algo- rithm, one of them was mismatched, and one of them is only available in MIRI data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Of the remaining five, three have a probability of being a YSO less than 10%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' As such, 3/26 objects give a contamination rate of 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='5%, which is similar to the 10% contamination rate identi- fied in Kuhn et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' (2022) over an analysis of 26 YSO candidates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' At this stage, we obtained a high F1-Score for the validation set, and we can assume a low contamination based off of the number of YSOs that we retrieved from the full dataset of 8632 objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' If even 10% of contami- nants were misclassified as YSOs, we would have greater than 800 objects classified as YSOs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' As it is, by boot- strapping the results, we obtained the probability of an object being a YSO based off the number of times it was classified by a PRF (whose validation F1-Score was approximately 81%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' We report an object as a YSO if the probability of being a YSO is greater than the prob- ability of being a contaminant (50%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' We include the probabilities in our published catalog for future refer- ence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Based upon these probabilities, we find that the PRF method (Reis & Baron 2019) holds promise for accurate YSO identification from JWST data, especially as we wait for more data to become available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' At this stage, we are limited by the relatively small amount of previ- ously classified data available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' We cannot yet, for in- stance, realistically apply the ML model to determine the stage of star formation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' The PRF, however, was able to recover previously identified YSOs to 85% F1- Score and retrieved a reasonable number of YSOs from the entire set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' With more JWST data becoming avail- able and the use of synthetic JWST data, these metrics can only improve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' The authors would like to thank Peter Stetson, Chris Willott, and Nicholas Martis for advice on JWST pho- tometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' In addition, we thank the staff of the NASA- funded Mikulski Archive for Space Telescopes (MAST) for providing the data products used for this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' JDF acknowledges the support of an NSERC Discovery Grant held at the University of Victoria.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' REFERENCES Bertin, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=', & Arnouts, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' 1996, A&AS, 117, 393, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='1051/aas:1996164 Breiman, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' 2001, Machine Learning, 45, 5, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='1023/A:1010933404324 Chiu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=', Ho, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=', Wang, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=', & Lai, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' 2021, Astronomy and Computing, 36, 100470, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='ascom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='100470 Cornu, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=', & Montillaud, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' 2021, A&A, 647, A116, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='1051/0004-6361/202038516 Evans, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=', I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=', Allen, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=', Blake, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' 2014, VizieR Online Data Catalog, II/332 Kinson, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=', Oliveira, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=', & van Loon, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' 2021, MNRAS, 507, 5106, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='1093/mnras/stab2386 —.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' 2022, MNRAS, 517, 140, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='1093/mnras/stac2692 Kuhn, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=', de Souza, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=', Krone-Martins, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' 2021, ApJS, 254, 33, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='3847/1538-4365/abe465 Kuhn, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=', Saber, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=', Povich, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' 2022, AJ, 165, 3, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='3847/1538-3881/ac9314 Miettinen, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' 2018, Ap&SS, 363, 197, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='1007/s10509-018-3418-7 Nelsen, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' 2007, An introduction to copulas (Springer Science & Business Media) Pontoppidan, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=', Barrientes, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=', Blome, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' 2022, ApJL, 936, L14, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='17909/67ft-nb86 Climbing the Cliffs 7 Preibisch, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=', Zeidler, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=', Ratzka, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=', Roccatagliata, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=', & Petr-Gotzens, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' 2014, A&A, 572, A116, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='1051/0004-6361/201424045 Reis, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=', & Baron, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' 2019, PRF: Probabilistic Random Forest, Astrophysics Source Code Library, record ascl:1903.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' http://ascl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='net/1903.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='009 Reiter, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=', Morse, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=', Smith, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' 2022, MNRAS, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='1093/mnras/stac2820 The Astropy Collaboration, Price-Whelan, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=', Sip˝ocz, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' 2018, AJ, 156, 123, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='3847/1538-3881/aabc4f 8 Crompvoets et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' JWST Number Kuhn et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' (2021) This work J103635.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='2-584029 CI - SPICY 7409 J103648.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='7-583803 CII - SPICY 7428 YSO J103652.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='5-583725 CI - SPICY 7435 YSO J103656.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='6-583659 CII - SPICY 7444 YSO J103657.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='4-583637 CII - SPICY 7447 YSO J103658.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='4-583619 FS - SPICY 7448 YSO J103658.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='9-583742 CII - SPICY 7452 J103659.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='1-583524 FS - SPICY 7454 YSO J103700.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='1-583528 FS - SPICY 7461 YSO J103700.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='4-583829 CII - SPICY 7462 YSO J103700.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='7-583545 CII - SPICY 7464 YSO J103700.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='8-583622 FS - SPICY 7465 YSO J103702.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='5-583403 CI - SPICY 7469 YSO J103705.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='7-583418 FS - SPICY 7473 YSO J103706.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='4-583517 CII - SPICY 7475 YSO J103706.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='7-583419 CII - SPICY 7476 YSO J103706.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='9-583655 CII - SPICY 7477 YSO J103708.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='4-583654 CII - SPICY 7479 YSO J103711.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='3-583445 CII - SPICY 7481 YSO J103711.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='7-583424 CII - SPICY 7482 J103642.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='3-583804 J103648.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='0-583819 J103647.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='3-583810 CI - SPICY 7423 YSO J103646.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='7-583805 J103651.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='5-583754 J103650.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='5-583752 J103651.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='4-583748 J103653.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='8-583748 J103651.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='5-583710 J103654.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='2-583626 J103654.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='4-583618 J103654.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='0-583720 CI - SPICY 7441 J103653.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='6-583520 J103653.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='1-583737 J103653.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='3-583754 UN - SPICY 7438 YSO J103652.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='7-583805 J103653.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='1-583708 J103651.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='6-583658 J103652.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='3-583809 CI - SPICY 7434 J103653.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='9-583629 FS - SPICY 7440 J103701.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='5-583751 J103702.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='1-583658 CII - SPICY 7467 YSO J103653.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content='9-583632 Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' The top half of this table shows the YSOs identi- fied with Kuhn et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' (2021) and whether or not they were classified as YSOs with our model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' Classes are included as CI = Class I, CII = Class II, FS = Flat Spectrum, and UN = Uncertain for those objects found within Kuhn et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' The bottom half of this table shows the objects identified by Reiter et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' (2022) as potential progenitors for jets and the comparable YSO candidates within this work and Kuhn et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} +page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/h9E3T4oBgHgl3EQf4gse/content/2301.04772v1.pdf'} diff --git 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Schneider1 +Emergent Complexity in Physical Systems Laboratory (ECPS), École Polytechnique Fédérale de Lausanne (EPFL), +CH-1015 Lausanne, Switzerland +(*Electronic mail: tobias.schneider@epfl.ch) +In a dynamical systems description of spatiotemporally chaotic PDEs including those describing turbulence, chaos is +viewed as a trajectory evolving within a network of non-chaotic, dynamically unstable, time-invariant solutions embed- +ded in the chaotic attractor of the system. While equilibria, periodic orbits and invariant tori can be constructed using +existing methods, computations of heteroclinic and homoclinic connections mediating the evolution between the former +invariant solutions remain challenging. We propose a robust matrix-free variational method for computing connecting +orbits between equilibrium solutions of a dynamical system that can be applied to high-dimensional problems. Instead +of a common shooting-based approach, we define a minimization problem in the space of smooth state space curves that +connect the two equilibria with a cost function measuring the deviation of a connecting curve from an integral curve +of the vector field. Minimization deforms a trial curve until, at a global minimum, a connecting orbit is obtained. The +method is robust, has no limitation on the dimension of the unstable manifold at the origin equilibrium, and does not +suffer from exponential error amplification associated with time-marching a chaotic system. Owing to adjoint-based +minimization techniques, no Jacobian matrices need to be constructed and the memory requirement scales linearly with +the size of the problem. The robustness of the method is demonstrated for the one-dimensional Kuramoto-Sivashinsky +equation. +The chaotic evolution of a dynamical system can be de- +scribed in terms of the non-chaotic time-invariant solu- +tions embedded within its chaotic attractor. Heteroclinic +and homoclincic connecting orbits between these invariant +solutions mediate the evolution of the chaotic trajectory +from the vicinity of one invariant solution to the vicinity +of another one. While a complete characterization of the +state space structures supporting chaos requires the iden- +tification of connecting orbits, constructing those has re- +mained a numerical challenge. We introduce a robust and +memory-efficient method for constructing connecting or- +bits between equilibrium solutions. Thereby, a more com- +plete characterization of the state space structures sup- +porting chaotic dynamics becomes feasible. +I. +INTRODUCTION +Many nonlinear driven out-of-equilibrium systems includ- +ing those describing fluid flows, nonlinear optics and ac- +tive suspensions exhibit spatiotemporally chaotic dynamics. +Within a dynamical systems description the spatiotemporal +chaos can be viewed as the evolution of a chaotic trajectory in +the state space of the governing equations. Embedded in the +state space are non-chaotic, time-invariant solutions includ- +ing equilibria, periodic orbits and higher-dimensional invari- +ant tori. These invariant solutions are dynamically unstable +so that the chaotic trajectory visits them transiently, yet re- +curringly. Spatiotemporal chaos can thus be viewed as a walk +through a forest of invariant solutions that form the elementary +building blocks of the chaotic solution1–3. Consequently, indi- +vidual invariant solutions can provide remarkable information +about the spatiotemporal chaos and physical mechanisms un- +derlying it, and collectively they promise an avenue towards +quantitatively predicting statistical properties of the chaotic +dynamics. Due to the significantly increasing computational +resources and algorithmic advances, these concepts, originally +developed in the context of low-dimensional chaotic dynami- +cal systems, are now applied to very high-dimensional prob- +lems including transitional fluid turbulence where dynamical +systems descriptions based on the analysis of invariant solu- +tions have proven to be particularly useful4–9. +While equilibria and periodic orbits form the building +blocks of the dynamics, the chaotic evolution from the neigh- +borhood of one unstable invariant solution to another is me- +diated by connecting orbits. These hetero- and homoclinic +connections provide dynamic pathways between different pe- +riodic orbits or equilibria within the chaotic attractor. There- +fore, a characterization of the chaotic dynamics in terms of +state-space structures requires both to identify equilibria, peri- +odic orbits and invariant tori embedded in the chaotic attractor, +and to compute connecting orbits between them. In the con- +text of fluid dynamics for example, van Veen and Kawahara +use connecting orbits to explain the turbulent bursting in plane +Couette flow10; Suri et al. study the network of connecting +orbits that underpins the transient dynamics in a quasi-two- +dimensional Kolmogorov flow11; and Reetz and Schneider +characterize the time-dependent dynamics of inclined layer +convection using connecting orbits between coexisting invari- +ant solutions12. +We specifically focus on connecting orbits between equi- +librium solutions. Such connecting orbits have been identi- +fied as dynamically relevant in fluid systems10–12 and they +are involved in global bifurcations, when for instance a pe- +riodic orbit bifurcates off a homoclinic orbit or a hetero- +clinic cycle13,14. Connecting orbits are located within the in- +tersection of the unstable manifold of one equilibrium with +the stable manifold of another or the same equilibrium so- +lution if they are of heteroclinic or homoclinic type, respec- +arXiv:2301.11704v1 [nlin.CD] 27 Jan 2023 + +Jacobian-Free Variational Method for Constructing Connecting Orbits +2 +tively. In the vicinity of an equilibrium solution, a trajectory +approaches/departs the equilibrium along its stable/unstable +manifold exponentially in time. Consequently, the time re- +quired to traverse the entire connecting orbit is not finite. This +infinite passage time makes computing connecting orbits very +challenging. +One approach to handle the computational challenge of the +infinite passage time is to truncate the connecting orbit and +compute an approximating part of the orbit that is traversed +in finite time. Under favourable conditions, the truncated or- +bit can be computed using shooting methods. Geometrically, +the truncation approach attempts to construct a trajectory that +starts at some point on the unstable manifold of the origin +equilibrium and ends at some other point on the stable man- +ifold of the destination equilibrium. Due to their curvature, +parametrizations of stable and unstable manifolds are usually +not accessible. Consequently, they need to be approximated +locally by the corresponding tangent spaces associated to the +origin and destination equilibrium. Practically, a connecting +orbit is thus found by identifying an initial condition in the in- +tersection of the unstable tangent space of and a hypersphere +around the origin equilibrium, which after forward time inte- +gration reaches a distance below a chosen threshold from the +destination equilibrium15. If the hypersphere is chosen small +enough, the unstable tangent space accurately approximates +the unstable manifold, and thus the obtained trajectory accu- +rately represents a connecting orbit. +Even if the unstable manifold can be accurately approx- +imated by the unstable tangent space, a systematic search +for an initial condition that eventually reaches the destina- +tion equilibrium is a formidable task, especially for a chaotic +system where nearby trajectories diverge exponentially with +time. When the unstable manifold at the origin equilibrium +solution is two-dimensional, an exhaustive search strategy can +be employed6,11,16,17. In this case, the search space is a circle +on the unstable tangent space with an angle being the only +variable. However, when the unstable tangent space at the +origin equilibrium has more than two dimensions, the search +space is too large for an exhaustive search. To improve the +dimensionality drawback, Farano et al.18 propose an adjoint- +based variational method for finding a state on an energy shell +around the origin equilibrium whose trajectory reaches an- +other energy shell around the destination equilibrium. They +do not constrain the initial condition to be located on the un- +stable tangent space at the origin equilibrium, hence as a sec- +ond step the trajectory is confirmed to shadow a connecting +orbit by matching the endpoints of the trajectory against the +linearized dynamics around the two equilibria. In all these +methods determining the size of the hypersphere around the +origin equilibrium solution is not a trivial task: the hyper- +sphere should be small enough in order for the tangent space +to accurately approximate the manifold, and large enough to +let the required time integration intervals be feasibly short. +An alternative to the shooting-based methods which search +for a single state on the connecting orbit is to search in the +space of connecting curves, i.e. +all smooth curves in the +state space which connect the two equilibria. Among all such +curves, only connecting orbits are integral curves of the vector +field induced by the governing equation. The idea is to start +from a connecting curve pivoted on the two fixed points, then +deform the curve until the tangent velocity coincides with the +local field vector along the entire curve, and thus a connecting +orbit is achieved. This approach has several advantages over +the reviewed shooting-based methods for computing connect- +ing orbits: First, there is no limitation on the dimensionality +of the unstable manifold at the origin equilibrium because no +exhaustive search is needed; Secondly, the approach does not +suffer from the exponential separation of trajectories with time +since the connecting curve is deformed locally and no time in- +tegration is required; And lastly, this approach yields the exact +and the entire connecting orbit without requiring to truncate it. +Despite the conceptual advantages of searching in the space +of connecting curves over the shooting-based alternatives, this +approach is not extensively developed on the practical side. +Liu et al.19 use rational Chebyshev basis functions for the +spectral representation of variables along the infinite tempo- +ral direction probably for the first time in this context. They +formulate the problem as a system of nonlinear equations by +setting the temporal derivative equal to the right-hand side of +the governing equation for every state variable at every tem- +poral collocation point, and solve the system of equations us- +ing standard Newton iterations. Dong and Lan20 extend the +variational method of Lan and Cvitanovi´c21, originally de- +veloped for finding periodic orbits, to the problem of con- +structing connecting orbits. They view the problem of de- +forming connecting curves towards a connecting orbit as a +minimization problem: a connecting orbit is found by min- +imizing a cost function which penalizes the deviation of a +connecting curve from being an integral curve of the vector +field. They employ an infinitesimal-step version of Newton +iterations for continuously deforming the curve, and use fi- +nite differences for calculating the tangent velocity vector. In +his PhD thesis, Pallantla22 employs the same spectral repre- +sentation of variables in the temporal direction as in Ref. 19, +and deforms the curve in the direction of the steepest descent +of the cost function. The common drawback of the afore- +mentioned algorithms is that they all require explicit con- +struction of the Jacobian matrix. In a system with M tem- +poral and N spatial degrees of freedom the size of the Jaco- +bian matrix scales as O(M2N2) which can be prohibitively +large for high-dimensional dynamical systems such as three- +dimensional fluid flows. +In order to transfer the advantages of searching in the +space of connecting curves to high-dimensional dynamical +systems, we propose a Jacobian-free variational method for +constructing connecting orbits between two equilibrium so- +lutions. The method employs an adjoint-based optimization +technique to minimize a cost function which measures the de- +viation of a connecting curve between two equilibria from an +integral curve of the vector field. We construct a globally con- +tracting dynamical system in the space of connecting curves. +Fixed points of this dynamical system are minima of the non- +negative cost function, hence global minima of the cost func- +tion, taking zero value, correspond to connecting orbits of the +original dynamical system. Connecting orbits are therefore +found by integrating the dynamics in the space of connect- + +Jacobian-Free Variational Method for Constructing Connecting Orbits +3 +ing curves. Due to the explicit construction of the dynamical +system in the space of connecting curves, the memory require- +ment scales as O(MN) which allows the proposed method to +be applied to high-dimensional dynamical systems. +The remainder of the present article is organized as fol- +lows. In Sec. II the problem of constructing a connecting or- +bit is set up as a minimization problem, and in Sec. III the +adjoint-based minimization technique is formulated for a gen- +eral autonomous dynamical system. In Sec. IV a spectral rep- +resentation suitable for the discretization along the unbounded +temporal domain is discussed. +To demonstrate the robust- +ness of the proposed variational method, in Sec. V we con- +sider the one-dimensional Kuramoto–Sivashinsky equation in +a spatiotemporally chaotic regime, and show that several con- +necting orbits can be converged reliably. Finally, in Sec. VI, +the manuscript is summarized, and an outlook for future re- +search is given. +II. +VARIATIONAL METHOD FOR FINDING +CONNECTING ORBITS +We consider general autonomous dynamical systems of the +form +∂u +∂t = f(u), +(1) +where the smooth nonlinear operator f governs the evolution +of an n-dimensional real field u ∈ M ⊂ Rn defined over a d- +dimensional spatial domain x ∈ Ω ⊂ Rd and time t ∈ R sub- +ject to time-independent boundary conditions (BCs) at ∂Ω, +the boundaries of the spatial domain Ω. +A connecting orbit between two equilibrium solutions is a +solution trajectory u(x,t) of the governing equation (1) such +that the asymptotic conditions +lim +t→−∞u = u− , +lim +t→+∞u = u+ , +f(u±) = 0, +(2) +are satisfied in the temporal direction. The connecting orbit is +a heteroclinic connection if u− ̸= u+, and a homoclinic con- +nection if u− = u+ (while implicitly assuming that the entire +orbit is not the equilibrium solution itself.) +In the (d + 1)-dimensional space-time domain of the dy- +namical system (1), connecting orbits are solutions to a +boundary value problem subject to the same BCs as Eq. (1) in +d spatial directions, augmented by the asymptotic BCs (2) in +the temporal direction. The idea of the proposed variational +method is to consider C∞ space-time fields that satisfy the +boundary conditions in all (d + 1) directions, and vary the +field until Eq. (1) is satisfied at each and every space-time +coordinate. +Geometrically, f(u) is a vector field in the n- +dimensional state space M , u− and u+ are two fixed points, +and connecting orbits are integral curves of this vector field +extending from u− to u+. In this picture, the search space +is the space of all smooth curves in the state space that con- +nect the two fixed points. We define the space of connecting +J +FIG. 1: Schematic of the variational method for constructing +a connecting orbit between two equilibrium solutions: A +connecting curve pivoted on the two fixed points is deformed +such that a cost function J measuring the deviation of the +connecting curve from being an integral curve of the vector +field is minimized. For a connecting orbit the tangent +velocity vector matches the field vector along the entire +curve, and thus the global minimum of the cost function, +J = 0, is achieved. +curves, denoted by Cg, as +Cg = +� +� +�u(x,s) +����� +u : Ω×R → M +lims→±∞ u = u± +u satisfies BCs at ∂Ω +� +� +�. +(3) +We parameterize connecting curves by s ∈ R in order to dis- +tinguish the evolution along a connecting curve from the evo- +lution along a solution trajectory of the governing equation (1) +which is parameterized by the physical time t. Connecting or- +bits form a subset C ⊂ Cg in which the tangent velocity vector, +∂u/∂s, coincides with the local field vector, ∂u/∂t = f(u), +along the entire connecting curve. As a measure of deviation +of a connecting curve from being a connecting orbit we define +the non-negative cost function J2 as +J2 = +� +∞ +−∞ +� +Ω r·r dxds, +(4) +where r is the local deviation of the tangent velocity vector +from the field vector, or the residual of Eq. (1): +r(u) = f(u)− ∂u +∂s , +(5) +and · indicates the standard Euclidean inner product. +The +residual r is zero everywhere along a connecting orbit. There- +fore, the cost function takes zero value for u ∈ C while it takes +a positive value for u ∈ Cg \ C . The problem of finding con- +necting orbits can now be viewed as a minimization problem +in Cg: Absolute minima of J2, for which J = 0, correspond to +connecting orbits u ∈ C . Fig. 1 schematically shows the idea +of this approach: Minimizing the cost function J deforms a +curve connecting two fixed points of the vector field towards +an integral curve of the vector field bounded between the two +equilibria, thereby a connecting orbit. + +Jacobian-Free Variational Method for Constructing Connecting Orbits +4 +III. +ADJOINT-BASED MINIMIZATION OF THE COST +FUNCTION +We have recast the problem of computing connecting or- +bits into a minimization problem in the space of connecting +curves extended between two equilibrium solutions. Abso- +lute minima of the non-negative cost function J2 with J = 0 +correspond to a connecting orbit. To solve the minimization +problem, we employ an adjoint-based technique inspired by +the recent works by Farazmand23 on constructing equilibria +and travelling waves, and by and Azimi et al.24 on construct- +ing periodic orbits of nonlinear dynamical systems. We con- +struct a dynamical system in the space of connecting curves, +Cg, such that along its trajectories the cost function is guaran- +teed to decrease monotonically. Therefore, connecting orbits +are found by integrating the constructed dynamics in Cg until +a minimum of the cost function is reached. Parametrizing this +dynamical system by a fictitious time τ we need to construct +the operator G(u) such that evolution of u governed by +∂u +∂τ = G(u), +(6) +guarantees +∂J2 +∂τ ≤ 0; +∀τ. +(7) +We define the inner product space Cs ⊃ Cg +Cs = +� +q(x,s) +����� +q : Ω×R → Rn +lims→±∞ q = v± ∈ Rn +� +, +(8) +together with the real-valued inner product +⟨ , ⟩ : Cs ×Cs → R, +⟨q1,q2⟩ = +� +∞ +−∞ +� +Ω q1 ·q2 dxds, +(9) +and L2-norm +∥q∥ = +� +⟨q,q⟩. +(10) +In contrast to the space of connecting curves Cg, the elements +of Cs have arbitrary asymptotic states v± ∈ Rn. The rate of +change of the cost function J2 = ∥r∥2 = ⟨r,r⟩ is obtained by +the inner product of r(u) with its directional derivative along +the to-be-determined operator ∂u/∂τ = G(u): +∂J2 +∂τ = 2 +� +(∇ur) ∂u +∂τ , r +� +. +(11) +The directional derivative of r(u) along G is defined as +L +L +L (u;G) = lim +ε→0 +r(u+εG)−r(u) +ε +. +(12) +Using the adjoint of the directional derivative we can write +Eq. (11) as +∂J2 +∂τ = 2 +� +L +L +L †(u;r),G +� +, +(13) +where L +L +L † is the adjoint operator of L +L +L , with +⟨L +L +L (u;G),r⟩ = +� +G,L +L +L †(u;r) +� +, +(14) +for all connecting curves u ∈ Cg. +The residual r (defined +in Eq. (5)) and the operator G (defined in Eq. (6)) are func- +tions of u, and belong to the inner product space Cs with cer- +tain properties that are detailed shortly. By choosing G(u) = +−L +L +L †(u;r) the monotonic decrease of the cost function is +guaranteed: +∂J2 +∂τ = 2 +� +L +L +L †(u;r),−L +L +L †(u;r) +� += −2 +��L +L +L †(u;r) +��2 ≤ 0. +(15) +The dynamical system ∂u/∂τ = G(u) = −L +L +L †(u;r) is glob- +ally contracting: All trajectories are eventually attracted to +stable fixed points at which ∂u/∂τ = 0 and J2 takes a min- +imum value. Although the monotonic decrease of the cost +function is guaranteed along trajectories of the dynamics in +Cg, reaching the global minimum is not. To find a connect- +ing orbit, therefore, the dynamics in the space of connecting +curves is integrated until a fixed point is reached. Those fixed +points of ∂u/∂τ = G(u) which correspond to the global min- +imum of the cost function, J = 0, are connecting orbits of +the original dynamical system ∂u/∂t = f(u), and those corre- +sponding to J > 0 are rejected. +The dynamical system ∂u/∂τ = G(u) is constructed in the +space of connecting curves Cg defined in Eq. (3). This im- +poses certain BCs on the residual r(u) and the operator G(u). +In the temporal direction, lims→±∞ r = 0 since u satisfies the +correct asymptotic BCs for all τ, and lims→±∞ G = 0 since the +correct asymptotic values of u must be preserved. In space, u +satisfies the correct BCs at ∂Ω for all τ; consequently, the +spatial BCs of r and G are determined following similar argu- +ments. For example, r and G will be periodic in directions +where u is periodic, will take zero value where u satisfies +Dirichlet boundary conditions, and so forth. These properties +must be taken into account while deriving the adjoint opera- +tor from the definition (14). Derivation of the adjoint operator +for the Kuramoto-Sivashinsky system, introduced in Sec. V, +is presented in Appendix A where the zero asymptotic values +of r and G in the temporal direction and their periodicity in +space enable us to derive the adjoint operator as an explicit +function of the space-time field u. +Both heteroclinic and homoclinic connections can be con- +structed using the introduced variational method. In the case +of a homoclinic connection to an equilibrium solutions, zero +variation in time, i.e. the equilibrium solution itself, is a trivial +solution satisfying the definition (2). Therefore, depending on +the initial connecting curve from which the integration starts, +a trivial or a nontrivial solution with J = 0 can be obtained. +The definition of a heteroclinic connection does not have any +trivial solution. +On an abstract level, we construct the operator G follow- +ing the same logic as that in Refs. 24 and 23. However, in +the different contexts the form of the operator differs as it +acts on different objects and the dynamical system guaran- +teeing the monotonic decrease of the cost function evolves + +Jacobian-Free Variational Method for Constructing Connecting Orbits +5 +objects representing the specific sought-after invariant solu- +tion: Farazmand23 converges equilibrium solutions, and thus +constructs G for evolving spatial fields, i.e. points in the state +space; Azimi et al.24 converge periodic orbits, hence they con- +struct G for evolving space-time fields that are periodic in +the temporal direction, i.e. closed loops in the state space; +and here we converge connecting orbits, thus we construct G +for evolving space-time fields satisfying the asymptotic con- +ditions (2) in the temporal direction, i.e. connecting curves +between two fixed points in the state space. +IV. +SPECTRAL REPRESENTATION IN TIME +An efficient implementation of the proposed adjoint-based +variational method is aided by an accurate spectral represen- +tation of a space-time field q(x,s) ∈ Cs in the s direction, such +that the asymptotic conditions at s → ±∞ are directly enforced +by the chosen expansion. The spectral accuracy significantly +reduces the number of time sections, and thereby memory, re- +quired for an accurate representation of connecting orbits. We +use rational Chebyshev basis functions for the spectral repre- +sentation in the temporal direction (see Chapter 17 of Ref. 25 +for details). +Rational Chebyshev functions, Rn(s), are given by +Rn(s) = cos(nθ); +n ∈ W, +(16) +where θ ∈ (0,π) and s ∈ R are related via +s = s0 +Scot(θ) ⇐⇒ θ = cot−1 +�s−s0 +S +� +, +(17) +with s0 ∈ R and S ∈ R+ being mapping parameters. +Rational Chebyshev collocation points are obtained by a +uniform discretization of θ. Therefore, M interior collocation +points are +sj = s0 +Scot +� +jπ +M +1 +� +; +j = 1,2,...,M, +(18) +with j = 0 and j = M + 1 being reserved for the asymptotic +values s → +∞ and s → −∞, respectively. The uniform dis- +cretization of θ results in a non-uniform distribution of grid +points in s. Collocation points are denser around s0, the center +of the distribution, and become sparser further away from the +center. The spacing between successive grid points is linearly +scaled by S. +A real function q(s) with s ∈ R and constant asymptotic val- +ues is approximated by the truncated expansion in a rational +Chebyshev basis, q(s) ≈ ∑M+1 +k=0 ckRk(s), where the expansion +coefficients are +ck = +2 +(M +1)¯ck +M+1 +∑ +m=0 +1 +¯cm +q(sm)cos +� mkπ +M +1 +� +, +(19) +with grid points sm defined in equation (18) and +¯c j = +� +2, +if j = 0 or M +1, +1, +otherwise. +(20) +Having a grid function q(s j) with j = 0,1,...,M + 1 over +rational Chebyshev grid points (18), the differentiation matrix +Dt is constructed as: +Dt j,m = +2 +S(M +1) sin2 +� +jπ +M +1 +� M+1 +∑ +k=0 +k +¯cm ¯ck +cos +� mkπ +M +1 +� +sin +� k jπ +M +1 +� +; +j,m = 0,1,...,M +1. +(21) +The expansion in a rational Chebyshev basis allows us to +represent the space-time objects in the unbounded temporal +direction, and we can expect spectral accuracy with fast con- +vergence as a function of the expansion’s truncation order. Ra- +tional Chebyshev functions form a generic basis for the spec- +tral representation of functions over the entire real axis with +constant asymptotic values and are thus a suitable expansion +for connecting orbits for any studied physical system. +V. +APPLICATION TO KURAMOTO-SIVASHINSKY +EQUATION +As a proof of concept, we apply the introduced method +for constructing connecting orbits to the one-dimensional +Kuramoto-Sivashinsky equation (KSE)26,27. +The KSE is a +nonlinear partial differential equation which emerges in var- +ious physical contexts such as flame propagation27, plasma +physics28, or interfacial fluids instability29. The KSE is also +commonly used as a model system for examining new meth- +ods developed for chaotic fluid flows and transitional turbu- +lence since it exhibits spatiotemporally chaotic behavior and +displays some similar features to the Navier-Stokes equations. +The one-dimensional KSE for a real field u(x,t) on the pe- +riodic spatial domain 0 ≤ x < L is +∂u +∂t = −u∂u +∂x − ∂ 2u +∂x2 −ν ∂ 4u +∂x4 , +(22) +with constant positive damping parameter ν. The dynamics +of the KSE is controlled by the single dimensionless group +L = L/√ν. Here, we fix ν = 1 and consider the domain size +L as the control parameter. For L < 2π, the trivial equilibrium +solution u(x,t) = const. is linearly stable, and is the global +attractor of the dynamics. By increasing L, solutions of the +KSE undergo a series of bifurcations, and for a sufficiently +large domain size the dynamics can exhibit spatiotemporally +chaotic behavior30. We demonstrate the application of the +proposed method by constructing connecting orbits between + +Jacobian-Free Variational Method for Constructing Connecting Orbits +6 +equilibrium solutions of the KSE for L = 22. This domain +size is large enough for the KSE to exhibit spatiotemporally +chaotic dynamics, yet small enough to have low-dimensional +unstable manifolds at the equilibria found, over which an ex- +haustive search for possible connecting orbits is practical. The +state space geometry of the KSE for this parameter value +has previously been explored in detail by Cvitanovi´c and +collaborators17. They identified several connecting orbits us- +ing the shooting method described in Section I. We construct +a complete set of connecting orbits between all known equi- +librium solutions of this system; complete in the sense that +at least one connecting orbit between any pair of equilibrium +solutions is computed, or it is confirmed by the exhaustive +search in Ref. 17 that no connecting orbit exists between the +two equilibria. +A. +Formulation of the adjoint-based variational method for +the KSE +The KSE (22) has the form of the general dynamical system +(1) with n = d = 1 and Ω = [0,L). The residual field, defined +in Eq. (5), for the KSE is +r = −∂u +∂s −u∂u +∂x − ∂ 2u +∂x2 − ∂ 4u +∂x4 . +(23) +The dynamical system along whose trajectories the cost func- +tion decreases monotonically is derived based on the adjoint +operator of the directional derivative of r. The adjoint operator +for the KSE system is constructed by a series of integrations +by part (see Appendix A for details): +L †(u;r) = ∂r +∂s +u∂r +∂x − ∂ 2r +∂x2 − ∂ 4r +∂x4 . +(24) +Therefore, the dynamical system in the space of connecting +curves, u(x,s;τ) ∈ Cg, that minimizes the cost function J2 is +∂u +∂τ = −L †(u;r) = −∂r +∂s −u∂r +∂x + ∂ 2r +∂x2 + ∂ 4r +∂x4 . +(25) +B. +Symmetry preservation +The KSE (22) is equivariant under continuous translations +in the x-direction +γ(α)u(x,t) = u(x+αL,t); +α ∈ [0,1), +(26) +and under inversions about the origin +σu(x,t) = −u(−x,t). +(27) +The translation operator γ(α) and inversion operator σ com- +mute with the residual (23) of the KSE. Consequently, the dy- +namics in the space of connecting curves, Eq. (25), is equivari- +ant under the action of γ(α) and σ. This means that if the in- +tegration of Eq. (25) starts from an initial space-time field that +is invariant under the action of σ ◦ γ(α), the dynamics pre- +serves the resulting point-inversion symmetry, and therefore +the constructed connecting orbit belongs to the same symmet- +ric subspace of the state space M . +The KSE (22) preserves the spatial mean value of the evolv- +ing field. Consequently, the spatial mean along a connecting +orbit is constant and the same as the end point equilibrium so- +lutions. We consider the dynamics of the KSE in the subspace +of fields with zero spatial mean. The zero mean value is not +enforced during the evolution of a connecting curve towards a +connecting orbit. However, since the two end point equilibria +do have zero spatial mean, a converged connecting orbit with +J = 0 takes zero mean value as well. +C. +Numerical implementation +1. +Spectral discretization +A connecting curve u(x,s) is discretized in the temporal +direction using M + 2 time sections (including the end point +equilibria) over the rational Chebyshev grid while each time +section is represented by N Fourier modes in space: +u(xn,sm) = +N +2 −1 +∑ +j=− N +2 +ˆuj(sm)exp +� +j2πxn +L +i +� +, +(28) +where xn = nL/N with indices 0 ≤ n < N are the uniform grid +points in space; sm with indices 0 ≤ m ≤ M + 1 are the non- +uniform rational Chebyshev collocation points in time; ˆuj(sm) +is the jth Fourier coefficient of the time section at sm; and i is +the imaginary unit. +In spectral space, the connecting curve u is represented by +an (M + 2) × N matrix of complex numbers ˆum,j = ˆuj(sm). +The derivative of order q ∈ W of this space-time field with +respect to x is obtained by the Hadamard product D(q) +x +⊙ ˆu +where D(q) +x +m, j = (2π ji/L)q, and its derivative of order q ∈ W +with respect to s is obtained by multiplying ˆu from the left +by Dq +t , where the temporal differentiation matrix Dt is de- +fined in Eq. (21). The residual r and the descent direction G +are discretized in the same way with the only difference that +their time sections at s0 and sM+1 (corresponding to s → +∞ +and s → −∞, respectively) are identically zero (see Sec. III). +The nonlinear terms are calculated in physical space where +products are of elementwise Hadamard type. Transforming +back and forward between physical and spectral representa- +tions of the space-time fields requires one-dimensional for- +ward or backward discrete Fourier transformation of each time +section. +2. +Initialization +The initial connecting curve is chosen as a convex combina- +tion of the equilibrium solutions u− and u+, plus a symmetry + +Jacobian-Free Variational Method for Constructing Connecting Orbits +7 +breaking term: +u0(x,s;a) =1 +2 [(1+tanh(s))u+(x)+(1−tanh(s))u−(x)] ++aexp(−s2)v(x); +a ∈ {0,1}, +(29) +with x ∈ [0,L) and s ∈ R. If u−(x) and u+(x) both are inver- +sion symmetric about the same point x = x0, then a = 0 results +in an initial space-time field for which all time sections are +invariant under the same inversion symmetry. Since the pro- +posed variational dynamics preserves the inversion symmetry, +we can set a = 0 in order to search in the inversion-symmetric +subspace of connecting trajectories. In order to break such a +symmetry, we add the second line, i.e. set a ̸= 0, where v(x) +is a field which does not have the inversion symmetry shared +between u−(x) and u+(x). +3. +Time stepping +The defined dynamical system ∂u/∂τ = G is globally con- +tracting and we are only concerned about the asymptotic state +u = u0 + +� ∞ +0 Gdτ. Consequently, we select the numerical in- +tegration scheme based on simplicity and stability rather than +accuracy. We use semi-implicit forward Euler time-stepping +scheme which has first-order accuracy in τ, and treats the lin- +ear terms of G in u implicitly and the nonlinear terms explic- +itly. The code was developed in C++ with OpenMP paral- +lelization of local calculations. +D. +Results and discussion +In the subspace of fields with zero spatial mean, the KSE +with L = 22 has four known equilibrium solutions includ- +ing the trivial solution u = 0. Hereafter we denote the triv- +ial equilibrium solution by E0, and the nontrivial ones by E1, +E2 and E3 as shown in Fig. 2. We construct these equilib- +rium solutions following the adjoint-based variational method +of Farazmand23. E1, E2 and E3 are invariant under inversion +about the origin, σ. E2 and E3 are also symmetric under dis- +crete shifts γ(1/2) and γ(1/3), respectively. Therefore, in ad- +dition to the inversion about x = 0 and L/2, E2 is symmetric +under inversion about x = L/4 and 3L/4, and E3 is symmetric +under inversion about x = L/6, L/3, 2L/3, and 5L/6 as well. +The repelling eigenvalues of all four equilibrium solutions are +listed in Table I, and their associated eigenvectors are shown +in Figs. 15 to 18 in Appendix B. +Connecting orbits are converged by integrating Eq. (25) un- +til a fixed point in the vector field of G, corresponding to a +minimum J, is achieved. Connecting orbits correspond to the +global minima of J, for which J = 0. In order to monitor the +convergence, we define the arc length weighted cost function +Jarc = +� +∞ +−∞ |r| +���� +∂u +∂s +����ds +� +∞ +−∞ +���� +∂u +∂s +����ds +, +(30) +0 +11 +22 +x +−2 +−1 +0 +1 +2 +u +(a) E1 +0 +11 +22 +x +−2 +−1 +0 +1 +2 +u +(b) E2 +0 +11 +22 +x +−2 +−1 +0 +1 +2 +u +(c) E3 +FIG. 2: Nontrivial equilibrium solutions of the KSE for +L = 22. E1, E2 and E3 are symmetric under inversion about +the origin. E2 and E3 are also symmetric under discrete shift +by L/2 and L/3, respectively. +TABLE I: Repelling eigenvalues of the equilibria of the KSE +for L = 22. The rest of the eigenvalues, except one zero +eigenvalue for E1, E2 and E3, have negative real part. +Solution +Unstable eigenvalues +E0 +λ1,2 =0.2198 +λ3,4 =0.1952 +λ5,6 =0.0749 +E1 +λ1,2 =0.1308±0.3341i +λ3,4 =0.0824±0.3402i +E2 +λ1,2 =0.1390±0.2384i +E3 +λ1,2 =0.0933 + +Jacobian-Free Variational Method for Constructing Connecting Orbits +8 +with | · | being +|q| = +�� +Ω q·q dx ; +q ∈ Cs. +(31) +Obviously, Jarc = 0 if and only if J = 0. However, the numer- +ical evaluation of Jarc is not subject to the error accumulation +associated with the numerical evaluation of the improper inte- +gral (4) that defines J. Moreover, since the trivial solution to +the definition of a homoclinic connection has zero arc length, +Jarc is undefined when the trivial solution is achieved, while +J = 0 for either trivial or nontrivial solutions. We consider the +algorithm converged when Jarc < 10−12. +Due to the continuous translational symmetry of the KSE, +Ei with i = 1,2,3 represent its so-called group orbit of all sym- +metry related states, i.e. γ(α)Ei where α ∈ [0,1). Every con- +necting orbit, therefore, has infinite dynamically equivalent +copies corresponding to similar translations of the origin and +the destination equilibrium solutions. We construct connect- +ing orbits of certain relative phase between the two end points +by fixing the origin equilibrium and shifting the destination +equilibrium solution when constructing the initial connecting +curve using Eq. (29). In the following, we first demonstrate +the application of the introduced method by constructing a +connecting orbit from E1 to E2. We then present converged +connecting orbits between other equilibrium solutions, and +compare to the same orbits obtained from other methods re- +ported in the literature if applicable. +The search for a heteroclinic connection from E1 to E2 is +initialized by a connecting curve constructed using Eq. (29) +in the inversion-symmetric subspace of M (a = 0). We dis- +cretize the space-time domain by N = 64 Fourier modes in +space and M = 550 rational Chebyshev grid points in time. +The scaling of the temporal discretization is set to S = 55, +and the center of the distribution to s0 = 0. For this system, +the integration scheme described in section V C is stable for +∆τ = 0.01. +After a sharp initial decrease, the arc length cost function +decays exponentially with the fictitious time, as shown in +Fig. 3, and reaches the convergence criterion, Jarc = 10−12, +at τ ≈ 1.25 × 104. In the vector field induced by G, hetero- +clinic connections are attracting fixed points. The exponential +decay of the cost function suggests that when the evolving +connecting curve gets close enough to the connecting orbit, +the dynamics is dominated by the leading, i.e. the slowest, +eigendirection of the linearized dynamics in the vicinity of +the fixed point of ∂u/∂τ = G. +Fig. 4 shows six snapshots of the continuous deformation of +the connecting curve from E1 to E2 governed by the dynamics +in the space of connecting curves (25) towards a heteroclinic +connection. A substantial deformation towards the final shape +of the connecting orbit takes place in the beginning of the evo- +lution. The major remaining part of the integration time is +spent on the slight remaining deviation from the final orbit. +The space-time field corresponding to the initial connecting +curve (snapshot (i) in Fig. 4) and the converged connecting +orbit (snapshot (vi) in Fig. 4) are displayed in panels (a) and +(b) of Fig. 5, respectively. +0 +2 +4 +6 +8 +10 +12 +10−3 τ +10−12 +10−10 +10−8 +10−6 +10−4 +10−2 +100 +Jarc +(i) +(ii) +(iii)(iv)(v) +(vi) +FIG. 3: Monotonic decrease of the arc length cost function +Jarc against the fictitious time τ as the dynamics in the space +of connecting curves evolves an initial connecting curve +towards a connecting orbit for which J = 0. A three +dimensional projection of the state space corresponding to +the marked times (i) to (vi) is shown in Fig. 4. +E1 +E2 +(i) +P3 +−10 +5 +20 +35 +(ii) +(iii) +P3 +−10 +5 +20 +35 +(iv) +P1 +−20 +0 +20 +40 +P2 +0 +20 +40 +(v) +P1 +−20 +0 +20 +40 +P2 +0 +20 +40 +P3 +−10 +5 +20 +35 +(vi) +FIG. 4: Continuous deformation of a connecting curve by the +dynamics constructed in the space of connecting curves +towards a heteroclinic connection from the fixed point E1 to +E2. The solid blue line is the evolving connecting curve at the +times marked on Fig. 3, and the dashed line is the converged +heteroclinic connection. The state space is projected on +Pk(s) = ℑ{ ˆuk(s)}; k = 1,2,3. + +Jacobian-Free Variational Method for Constructing Connecting Orbits +9 +π +0 +θ +0 +22 +x +(a) The initial connecting curve at τ = 0. See marker (i) on Fig. 3 +and panel (i) of Fig. 4. +π +0 +θ +0 +22 +x +(b) The converged connecting orbit at τ = 1.25×104. See marker +(vi) on Fig. 3 and panel (vi) of Fig. 4. +FIG. 5: The space-time contour of the initial connecting +curve and the converged connecting orbit from the +equilibrium solution E1 to E2. The initial connecting curve is +symmetric under inversion about the origin. Since the +dynamics in the space of connecting curves preserves the +center symmetry, the converged connecting orbit belongs to +center-symmetric subspace as well. The temporal dimension +is mapped on the uniformly discretized finite interval [π,0] +where θ = π and θ = 0 correspond to s → −∞ and s → +∞, +respectively (see Eq. (18)). +The spatial resolution is chosen by monitoring the energy +spectrum of spatial Fourier modes in a direct numerical sim- +ulation of the KSE for L = 22. The spatial resolution N = 64 +ensures at least six orders of magnitude drop in the modu- +lus of spatial Fourier coefficients at all times. The converged +connecting orbit from E1 to E2, as an equilibrium solution to +Eq. (25), is structurally stable for a wide range of temporal res- +olutions M. However, the accuracy of the spectral representa- +tion in time, and therefore the minimum achieved value of the +cost function, Jarc,min := limτ→∞ Jarc(τ), varies with M. Fig. 6 +show the spectral convergence of Jarc,min with M. Notice that +Jarc,min can be considerably higher than the convergence crite- +rion when M is not large enough. If a local minimum of the +cost function is reached, in contrast, Jarc,min does not improve +as the temporal resolution is increased. As an example of a +failing search, we try to converge a connecting orbit between +E2 and γ(1/4)E2 from an initial connecting curve constructed +using Eq. (29) with a = 0 (see Sec. V D 3 why such connec- +tion cannot exist). The integration from this initial connecting +curve does not reach a global minimum but approaches a local +minimum with Jarc,min = 5.1×10−2. As shown on Fig. 6, the +minimum value does not decrease as the temporal discretiza- +tion is refined, confirming that a converged local minimum +has been identified and no connecting orbit was found. +100 +200 +300 +400 +500 +M +10−13 +10−11 +10−9 +10−7 +10−5 +10−3 +10−1 +Jarc,min +FIG. 6: Variation of the asymptotic value of the arc length +cost function Jarc by refining the temporal resolution M. +Filled circles: Exponential decrease of Jarc,min to zero in +successfully converging to a connecting orbit from E1 to E2. +Open circles: The cost function getting stuck in a local +minimum in the failed search for a connecting orbit from E2 +to γ(1/4)E2 in an over-constrained subspace. +1. +Connecting orbits originating from E0: Six-dimensional +unstable manifold +We converge a heteroclinic connection from E0 to E1, E2 +and E3 from an initial connecting curve constructed using +Eq. (29) with a = 0. A three-dimensional state space projec- +tion and the space-time contour of heteroclinic connections +from E0 to the other three equilibrium solutions are exhibited +in Figs. 7 and 8, respectively. The algorithm settings are pre- +sented in Appendix C. +The unstable manifold of E0 is six-dimensional. Each of +the repeated unstable eigenvalues of E0, Table I, is associated +to one eigenvector symmetric under reflection across x = 0 +and another one symmetric under inversion about the origin +(see Fig. 15). An exhaustive search in the unstable tangent +space at E0 is not practical even in the inversion-symmetric +subspace of the KSE where the reflection-symmetric eigen- +vectors do not exist, and the unstable manifold is three- +dimensional. Dong and Lan20 have computed a heteroclinic +connection from E0 to E1 using their variational method which +employs finite differences for calculating tangent velocity vec- +tors. They have used 6 000 sections to discretize this connect- +ing orbit in time, and obtain residuals of order O(10−6). To +achieve this value of Jarc (and similarly the suprimum norm of +the residual r), M = 25 interior time sections suffice for the +proposed variational method. +2. +Connecting orbits originating from E1: Four-dimensional +unstable manifold +We demonstrated the details of converging a heteroclinic +connection from E1 to E2 in the beginning of this section (see +Figs. 3 to 6). We also converge a heteroclinic connection from +E1 to E3 from an initial connecting curve constructed using + +Jacobian-Free Variational Method for Constructing Connecting Orbits +10 +P1 +0 +5 +10 +15 +20 +25 +P2 +−10 1 2 3 4 5 6 +P3 +0 +2 +4 +6 +8 +10 +12 +14 +E0 +E1 +(a) From E0 to E1 +P1 +0 +10 +20 +30 +40 +P2 +0 +5 +10 +15 +20 +P3 +0 +1 +2 +3 +4 +E0 +E2 +(b) From E0 to E2 +P1 +0 +20 +40 +60 +80 +P2 +0 2 4 6 8 101214 +P3 +0.0 +0.2 +0.4 +0.6 +0.8 +1.0 +1.2 +E0 +E3 +(c) From E0 to E3 +FIG. 7: Connecting orbits from E0 to the other three +equilibrium solutions in the center-symmetric subspace. The +orange line shows the initial connecting curve, and the blue +line shows the converged connecting orbit. The state space is +projected on Pk(s) = ℑ{ ˆubk(s)}; k = 1,2,3 with b = 1 in (a), +b = 2 in (b), and b = 3 in (c). +Eq. (29) with a = 0. Figs. 9 and 10 show a three-dimensional +state space projection and the space-time contour plot of the +converged heteroclinic connection from E1 to E3, respectively. +The algorithm settings are presented in Appendix C. +The unstable manifold of E1 is four-dimensional. One pair +of complex conjugate unstable eigenvalues of E1, Table I, is +associated to eigenvectors invariant under reflection across +x = 0, while the other pair is associated to eigenvectors in- +variant under inversion about the origin (see Fig. 16). An +exhaustive search in the four-dimensional unstable tangent +space at E1 is not practical. Cvitanovi´c et al.17 perform an +exhaustive search in the two-dimensional plane spanned by +the reflection-symmetric eigenvectors at E1, and show that all +π +0 +θ +0 +22 +x +(a) From E0 to E1 +π +0 +θ +0 +22 +x +(b) From E0 to E2 +π +0 +θ +0 +22 +x +(c) From E0 to E3 +FIG. 8: The space-time contour of the converged connecting +orbits from E0 to the other three equilibrium solutions in the +center-symmetric subspace. +P1 +0 +5 +10 15 20 25 30 35 +P2 +−5 0 5 10 15 20 +P3 +0 +20 +40 +60 +80 +E1 +E3 +FIG. 9: Connecting orbit from E1 to E3 in the +center-symmetric subspace. The orange line shows the initial +connecting curve, and the blue line shows the converged +connecting orbit. The state space is projected on +Pk(s) = ℑ{ ˆuk(s)}; k = 1,2,3. +trajectories starting from that plane are chaotic, and do not +reach any of the equilibrium solutions. They perform another +exhaustive search in the two-dimensional plane spanned by +the inversion-symmetric eigenvectors, and show that trajecto- +ries starting from that plane form a one-parameter family of +heteroclinic connections from E1 to E2, except one bordering +orbit that converges to E3. + +Jacobian-Free Variational Method for Constructing Connecting Orbits +11 +π +0 +θ +0 +22 +x +FIG. 10: The space-time contour of the converged connecting +orbit from E1 to E3 in the center-symmetric subspace. +3. +Connecting orbits originating from E2: Two-dimensional +unstable manifold +We converge two heteroclinic connections from E2 to E3 +and γ(1/4)E2. The initial conditions are constructed using +Eq. (29) by setting a = 0 for the connecting orbit between +E2 and E3, and setting a = −1 and v = ℜ{v1,2} for the con- +necting orbit between E2 and γ(1/4)E2 where ℜ{v1,2} is the +real part of the complex conjugate unstable eigenvectors at +E2 (see Fig. 17). In the latter, adding the symmetry breaking +term (a ̸= 0) is necessary because E2 and γ(1/4)E2 are both +symmetric under inversion about x = kL/4 with k = 0,1,2,3, +thus an initial connecting curve constructed by setting a = 0 is +symmetric under inversion about all these points. The dynam- +ics (25) preserves all the four inversion symmetries while no +connecting orbit can exist in such subspace of M , because the +unstable eigenvectors of E2 are symmetric only about x = 0 +and L/2, meaning that as soon as a trajectory of the KSE +leaves E2, the inversion symmetries about x = L/4 and 3L/4 +are broken. Consequently, as shown on Fig. 6, a = 0 results +in getting stuck in a local minimum of the cost function as the +dynamics (25) is integrated. A three-dimensional state space +projection and the space-time contour plot of the connecting +orbits from E2 to E3 and γ(1/4)E2 are shown in Figs. 11 and +12, respectively. The algorithm settings are presented in Ap- +pendix C. +By an exhaustive search in the two-dimensional unstable +tangent space at E2, Cvitanovi´c et al.17 show that the unstable +manifold of E2 is a one-parameter family of connecting orbits +that converge to γ(1/4)E2, except one orbit that connects E2 +to E3. +4. +Connecting orbits originating from E3: Two-dimensional +unstable manifold +We converge two heteroclinic connections from E3 to E2. +The initial conditions are constructed using Eq. (29) by set- +ting a = 0 in one, and a = −1 and v = sin(x) in the other. +A three-dimensional state space projection and the space-time +contour of these connecting orbits are shown in Figs. 13 and +14, respectively. The algorithm settings are presented in Ap- +pendix C. +The unstable manifold of E3 is two-dimensional. The re- +peated positive eigenvalue of E3, Table I, is associated to one +eigenvector symmetric under reflection across x = 0, and an- +other eigenvector symmetric under inversion about the origin +P1 +−15 +−10 +−5 +0 +P2 +−30 +−20 +−10 +0 +P3 +−20 +0 +20 +40 +60 +80 +E2 +E3 +(a) From E2 to E3 +P1 +−30 +−20 +−10 +0 +10 +P2 +−40 +−20 +0 +20 +40 +P3 +−40 +−20 +0 +20 +E2 +γ(1/4)E2 +(b) From E2 to γ(1/4)E2 +FIG. 11: Connecting orbits from E2 to E3 and γ(1/4)E2 in +the center-symmetric subspace. The orange line shows the +initial connecting curve, and the blue line shows the +converged connecting orbit. The state space is projected on +Pk(s) = ℑ{ ˆuk(s)}; k = 1,2,3. +(see Fig. 18). Cvitanovi´c et al.17 conduct an exhaustive search +in the two-dimensional unstable tangent space at E3, and iden- +tify two heteroclinic connections from E3 to E2 corresponding +to the perturbation of E3 along the inversion-symmetric eigen- +vector and its opposite direction. Fixing E3 and shifting E2 in +space by L/3 and 2L/3 puts the translated copy of E2 in the +same relative phase to E3 as the original configuration. There- +fore, the exhaustive search identifies two other pairs of hete- +roclinic connections from E3 to the group orbit of E2, which +are copies of the first pair of connecting orbits shifted by L/3 +and 2L/3 in the x-direction. +VI. +SUMMARY AND CONCLUDING REMARKS +Connecting orbits are of significant importance for study- +ing spatiotemporally chaotic dynamical systems in terms of +their invariant state space structures. We introduce a varia- +tional method for computing connecting orbits between two +equilibrium solutions by searching in the space of all smooth +curves in the state space that connect the two equilibria. In +this method, the deviation of a connecting curve from an in- +tegral curve of the vector field is penalized by a non-negative +cost function. A dynamical system in the space of connecting +curves is set up such that along its trajectories the cost function +is guaranteed to decrease monotonically. All trajectories of + +Jacobian-Free Variational Method for Constructing Connecting Orbits +12 +π +0 +θ +0 +22 +x +(a) From E2 to E3 +π +0 +θ +0 +22 +x +(b) From E2 to γ(1/4)E2 +FIG. 12: The space-time contour of the converged connecting +orbits from E1 to E3 and γ(1/4)E2 in the center-symmetric +subspace. +this dynamical system eventually converge to an equilibrium, +which corresponds to a minimum of the cost function. Global +minima of the cost function, taking zero value, correspond to +the connecting orbits of the original dynamics. This method +is not limited by the dimensionality of the unstable manifold +at the origin equilibrium solution, does not suffer from ex- +ponential separation of trajectories, and does not require any +domain truncation. The introduced method is Jacobian-free, +and its memory requirement scales linearly with the number +of degrees of freedom, which allows this method to be ap- +plied to high-dimensional dynamical systems including three- +dimensional fluid dynamics problems. +As a proof of concept, we apply the introduced variational +method to the one-dimensional KSE, and compute several +connecting orbits between known equilibrium solutions of the +system with domain size L = 22. The set of converged solu- +tions contains at least one connecting orbit between any two +equilibrium solutions unless it is known from an exhaustive +search in the unstable manifold of the origin equilibrium so- +lution that they are not connected. +After demonstrating the feasibility of the introduced +method for computing connecting orbits between equilibrium +solutions of the one-dimensional KSE, we are extending the +present work in two directions: One is applying this method +to the three-dimensional wall-bounded fluid flows governed +by the Navier-Stokes equations (NSE). The challenge in ap- +plying this method to the wall-bounded NSE lies not only in +dealing with a dynamical system of considerably larger size, +but also in handling the incompressibility constraint and the +pressure field: Pressure is not governed by an explicit evolu- +tion equation, but by the so-called pressure Poisson equation +to adapt itself to the velocity such that the velocity field re- +mains divergence-free. Construction of the pressure field as- +sociated to an instantaneous divergence-free velocity field in +a wall-bounded domain is not a trivial task31, let alone the +derivation of the adjoint operator in the presence of this non- +P1 +−25 −20 −15 −10 −5 +0 +P2 +0 102030405060 +P3 +0 +20 +40 +60 +80 +E3 +E2 +(a) Orbit 1: The initial connecting curve is constructed via Eq. (29) +by setting a = 0. +P1 +−10 +0 +10 +20 +30 +P2 +−20 +−100 10203040 +P3 +−20 +0 +20 +40 +60 +80 +E3 +E2 +(b) Orbit 2: The initial connecting curve is constructed via Eq. (29) +by setting a = −1 and v = sin(x). +FIG. 13: Two connecting orbits from E3 to E2 in the +center-symmetric subspace. The orange line shows the initial +connecting curve, and the blue line shows the converged +connecting orbit. The state space is projected on +Pk(s) = ℑ{ ˆuk(s)}; k = 1,2,3. +local, nonlinear operator. The second direction is developing +methods following a similar idea for computing connecting +orbits between invariant solutions of other types, including +between two periodic orbits and eventually between invariant +tori. Together with improved methods for constructing invari- +ant solutions24,32,33, the proposed methodology for computing +connecting orbits represents a step towards a more complete +characterization of the state-space structures supporting spa- +tiotemporally chaotic dynamics. Eventually, the characteriza- +tion of connecting orbits mediating transitions between invari- +ant solutions may allow for efficient forecasting of chaos even +in high-dimensional systems including fluid turbulence. +Appendix A: Derivation of the adjoint operator for the KSE +The directional derivative of the residual of the KSE, de- +fined in Eq. (23), along G is obtained by the definition (12) +as +L (u;G) = −∂G +∂s − ∂(uG) +∂x +− ∂ 2G +∂x2 − ∂ 4G +∂x4 . +(A1) + +Jacobian-Free Variational Method for Constructing Connecting Orbits +13 +π +0 +θ +0 +22 +x +(a) Orbit 1. +π +0 +θ +0 +22 +x +(b) Orbit 2. +FIG. 14: The space-time contour of the two converged +connecting orbits from E3 to E2 in the center-symmetric +subspace. +In order to find the adjoint operator, we expand the inner prod- +uct of L (u;G) and r +� +L (u;G),r +� += +� +∞ +−∞ +� L +0 +� +−∂G +∂s − ∂(uG) +∂x +− ∂ 2G +∂x2 − ∂ 4G +∂x4 +� +rdxds +=− +� L +0 +�� +∞ +−∞ +∂G +∂s rds +� +dx +− +� +∞ +−∞ +�� L +0 +�∂(uG) +∂x ++ ∂ 2G +∂x2 + ∂ 4G +∂x4 +� +rdx +� +ds (A2) +Integrating by parts we can write the first and the second inte- +gral as follows +� L +0 +�� +∞ +−∞ +∂G +∂s rds +� +dx = +� L +0 +� +lim +T→∞ +� +Gr +�s=T +s=−T − +� +∞ +−∞ G∂r +∂sds +� +dx, +� +∞ +−∞ +�� L +0 +� +∂(uG) +∂x ++ ∂ 2G +∂x2 + ∂ 4G +∂x4 +� +rdx +� +ds = +� +∞ +−∞ +�� +uGr +�x=L +x=0 − +� L +0 uG∂r +∂xdx+ +� +∂G +∂x r −G∂r +∂x +�x=L +x=0 ++ +� L +0 G∂ 2r +∂x2 dx ++ +� +∂ 3G +∂x3 r − ∂ 2G +∂x2 +∂r +∂x + ∂G +∂x +∂ 2r +∂x2 −G∂ 3r +∂x3 +�x=L +x=0 ++ +� L +0 G∂ 4r +∂x4 dx +� +ds. +In the limit T → ∞ the boundary term [Gr]s=T +s=−T vanishes since +both G and r are asymptotically zero. All boundary terms +[·]x=L +x=0 vanish too due to periodicity of u, r and G in x. There- +fore, Eq. (A2) becomes +⟨L (u;G),r⟩ = +� +∞ +−∞ +� L +0 +�∂r +∂s +u∂r +∂x − ∂ 2r +∂x2 − ∂ 4r +∂x4 +� +Gdxds. +(A3) +From the definition of the adjoint operator (14), this inner +product equals +� +L †(u;r),G +� += +� +∞ +−∞ +� L +0 L †Gdxds. +(A4) +Comparing Eqs. (A3) and (A4), L †(u;r) is given by +L †(u;r) = ∂r +∂s +u∂r +∂x − ∂ 2r +∂x2 − ∂ 4r +∂x4 . +(A5) +Appendix B: Unstable eigenvectors of the equilibria of the +KSE +The KSE with L = 22 has four known equilibrium solu- +tions including the trivial solution E0 = 0, and three nontrivial +solutions E1, E2 and E3 as shown in Fig. 2. The repelling +eigenvalues of these equilibrium solutions are listed in Table +I. The corresponding eigenvectors of E0, E1, E2 and E3, are +shown in Figs. 15 to 18, respectively. +Appendix C: Parameters used in constructing connecting +orbits of the KSE +In all calculations presented in Section V we have used N = +64 Fourier modes in space, have set the center of the temporal +distribution at the origin s0 = 0, and have used time step size +∆τ = 0.01. The temporal resolution M and the scaling S are +listed in Table II. The temporal resolution is set high enough +so that the convergence criterion Jarc,min < 10−12 is achieved +(see Section V D.) +ACKNOWLEDGEMENTS +This research has been supported by the European Re- +search Council (ERC) under the European Union’s Horizon +2020 research and innovation programme (grant agreement +no. 865677). The authors would like to thank Sajjad Azimi +and Jeremy P. Parker for helpful discussions. + +Jacobian-Free Variational Method for Constructing Connecting Orbits +14 +0 +11 +22 +x +−1.0 +−0.5 +0.0 +0.5 +1.0 +v1 +(a) λ1 = 0.2198 +0 +11 +22 +x +−1.0 +−0.5 +0.0 +0.5 +1.0 +v2 +(b) λ2 = 0.2198 +0 +11 +22 +x +−1.0 +−0.5 +0.0 +0.5 +1.0 +v3 +(c) λ3 = 0.1952 +0 +11 +22 +x +−1.0 +−0.5 +0.0 +0.5 +1.0 +v4 +(d) λ4 = 0.1952 +0 +11 +22 +x +−1.0 +−0.5 +0.0 +0.5 +1.0 +v5 +(e) λ5 = 0.0749 +0 +11 +22 +x +−1.0 +−0.5 +0.0 +0.5 +1.0 +v6 +(f) λ6 = 0.0749 +FIG. 15: Unstable eigenvectors vi of the trivial equilibrium +solution E0. λi is the eigenvalue associated with vi. +0 +11 +22 +x +−1.0 +−0.5 +0.0 +0.5 +1.0 +ℜ{v1,2} +(a) λ1,2 = 0.1308±0.3341i +0 +11 +22 +x +−1.0 +−0.5 +0.0 +0.5 +1.0 +ℑ{v1,2} +(b) λ1,2 = 0.1308±0.3341i +0 +11 +22 +x +−1.0 +−0.5 +0.0 +0.5 +1.0 +ℜ{v3,4} +(c) λ3,4 = 0.0824±0.3402i +0 +11 +22 +x +−1.0 +−0.5 +0.0 +0.5 +1.0 +ℑ{v3,4} +(d) λ3,4 = 0.0824±0.3402i +FIG. 16: Unstable eigenvectors vi of the equilibrium solution +E1. λi is the eigenvalue associated with vi. +0 +11 +22 +x +−1.0 +−0.5 +0.0 +0.5 +1.0 +ℜ{v1,2} +(a) λ1,2 = 0.1390±0.2384i +0 +11 +22 +x +−1.0 +−0.5 +0.0 +0.5 +1.0 +ℑ{v1,2} +(b) λ1,2 = 0.1390±0.2384i +FIG. 17: Unstable eigenvectors vi of the equilibrium solution +E2. λi is the eigenvalue associated with vi. +0 +11 +22 +x +−1.0 +−0.5 +0.0 +0.5 +1.0 +v1 +(a) λ1 = 0.0933 +0 +11 +22 +x +−1.0 +−0.5 +0.0 +0.5 +1.0 +v2 +(b) λ2 = 0.0933 +FIG. 18: Unstable eigenvectors vi of the equilibrium solution +E3. λi is the eigenvalue associated with vi. +DATA AVAILABILITY STATEMENT +The data that support the findings of this study are available +from the corresponding author upon reasonable request. +REFERENCES +1P. Cvitanovi´c, “Recurrent flows : the clockwork behind turbulence,” Journal +of Fluid Mechanics 726, 1–4 (2013). +TABLE II: Parameters used for numerically integrating the +dynamics in the space of connecting curves between different +equilibrium solutions of the KSE for L = 22 to construct +connecting orbits. +row +from +to +M +S +Figure +1 +E0 +E1 +80 +40 +7a & 8a +2 +E2 +130 +35 +7b & 8b +3 +E3 +120 +40 +7c & 8c +4 +E1 +E2 +550 +55 +4 & 5 +5 +E3 +500 +60 +9 & 10 +6 +E2 +τ(1/4)E2 +400 +35 +11a & 12a +7 +E3 +450 +50 +11b & 12b +8 +E3 +E2 +600 +50 +13a & 14a +9 +500 +40 +13b & 14b + +Jacobian-Free Variational Method for Constructing Connecting Orbits +15 +2G. J. Chandler and R. R. Kerswell, “Invariant recurrent solutions embedded +in a turbulent two-dimensional Kolmogorov flow,” Journal of Fluid Me- +chanics 722, 554–595 (2013). +3C. J. Crowley, J. L. Pughe-Sanford, W. Toler, M. C. Krygier, R. O. Grig- +oriev, and M. F. Schatz, “Turbulence tracks recurrent solutions,” Proceed- +ings of the National Academy of Sciences 119, 1–7 (2022). +4R. R. Kerswell, “Recent progress in understanding the transition to turbu- +lence in a pipe,” Nonlinearity 18, R17–R44 (2005). +5B. Eckhardt, T. M. Schneider, B. Hof, +and J. Westerweel, “Turbulence +Transition in Pipe Flow,” Annual Review of Fluid Mechanics 39, 447–468 +(2007). +6J. F. Gibson, J. Halcrow, and P. Cvitanovi´c, “Visualizing the geometry of +state space in plane Couette flow,” Journal of Fluid Mechanics 611, 107– +130 (2008). +7G. Kawahara, M. Uhlmann, and L. van Veen, “The Significance of Simple +Invariant Solutions in Turbulent Flows,” Annual Review of Fluid Mechan- +ics 44, 203–225 (2012). +8B. Suri, J. Tithof, R. O. Grigoriev, and M. F. Schatz, “Forecasting Fluid +Flows Using the Geometry of Turbulence,” Physical Review Letters 118, +114501 (2017). +9M. D. Graham and D. Floryan, “Exact Coherent States and the Nonlin- +ear Dynamics of Wall-Bounded Turbulent Flows,” Annual Review of Fluid +Mechanics 53, 227–253 (2021). +10L. van Veen and G. Kawahara, “Homoclinic tangle on the edge of shear +turbulence,” Physical Review Letters 107, 114501 (2011). +11B. Suri, R. K. Pallantla, M. F. Schatz, and R. O. Grigoriev, “Heteroclinic +and homoclinic connections in a Kolmogorov-like flow,” Physical Review +E 100, 1–14 (2019). +12F. Reetz and T. M. Schneider, “Invariant states in inclined layer convection. +Part 1. Temporal transitions along dynamical connections between invariant +states,” Journal of Fluid Mechanics 898 (2020), 10.1017/jfm.2020.317. +13A. J. Homburg and B. Sandstede, “Homoclinic and heteroclinic bifurcations +of vector fields,” in Handbook of dynamical systems 3, edited by H. Broer, +F. Takens, and B. Hasselblatt (Elsevier, 2010) pp. 1–124. +14F. Reetz, P. Subramanian, and T. M. Schneider, “Invariant states in inclined +layer convection. Part 2. Bifurcations and connections between branches of +invariant states,” under revision at JFM , 1–36 (2020). +15W.-J. Beyn, “The Numerical Computation of Connecting Orbits in Dynam- +ical Systems,” IMA Journal of Numerical Analysis 10, 379–405 (1990). +16J. Halcrow, J. F. Gibson, P. Cvitanovi´c, and D. Viswanath, “Heteroclinic +connections in plane Couette flow,” Journal of Fluid Mechanics 621, 365– +376 (2009). +17P. Cvitanovi´c, R. L. Davidchack, and E. Siminos, “On the state space ge- +ometry of the Kuramoto-Sivashinsky flow in a periodic domain,” SIAM +Journal on Applied Dynamical Systems 9, 1–33 (2010). +18M. Farano, S. Cherubini, J.-C. Robinet, P. De Palma, and T. M. Schneider, +“Computing heteroclinic orbits using adjoint-based methods,” Journal of +Fluid Mechanics 858, R3 (2019). +19Y. Liu, L. Liu, and T. Tang, “The numerical computation of connecting or- +bits in dynamical systems: A rational spectral approach,” Journal of Com- +putational Physics 111, 373–380 (1994). +20C. Dong and Y. Lan, “A variational approach to connecting orbits in nonlin- +ear dynamical systems,” Physics Letters, Section A: General, Atomic and +Solid State Physics 378, 705–712 (2014). +21Y. Lan and P. Cvitanovi´c, “Variational method for finding periodic orbits in +a general flow,” Physical Review E 69, 016217 (2004). +22R. K. Pallantla, Exact coherent structures and dynamical connections in a +quasi 2D Kolmogorov like flow, Ph.D. thesis, Georgia Institute of Technol- +ogy (2018). +23M. Farazmand, “An adjoint-based approach for finding invariant solutions +of Navier-Stokes equations,” Journal of Fluid Mechanics 795, 278–312 +(2016). +24S. Azimi, O. Ashtari, and T. M. Schneider, “Constructing periodic orbits of +high-dimensional chaotic systems by an adjoint-based variational method,” +Physical Review E 105, 014217 (2022). +25J. P. Boyd, “Chebyshev and Fourier Spectral Methods,” New York , 688 +(2000). +26Y. Kuramoto and T. Tsuzuki, “Persistent Propagation of Concentration +Waves in Dissipative Media Far from Thermal Equilibrium,” Progress of +Theoretical Physics 55, 356–369 (1976). +27G. I. Sivashinsky, “Nonlinear analysis of hydrodynamic instability in lam- +inar flames—I. Derivation of basic equations,” Acta Astronautica 4, 1177– +1206 (1977). +28R. E. LaQuey, S. M. Mahajan, P. H. Rutherford, and W. M. Tang, “Non- +linear Saturation of the Trapped-Ion Mode,” Physical Review Letters 34, +391–394 (1975). +29A. P. Hooper and R. Grimshaw, “Nonlinear instability at the interface be- +tween two viscous fluids,” Physics of Fluids 28, 37–45 (1985). +30Y. S. Smyrlis and D. T. Papageorgiou, “Computational study of chaotic +and ordered solutions of the Kuramoto-Sivashinsky equation,” Tech. Rep. +(Institute for Computer Applications in Science and Engineering, NASA +Langley Research Center, 1996). +31D. Rempfer, “On Boundary Conditions for Incompressible Navier-Stokes +Problems,” Applied Mechanics Reviews 59, 107–125 (2006). +32J. P. Parker and T. M. Schneider, “Invariant tori in dissipative hyperchaos,” +Chaos: An Interdisciplinary Journal of Nonlinear Science 32, 113102 +(2022). +33J. P. Parker, O. Ashtari, and T. M. Schneider, “Predicting chaotic statistics +with unstable invariant tori,” arXiv preprint 2301.10626, 1–11 (2023). + diff --git a/jtFKT4oBgHgl3EQfBi3I/content/tmp_files/load_file.txt b/jtFKT4oBgHgl3EQfBi3I/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..b5aab0fd1a88737f0d5e929aa2f7b4156d28d0fb --- /dev/null +++ b/jtFKT4oBgHgl3EQfBi3I/content/tmp_files/load_file.txt @@ -0,0 +1,794 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf,len=793 +page_content='Jacobian-Free Variational Method for Constructing Connecting Orbits Jacobian-Free Variational Method for Constructing Connecting Orbits in Nonlinear Dynamical Systems Omid Ashtari1 and Tobias M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Schneider1 Emergent Complexity in Physical Systems Laboratory (ECPS), École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland (*Electronic mail: tobias.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='schneider@epfl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='ch) In a dynamical systems description of spatiotemporally chaotic PDEs including those describing turbulence, chaos is viewed as a trajectory evolving within a network of non-chaotic, dynamically unstable, time-invariant solutions embed- ded in the chaotic attractor of the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' While equilibria, periodic orbits and invariant tori can be constructed using existing methods, computations of heteroclinic and homoclinic connections mediating the evolution between the former invariant solutions remain challenging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' We propose a robust matrix-free variational method for computing connecting orbits between equilibrium solutions of a dynamical system that can be applied to high-dimensional problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Instead of a common shooting-based approach, we define a minimization problem in the space of smooth state space curves that connect the two equilibria with a cost function measuring the deviation of a connecting curve from an integral curve of the vector field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Minimization deforms a trial curve until, at a global minimum, a connecting orbit is obtained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The method is robust, has no limitation on the dimension of the unstable manifold at the origin equilibrium, and does not suffer from exponential error amplification associated with time-marching a chaotic system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Owing to adjoint-based minimization techniques, no Jacobian matrices need to be constructed and the memory requirement scales linearly with the size of the problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The robustness of the method is demonstrated for the one-dimensional Kuramoto-Sivashinsky equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The chaotic evolution of a dynamical system can be de- scribed in terms of the non-chaotic time-invariant solu- tions embedded within its chaotic attractor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Heteroclinic and homoclincic connecting orbits between these invariant solutions mediate the evolution of the chaotic trajectory from the vicinity of one invariant solution to the vicinity of another one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' While a complete characterization of the state space structures supporting chaos requires the iden- tification of connecting orbits, constructing those has re- mained a numerical challenge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' We introduce a robust and memory-efficient method for constructing connecting or- bits between equilibrium solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Thereby, a more com- plete characterization of the state space structures sup- porting chaotic dynamics becomes feasible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' INTRODUCTION Many nonlinear driven out-of-equilibrium systems includ- ing those describing fluid flows, nonlinear optics and ac- tive suspensions exhibit spatiotemporally chaotic dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Within a dynamical systems description the spatiotemporal chaos can be viewed as the evolution of a chaotic trajectory in the state space of the governing equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Embedded in the state space are non-chaotic, time-invariant solutions includ- ing equilibria, periodic orbits and higher-dimensional invari- ant tori.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' These invariant solutions are dynamically unstable so that the chaotic trajectory visits them transiently, yet re- curringly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Spatiotemporal chaos can thus be viewed as a walk through a forest of invariant solutions that form the elementary building blocks of the chaotic solution1–3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Consequently, indi- vidual invariant solutions can provide remarkable information about the spatiotemporal chaos and physical mechanisms un- derlying it, and collectively they promise an avenue towards quantitatively predicting statistical properties of the chaotic dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Due to the significantly increasing computational resources and algorithmic advances, these concepts, originally developed in the context of low-dimensional chaotic dynami- cal systems, are now applied to very high-dimensional prob- lems including transitional fluid turbulence where dynamical systems descriptions based on the analysis of invariant solu- tions have proven to be particularly useful4–9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' While equilibria and periodic orbits form the building blocks of the dynamics, the chaotic evolution from the neigh- borhood of one unstable invariant solution to another is me- diated by connecting orbits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' These hetero- and homoclinic connections provide dynamic pathways between different pe- riodic orbits or equilibria within the chaotic attractor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' There- fore, a characterization of the chaotic dynamics in terms of state-space structures requires both to identify equilibria, peri- odic orbits and invariant tori embedded in the chaotic attractor, and to compute connecting orbits between them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' In the con- text of fluid dynamics for example, van Veen and Kawahara use connecting orbits to explain the turbulent bursting in plane Couette flow10;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Suri et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' study the network of connecting orbits that underpins the transient dynamics in a quasi-two- dimensional Kolmogorov flow11;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' and Reetz and Schneider characterize the time-dependent dynamics of inclined layer convection using connecting orbits between coexisting invari- ant solutions12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' We specifically focus on connecting orbits between equi- librium solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Such connecting orbits have been identi- fied as dynamically relevant in fluid systems10–12 and they are involved in global bifurcations, when for instance a pe- riodic orbit bifurcates off a homoclinic orbit or a hetero- clinic cycle13,14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Connecting orbits are located within the in- tersection of the unstable manifold of one equilibrium with the stable manifold of another or the same equilibrium so- lution if they are of heteroclinic or homoclinic type, respec- arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='11704v1 [nlin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='CD] 27 Jan 2023 Jacobian-Free Variational Method for Constructing Connecting Orbits 2 tively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' In the vicinity of an equilibrium solution, a trajectory approaches/departs the equilibrium along its stable/unstable manifold exponentially in time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Consequently, the time re- quired to traverse the entire connecting orbit is not finite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' This infinite passage time makes computing connecting orbits very challenging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' One approach to handle the computational challenge of the infinite passage time is to truncate the connecting orbit and compute an approximating part of the orbit that is traversed in finite time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Under favourable conditions, the truncated or- bit can be computed using shooting methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Geometrically, the truncation approach attempts to construct a trajectory that starts at some point on the unstable manifold of the origin equilibrium and ends at some other point on the stable man- ifold of the destination equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Due to their curvature, parametrizations of stable and unstable manifolds are usually not accessible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Consequently, they need to be approximated locally by the corresponding tangent spaces associated to the origin and destination equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Practically, a connecting orbit is thus found by identifying an initial condition in the in- tersection of the unstable tangent space of and a hypersphere around the origin equilibrium, which after forward time inte- gration reaches a distance below a chosen threshold from the destination equilibrium15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' If the hypersphere is chosen small enough, the unstable tangent space accurately approximates the unstable manifold, and thus the obtained trajectory accu- rately represents a connecting orbit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Even if the unstable manifold can be accurately approx- imated by the unstable tangent space, a systematic search for an initial condition that eventually reaches the destina- tion equilibrium is a formidable task, especially for a chaotic system where nearby trajectories diverge exponentially with time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' When the unstable manifold at the origin equilibrium solution is two-dimensional, an exhaustive search strategy can be employed6,11,16,17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' In this case, the search space is a circle on the unstable tangent space with an angle being the only variable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' However, when the unstable tangent space at the origin equilibrium has more than two dimensions, the search space is too large for an exhaustive search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' To improve the dimensionality drawback, Farano et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='18 propose an adjoint- based variational method for finding a state on an energy shell around the origin equilibrium whose trajectory reaches an- other energy shell around the destination equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' They do not constrain the initial condition to be located on the un- stable tangent space at the origin equilibrium, hence as a sec- ond step the trajectory is confirmed to shadow a connecting orbit by matching the endpoints of the trajectory against the linearized dynamics around the two equilibria.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' In all these methods determining the size of the hypersphere around the origin equilibrium solution is not a trivial task: the hyper- sphere should be small enough in order for the tangent space to accurately approximate the manifold, and large enough to let the required time integration intervals be feasibly short.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' An alternative to the shooting-based methods which search for a single state on the connecting orbit is to search in the space of connecting curves, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' all smooth curves in the state space which connect the two equilibria.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Among all such curves, only connecting orbits are integral curves of the vector field induced by the governing equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The idea is to start from a connecting curve pivoted on the two fixed points, then deform the curve until the tangent velocity coincides with the local field vector along the entire curve, and thus a connecting orbit is achieved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' This approach has several advantages over the reviewed shooting-based methods for computing connect- ing orbits: First, there is no limitation on the dimensionality of the unstable manifold at the origin equilibrium because no exhaustive search is needed;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Secondly, the approach does not suffer from the exponential separation of trajectories with time since the connecting curve is deformed locally and no time in- tegration is required;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' And lastly, this approach yields the exact and the entire connecting orbit without requiring to truncate it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Despite the conceptual advantages of searching in the space of connecting curves over the shooting-based alternatives, this approach is not extensively developed on the practical side.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='19 use rational Chebyshev basis functions for the spectral representation of variables along the infinite tempo- ral direction probably for the first time in this context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' They formulate the problem as a system of nonlinear equations by setting the temporal derivative equal to the right-hand side of the governing equation for every state variable at every tem- poral collocation point, and solve the system of equations us- ing standard Newton iterations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Dong and Lan20 extend the variational method of Lan and Cvitanovi´c21, originally de- veloped for finding periodic orbits, to the problem of con- structing connecting orbits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' They view the problem of de- forming connecting curves towards a connecting orbit as a minimization problem: a connecting orbit is found by min- imizing a cost function which penalizes the deviation of a connecting curve from being an integral curve of the vector field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' They employ an infinitesimal-step version of Newton iterations for continuously deforming the curve, and use fi- nite differences for calculating the tangent velocity vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' In his PhD thesis, Pallantla22 employs the same spectral repre- sentation of variables in the temporal direction as in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 19, and deforms the curve in the direction of the steepest descent of the cost function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The common drawback of the afore- mentioned algorithms is that they all require explicit con- struction of the Jacobian matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' In a system with M tem- poral and N spatial degrees of freedom the size of the Jaco- bian matrix scales as O(M2N2) which can be prohibitively large for high-dimensional dynamical systems such as three- dimensional fluid flows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' In order to transfer the advantages of searching in the space of connecting curves to high-dimensional dynamical systems, we propose a Jacobian-free variational method for constructing connecting orbits between two equilibrium so- lutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The method employs an adjoint-based optimization technique to minimize a cost function which measures the de- viation of a connecting curve between two equilibria from an integral curve of the vector field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' We construct a globally con- tracting dynamical system in the space of connecting curves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Fixed points of this dynamical system are minima of the non- negative cost function, hence global minima of the cost func- tion, taking zero value, correspond to connecting orbits of the original dynamical system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Connecting orbits are therefore found by integrating the dynamics in the space of connect- Jacobian-Free Variational Method for Constructing Connecting Orbits 3 ing curves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Due to the explicit construction of the dynamical system in the space of connecting curves, the memory require- ment scales as O(MN) which allows the proposed method to be applied to high-dimensional dynamical systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The remainder of the present article is organized as fol- lows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' In Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' II the problem of constructing a connecting or- bit is set up as a minimization problem, and in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' III the adjoint-based minimization technique is formulated for a gen- eral autonomous dynamical system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' In Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' IV a spectral rep- resentation suitable for the discretization along the unbounded temporal domain is discussed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' To demonstrate the robust- ness of the proposed variational method, in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' V we con- sider the one-dimensional Kuramoto–Sivashinsky equation in a spatiotemporally chaotic regime, and show that several con- necting orbits can be converged reliably.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Finally, in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' VI, the manuscript is summarized, and an outlook for future re- search is given.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' VARIATIONAL METHOD FOR FINDING CONNECTING ORBITS We consider general autonomous dynamical systems of the form ∂u ∂t = f(u), (1) where the smooth nonlinear operator f governs the evolution of an n-dimensional real field u ∈ M ⊂ Rn defined over a d- dimensional spatial domain x ∈ Ω ⊂ Rd and time t ∈ R sub- ject to time-independent boundary conditions (BCs) at ∂Ω, the boundaries of the spatial domain Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' A connecting orbit between two equilibrium solutions is a solution trajectory u(x,t) of the governing equation (1) such that the asymptotic conditions lim t→−∞u = u− , lim t→+∞u = u+ , f(u±) = 0, (2) are satisfied in the temporal direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The connecting orbit is a heteroclinic connection if u− ̸= u+, and a homoclinic con- nection if u− = u+ (while implicitly assuming that the entire orbit is not the equilibrium solution itself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=') In the (d + 1)-dimensional space-time domain of the dy- namical system (1), connecting orbits are solutions to a boundary value problem subject to the same BCs as Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' (1) in d spatial directions, augmented by the asymptotic BCs (2) in the temporal direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The idea of the proposed variational method is to consider C∞ space-time fields that satisfy the boundary conditions in all (d + 1) directions, and vary the field until Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' (1) is satisfied at each and every space-time coordinate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Geometrically, f(u) is a vector field in the n- dimensional state space M , u− and u+ are two fixed points, and connecting orbits are integral curves of this vector field extending from u− to u+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' In this picture, the search space is the space of all smooth curves in the state space that con- nect the two fixed points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' We define the space of connecting J FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 1: Schematic of the variational method for constructing a connecting orbit between two equilibrium solutions: A connecting curve pivoted on the two fixed points is deformed such that a cost function J measuring the deviation of the connecting curve from being an integral curve of the vector field is minimized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' For a connecting orbit the tangent velocity vector matches the field vector along the entire curve, and thus the global minimum of the cost function, J = 0, is achieved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' curves, denoted by Cg, as Cg = � � �u(x,s) ����� u : Ω×R → M lims→±∞ u = u± u satisfies BCs at ∂Ω � � �.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' (3) We parameterize connecting curves by s ∈ R in order to dis- tinguish the evolution along a connecting curve from the evo- lution along a solution trajectory of the governing equation (1) which is parameterized by the physical time t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Connecting or- bits form a subset C ⊂ Cg in which the tangent velocity vector, ∂u/∂s, coincides with the local field vector, ∂u/∂t = f(u), along the entire connecting curve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' As a measure of deviation of a connecting curve from being a connecting orbit we define the non-negative cost function J2 as J2 = � +∞ −∞ � Ω r·r dxds, (4) where r is the local deviation of the tangent velocity vector from the field vector, or the residual of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' (1): r(u) = f(u)− ∂u ∂s , (5) and · indicates the standard Euclidean inner product.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The residual r is zero everywhere along a connecting orbit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' There- fore, the cost function takes zero value for u ∈ C while it takes a positive value for u ∈ Cg \\ C .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The problem of finding con- necting orbits can now be viewed as a minimization problem in Cg: Absolute minima of J2, for which J = 0, correspond to connecting orbits u ∈ C .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 1 schematically shows the idea of this approach: Minimizing the cost function J deforms a curve connecting two fixed points of the vector field towards an integral curve of the vector field bounded between the two equilibria, thereby a connecting orbit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Jacobian-Free Variational Method for Constructing Connecting Orbits 4 III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' ADJOINT-BASED MINIMIZATION OF THE COST FUNCTION We have recast the problem of computing connecting or- bits into a minimization problem in the space of connecting curves extended between two equilibrium solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Abso- lute minima of the non-negative cost function J2 with J = 0 correspond to a connecting orbit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' To solve the minimization problem, we employ an adjoint-based technique inspired by the recent works by Farazmand23 on constructing equilibria and travelling waves, and by and Azimi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='24 on construct- ing periodic orbits of nonlinear dynamical systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' We con- struct a dynamical system in the space of connecting curves, Cg, such that along its trajectories the cost function is guaran- teed to decrease monotonically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Therefore, connecting orbits are found by integrating the constructed dynamics in Cg until a minimum of the cost function is reached.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Parametrizing this dynamical system by a fictitious time τ we need to construct the operator G(u) such that evolution of u governed by ∂u ∂τ = G(u), (6) guarantees ∂J2 ∂τ ≤ 0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' ∀τ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' (7) We define the inner product space Cs ⊃ Cg Cs = � q(x,s) ����� q : Ω×R → Rn lims→±∞ q = v± ∈ Rn � , (8) together with the real-valued inner product ⟨ , ⟩ : Cs ×Cs → R, ⟨q1,q2⟩ = � +∞ −∞ � Ω q1 ·q2 dxds, (9) and L2-norm ∥q∥ = � ⟨q,q⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' (10) In contrast to the space of connecting curves Cg, the elements of Cs have arbitrary asymptotic states v± ∈ Rn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The rate of change of the cost function J2 = ∥r∥2 = ⟨r,r⟩ is obtained by the inner product of r(u) with its directional derivative along the to-be-determined operator ∂u/∂τ = G(u): ∂J2 ∂τ = 2 � (∇ur) ∂u ∂τ , r � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' (11) The directional derivative of r(u) along G is defined as L L L (u;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='G) = lim ε→0 r(u+εG)−r(u) ε .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' (12) Using the adjoint of the directional derivative we can write Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' (11) as ∂J2 ∂τ = 2 � L L L †(u;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='r),G � , (13) where L L L † is the adjoint operator of L L L , with ⟨L L L (u;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='G),r⟩ = � G,L L L †(u;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='r) � , (14) for all connecting curves u ∈ Cg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The residual r (defined in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' (5)) and the operator G (defined in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' (6)) are func- tions of u, and belong to the inner product space Cs with cer- tain properties that are detailed shortly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' By choosing G(u) = −L L L †(u;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='r) the monotonic decrease of the cost function is guaranteed: ∂J2 ∂τ = 2 � L L L †(u;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='r),−L L L †(u;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='r) � = −2 ��L L L †(u;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='r) ��2 ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' (15) The dynamical system ∂u/∂τ = G(u) = −L L L †(u;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='r) is glob- ally contracting: All trajectories are eventually attracted to stable fixed points at which ∂u/∂τ = 0 and J2 takes a min- imum value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Although the monotonic decrease of the cost function is guaranteed along trajectories of the dynamics in Cg, reaching the global minimum is not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' To find a connect- ing orbit, therefore, the dynamics in the space of connecting curves is integrated until a fixed point is reached.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Those fixed points of ∂u/∂τ = G(u) which correspond to the global min- imum of the cost function, J = 0, are connecting orbits of the original dynamical system ∂u/∂t = f(u), and those corre- sponding to J > 0 are rejected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The dynamical system ∂u/∂τ = G(u) is constructed in the space of connecting curves Cg defined in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' (3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' This im- poses certain BCs on the residual r(u) and the operator G(u).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' In the temporal direction, lims→±∞ r = 0 since u satisfies the correct asymptotic BCs for all τ, and lims→±∞ G = 0 since the correct asymptotic values of u must be preserved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' In space, u satisfies the correct BCs at ∂Ω for all τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' consequently, the spatial BCs of r and G are determined following similar argu- ments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' For example, r and G will be periodic in directions where u is periodic, will take zero value where u satisfies Dirichlet boundary conditions, and so forth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' These properties must be taken into account while deriving the adjoint opera- tor from the definition (14).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Derivation of the adjoint operator for the Kuramoto-Sivashinsky system, introduced in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' V, is presented in Appendix A where the zero asymptotic values of r and G in the temporal direction and their periodicity in space enable us to derive the adjoint operator as an explicit function of the space-time field u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Both heteroclinic and homoclinic connections can be con- structed using the introduced variational method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' In the case of a homoclinic connection to an equilibrium solutions, zero variation in time, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' the equilibrium solution itself, is a trivial solution satisfying the definition (2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Therefore, depending on the initial connecting curve from which the integration starts, a trivial or a nontrivial solution with J = 0 can be obtained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The definition of a heteroclinic connection does not have any trivial solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' On an abstract level, we construct the operator G follow- ing the same logic as that in Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 24 and 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' However, in the different contexts the form of the operator differs as it acts on different objects and the dynamical system guaran- teeing the monotonic decrease of the cost function evolves Jacobian-Free Variational Method for Constructing Connecting Orbits 5 objects representing the specific sought-after invariant solu- tion: Farazmand23 converges equilibrium solutions, and thus constructs G for evolving spatial fields, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' points in the state space;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Azimi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='24 converge periodic orbits, hence they con- struct G for evolving space-time fields that are periodic in the temporal direction, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' closed loops in the state space;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' and here we converge connecting orbits, thus we construct G for evolving space-time fields satisfying the asymptotic con- ditions (2) in the temporal direction, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' connecting curves between two fixed points in the state space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' SPECTRAL REPRESENTATION IN TIME An efficient implementation of the proposed adjoint-based variational method is aided by an accurate spectral represen- tation of a space-time field q(x,s) ∈ Cs in the s direction, such that the asymptotic conditions at s → ±∞ are directly enforced by the chosen expansion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The spectral accuracy significantly reduces the number of time sections, and thereby memory, re- quired for an accurate representation of connecting orbits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' We use rational Chebyshev basis functions for the spectral repre- sentation in the temporal direction (see Chapter 17 of Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 25 for details).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Rational Chebyshev functions, Rn(s), are given by Rn(s) = cos(nθ);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' n ∈ W, (16) where θ ∈ (0,π) and s ∈ R are related via s = s0 +Scot(θ) ⇐⇒ θ = cot−1 �s−s0 S � , (17) with s0 ∈ R and S ∈ R+ being mapping parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Rational Chebyshev collocation points are obtained by a uniform discretization of θ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Therefore, M interior collocation points are sj = s0 +Scot � jπ M +1 � ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' j = 1,2,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=',M, (18) with j = 0 and j = M + 1 being reserved for the asymptotic values s → +∞ and s → −∞, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The uniform dis- cretization of θ results in a non-uniform distribution of grid points in s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Collocation points are denser around s0, the center of the distribution, and become sparser further away from the center.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The spacing between successive grid points is linearly scaled by S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' A real function q(s) with s ∈ R and constant asymptotic val- ues is approximated by the truncated expansion in a rational Chebyshev basis, q(s) ≈ ∑M+1 k=0 ckRk(s), where the expansion coefficients are ck = 2 (M +1)¯ck M+1 ∑ m=0 1 ¯cm q(sm)cos � mkπ M +1 � , (19) with grid points sm defined in equation (18) and ¯c j = � 2, if j = 0 or M +1, 1, otherwise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' (20) Having a grid function q(s j) with j = 0,1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=',M + 1 over rational Chebyshev grid points (18), the differentiation matrix Dt is constructed as: Dt j,m = 2 S(M +1) sin2 � jπ M +1 � M+1 ∑ k=0 k ¯cm ¯ck cos � mkπ M +1 � sin � k jπ M +1 � ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' j,m = 0,1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=',M +1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' (21) The expansion in a rational Chebyshev basis allows us to represent the space-time objects in the unbounded temporal direction, and we can expect spectral accuracy with fast con- vergence as a function of the expansion’s truncation order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Ra- tional Chebyshev functions form a generic basis for the spec- tral representation of functions over the entire real axis with constant asymptotic values and are thus a suitable expansion for connecting orbits for any studied physical system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' APPLICATION TO KURAMOTO-SIVASHINSKY EQUATION As a proof of concept, we apply the introduced method for constructing connecting orbits to the one-dimensional Kuramoto-Sivashinsky equation (KSE)26,27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The KSE is a nonlinear partial differential equation which emerges in var- ious physical contexts such as flame propagation27, plasma physics28, or interfacial fluids instability29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The KSE is also commonly used as a model system for examining new meth- ods developed for chaotic fluid flows and transitional turbu- lence since it exhibits spatiotemporally chaotic behavior and displays some similar features to the Navier-Stokes equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The one-dimensional KSE for a real field u(x,t) on the pe- riodic spatial domain 0 ≤ x < L is ∂u ∂t = −u∂u ∂x − ∂ 2u ∂x2 −ν ∂ 4u ∂x4 , (22) with constant positive damping parameter ν.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The dynamics of the KSE is controlled by the single dimensionless group L = L/√ν.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Here, we fix ν = 1 and consider the domain size L as the control parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' For L < 2π, the trivial equilibrium solution u(x,t) = const.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' is linearly stable, and is the global attractor of the dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' By increasing L, solutions of the KSE undergo a series of bifurcations, and for a sufficiently large domain size the dynamics can exhibit spatiotemporally chaotic behavior30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' We demonstrate the application of the proposed method by constructing connecting orbits between Jacobian-Free Variational Method for Constructing Connecting Orbits 6 equilibrium solutions of the KSE for L = 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' This domain size is large enough for the KSE to exhibit spatiotemporally chaotic dynamics, yet small enough to have low-dimensional unstable manifolds at the equilibria found, over which an ex- haustive search for possible connecting orbits is practical.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The state space geometry of the KSE for this parameter value has previously been explored in detail by Cvitanovi´c and collaborators17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' They identified several connecting orbits us- ing the shooting method described in Section I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' We construct a complete set of connecting orbits between all known equi- librium solutions of this system;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' complete in the sense that at least one connecting orbit between any pair of equilibrium solutions is computed, or it is confirmed by the exhaustive search in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 17 that no connecting orbit exists between the two equilibria.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Formulation of the adjoint-based variational method for the KSE The KSE (22) has the form of the general dynamical system (1) with n = d = 1 and Ω = [0,L).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The residual field, defined in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' (5), for the KSE is r = −∂u ∂s −u∂u ∂x − ∂ 2u ∂x2 − ∂ 4u ∂x4 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' (23) The dynamical system along whose trajectories the cost func- tion decreases monotonically is derived based on the adjoint operator of the directional derivative of r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The adjoint operator for the KSE system is constructed by a series of integrations by part (see Appendix A for details): L †(u;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='r) = ∂r ∂s +u∂r ∂x − ∂ 2r ∂x2 − ∂ 4r ∂x4 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' (24) Therefore, the dynamical system in the space of connecting curves, u(x,s;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='τ) ∈ Cg, that minimizes the cost function J2 is ∂u ∂τ = −L †(u;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='r) = −∂r ∂s −u∂r ∂x + ∂ 2r ∂x2 + ∂ 4r ∂x4 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' (25) B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Symmetry preservation The KSE (22) is equivariant under continuous translations in the x-direction γ(α)u(x,t) = u(x+αL,t);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' α ∈ [0,1), (26) and under inversions about the origin σu(x,t) = −u(−x,t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' (27) The translation operator γ(α) and inversion operator σ com- mute with the residual (23) of the KSE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Consequently, the dy- namics in the space of connecting curves, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' (25), is equivari- ant under the action of γ(α) and σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' This means that if the in- tegration of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' (25) starts from an initial space-time field that is invariant under the action of σ ◦ γ(α), the dynamics pre- serves the resulting point-inversion symmetry, and therefore the constructed connecting orbit belongs to the same symmet- ric subspace of the state space M .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The KSE (22) preserves the spatial mean value of the evolv- ing field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Consequently, the spatial mean along a connecting orbit is constant and the same as the end point equilibrium so- lutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' We consider the dynamics of the KSE in the subspace of fields with zero spatial mean.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The zero mean value is not enforced during the evolution of a connecting curve towards a connecting orbit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' However, since the two end point equilibria do have zero spatial mean, a converged connecting orbit with J = 0 takes zero mean value as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Numerical implementation 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Spectral discretization A connecting curve u(x,s) is discretized in the temporal direction using M + 2 time sections (including the end point equilibria) over the rational Chebyshev grid while each time section is represented by N Fourier modes in space: u(xn,sm) = N 2 −1 ∑ j=− N 2 ˆuj(sm)exp � j2πxn L i � , (28) where xn = nL/N with indices 0 ≤ n < N are the uniform grid points in space;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' sm with indices 0 ≤ m ≤ M + 1 are the non- uniform rational Chebyshev collocation points in time;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' ˆuj(sm) is the jth Fourier coefficient of the time section at sm;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' and i is the imaginary unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' In spectral space, the connecting curve u is represented by an (M + 2) × N matrix of complex numbers ˆum,j = ˆuj(sm).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The derivative of order q ∈ W of this space-time field with respect to x is obtained by the Hadamard product D(q) x ⊙ ˆu where D(q) x m, j = (2π ji/L)q, and its derivative of order q ∈ W with respect to s is obtained by multiplying ˆu from the left by Dq t , where the temporal differentiation matrix Dt is de- fined in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' (21).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The residual r and the descent direction G are discretized in the same way with the only difference that their time sections at s0 and sM+1 (corresponding to s → +∞ and s → −∞, respectively) are identically zero (see Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' III).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The nonlinear terms are calculated in physical space where products are of elementwise Hadamard type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Transforming back and forward between physical and spectral representa- tions of the space-time fields requires one-dimensional for- ward or backward discrete Fourier transformation of each time section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Initialization The initial connecting curve is chosen as a convex combina- tion of the equilibrium solutions u− and u+, plus a symmetry Jacobian-Free Variational Method for Constructing Connecting Orbits 7 breaking term: u0(x,s;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='a) =1 2 [(1+tanh(s))u+(x)+(1−tanh(s))u−(x)] +aexp(−s2)v(x);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' a ∈ {0,1}, (29) with x ∈ [0,L) and s ∈ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' If u−(x) and u+(x) both are inver- sion symmetric about the same point x = x0, then a = 0 results in an initial space-time field for which all time sections are invariant under the same inversion symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Since the pro- posed variational dynamics preserves the inversion symmetry, we can set a = 0 in order to search in the inversion-symmetric subspace of connecting trajectories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' In order to break such a symmetry, we add the second line, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' set a ̸= 0, where v(x) is a field which does not have the inversion symmetry shared between u−(x) and u+(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Time stepping The defined dynamical system ∂u/∂τ = G is globally con- tracting and we are only concerned about the asymptotic state u = u0 + � ∞ 0 Gdτ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Consequently, we select the numerical in- tegration scheme based on simplicity and stability rather than accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' We use semi-implicit forward Euler time-stepping scheme which has first-order accuracy in τ, and treats the lin- ear terms of G in u implicitly and the nonlinear terms explic- itly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The code was developed in C++ with OpenMP paral- lelization of local calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Results and discussion In the subspace of fields with zero spatial mean, the KSE with L = 22 has four known equilibrium solutions includ- ing the trivial solution u = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Hereafter we denote the triv- ial equilibrium solution by E0, and the nontrivial ones by E1, E2 and E3 as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' We construct these equilib- rium solutions following the adjoint-based variational method of Farazmand23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' E1, E2 and E3 are invariant under inversion about the origin, σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' E2 and E3 are also symmetric under dis- crete shifts γ(1/2) and γ(1/3), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Therefore, in ad- dition to the inversion about x = 0 and L/2, E2 is symmetric under inversion about x = L/4 and 3L/4, and E3 is symmetric under inversion about x = L/6, L/3, 2L/3, and 5L/6 as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The repelling eigenvalues of all four equilibrium solutions are listed in Table I, and their associated eigenvectors are shown in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 15 to 18 in Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Connecting orbits are converged by integrating Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' (25) un- til a fixed point in the vector field of G, corresponding to a minimum J, is achieved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Connecting orbits correspond to the global minima of J, for which J = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' In order to monitor the convergence, we define the arc length weighted cost function Jarc = � +∞ −∞ |r| ���� ∂u ∂s ����ds � +∞ −∞ ���� ∂u ∂s ����ds , (30) 0 11 22 x −2 −1 0 1 2 u (a) E1 0 11 22 x −2 −1 0 1 2 u (b) E2 0 11 22 x −2 −1 0 1 2 u (c) E3 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 2: Nontrivial equilibrium solutions of the KSE for L = 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' E1, E2 and E3 are symmetric under inversion about the origin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' E2 and E3 are also symmetric under discrete shift by L/2 and L/3, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' TABLE I: Repelling eigenvalues of the equilibria of the KSE for L = 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The rest of the eigenvalues, except one zero eigenvalue for E1, E2 and E3, have negative real part.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Solution Unstable eigenvalues E0 λ1,2 =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='2198 λ3,4 =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='1952 λ5,6 =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='0749 E1 λ1,2 =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='1308±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='3341i λ3,4 =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='0824±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='3402i E2 λ1,2 =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='1390±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='2384i E3 λ1,2 =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='0933 Jacobian-Free Variational Method for Constructing Connecting Orbits 8 with | · | being |q| = �� Ω q·q dx ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' q ∈ Cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' (31) Obviously, Jarc = 0 if and only if J = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' However, the numer- ical evaluation of Jarc is not subject to the error accumulation associated with the numerical evaluation of the improper inte- gral (4) that defines J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Moreover, since the trivial solution to the definition of a homoclinic connection has zero arc length, Jarc is undefined when the trivial solution is achieved, while J = 0 for either trivial or nontrivial solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' We consider the algorithm converged when Jarc < 10−12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Due to the continuous translational symmetry of the KSE, Ei with i = 1,2,3 represent its so-called group orbit of all sym- metry related states, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' γ(α)Ei where α ∈ [0,1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Every con- necting orbit, therefore, has infinite dynamically equivalent copies corresponding to similar translations of the origin and the destination equilibrium solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' We construct connect- ing orbits of certain relative phase between the two end points by fixing the origin equilibrium and shifting the destination equilibrium solution when constructing the initial connecting curve using Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' (29).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' In the following, we first demonstrate the application of the introduced method by constructing a connecting orbit from E1 to E2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' We then present converged connecting orbits between other equilibrium solutions, and compare to the same orbits obtained from other methods re- ported in the literature if applicable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The search for a heteroclinic connection from E1 to E2 is initialized by a connecting curve constructed using Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' (29) in the inversion-symmetric subspace of M (a = 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' We dis- cretize the space-time domain by N = 64 Fourier modes in space and M = 550 rational Chebyshev grid points in time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The scaling of the temporal discretization is set to S = 55, and the center of the distribution to s0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' For this system, the integration scheme described in section V C is stable for ∆τ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='01.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' After a sharp initial decrease, the arc length cost function decays exponentially with the fictitious time, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 3, and reaches the convergence criterion, Jarc = 10−12, at τ ≈ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='25 × 104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' In the vector field induced by G, hetero- clinic connections are attracting fixed points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The exponential decay of the cost function suggests that when the evolving connecting curve gets close enough to the connecting orbit, the dynamics is dominated by the leading, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' the slowest, eigendirection of the linearized dynamics in the vicinity of the fixed point of ∂u/∂τ = G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 4 shows six snapshots of the continuous deformation of the connecting curve from E1 to E2 governed by the dynamics in the space of connecting curves (25) towards a heteroclinic connection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' A substantial deformation towards the final shape of the connecting orbit takes place in the beginning of the evo- lution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The major remaining part of the integration time is spent on the slight remaining deviation from the final orbit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The space-time field corresponding to the initial connecting curve (snapshot (i) in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 4) and the converged connecting orbit (snapshot (vi) in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 4) are displayed in panels (a) and (b) of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 5, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 0 2 4 6 8 10 12 10−3 τ 10−12 10−10 10−8 10−6 10−4 10−2 100 Jarc (i) (ii) (iii)(iv)(v) (vi) FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 3: Monotonic decrease of the arc length cost function Jarc against the fictitious time τ as the dynamics in the space of connecting curves evolves an initial connecting curve towards a connecting orbit for which J = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' A three dimensional projection of the state space corresponding to the marked times (i) to (vi) is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' E1 E2 (i) P3 −10 5 20 35 (ii) (iii) P3 −10 5 20 35 (iv) P1 −20 0 20 40 P2 0 20 40 (v) P1 −20 0 20 40 P2 0 20 40 P3 −10 5 20 35 (vi) FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 4: Continuous deformation of a connecting curve by the dynamics constructed in the space of connecting curves towards a heteroclinic connection from the fixed point E1 to E2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The solid blue line is the evolving connecting curve at the times marked on Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 3, and the dashed line is the converged heteroclinic connection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The state space is projected on Pk(s) = ℑ{ ˆuk(s)};' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' k = 1,2,3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Jacobian-Free Variational Method for Constructing Connecting Orbits 9 π 0 θ 0 22 x (a) The initial connecting curve at τ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' See marker (i) on Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 3 and panel (i) of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' π 0 θ 0 22 x (b) The converged connecting orbit at τ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='25×104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' See marker (vi) on Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 3 and panel (vi) of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 5: The space-time contour of the initial connecting curve and the converged connecting orbit from the equilibrium solution E1 to E2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The initial connecting curve is symmetric under inversion about the origin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Since the dynamics in the space of connecting curves preserves the center symmetry, the converged connecting orbit belongs to center-symmetric subspace as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The temporal dimension is mapped on the uniformly discretized finite interval [π,0] where θ = π and θ = 0 correspond to s → −∞ and s → +∞, respectively (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' (18)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The spatial resolution is chosen by monitoring the energy spectrum of spatial Fourier modes in a direct numerical sim- ulation of the KSE for L = 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The spatial resolution N = 64 ensures at least six orders of magnitude drop in the modu- lus of spatial Fourier coefficients at all times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The converged connecting orbit from E1 to E2, as an equilibrium solution to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' (25), is structurally stable for a wide range of temporal res- olutions M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' However, the accuracy of the spectral representa- tion in time, and therefore the minimum achieved value of the cost function, Jarc,min := limτ→∞ Jarc(τ), varies with M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 6 show the spectral convergence of Jarc,min with M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Notice that Jarc,min can be considerably higher than the convergence crite- rion when M is not large enough.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' If a local minimum of the cost function is reached, in contrast, Jarc,min does not improve as the temporal resolution is increased.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' As an example of a failing search, we try to converge a connecting orbit between E2 and γ(1/4)E2 from an initial connecting curve constructed using Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' (29) with a = 0 (see Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' V D 3 why such connec- tion cannot exist).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The integration from this initial connecting curve does not reach a global minimum but approaches a local minimum with Jarc,min = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='1×10−2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' As shown on Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 6, the minimum value does not decrease as the temporal discretiza- tion is refined, confirming that a converged local minimum has been identified and no connecting orbit was found.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 100 200 300 400 500 M 10−13 10−11 10−9 10−7 10−5 10−3 10−1 Jarc,min FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 6: Variation of the asymptotic value of the arc length cost function Jarc by refining the temporal resolution M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Filled circles: Exponential decrease of Jarc,min to zero in successfully converging to a connecting orbit from E1 to E2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Open circles: The cost function getting stuck in a local minimum in the failed search for a connecting orbit from E2 to γ(1/4)E2 in an over-constrained subspace.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Connecting orbits originating from E0: Six-dimensional unstable manifold We converge a heteroclinic connection from E0 to E1, E2 and E3 from an initial connecting curve constructed using Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' (29) with a = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' A three-dimensional state space projec- tion and the space-time contour of heteroclinic connections from E0 to the other three equilibrium solutions are exhibited in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 7 and 8, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The algorithm settings are pre- sented in Appendix C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The unstable manifold of E0 is six-dimensional.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Each of the repeated unstable eigenvalues of E0, Table I, is associated to one eigenvector symmetric under reflection across x = 0 and another one symmetric under inversion about the origin (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 15).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' An exhaustive search in the unstable tangent space at E0 is not practical even in the inversion-symmetric subspace of the KSE where the reflection-symmetric eigen- vectors do not exist, and the unstable manifold is three- dimensional.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Dong and Lan20 have computed a heteroclinic connection from E0 to E1 using their variational method which employs finite differences for calculating tangent velocity vec- tors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' They have used 6 000 sections to discretize this connect- ing orbit in time, and obtain residuals of order O(10−6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' To achieve this value of Jarc (and similarly the suprimum norm of the residual r), M = 25 interior time sections suffice for the proposed variational method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Connecting orbits originating from E1: Four-dimensional unstable manifold We demonstrated the details of converging a heteroclinic connection from E1 to E2 in the beginning of this section (see Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 3 to 6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' We also converge a heteroclinic connection from E1 to E3 from an initial connecting curve constructed using Jacobian-Free Variational Method for Constructing Connecting Orbits 10 P1 0 5 10 15 20 25 P2 −10 1 2 3 4 5 6 P3 0 2 4 6 8 10 12 14 E0 E1 (a) From E0 to E1 P1 0 10 20 30 40 P2 0 5 10 15 20 P3 0 1 2 3 4 E0 E2 (b) From E0 to E2 P1 0 20 40 60 80 P2 0 2 4 6 8 101214 P3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='2 E0 E3 (c) From E0 to E3 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 7: Connecting orbits from E0 to the other three equilibrium solutions in the center-symmetric subspace.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The orange line shows the initial connecting curve, and the blue line shows the converged connecting orbit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The state space is projected on Pk(s) = ℑ{ ˆubk(s)};' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' k = 1,2,3 with b = 1 in (a), b = 2 in (b), and b = 3 in (c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' (29) with a = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 9 and 10 show a three-dimensional state space projection and the space-time contour plot of the converged heteroclinic connection from E1 to E3, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The algorithm settings are presented in Appendix C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The unstable manifold of E1 is four-dimensional.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' One pair of complex conjugate unstable eigenvalues of E1, Table I, is associated to eigenvectors invariant under reflection across x = 0, while the other pair is associated to eigenvectors in- variant under inversion about the origin (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 16).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' An exhaustive search in the four-dimensional unstable tangent space at E1 is not practical.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Cvitanovi´c et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='17 perform an exhaustive search in the two-dimensional plane spanned by the reflection-symmetric eigenvectors at E1, and show that all π 0 θ 0 22 x (a) From E0 to E1 π 0 θ 0 22 x (b) From E0 to E2 π 0 θ 0 22 x (c) From E0 to E3 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 8: The space-time contour of the converged connecting orbits from E0 to the other three equilibrium solutions in the center-symmetric subspace.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' P1 0 5 10 15 20 25 30 35 P2 −5 0 5 10 15 20 P3 0 20 40 60 80 E1 E3 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 9: Connecting orbit from E1 to E3 in the center-symmetric subspace.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The orange line shows the initial connecting curve, and the blue line shows the converged connecting orbit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The state space is projected on Pk(s) = ℑ{ ˆuk(s)};' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' k = 1,2,3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' trajectories starting from that plane are chaotic, and do not reach any of the equilibrium solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' They perform another exhaustive search in the two-dimensional plane spanned by the inversion-symmetric eigenvectors, and show that trajecto- ries starting from that plane form a one-parameter family of heteroclinic connections from E1 to E2, except one bordering orbit that converges to E3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Jacobian-Free Variational Method for Constructing Connecting Orbits 11 π 0 θ 0 22 x FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 10: The space-time contour of the converged connecting orbit from E1 to E3 in the center-symmetric subspace.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Connecting orbits originating from E2: Two-dimensional unstable manifold We converge two heteroclinic connections from E2 to E3 and γ(1/4)E2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The initial conditions are constructed using Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' (29) by setting a = 0 for the connecting orbit between E2 and E3, and setting a = −1 and v = ℜ{v1,2} for the con- necting orbit between E2 and γ(1/4)E2 where ℜ{v1,2} is the real part of the complex conjugate unstable eigenvectors at E2 (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 17).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' In the latter, adding the symmetry breaking term (a ̸= 0) is necessary because E2 and γ(1/4)E2 are both symmetric under inversion about x = kL/4 with k = 0,1,2,3, thus an initial connecting curve constructed by setting a = 0 is symmetric under inversion about all these points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The dynam- ics (25) preserves all the four inversion symmetries while no connecting orbit can exist in such subspace of M , because the unstable eigenvectors of E2 are symmetric only about x = 0 and L/2, meaning that as soon as a trajectory of the KSE leaves E2, the inversion symmetries about x = L/4 and 3L/4 are broken.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Consequently, as shown on Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 6, a = 0 results in getting stuck in a local minimum of the cost function as the dynamics (25) is integrated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' A three-dimensional state space projection and the space-time contour plot of the connecting orbits from E2 to E3 and γ(1/4)E2 are shown in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 11 and 12, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The algorithm settings are presented in Ap- pendix C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' By an exhaustive search in the two-dimensional unstable tangent space at E2, Cvitanovi´c et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='17 show that the unstable manifold of E2 is a one-parameter family of connecting orbits that converge to γ(1/4)E2, except one orbit that connects E2 to E3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Connecting orbits originating from E3: Two-dimensional unstable manifold We converge two heteroclinic connections from E3 to E2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The initial conditions are constructed using Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' (29) by set- ting a = 0 in one, and a = −1 and v = sin(x) in the other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' A three-dimensional state space projection and the space-time contour of these connecting orbits are shown in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 13 and 14, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The algorithm settings are presented in Ap- pendix C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The unstable manifold of E3 is two-dimensional.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The re- peated positive eigenvalue of E3, Table I, is associated to one eigenvector symmetric under reflection across x = 0, and an- other eigenvector symmetric under inversion about the origin P1 −15 −10 −5 0 P2 −30 −20 −10 0 P3 −20 0 20 40 60 80 E2 E3 (a) From E2 to E3 P1 −30 −20 −10 0 10 P2 −40 −20 0 20 40 P3 −40 −20 0 20 E2 γ(1/4)E2 (b) From E2 to γ(1/4)E2 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 11: Connecting orbits from E2 to E3 and γ(1/4)E2 in the center-symmetric subspace.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The orange line shows the initial connecting curve, and the blue line shows the converged connecting orbit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The state space is projected on Pk(s) = ℑ{ ˆuk(s)};' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' k = 1,2,3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 18).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Cvitanovi´c et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='17 conduct an exhaustive search in the two-dimensional unstable tangent space at E3, and iden- tify two heteroclinic connections from E3 to E2 corresponding to the perturbation of E3 along the inversion-symmetric eigen- vector and its opposite direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Fixing E3 and shifting E2 in space by L/3 and 2L/3 puts the translated copy of E2 in the same relative phase to E3 as the original configuration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' There- fore, the exhaustive search identifies two other pairs of hete- roclinic connections from E3 to the group orbit of E2, which are copies of the first pair of connecting orbits shifted by L/3 and 2L/3 in the x-direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' SUMMARY AND CONCLUDING REMARKS Connecting orbits are of significant importance for study- ing spatiotemporally chaotic dynamical systems in terms of their invariant state space structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' We introduce a varia- tional method for computing connecting orbits between two equilibrium solutions by searching in the space of all smooth curves in the state space that connect the two equilibria.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' In this method, the deviation of a connecting curve from an in- tegral curve of the vector field is penalized by a non-negative cost function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' A dynamical system in the space of connecting curves is set up such that along its trajectories the cost function is guaranteed to decrease monotonically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' All trajectories of Jacobian-Free Variational Method for Constructing Connecting Orbits 12 π 0 θ 0 22 x (a) From E2 to E3 π 0 θ 0 22 x (b) From E2 to γ(1/4)E2 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 12: The space-time contour of the converged connecting orbits from E1 to E3 and γ(1/4)E2 in the center-symmetric subspace.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' this dynamical system eventually converge to an equilibrium, which corresponds to a minimum of the cost function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Global minima of the cost function, taking zero value, correspond to the connecting orbits of the original dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' This method is not limited by the dimensionality of the unstable manifold at the origin equilibrium solution, does not suffer from ex- ponential separation of trajectories, and does not require any domain truncation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The introduced method is Jacobian-free, and its memory requirement scales linearly with the number of degrees of freedom, which allows this method to be ap- plied to high-dimensional dynamical systems including three- dimensional fluid dynamics problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' As a proof of concept, we apply the introduced variational method to the one-dimensional KSE, and compute several connecting orbits between known equilibrium solutions of the system with domain size L = 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The set of converged solu- tions contains at least one connecting orbit between any two equilibrium solutions unless it is known from an exhaustive search in the unstable manifold of the origin equilibrium so- lution that they are not connected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' After demonstrating the feasibility of the introduced method for computing connecting orbits between equilibrium solutions of the one-dimensional KSE, we are extending the present work in two directions: One is applying this method to the three-dimensional wall-bounded fluid flows governed by the Navier-Stokes equations (NSE).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The challenge in ap- plying this method to the wall-bounded NSE lies not only in dealing with a dynamical system of considerably larger size, but also in handling the incompressibility constraint and the pressure field: Pressure is not governed by an explicit evolu- tion equation, but by the so-called pressure Poisson equation to adapt itself to the velocity such that the velocity field re- mains divergence-free.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Construction of the pressure field as- sociated to an instantaneous divergence-free velocity field in a wall-bounded domain is not a trivial task31, let alone the derivation of the adjoint operator in the presence of this non- P1 −25 −20 −15 −10 −5 0 P2 0 102030405060 P3 0 20 40 60 80 E3 E2 (a) Orbit 1: The initial connecting curve is constructed via Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' (29) by setting a = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' P1 −10 0 10 20 30 P2 −20 −100 10203040 P3 −20 0 20 40 60 80 E3 E2 (b) Orbit 2: The initial connecting curve is constructed via Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' (29) by setting a = −1 and v = sin(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 13: Two connecting orbits from E3 to E2 in the center-symmetric subspace.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The orange line shows the initial connecting curve, and the blue line shows the converged connecting orbit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The state space is projected on Pk(s) = ℑ{ ˆuk(s)};' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' k = 1,2,3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' local, nonlinear operator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The second direction is developing methods following a similar idea for computing connecting orbits between invariant solutions of other types, including between two periodic orbits and eventually between invariant tori.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Together with improved methods for constructing invari- ant solutions24,32,33, the proposed methodology for computing connecting orbits represents a step towards a more complete characterization of the state-space structures supporting spa- tiotemporally chaotic dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Eventually, the characteriza- tion of connecting orbits mediating transitions between invari- ant solutions may allow for efficient forecasting of chaos even in high-dimensional systems including fluid turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Appendix A: Derivation of the adjoint operator for the KSE The directional derivative of the residual of the KSE, de- fined in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' (23), along G is obtained by the definition (12) as L (u;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='G) = −∂G ∂s − ∂(uG) ∂x − ∂ 2G ∂x2 − ∂ 4G ∂x4 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' (A1) Jacobian-Free Variational Method for Constructing Connecting Orbits 13 π 0 θ 0 22 x (a) Orbit 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' π 0 θ 0 22 x (b) Orbit 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 14: The space-time contour of the two converged connecting orbits from E3 to E2 in the center-symmetric subspace.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' In order to find the adjoint operator, we expand the inner prod- uct of L (u;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='G) and r � L (u;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='G),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='r � = � +∞ −∞ � L 0 � −∂G ∂s − ∂(uG) ∂x − ∂ 2G ∂x2 − ∂ 4G ∂x4 � rdxds =− � L 0 �� +∞ −∞ ∂G ∂s rds � dx − � +∞ −∞ �� L 0 �∂(uG) ∂x + ∂ 2G ∂x2 + ∂ 4G ∂x4 � rdx � ds (A2) Integrating by parts we can write the first and the second inte- gral as follows � L 0 �� +∞ −∞ ∂G ∂s rds � dx = � L 0 � lim T→∞ � Gr �s=T s=−T − � +∞ −∞ G∂r ∂sds � dx,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' � +∞ −∞ �� L 0 � ∂(uG) ∂x + ∂ 2G ∂x2 + ∂ 4G ∂x4 � rdx � ds = � +∞ −∞ �� uGr �x=L x=0 − � L 0 uG∂r ∂xdx+ � ∂G ∂x r −G∂r ∂x �x=L x=0 + � L 0 G∂ 2r ∂x2 dx + � ∂ 3G ∂x3 r − ∂ 2G ∂x2 ∂r ∂x + ∂G ∂x ∂ 2r ∂x2 −G∂ 3r ∂x3 �x=L x=0 + � L 0 G∂ 4r ∂x4 dx � ds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' In the limit T → ∞ the boundary term [Gr]s=T s=−T vanishes since both G and r are asymptotically zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' All boundary terms [·]x=L x=0 vanish too due to periodicity of u, r and G in x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' There- fore, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' (A2) becomes ⟨L (u;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='G),r⟩ = � +∞ −∞ � L 0 �∂r ∂s +u∂r ∂x − ∂ 2r ∂x2 − ∂ 4r ∂x4 � Gdxds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' (A3) From the definition of the adjoint operator (14), this inner product equals � L †(u;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='r),G � = � +∞ −∞ � L 0 L †Gdxds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' (A4) Comparing Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' (A3) and (A4), L †(u;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='r) is given by L †(u;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='r) = ∂r ∂s +u∂r ∂x − ∂ 2r ∂x2 − ∂ 4r ∂x4 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' (A5) Appendix B: Unstable eigenvectors of the equilibria of the KSE The KSE with L = 22 has four known equilibrium solu- tions including the trivial solution E0 = 0, and three nontrivial solutions E1, E2 and E3 as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The repelling eigenvalues of these equilibrium solutions are listed in Table I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The corresponding eigenvectors of E0, E1, E2 and E3, are shown in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 15 to 18, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Appendix C: Parameters used in constructing connecting orbits of the KSE In all calculations presented in Section V we have used N = 64 Fourier modes in space, have set the center of the temporal distribution at the origin s0 = 0, and have used time step size ∆τ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='01.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The temporal resolution M and the scaling S are listed in Table II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The temporal resolution is set high enough so that the convergence criterion Jarc,min < 10−12 is achieved (see Section V D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=') ACKNOWLEDGEMENTS This research has been supported by the European Re- search Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 865677).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' The authors would like to thank Sajjad Azimi and Jeremy P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Parker for helpful discussions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Jacobian-Free Variational Method for Constructing Connecting Orbits 14 0 11 22 x −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='0 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='0 v1 (a) λ1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='2198 0 11 22 x −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='0 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='0 v2 (b) λ2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='2198 0 11 22 x −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='0 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='0 v3 (c) λ3 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='1952 0 11 22 x −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='0 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='0 v4 (d) λ4 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='1952 0 11 22 x −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='0 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='0 v5 (e) λ5 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='0749 0 11 22 x −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='0 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='0 v6 (f) λ6 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='0749 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 15: Unstable eigenvectors vi of the trivial equilibrium solution E0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' λi is the eigenvalue associated with vi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 0 11 22 x −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='0 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='0 ℜ{v1,2} (a) λ1,2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='1308±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='3341i 0 11 22 x −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='0 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='0 ℑ{v1,2} (b) λ1,2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='1308±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='3341i 0 11 22 x −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='0 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='0 ℜ{v3,4} (c) λ3,4 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='0824±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='3402i 0 11 22 x −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='0 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='0 ℑ{v3,4} (d) λ3,4 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='0824±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='3402i FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 16: Unstable eigenvectors vi of the equilibrium solution E1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' λi is the eigenvalue associated with vi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 0 11 22 x −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='0 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='0 ℜ{v1,2} (a) λ1,2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='1390±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='2384i 0 11 22 x −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='0 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='0 ℑ{v1,2} (b) λ1,2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='1390±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='2384i FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 17: Unstable eigenvectors vi of the equilibrium solution E2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' λi is the eigenvalue associated with vi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 0 11 22 x −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='0 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='0 v1 (a) λ1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='0933 0 11 22 x −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='0 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='0 v2 (b) λ2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='0933 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 18: Unstable eigenvectors vi of the equilibrium solution E3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' λi is the eigenvalue associated with vi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' DATA AVAILABILITY STATEMENT The data that support the findings of this study are available from the corresponding author upon reasonable request.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' REFERENCES 1P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Cvitanovi´c, “Recurrent flows : the clockwork behind turbulence,” Journal of Fluid Mechanics 726, 1–4 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' TABLE II: Parameters used for numerically integrating the dynamics in the space of connecting curves between different equilibrium solutions of the KSE for L = 22 to construct connecting orbits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' row from to M S Figure 1 E0 E1 80 40 7a & 8a 2 E2 130 35 7b & 8b 3 E3 120 40 7c & 8c 4 E1 E2 550 55 4 & 5 5 E3 500 60 9 & 10 6 E2 τ(1/4)E2 400 35 11a & 12a 7 E3 450 50 11b & 12b 8 E3 E2 600 50 13a & 14a 9 500 40 13b & 14b Jacobian-Free Variational Method for Constructing Connecting Orbits 15 2G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Chandler and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Kerswell, “Invariant recurrent solutions embedded in a turbulent two-dimensional Kolmogorov flow,” Journal of Fluid Me- chanics 722, 554–595 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 3C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Crowley, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Pughe-Sanford, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Toler, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Krygier, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Grig- oriev, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Schatz, “Turbulence tracks recurrent solutions,” Proceed- ings of the National Academy of Sciences 119, 1–7 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 4R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Kerswell, “Recent progress in understanding the transition to turbu- lence in a pipe,” Nonlinearity 18, R17–R44 (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 5B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Eckhardt, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Schneider, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Hof, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Westerweel, “Turbulence Transition in Pipe Flow,” Annual Review of Fluid Mechanics 39, 447–468 (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 6J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Gibson, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Halcrow, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Cvitanovi´c, “Visualizing the geometry of state space in plane Couette flow,” Journal of Fluid Mechanics 611, 107– 130 (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 7G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Kawahara, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Uhlmann, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' van Veen, “The Significance of Simple Invariant Solutions in Turbulent Flows,” Annual Review of Fluid Mechan- ics 44, 203–225 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 8B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Suri, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Tithof, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Grigoriev, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Schatz, “Forecasting Fluid Flows Using the Geometry of Turbulence,” Physical Review Letters 118, 114501 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 9M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Graham and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Floryan, “Exact Coherent States and the Nonlin- ear Dynamics of Wall-Bounded Turbulent Flows,” Annual Review of Fluid Mechanics 53, 227–253 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 10L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' van Veen and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Kawahara, “Homoclinic tangle on the edge of shear turbulence,” Physical Review Letters 107, 114501 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 11B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Suri, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Pallantla, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Schatz, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Grigoriev, “Heteroclinic and homoclinic connections in a Kolmogorov-like flow,” Physical Review E 100, 1–14 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 12F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Reetz and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Schneider, “Invariant states in inclined layer convection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Part 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Temporal transitions along dynamical connections between invariant states,” Journal of Fluid Mechanics 898 (2020), 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='1017/jfm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='317.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 13A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Homburg and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Sandstede, “Homoclinic and heteroclinic bifurcations of vector fields,” in Handbook of dynamical systems 3, edited by H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Broer, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Takens, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Hasselblatt (Elsevier, 2010) pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 1–124.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 14F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Reetz, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Subramanian, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Schneider, “Invariant states in inclined layer convection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Part 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Bifurcations and connections between branches of invariant states,” under revision at JFM , 1–36 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 15W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Beyn, “The Numerical Computation of Connecting Orbits in Dynam- ical Systems,” IMA Journal of Numerical Analysis 10, 379–405 (1990).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 16J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Halcrow, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Gibson, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Cvitanovi´c, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Viswanath, “Heteroclinic connections in plane Couette flow,” Journal of Fluid Mechanics 621, 365– 376 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 17P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Cvitanovi´c, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Davidchack, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Siminos, “On the state space ge- ometry of the Kuramoto-Sivashinsky flow in a periodic domain,” SIAM Journal on Applied Dynamical Systems 9, 1–33 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 18M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Farano, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Cherubini, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Robinet, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' De Palma, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Schneider, “Computing heteroclinic orbits using adjoint-based methods,” Journal of Fluid Mechanics 858, R3 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 19Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Liu, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Liu, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Tang, “The numerical computation of connecting or- bits in dynamical systems: A rational spectral approach,” Journal of Com- putational Physics 111, 373–380 (1994).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 20C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Dong and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Lan, “A variational approach to connecting orbits in nonlin- ear dynamical systems,” Physics Letters, Section A: General, Atomic and Solid State Physics 378, 705–712 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 21Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Lan and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Cvitanovi´c, “Variational method for finding periodic orbits in a general flow,” Physical Review E 69, 016217 (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 22R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Pallantla, Exact coherent structures and dynamical connections in a quasi 2D Kolmogorov like flow, Ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' thesis, Georgia Institute of Technol- ogy (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 23M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Farazmand, “An adjoint-based approach for finding invariant solutions of Navier-Stokes equations,” Journal of Fluid Mechanics 795, 278–312 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 24S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Azimi, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Ashtari, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Schneider, “Constructing periodic orbits of high-dimensional chaotic systems by an adjoint-based variational method,” Physical Review E 105, 014217 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 25J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Boyd, “Chebyshev and Fourier Spectral Methods,” New York , 688 (2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 26Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Kuramoto and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Tsuzuki, “Persistent Propagation of Concentration Waves in Dissipative Media Far from Thermal Equilibrium,” Progress of Theoretical Physics 55, 356–369 (1976).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 27G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Sivashinsky, “Nonlinear analysis of hydrodynamic instability in lam- inar flames—I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Derivation of basic equations,” Acta Astronautica 4, 1177– 1206 (1977).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 28R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' LaQuey, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Mahajan, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Rutherford, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Tang, “Non- linear Saturation of the Trapped-Ion Mode,” Physical Review Letters 34, 391–394 (1975).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 29A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Hooper and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Grimshaw, “Nonlinear instability at the interface be- tween two viscous fluids,” Physics of Fluids 28, 37–45 (1985).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 30Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Smyrlis and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Papageorgiou, “Computational study of chaotic and ordered solutions of the Kuramoto-Sivashinsky equation,” Tech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' (Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1996).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 31D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Rempfer, “On Boundary Conditions for Incompressible Navier-Stokes Problems,” Applied Mechanics Reviews 59, 107–125 (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 32J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Parker and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Schneider, “Invariant tori in dissipative hyperchaos,” Chaos: An Interdisciplinary Journal of Nonlinear Science 32, 113102 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' 33J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Parker, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Ashtari, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content=' Schneider, “Predicting chaotic statistics with unstable invariant tori,” arXiv preprint 2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} +page_content='10626, 1–11 (2023).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jtFKT4oBgHgl3EQfBi3I/content/2301.11704v1.pdf'} diff --git a/kdE4T4oBgHgl3EQfTgyJ/content/tmp_files/2301.05008v1.pdf.txt b/kdE4T4oBgHgl3EQfTgyJ/content/tmp_files/2301.05008v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..19de6d271a482554f6b8cb3bc6d1d16b443fc800 --- /dev/null +++ b/kdE4T4oBgHgl3EQfTgyJ/content/tmp_files/2301.05008v1.pdf.txt @@ -0,0 +1,1462 @@ +1 + +Applied Catalysis B, Volume 303, p. 120896, 2022 +https://doi.org/10.1016/j.apcatb.2021.120896 +Received on 24 August 2021; Revised on 22 October 2021; Accepted on:2 November 202; +Available online 8 November 2021 + +Defective high-entropy oxide photocatalyst with high activity for +CO2 conversion + + +Saeid Akrami1, Yasushi Murakami2, Monotori Watanabe3, Tatsumi Ishihara2,3, Makoto Arita4, +Masayoshi Fuji1,5,* and Kaveh Edalati3,* + + +1 Department of Life Science and Applied Chemistry, Nagoya Institute of Technology, Tajimi +507-0071, Japan +2 Department of Applied Chemistry, Faculty of Engineering, Kyushu University, Fukuoka 819- +0395, Japan +3 WPI, International Institute for Carbon-Neutral Energy Research (WPI-I2CNER), Kyushu +University, Fukuoka 819-0395, Japan +4 Department of Materials Science and Engineering, Faculty of Engineering, Kyushu University, +Fukuoka 819-0395, Japan +5 Advanced Ceramics Research Center, Nagoya Institute of Technology, Tajimi 507-0071, Japan + + +Abstract +High-entropy oxides (HEOs), as a new family of materials with five or more principal +cations, have shown promising properties for various applications. In this work and inspired by +inherent defective and strained structure of HEOs, photocatalytic CO2 conversion is examined on +a dual-phase TiZrNbHfTaO11 synthesized by a two-step high-pressure torsion mechanical alloying +and high-temperature oxidation. The HEO, which had various structural defects, showed +simultaneous photocatalytic activity for CO2 to CO and H2O to H2 conversion without the addition +of a co-catalyst. The photocatalytic activity of this HEO for CO2 conversion was better than +conventional photocatalysts such as anatase TiO2 and BiVO4 and similar to P25 TiO2. The high +activity of HEO was discussed in terms of lattice defects, lattice strain, light absorbance, band +structure, photocurrent generation and charge carrier mobility to activation centers. The current +study confirms the high potential of HEOs as a new family of photocatalysts for CO2 conversion. + +Keywords: High-entropy alloys (HEAs); High-entropy oxide (HEO); Photocatalyst, +Photocatalytic CO2 conversion; Oxygen vacancy + + +*Corresponding authors: +Masayoshi Fuji (E-mail: fuji@ fuji@nitech.ac.jp; Tel: +81-57-227-6811) +Kaveh Edalati (E-mail: kaveh.edalati@kyudai.jp; Tel: +81-92-802-6744) + + + +2 + +1. Introduction +Carbon dioxide (CO2) is a stable molecule, which is produced mainly from human +activities such as combustion of hydrocarbons and partly from natural sources such as +decomposition of organisms. Emission of CO2 from combustion of hydrocarbon fuels is +considered as a main reason for the global warming on the earth [1,2]. There are currently +significant attempts to explore effective strategies to reduce the human-activity-based CO2 +emission or to convert CO2 to useful products [1]. Photocatalytic CO2 conversion is considered as +a clean technology to reduce the amount of this stable gas in the atmosphere, although the research +on photocatalytic CO2 conversion is still at the early stages and significant efforts are required to +enhance its efficiency for practical applications [2]. In photocatalytic CO2 conversion, following +the light absorbance by a semiconductor which is known as photocatalyst, electrons are excited +from the valence band to the conduction band and contribute to CO2 conversion [2]. Such a CO2 +conversion occurs through different pathways including carbene pathway, formaldehyde pathway +and glyoxal pathway [3,4], leading to different conversion products, as shown in Table 1 [5,6]. + +Table 1. Reactions in CO2 conversion with their standard potentials [5,6]. +Reaction +Standard Potential vs. NHE (eV) at PH = 0 +CO2 + 2H+ + 2e- → HCOOH +-0.20 +CO2 + 2H+ + 2e- → CO + H2O +-0.11 +CO2 + 4H+ + 4e- → HCHO + H2O +-0.07 +CO2 + 6H+ + 6e- → CH3OH + H2O +0.03 +CO2 + 8H+ + 8e- → CH4 + 2H2O +0.17 + +For photocatalytic CO2 conversion, a photocatalyst should have appropriate bandgap to +absorb light photons, appropriate band structure to satisfy the standard potentials for each reaction +shown in Table 1, long exited electron lifetime and appropriate charge carrier mobility [7]. TiO2 +[8], C3N4-based catalysts [9], bismuth-based compounds such as BiVO4 [10], Cu-based +semiconductors [11] and WO3 [12] are some popular photocatalysts for CO2 conversion. Although +the improvement of existing photocatalysts by different strategies such as heterostructure +generation [7], nanosheet production [8], surface defect introduction [9], oxygen vacancy +generation [12], mesoporous structure formation [13] and strain engineering [14,15] is currently +the major research activity, there are high demands to explore new family of materials as highly +active photocatalysts. +High-entropy ceramics are a new type of materials which show high stability and promising +structural and functional properties due to the so-called cocktail effect, lattice strain/defects, +heterogenous valence electron distribution and high configurational entropy [16]. As shown in Fig. +1a, high-entropy ceramics are defined as multi-component materials with at least five principal +elements and a configurational entropy higher than 1.5R (R: the gas constant) [17]. These materials +have a low Gibbs free energy due to their high entropy and this gives a high stability to these +materials under different conditions [16] including catalytic reactions [18,19]. Moreover, the +presence of at least five cations with different atomic sizes in these materials results in the +formation of inherent lattice strain and defects [17]. Since lattice strain and defects are effective to +enhance photocatalytic CO2 conversion [9,12,14,15], the high-entropy ceramics are expected to + +3 + +show good activity for such a conversion. High-entropy oxides (HEOs) are the most popular high- +entropy ceramics which have been investigated for various applications and properties such as +thermal barrier coatings [20,21], magnetic components [22,23], dielectric components [24,25], Li- +ion batteries [26,27], Li-S batteries [28], Zn-air batteries [29], catalysts [30,31], electrocatalysts +[32], and photocatalytic hydrogen production [33,34]. Despite the inherent defective and strained +structure of HEOs, there have been no attempts to employ these materials for photocatalytic CO2 +conversion. +In this study, a HEO photocatalyst, TiZrNbHfTaO11, is synthesized and its activity for CO2 +conversion is examined. The transition elements titanium, zirconium, niobium, hafnium, and +tantalum are selected simply because their binary oxides with the d0 electronic structure can act as +photocatalysts. This first application of HEOs for photocatalytic CO2 conversion confirms that the +HEO photocatalyst shows higher activity compared to common binary or ternary photocatalysts +such as TiO2 and BiVO4, suggesting HEOs as a new family of photocatalysts for CO2 conversion. + +2. Experimental +2.1. Sample preparation +Although various methods have been developed in recent years for the synthesis of HEO +[16-34], a two-step high-pressure mechanical alloying and high-temperature oxidation which is +available in the authors’ laboratory was used to synthesize the HEO. In the first step, equiatomic +amounts of Ti (99.9%), Zr (95.0%), Hf (99.5%), Nb (99.9%) and Ta (99.9%) powders were mixed +in acetone, treated by ultrasonic and then dried. The dried powder mixture was processed by high- +pressure torsion (HPT), shown in Fig. 1b, to fabricate TiZrNbHfTa high entropy alloy (HEA) with +the body-centered cubic (BCC) structure (see the principles of HPT and its applications to oxides +in [35,36]). To produce the TiZrNbHfTa alloy, a 10 mm diameter and 1 mm thick disc was +prepared by compacting the powder mixture under a pressure of 400 MPa. The compacted disc +was then compressed between two HPT anvils under a high pressure of 6 GPa at room temperature +and simultaneously processed by rotating the lower HPT anvil with respect to the upper one for +100 turns with a rotation rate of one turn per minute. In the second step, the HPT-processed +TiZrNbHfTa alloy was exposed to hot air at a temperature of 1373 K for 24 h to produce an oxide, +with the appearance shown in Fig. 1c. Examination of the mass of sample before and after +oxidation suggested a composition of TiZrNbHfTaO11 for the produced oxide. The oxide was +crushed after oxidation into the powder form using a mortar and examined by various +characterization methods, as described below. + +2.2. Characterization +To examine the crystal structure, X-ray diffraction (XRD) using the Cu Kα radiation with +a wavelength of λ = 0.1542 nm and micro-Raman spectroscopy using a laser source with a +wavelength of λ = 532 nm were utilized. +Examination of microstructure was conducted by (i) scanning electron microscopy (SEM) +with energy dispersive X-ray spectroscopy (EDS) analysis under 15 keV, (ii) transmission electron +microscopy (TEM) with selected area electron diffraction (SAED), bright-field (BF) images, dark- +field (DF) images, high-resolution images and fast Fourier transform (FFT) analysis under 200 + +4 + +keV, and (iii) scanning-transmission electron microscopy (STEM) with high-angle annular dark- +field (HAADF) images and EDS analysis under 200 keV. + + +Fig. 1. (a) Relationship between number of elements and configurational entropy and definition of +high-entropy ceramics with equiatomic fractions of elements, (b) schematic illustration of high- +pressure torsion (HPT), and (c) appearance of high-entropy oxide synthesized in this study. + + +To investigate the presence of point defects such as oxygen vacancies, electron +paramagnetic resonance (EPR) was performed at ambient temperature using a microwave source +with a frequency of 9.4688 GHz. +To study the oxidation states of different elements and to estimate the valence band top +position, X-ray photoelectron spectroscopy (XPS) using the Al Kα radiation with a wavelength of +λ = 0.989 nm was used. The XPS energy position for each element was adjusted by considering +the peak position of C 1s at 284.8 eV. After correction of the energy positions, the peaks for +different elements were analyzed by peak deconvolution by considering the standard energy +relations and differences reported in the handbook [37]: f7/2:f5/2 = 4:3, d5/2:d3/2 = 3:2, p3/2:p1/2 = 2:1, +Ti 2p1/2 - Ti 2p3/2 = 5.54 eV, Zr 3d3/2 - Zr 3d5/2 = 2.43 eV, Hf 4f5/2 - Hf 4f7/2 = 1.71 eV, Nb 3d3/2 - +Nb 3d5/2 = 2.72 eV, Ta 4f5/2 - Ta 4f7/2 = 1.91 eV. + +(a) +2.0R +High-Entropy +Ceramics +1.5R +Medium-Entropy +Ceramics +1.0R +0.5R +0 +1 +2 +3 +4 +5 +6 +7 +8 +Number of Elements, N +(b) +Upper Anvil +(c) +Pressure +Disc Sample +个 +个 +10 mm +Pressure +LowerAnvil +Torsion5 + +To investigate the light absorbance and bandgap (Kubelka-Munk analysis), UV-vis diffuse +reflectance spectroscopy was conducted, and the band structure was calculated by considering both +XPS and UV-vis spectra. +To study the lifetime of exited electrons, steady-state photoluminescence (PL) emission +spectroscopy with a 325 nm laser source and time-resolved photoluminescence decay (PL decay) +with a 285 nm laser source were conducted. +The specific surface area of powder was examined by nitrogen gas adsorption and using +the Brunauer-Emmett-Teller (BET) method. + +2.3. Photocurrent test +Photocurrent generation was examined using a thin film of sample in a 1 M Na2SO4 +electrolyte under the full arc of Xe lamp (without using any filter), as described in detail earlier +[38]. The thin film was prepared by deposition of HEO powder on FTO (fluorine-doped tin oxide) +glass with 2.25 mm thickness and 15×25 mm2 surface area. about 5 mg of sample was crushed in +0.2 mL ethanol and carefully dispersed on the FTO glass using a drop and annealed at 473 K for +24 h. The average thickness of HEO on FTO glass was about 0.04 mm, which was estimated by +measuring the thickness of glass before and after deposition of HEO using a micrometer with 0.01 +mm accuracy. Photocurrent generation was examined by an electrochemical analyzer in the +potentiostatic amperometry mode during time (30 s light ON and 60 s light OFF), while the counter +electrode was Pt wire, the reference electrode was Ag/AgCl, and the external potential was 0.7 V +vs. Ag/AgCl. + +2.4. Photocatalytic test +Photocatalytic CO2 conversion was conducted using the powder of HEO in a continuous +flow quartz photoreactor. The photoreactor, as shown in Fig. 2a, had a cylindrical shape with a +total inner volume of 858 mL. The reactor had an inner space to insert the light source. There were +two holes on the top of photoreactor: one for the inlet of CO2 flow, which was connected to a gas +cylinder; and another one for the outlet of gas and sampling the reaction products for analysis, +which was connected to a vent and gas chromatograph. For the photocatalytic reaction, 120 mg of +HEO was mixed with 500 mL of deionized water and NaHCO3 with 1 M concentration and then +bubbled with CO2 with a flow rate of 3 mL/min. The temperature was controlled as 288 K using a +water chiller and the suspension was continuously stirred using a magnetic stirrer. The process was +first conducted for 2 h without light irradiation, and after confirmation that no reaction products +appear, the photocatalytic test was conducted under irradiation with a high-pressure Hg light +source (Sen Lights Corporation, HL400BH-8, 400 W, with the spectral composition shown in Fig. +2b). The light intensity irradiated on the photocatalysts was 0.5 W/cm2 and no filter was used +during the irradiation. The reaction products were analyzed by a gas chromatograph (Shimadzu +GC-8A, Ar Carrier). A flame ionization detector equipped with a methanizer (Shimadzu MTN-1) +was used to measure the CO and CH4 production rate. A thermal conductivity detector also was +utilized to evaluate the H2 and O2 production. To be sure about the absence of CO from other +sources such as contamination, blank tests were conducted (i) under irradiation in the presence of +CO2, NaHCO3 and H2O and without the photocatalyst addition and (ii) under irradiation in the +presence of Ar, NaHCO3 and H2O and with photocatalyst addition. + + +6 + + + +Fig. 2. (a) Description of experimental setting for photocatalytic CO2 conversion including +photograph of photoreactor, and (b) spectroscopy of light source used for photocatalytic test. + + +3. Results +3.1. Crystal structure and microstructure +Fig. 3 shows the SEM images of HEO in various scales. Particle size measured by SEM is +25 µm. The HEO contains particles with different sizes, as shown in Fig. 3, and its specific surface +area, achieved by the BET method, is 0.66 m2/g. Although big size of some particles can have +negative effect on photocatalytic activity due to decreasing the active surface area, this issue can +be addressed in the future by using other synthesis method or advanced crushing techniques. The +presence of numerous nanograins in each particle is obvious in higher magnification images in +Fig. 3b, c and d. The average grain size for this material is estimated to be 192 nm, while some +pores are also visible within the particles. Here, it should be noted that low specific surface area +and small grain size are characteristics of materials which are synthesized/processed by the HPT +method [33-36]. +To confirm the successful oxidation of the material, electronic states of each element in the +HEO are presented in Fig. 4 using the XPS analysis and corresponding peak deconvolution. Fig. +4 shows that the main cations in the sample are Ti4+, Zr4+, Nb5+, Hf4+ and Ta5+, suggesting that the +material is successfully oxidized to a d0 electronic configuration during the high-temperature +oxidation [37]. However, it should be noted that the peaks for Ti, Zr, Nb, Hf and Ta have some +shoulders to the lower energy sides, suggesting that some oxygen-deficient regions with lower +oxidation states should exist within the material, as confirmed by the peak deconvolution analysis +(i.e., some oxygen vacancies present). The presence of vacancies is not surprising as similar issue +can be observed in other HPT-processed materials due to the strain effect [35,36] and in other +HEOs due to the atomic size mismatch effect [16,17]. + + +MassFlow +Gas +(a) +(q) +Chromatograph +High-Pressure Hg Lamp +Controller +Relative Intensity +00 +0 +a +Vent +CO2 +Lamp +300 +400 +500 +600 +Stirring +Photoreactor +Wavelength (nm)7 + + +Fig. 3. Morphology of high-entropy oxide examined by SEM at different magnifications. + + +To confirm the distribution of elements in the material, Fig. 5a and Fig. 5b illustrate the +elemental distribution mappings in the micrometer and nanometer scales, respectively. Fig. 5 +shows that the elements distribute appropriately in both micrometer and nanometer scales. It is +confirmed that the elements are successfully mixed by high-pressure mechanical alloying and their +distribution remains reasonably homogeneous even after high-temperature oxidation. SEM-EDS +analysis suggests that the material should have a general composition of TiZrNbHfTaO11. Uniform +distribution of elements is a general requirement of high-entropy materials [16-32]. + + + +100um +500mm +200 nm8 + + + +Fig. 4. Electronic states and relevant peak deconvolution of (a) Ti, (b) Zr, (c) Nb, (d) Hf, (e) Ta +and (f) O in high-entropy oxide examined by XPS analysis. + + + + +(a) +TiZrNbHfTaO11 +(b) +TiZrNbHfTaO11 +Ti2p1/2 +T: +41 +2p1/2 +r +4+ +3d3/2 +Intensity (a.u.) +... Ti2p3/2 +T:4 +41 +2p3/2 +(a.u.) +-0- Sum +T:o +2p1/2 +Zr3d3/2 +Ti3*2p3/2 +Intensity +---Zr 3d5/2 +-o-Sum +456 +458 +460 +462 +464 +466 +178 +180 +182 +184 +186 +188 +Binding Energy (eV) +Binding Energy (eV) +(c) +TiZrNbHfTaO11 +(d) +TiZrNbHfTaO11 +Intensity (a.u.) +Intensity (a.u.) +- Nb3*3d3/2 +— Hf 4f 5/2 +--- Hf 4f7/2 +—Nb 3d3/2 +-o-Sum +---Nb 3d5/2 +-0-Sum +202 +204206208210212214 +1314 +15 +17 +18 +19 +20 +21 +Binding Energy (eV) +Binding Energy (eV) +(e) +5+ +TiZrNbHfTaO11 +(f) +TiZrNbHfTaO11 +Ta +5+ +Intensity (a.u.) +Intensity (a.u.) +-o-Sum +3+ +—Ta 4f5/2 +--. Ta 4f712 +-o-Sum +22 +24 +26 +28 +30 +524 +526 +528 +530 +532 +534 +536 +BindingEnergy(ev) +BindingEnergy(ev)9 + + +Fig. 5. Distribution of elements in high-entropy oxide examined at (a) micrometer scale using +SEM-EDS and (b) nanometer scale using STEM-EDS. + + +Crystal structure of HEO was examined using XRD analysis, as shown in Fig. 6a. The +material contains two phases with the monoclinic and orthorhombic structures. Based on the +Rietveld analysis, the HEO consists of 40 wt% of monoclinic phase (A2/m space group, a = 1.193 +nm, b = 0.381 nm, c = 2.044 nm, α = 90°, β = 120.16°, γ = 90°) and 60 wt% of orthorhombic phase +(Ima2 space group, a = 4.092 nm, b = 0.493 nm, c = 0.527 nm, α = β = γ = 90°). Raman spectra, +shown in Fig. 6b from three different positions, illustrate similar patterns in different positions, +suggesting the size of phases should be smaller than the spatial resolution of micro-Raman. Taken +altogether, a combination of XPS, EDS and XRD confirms that a dual-phase HEO could be +successfully produced in this study. +Examination of microstructural/nanostructural features of this dual-phase HEO is shown +in Fig. 7, where a is a BF image, b is a corresponding SAED pattern, c is a DF image, d and e are +HR images, and f is a magnified lattice image of the selected squared region in e. Fig. 7 reveals +several important points. (i) A ring pattern of SAED image confirms the presence of many +nanocrystals with random orientation in Fig. 7a. (ii) The BF and DF images confirm that the grain + +(b) +100um +100 μm +20 nm +20 nm +BF +HAADF +SM +100 μm +20 nm +100 μm +20 nm +Ti +Zr +Nb +100 μm +100 μm +20 nm +20 nm +Nb +Hf +Hf +100 μm +20nm +20 nm +Ta10 + +sizes are quite small and less than 100 nm. This indicates that there are still smaller crystals within +the grain-like regions observed in the SEM images of Fig. 3. (iii) The HR images confirm the co- +existence of two monoclinic and orthorhombic phases at the nanoscale and large fraction of +interphase boundaries. It was shown that the presence of interphases as charge heterojunctions can +improve the photocatalytic activity through enhanced charge carrier separation and mobility [7]. +(iv) The lattice images are quite distorted and close examination of the lattice confirms the +presence of many dislocation defects within the grains. Since it was reported that the dislocations +can enhance the light absorbance and photocatalytic activity at least in some semiconductors [39], +the presence of dislocations in this HEO may positively act for enhancement of photocatalytic +activity. + + + +Fig. 6. Dual-phase structure of high-entropy oxide examined by (a) XRD profile and (b) micro- +Raman spectra at three different positions. + +(a) +TiZrNbHfTaO11 +Oxidation: T= 1373 K, t = 24 h +Intensity (a.u.) +800888 +8 +880 +Monoclinic +MMMM +W +V +Orthorhombic +20 +30 +40 +50 +60 +70 +80 +Diffraction Angle, 20 (deg.) +(b) +TiZrNbHfTaO11 +Normalized Intensity +Position 3 +Position 2 +Position 1 +200 +400 +600 +800 +Raman Shift, o (cm11 + + + +Fig. 7. Presence of nanoscaled dual phases with large fraction of interfaces and dislocations in +high-entropy oxide examined by TEM (a) BF image, (b) SAED analysis, (c) DF image and (d-f) +HR images, where (c) was taken with diffracted beams indicated by arrow in (a), and (f) is a +magnified view of squared region in (e). + + +3.2. Electronic structure and defect states +Fig. 8 shows (a) UV-vis absorbance spectrum, (b) Kubelka-Munk plot, (c) XPS spectrum +of top of valence band and (d) electronic structure determined by a combination of UV-vis and + +(a) +(b) +(c) +20 nm +20 nm +BF +DF +(d) +Orthorhombic +Monoclinic +[122] +[311] +5.nmm +(e) +[310] +1. (602] +Monoclinic[133] +2nm +uu12 + +XPS analyses. Fig. 8a indicates that the HEO can absorb light in both ultraviolet and visible light +regions, although the quantity of absorbed light in the ultraviolet region is higher than that in the +visible light region. Such a visible light absorbance is not detected in binary oxides such as TiO2, +ZrO2, HfO2, Nb2O5 and Ta2O5 [38,39]. Based on the Kubelka-Munk analysis, there are two +apparent bandgaps of 3.0 and 2.3 eV for this HEO. The first energy gap should be related to the +energy difference between the valence band and conduction band which is reasonably similar to +the bandgap of TiO2 and smaller than the bandgap of other binary oxides in the Ti-Zr-Hf-Nb-Ta- +O system (3.1-5.7 eV) [40,41], and the second gap should be due to the defect level between the +valence band and conduction band. The presence of defects (i.e., oxygen vacancies or color +centers), which can be confirmed from the low energy shoulders in XPS spectra of cations, should +be a main reason for the orange color of sample. The top of valence band calculated by XPS is 1.8 +eV vs. NHE, which is shown by an arrow in Fig. 8c. The bottom of conduction band is calculated +as -1.2 vs. NHE by considering an indirect bandgap of 3.0 eV and the defect state is estimated as +-0.5 eV vs. NHE. As summarized in Fig. 8d, the potential of reactions for CO2 conversion and +water splitting (see Table 1) are between the energy levels for the top of valence band and the +bottom of conduction band, and thus, this HEO can basically satisfy the requirements for +photocatalytic reactions [5-7]. + + + +Fig. 8. Appropriate electronic structure of high-entropy oxide for photocatalytic CO2 conversion. +(a) UV-vis light absorbance spectrum, (b) Kubelka-Munk plot to calculate indirect bandgap (α: +light absorption, h: Planck's constant, ν: light frequency), (c) XPS spectrum to estimate top of +valence band, and (d) electronic band structure in comparison with potentials for photocatalytic +CO2 conversion. + +(a) +Uv +IR +(b) +TiZrNbHfTaO11 +TiZrNbHfTaO11, +14 +(a.u.) +0.8 +12 +(ahu) (eV/cm) +0 +10 +rbance, +0.6 +8 +2 +6 +0.4 +Absor +4 +0.2 +2 +0 +200 +400 +600 +800 +2 +3 +4 +5 +Wavelength (nm) +Photon Energy, hv(eV) +(c) +(d) +TiZrNbHfTaO11 +Conduction Band +Intensity (a.u.) +CO./HCOOH +Defect State +CO2/CO +CO2/CH20 +:2H/H2 +1 +CO,/CHOH +CO2/CH4 +Valence Band +O,/H,0 +-2 +0 +2 +4 +8 +10 +12 +Binding Energy (eV)13 + + +3.3. Charge-carrier dynamics +Charge-carrier dynamics were examined by (a) steady-state PL spectroscopy, (b) PL decay +spectroscopy, (c) EPR spectroscopy and (d) photocurrent measurement, as shown in Fig. 9. The +PL spectrum in Fig. 9a shows a peak at 580 nm which is equivalent to an energy level of 2.14 eV. +Since this energy level is close to the energy gap of 2.3 eV, calculated using the Kubelka-Munk +analysis for the defect states, it can be concluded that this peak corresponds to the recombination +of excited electrons at the defect state. To have an insight into the significance of these electron- +hole recombination, Table 2 compares the PL intensity and PL wavelength of the HEO with those +measured by the current authors for anatase TiO2 and BiVO4 (as two popular photocatalysts for +CO2 conversion [2-5]). It is obvious that the PL intensity of HEO is lower than that of anatase TiO2 +and BiVO2, despite its high light absorbance which is an indication of large electron-hole +production. The lower PL intensity suggests that the recombination in this HEO is not higher than +TiO2 and BiVO2, provided that the heat energy generation through the electron-hole recombination +is considered identical for the three oxides. +Evaluation of PL decay intensity versus time, as shown in Fig. 9b, indicates that the PL +decay of the HEO follows an exponential equation. + +𝐼(𝑡) = 𝐴1 exp (− 𝑡 +𝜏1 +) + 𝐴2 exp (− 𝑡 +𝜏2 +) +(1) + +where, I(t), 𝐴1, 𝐴2, 𝜏1 and 𝜏2 are PL decay intensity at time t, amplitude of the first exponential +function, amplitude of the second exponential function, fast decay time and slow decay time, +respectively. Analysis of data in Fig. 9b suggests the values of 1.53 and 10.39 ns for 𝜏1 and 𝜏2, +respectively. Here, the following equation can be used to estimate the average lifetime, 𝜏𝑎𝑣𝑒 [42]. + +𝜏𝑎𝑣𝑒 = 𝐴1𝜏1 +2 + 𝐴2𝜏2 +2 +𝐴1𝜏1 + 𝐴1𝜏1 +(2) + +Table 2 compares the average lifetime for the HEO with those for anatase TiO2 and BiVO4. The +average lifetime for the HEO is 10.5 ns which is close to the lifetime of TiO2 anatase (10.7 ns). +Low recombination intensity of the HEO, measured by steady-state PL spectroscopy, and an +appropriate electron lifetime close to TiO2 anatase, show that the exited electrons on the surface +of this material can be active for appropriate time to take part in photocatalytic reaction before +recombination with holes. One reason for the appropriate charge carrier lifetime and low-intensity +recombination for this HEO can be the presence of oxygen vacancies on the surface [43,44]. +Prescence of oxygen vacancies, which was suggested by the orange color of sample in Fig. +1c, XPS spectroscopy in Fig. 4 and UV-vis spectroscopy in Fig. 8a, was examined further by EPR +spectroscopy, as shown in Fig. 9c. Two symmetric hump peaks with a g factor of 2.15 appear +which may be due to the oxygen vacancies, as reported in some oxides such as Nb2O5 [45]. It +should be noted that the oxygen vacancies on the surface can act as active sites for electron-hole +separation and photocatalytic reaction [4]. Moreover, it was shown that the surface oxygen +vacancies have a direct effect on photocatalytic CO production rate: surface oxygen vacancies can +absorb CO2 and contribute to breaking the C=O bonds to produce CO [4]. + + +14 + +Table 2. PL wavelength and intensity, fitted parameters of PL decay spectra and photocurrent +density for high-entropy oxide in comparison with anatase TiO2 and BiVO4 photocatalysts. +PL +Wavelength (nm) +Intensity (cps) +TiZrNbHfTaO11 +580 +190 +Anatase TiO2 +510 +12300 +BiVO4 +640 +300 +PL Decay +τ1 (ns) +τ2 (ns) +A1 +A2 +τ ave (ns) +TiZrNbHfTaO11 +1.53 +10.39 +42.34 +57.66 +10.5 +Anatase TiO2 +1.24 +11.46 +41.98 +58.02 +10.7 +BiVO4 +2.17 +14.90 +56.56 +43.44 +12.9 +Photocurrent (mA/m2) +Cycle 1 +Cycle 2 +Cycle 3 +Cycle 4 +TiZrNbHfTaO11 +9.6 +8.9 +8.4 +8.2 +Anatase TiO2 +43.5 +32.2 +27.9 +25.2 +BiVO4 +18.6 +17.1 +17.0 +16.7 + + + +Fig. 9. (a) Steady-state PL emission, (b) time-resolved PL decay, (c) EPR spectra and (d) +photocurrent generation for high-entropy oxide. + + +(a) +(b) +200 +TiZrNbHfTaO11 +TiZrNbHfTaO11 +1.0 +(cps) +Intensity (a.u.) +150 +0.8 +Intensity +100 +0.6 +0.4 +50 +PL +0.2 +0 +400 +500 +600 +700 +800 +0 +2 +4 +6 +8 +10 +Wavelength(nm) +Time (ns) +(c) +(d) +TiZrNbHfTaO11 +2 +Current Density (mA/m +TiZrNbHfTaO11 +10 +Vo +LightON +Intensity (a.u.) +8 +9 +4 +1.6 +1.8 +2.0 +2.2 +2.4 +2.6 +0 +300 +600 +900 +1200 +1500 +Time (s) +g Factor15 + +Fig. 9d shows photocurrent measurement on HEO thin film. The material successfully +generates photocurrent, although its photocurrent density decreases during the time due to the +accumulation of holes with positive charge on the surface. Table 2 compares the photocurrent +density of the HEO with that of reference anatase TiO2 and BiVO4 for the first four cycles. It +should be noted that the quantitative comparison of the photocurrent density of these three +materials should be conducted by care due to the technical limits in making dense films with good +FTO-oxide bonding by annealing at 473 K. The photocurrent density of HEO is apparently lower +than that of the reference oxides. Despite the low photocurrent density of HEO, photocurrent +generation on this material indicates that the exited electrons can have enough lifetime to separate +from the surface of material and take part in the photocurrent generation. The generation of +photocurrent is a positive sign for possible photocatalytic activity of this HEO, as discussed earlier +for other photocatalysts [38]. + +3.4. Photocatalytic activity +Photocatalytic activity of HEO for CO2 conversion is summarized in Fig. 10. As shown in +Fig. 10a and b, the HEO could successfully produce both CO and H2 under the full arc emission +of high-pressure Hg lamp without any co-catalyst addition, despite its low specific surface area as +0.66 m2/g (the error bar of gas amount measurement for three repeated tests was lower than 10%). +Independent synthesis of the HEO material and repeating the photocatalytic test, as indicated as +Sample #2 in Fig. 10a, also confirm the high activity of this material for photocatalytic CO2 +conversion with a reasonably constant CO and H2 production rate within an extended irradiation +time of 10 h. The amount of CO production is higher and the amount of H2 production is lower for +Sample #2 compared to Sample #1, suggesting that the activity of this HEO can be still improved +by modification of the synthesis method. Two points should be noted here. First, CO and H2 were +the only reaction products within the detection limits of analyses and no other products including +methane could be detected. Second, blank tests confirmed that no CO and H2 are produced by (i) +CO2 injection in the presence of HEO under the dark condition for 2 h, (ii) Ar injection in the +presence of HEO under the light irradiation for 1 h, and (iii) CO2 injection without the presence of +HEO under the light irradiation for 5 h. The stability of HEO, examined by XRD analysis after the +photocatalytic test, is shown in Fig. 10c, indicating that the crystal structure of the HEO is stable +after photocatalytic test. The stability of HEOs, which was also reported for other applications +such thermal barrier coatings [20,21], magnetic components [22,23], dielectric components +[24,25], Li-ion batteries [26,27], Li-S batteries [28], Zn-air batteries [29], catalysts [30,31] and +electrocatalysts [32], is usually due to their low Gibbs free energy resulting from their high entropy +[16,17]. + +16 + + +Fig. 10. Photocatalytic activity of high-entropy oxide for CO2 conversion and H2O decomposition. +(a) CO production rate versus time, (b) H2 production rate versus time, and (c) XRD pattern before +and after photocatalytic test. + + +4. Discussion +Three issues need to be discussed in detail here: (i) comparison of photocatalytic activity +of the HEO with available photocatalysts, (ii) factors influencing the photocatalytic activity of the +HEO, and (iii) mechanism of CO2 conversion on the HEO photocatalyst. + +(a) +TiZrNbHfTaO11 +0.6 +0.5 +Sample#2 +0.4 +Sample#1 +0.3 +0.2 +0.1 +co +0 +0 +1 +2 +3 +4 +5 +6 +7 +8 +9 +10 +Time (h) +(b) +5 +TiZrNbHfTaO11 +4 +Sample#1 +3 +Sample#2 +2 +0 +0 +1 +2 +3 +4 +5 +6 +7 +8 +9 +10 +Time (h) +(c) +TiZrNbHfTaO11 +Normalized Intensity +80088 +8 +880 +Monoclinic +WV +Orthorhombic +AfterPhotocatalysis +BeforePhotocatalysis +L +w +20 +30 +40 +50 +60 +70 +80 +Diffraction Angle, 20(deg.)17 + +Although the current results confirm the potential of HEOs as a new family of +photocatalysts for CO2 conversion, their activity should be compared with other photocatalysts to +have an insight into their significance. To understand this issue, photocatalytic CO2 conversion +activity of the HEO with a specific surface area of 0.66 m2/g was compared with anatase TiO2 +(99.8%), BiVO4 (99.9%) and P25 TiO2 (99.5%) with the surface areas of 10.2, 0.3 and 38.7 m2/g, +respectively. Since various parameter such as catalyst concentration, temperature, reactor type, +light source type and light intensity can influence the CO production rate, photocatalytic activity +of these materials were compared in the same conditions. Fig. 11 shows the activity of these +materials per 1 g of catalyst. The CO production rate for HEO is significantly higher than anatase +TiO2 and BiVO4 which are some of the most popular photocatalysts for photocatalytic CO2 +conversion. Moreover, the CO and H2 production rate on this HEO is comparable with P25 TiO2 +as a benchmark photocatalyst, although the surface area of current HEO is 60 times smaller than +that of P25 TiO2. It should be noted that the quantity of H2 production on anatase TiO2 and BiVO4 +was not within the detection limits of gas chromatograph. To get more insight on the significance +of photocatalytic CO2 conversion on this HEO, its activity was compared with some reported data +in the literature [8,9,11,46-53]. Although the experiments in the literature are not conducted under +a consistent and standard condition, it is still useful to have a comparison. As given in Table 3, the +amount of CO production rate varies in a wide range of 0.12-10.16 μmolh-1 g-1. The average CO +production for HEO is 4.64±0.30 μmolh-1g-1 which is higher than many of the reported values in +Table 3. +The reason for high CO production rate on current HEO can be attributed to various factors: +the presence of lattice defects such as oxygen vacancies which can act as activation sites [9,12], +the presence of five cations which can enhance the activity by straining effect [14,15], appropriate +electronic structure which satisfy most of the reactions for CO2 conversion and water splitting +[5,6], and appropriate lifetime of charge carriers to participate in photocatalytic reaction due to the +defective nature of HEOs [43,44]. Moreover, the presence of two phases can improve the charge +carrier separation through interfaces and enhance the photocatalytic activity [7,38]. The presence +of several cations in the HEO can also produce hybridized orbitals with higher activity for chemical +reactions [16,17]. To further enhance the efficiency of current HEO for photocatalytic CO2 +conversion, future works are required to enhance its specific surface area by improving the +synthesis or crushing techniques. +Regarding the third issue, three main mechanisms for photocatalytic CO2 reduction have +been suggested, as summarized in Table 4: carbene pathway, formaldehyde pathway and glyoxal +pathway [3,4]. The behavior of current HEO is similar to P25 TiO2, suggesting that both materials +probably follow the same pathway. Although even for TiO2 with different impurities and lattice +defects, there are still significant arguments regarding the CO2 reduction pathways, it is still +possible to discuss about the possible mechanisms for current HEO photocatalyst. The +nonappearance of HCOOH, CH3OH and CH4 in the gas and liquid phases within the detection +limits of analyses suggests that the formaldehyde pathway may not be the major mechanism [3,4]. +The nonappearance of HCOOH and CH4 also indicates that the glyoxal pathway may not be the +major mechanism [3,4]. The production of CO suggests that the carbene pathway is probably the +major mechanism. However, the absence of CH4 and the presence of H2, which is similar to the +behavior of P25 TiO2 in this study, indicates that the carbene pathway possibly stops at some +intermediate stages due to the formation of H2 gas [54]. The absence of CH4 can also be explained +by the defective structure of HEO. Since the HEO material has oxygen vacancies as surface +defects, CO2 in connection with H2O as a Lewis acid tends to adsorb on oxygen vacancies [54]. + +18 + +This adsorption degrades C=O bonding and produce •CO radicals and consequently generates CO +gas [4]. Compared with CO2, the generated CO has lower tendency to be adsorbed on the surface +defects [54], and thus, the carbene pathway does no continue to produce detectable quantity of +CH4. For TiO2, it was also reported that although the CH4 formation in the carbene pathway is +thermodynamically more favorable than CO and H2 formation, the formation of CH4 is kinetically +more difficult because it needs higher numbers of electrons and protons [55]. +Taken altogether, this study introduces HEOs as active photocatalysts for CO2 conversion, +and this opens a path to explore numerous photocatalysts by considering the state-of-art on +engineering of catalysts for CO2 photoreduction [56]. Despite high activity of current HEO, future +studies are required to clarify the exact CO2 conversion mechanism on this new family of materials. +It should be noted that although the material in this study was synthesized by a two-step high- +pressure mechanical alloying and high-temperature oxidation, other methods developed earlier for +the synthesis of high-entropy ceramics [57] can be used in the future to synthesize powders with +high specific surface area and low economical cost. Moreover, since earlier studies showed that +the semiconductor photocatalysts with CO2 conversion capability can have good activity for +degradation of organic pollutants as well [58,59], it is expected that the photocatalytic activity of +HEOs is not limited to CO and H2 production. + + +Fig. 11. High efficiency of high-entropy oxide compared with TiO2 and BiVO4 for photocatalytic +CO2 conversion. (a) CO production rate and (b) H2 production rate versus time. + + +(a) +5 +P25TiO2 +COProduction +4 +TiZrNbHfTaO11 +(6. yown) +3 +BivO4 +2 +Anatase TiO2 +1 +Blank +0 +Y +0 +1 +2 +3 +4 +5 +Time (h) +(b) +P25TiO2 +30 +25 +(umolh"g" +TiZrNbHfTaO11 +20 +15 +10 +5 +Blank +BivO4 +AnataseTiO, +0 +1 +2 +3 +4 +5 +Time (h)19 + +Table 3. Summary of some reported photocatalytic CO2 conversion rates in literature in +comparison with results of current study. +Photocatalyst +Light Source +CO Production +(µmolh-1g-1) +References +TiO2 Nanosheet -CN +150 W Xe lamp +2.04 +[8] +TiO2- Graphitic carbon +300 W Xe lamp +10.16 +[46] +TiO2 nanosheets exposed {001} facet +2 *18W Hg lamps +0.12 +[47] +TiO2 - Hydrogenated CoOx +150W UV lamp +1.24 +[48] +TiO2 3D Ordered Microporous - Pd +300 W Xe lamp +3.9 +[49] +C3N4 by Thermal Condensation +350 W Xe lamp +4.83 +[9] +Cd1−xZnxS +100 W LED plate +2.9 +[50] +BiOI +300 W Xe lamp +4.1 +[51] +xCu2O-Zn2−2xCr +200-W Hg-Xe lamp +2.5 +[11] +CeO2-x +300 W Xe lamp +1.65 +[52] +Cu2O/RuOx +150 W Xe lamp +0.88 +[53] +TiO2 Anatase +400 W Hg Lamp +0.58±0.12 +This Work +BiVO4 +400 W Hg Lamp +2.16±0.21 +This Work +TiO2 P25 +400 W Hg Lamp +4.63±0.33 +This Work +TiZrNbHfTaO11 +400 W Hg Lamp +4.64±0.30 +This Work + + +Table 4. Main mechanisms for CO2 photocatalytic reduction pathway [3]. +Carbene Pathway +Formaldehyde Pathway +Glyoxal Pathway +(1) CO2 + e− → CO2 +•− +(1) CO2 + e− → CO2 +•− +(1) CO2 + e− → CO2 +•− +(2) CO2 +•− + e− + H+ → CO + OH− (2) CO2 +•− + H+ → •COOH +(2) CO2 +•− + e− + H+ → CHOO− +(3) CO + e− → CO•− +(3) •COOH + e− + H+ → HCOOH +(3) CHOO− + H+ → HCOOH +(4) CO•− + e− + H+ → C + OH− +(4) HCOOH + e− + H+ → H3OOC• +(4) HCOOH + e− → HOC• +(5) C + e− + H+ → CH• +(5) HCOOH2 +• + e− + H+ → HCOH+ H2O +(5) HOC• + OH− → C2H2O2 +(6) CH• + e− + H+ → CH2 +(6) HCOH + e− → H2C•O− +(6) C2H2O2 + e− + H+ → H3O2C2 +• +(7) CH2 + e− + H+ → CH3 +• +(7) H2C•O− + H+ → H2OHC• +(7) H3O2C2 +• + e− + H+ → C2H4O2 +(8) CH3 +• + e− + H+ → CH4 +(8) H2OHC• + e− + H+ → CH3OH +(8) C2H4O2 + e− + H+ → H3OC2 +•+ H2O +(9) CH3 +• + OH− → CH3OH +(9) CH3OH + e− + H+ → •CH3 + H2O +(9) H3OC2 +• + e− + H+ → C2H4O + +(10) •CH3 + e− + H+ → CH4 +(10) C2H4O + h+ → H3OC2 +• + H+ + + +(11) H3OC2 +• → CH3 +• + CO + + +(12) CH3 +• + e− + H+ → CH4 + +5. Conclusion +A high-entropy oxide with a general composition of TiZrNbHfTaO11 was synthesized and +used for photocatalytic CO2 conversion. Due to appropriate electronic band structure, good charge +carrier lifetime and a defective and strained dual-phase structure, the material acted as a +photocatalyst for CO2 to CO conversion and H2O to H2 production without addition of any co- +catalyst. The photocatalytic activity of this oxide was better than well-known anatase TiO2 and +BiVO4 photocatalysts and comparable with P25 TiO2 as a benchmark photocatalyst, suggesting +high-entropy oxides as a new family of photocatalysts for CO2 conversion. + + + +20 + +Acknowledgments +This work is supported in part by the WPI-I2CNER, Japan, and in part by Grants-in-Aid +for Scientific Research on Innovative Areas from the MEXT, Japan (19H05176 & 21H00150). + + +References +[1] M. Forkel, N. Carvalhais, C. Rödenbeck, R. Keeling, M. Heimann, K. Thonicke, S. Zaehle, M. +Reichstein, Enhanced seasonal CO2 exchange caused by amplified plant productivity in northern +ecosystems, Science 351 (2016) 696-699. https://doi.org/10.1126/science.aac4971. +[2] A.J. Morris, G.J. Meyer, E. Fujita, Molecular approaches to the photocatalytic reduction of +carbon +dioxide +for +solar +fuels, +Acc. +Chem. +Res. +42 +(2009) +1983-1994. +https://doi.org/10.1021/ar9001679. +[3] S.N. Habisreutinger, L. Schmidt-Mende, J.K. Stolarczyk, Photocatalytic reduction of CO2 on +TiO2 and other semiconductors, Angew. Chem. Int. Ed. 52 (2013) 7372-7408. +https://doi.org/10.1002/anie.201207199. +[4] K. Wang, J. Lu, Y. Lu, C.H. Lau, Y. Zheng, X. Fan, Unravelling the C-C coupling in CO2 +photocatalytic reduction with H2O on Au/TiO2-x: combination of plasmonic excitation and oxygen +vacancy, Appl. Catal. B 292 (2021) 120147. https://doi.org/10.1016/j.apcatb.2021.120147. +[5] X. Li, J. Yu, M. Jaroniec, Hierarchical photocatalysts, Chem. Soc. Rev. 45 (2016) 2603-2636. +https://doi.org/10.1039/C5CS00838G. +[6] E. Kalamaras, M.M. Maroto-Valer, M. Shao, J. Xuan, H. Wang, Solar carbon fuel via +photoelectrochemistry, +Catal. +Today +317 +(2018) +56-75. +https://doi.org/10.1016/j.cattod.2018.02.045. +[7] K. Li, B. Peng, T. Peng, Recent advances in heterogeneous photocatalytic CO2 conversion to +solar fuels, ACS Catal. 6 (2016) 7485-7527. https://doi.org/10.1021/acscatal.6b02089. +[8] A. Crake, K.C. Christoforidis, R. Godin, B. Moss, A. Kafizas, S. Zafeiratos, J.R. Durrant, C. +Petit, Titanium dioxide/carbon nitride nanosheet nanocomposites for gas phase CO2 +photoreduction under UV-visible irradiation, Appl. Catal. B 242 (2019) 369-378. +https://doi.org/10.1016/j.apcatb.2018.10.023. +[9] P. Xia, M. Antonietti, B. Zhu, T. Heil, J. Yu, S. Cao, Designing defective crystalline carbon +nitride to enable selective CO2 photoreduction in the gas phase, Adv. Funct. Mater. 29 (2019) +1900093. https://doi.org/10.1002/adfm.201900093. +[10] J. Bian, J. Feng, Z. Zhang, Z. Li, Y. Zhang, Y. Liu, S. Ali, Y. Qu, L. Bai, J. Xie, D. Tang, X. +Li, F. Bai, J. Tang, L. Jing, Dimension-matched zinc phthalocyanine/BiVO4 ultrathin +nanocomposites for CO2 reduction as efficient wide-visible-light-driven photocatalysts via a +cascade +charge +transfer, +Angew. +Chem. +131 +(2019) +10989-10994. +https://doi.org/10.1002/ange.201905274. +[11] H. Jiang, K. Katsumata, J. Hong, A. Yamaguchi, K. Nakata, C. Terashima, N. Matsushita, M. +Miyauchi, A. Fujishima, Photocatalytic reduction of CO2 on Cu2O-loaded Zn-Cr layered double +hydroxides, Appl. Catal. B 224 (2018) 783-790. https://doi.org/10.1016/j.apcatb.2017.11.011. +[12] J.J. Li, M. Zhang, B. Weng, X. Chen, J. Chen, H.P. Jia, Oxygen vacancies mediated charge +separation and collection in Pt/WO3 nanosheets for enhanced photocatalytic performance, Appl. +Surf. Sci. 507 (2020) 145133. https://doi.org/10.1016/j.apsusc.2019.145133. + +21 + +[13] Y. Li, W.N. Wang, Z. Zhan, M.H. Woo, C.Y. Wu, P. Biswas, Photocatalytic reduction of CO2 +with H2O on mesoporous silica supported Cu/TiO2 catalysts, Appl. Catal. B 100 (2010) 386-392. +https://doi.org/10.1016/j.apcatb.2010.08.015. +[14] Z. Liu, C. Menéndez, J. Shenoy, J.N. Hart, C.C. Sorrell, C. Cazorl, Strain engineering of oxide +thin +films +for +photocatalytic +applications, +Nano +Energy +72 +(2020) +104732. +https://doi.org/10.1016/j.nanoen.2020.104732. +[15] J. Di, P. Song, C. Zhu, C. Chen, J. Xiong, M. Duan, R. Long, W. Zhou, M. Xu, L. Kang, B. +Lin, D. Liu, S. Chen, C. Liu, H. Li, Y. Zhao, S. Li, Q. Yan, L. Song, Z. Liu, Strain-engineering of +Bi2O17Br2 nanotubes for boosting photocatalytic CO2 reduction, ACS Mater. Lett. 2 (2020)1025– +1032. https://doi.org/10.1021/acsmaterialslett.0c00306. +[16] C. Oses, C. Toher, S. Curtarolo, High-entropy ceramics, Nat. Rev. Mater. 5 (2020) 295-309. +https://doi.org/10.1038/s41578-019-0170-8. +[17] A.J. Wright, Q. Wang, C. Huang, A. Nieto, R. Chen, J. Luo, From high-entropy ceramics to +compositionally-complex ceramics: a case study of fluorite oxides, J. Eur. Ceram. Soc. 40 (2020) +2120-2129. https://doi.org/10.1016/j.jeurceramsoc.2020.01.015. +[18] H. Chen, K. Jie, C.J. Jafta, Z. Yang, S. Yao, M. Liu, Z. Zhang, J. Liu, M. Chi, J. Fu, S. Dai, +An ultrastable heterostructured oxide catalyst based on high-entropy materials: a new strategy +toward catalyst stabilization via synergistic interfacial interaction, Appl. Catal. B 276 (2020) +119155. https://doi.org/10.1016/j.apcatb.2020.119155. +[19] H. Chen, J. Fu, P. Zhang, H. Peng, C.W. Abney, K. Jie, X. Liu, M. Chi, S. Dai, Entropy- +stabilized metal oxide solid solutions as CO oxidation catalysts with high-temperature stability, J. +Mater. Chem. A 6 (2018) 11129-11133. https://doi.org/10.1039/C8TA01772G. +[20] J.L. Braun, C.M. Rost, M. Lim, A. Giri, D.H. Olson, G.N. Kotsonis, G. Stan, D.W. Brenner, +J.P. Maria, P.E. Hopkins, Charge‐induced disorder controls the thermal conductivity of entropy‐ +stabilized oxides, Adv. Mater. 30 (2018) 1805004. https://doi.org/10.1002/adma.201805004. +[21] A.J. Wright, C. Huang, M.J. Walock, A. Ghoshal, M. Murugan, J. Luo, Sand corrosion, +thermal expansion, and ablation of medium‐and high‐entropy compositionally complex fluorite +oxides, J. Am. Ceram. Soc. 104 (2021) 448-462. https://doi.org/10.1111/jace.17448. +[22] R. Witte, A. Sarkar, R. Kruk, B. Eggert, R.A. Brand, H. Wende, H. Hahn, High-entropy +oxides: an emerging prospect for magnetic rare-earth transition metal perovskites, Phys. Rev. +Mater. 3 (2019) 034406. https://doi.org/10.1103/PhysRevMaterials.3.034406. +[23] A. Mao, H.Z. Xiang, Z.G. Zhang, K. Kuramoto, H. Zhang, Y. Jia, A new class of spinel high- +entropy oxides with controllable magnetic properties, J. Magn. Magn. Mater. 497 (2020) 165884. +https://doi.org/10.1016/j.jmmm.2019.165884. +[24] A. Radoń, Ł. Hawełek, D. Łukowiec, J. Kubacki, P. Włodarczyk, Dielectric and +electromagnetic interference shielding properties of high entropy (Zn,Fe,Ni,Mg,Cd)Fe2O4 ferrite, +Sci. Rep. 9 (2019) 20078. https://doi.org/10.1038/s41598-019-56586-6. +[25] S. Zhou, Y. Pu, Q. Zhang, R. Shi, X. Guo, W. Wang, J. Ji, T. Wei, T. Ouyang, Microstructure +and dielectric properties of high entropy Ba(Zr0.2Ti0.2Sn0.2Hf0.2Me0.2)O3 perovskite oxides, Ceram. +Int. 46 (2020) 7430-7437. https://doi.org/10.1016/j.ceramint.2019.11.239. +[26] A. Sarkar, L. Velasco, D. Wang, Q. Wang, G. Talasila, L. de Biasi, C. Kübel, T. Brezesinski, +S.S. Bhattacharya, H. Hahn, B. Breitung, High entropy oxides for reversible energy storage, Nat. +Commun. 9 (2018) 3400. https://doi.org/10.1038/s41467-018-05774-5. + +22 + +[27] T.X. Nguyen, J. Patra, J.K. Chang, J.M. Ting, High entropy spinel oxide nanoparticles for +superior lithiation-delithiation performance, J. Mater. Chem. A 8 (2020) 18963-18973. +https://doi.org/10.1039/D0TA04844E. +[28] Y. Zheng, Y. Yi, M. Fan, H. Liu, X. Li, R. Zhang, M. Li, Z.-A. Qiao, A high-entropy metal +oxide as chemical anchor of polysulfide for lithium-sulfur batteries, Energy Storage Mater. 23 +(2019) 678-683. https://doi.org/10.1016/j.ensm.2019.02.030. +[29] G. Fang, J. Gao, J. Lv, H. Jia, H. Li, W. Liu, G. Xie, Z. Chen, Y. Huang, Q. Yuan,X. Liu, X. +Lin, S. Sun, H.J. Qiu, Multi-component nanoporous alloy/(oxy) hydroxide for bifunctional oxygen +electrocatalysis and rechargeable Zn-air batteries, Appl. Catal. B 268 (2020) 118431. +https://doi.org/10.1016/j.apcatb.2019.118431. +[30] H. Chen, W. Lin, Z. Zhang, K. Jie, D.R. Mullins, X. Sang, S.-Z. Yang, C.J. Jafta, C.A. +Bridges, X. Hu, Mechanochemical synthesis of high entropy oxide materials under ambient +conditions: dispersion of catalysts via entropy maximization, ACS Mater. Lett. 1 (2019) 83-88. +https://doi.org/10.1021/acsmaterialslett.9b00064. +[31] M.S. Lal, R. Sundara, High entropy oxides - a cost-effective catalyst for the growth of high +yield carbon nanotubes and their energy applications, ACS Appl. Mater. Interfaces 11 (2019) +30846-30857. https://doi.org/10.1021/acsami.9b08794. +[32] T.X. Nguyen, Y.C. Liao, C.C. Lin, Y.H. Su, J.M. Ting, Advanced high entropy perovskite +oxide electrocatalyst for oxygen evolution reaction, Adv. Funct. Mater. 31 (2021) 2101632. +https://doi.org/10.1002/adfm.202101632 +[33] P. Edalati, Q. Wang, H. Razavi-Khosroshahi, M. Fuji, T. Ishihara, K. Edalati, Photocatalytic +hydrogen evolution on a high-entropy oxide, J. Mater. Chem. A 8 (2020) 3814-3821. +https://doi.org/10.1039/C9TA12846H. +[34] P. Edalati, X.F. Shen, M. Watanabe, T. Ishihara, M. Arita, M. Fuji, K. Edalati, High-entropy +oxynitride as a low-bandgap and stable photocatalyst for hydrogen production, J. Mater. Chem. A +9 (2021) 15076-15086. https://doi.org/10.1039/D1TA03861C. +[35] K. Edalati, Z. Horita, A review on high-pressure torsion (HPT) from 1935 to 1988, Mater. +Sci. Eng. A 652 (2016) 325–352. https://doi.org/10.1016/j.msea.2015.11.074. +[36] K. Edalati, Review on recent advancements in severe plastic deformation of oxides by high- +pressure +torsion +(HPT), +Adv. +Eng. +Mater. +21 +(2019) +1800272. +https://doi.org/10.1002/adem.201800272. +[37] J. Chastain, Handbook of X-ray Photoelectron Spectroscopy, Perkin-Elmer Corporation, Eden +Prairie, MN, USA, 1992. +[38] S. Akrami, M. Watanabe, T.H. Ling, T. Ishihara, M. Arita, M. Fuji, K. Edalati, High-pressure +TiO2-II polymorph as an active photocatalyst for CO2 to CO conversion, Appl. Catal. B 298 (2021) +120566. https://doi.org/10.1016/j.apcatb.2021.120566. +[39] L. Ran, J. Hou, S. Cao, Z. Li, Y. Zhang, Y. Wu, B. Zhang, P. Zhai, L. Sun, Defect engineering +of +photocatalysts +for +solar +energy +conversion, +Sol. +RRL +4 +(2020) +1900487. +https://doi.org/10.1002/solr.201900487. +[40] M. R. Hoffmann, S. T. Martin, W. Choi and D. W. Bahnemann, Environmental applications +of +semiconductor +photocatalysis, +Chem. +Rev. +95 +(1995) +69–96. +https://doi.org/10.1021/cr00033a004. +[41] K. Maeda and K. Domen, New non-oxide photocatalysts designed for overall water splitting +under visible light, J. Phys. Chem. C, 111 (2007) 7851–7861. https://doi.org/10.1021/jp070911w. + +23 + +[42] Z. Zhang, K. Liu, Z. Feng, Y. Bao, B. Dong, Hierarchical sheet-on-sheet ZnIn2S4/g-C3N4 +heterostructure with highly efficient photocatalytic H2 production based on photoinduced +interfacial charge transfer, Sci. Rep. 6 (2016) 19221. https://doi.org/10.1038/srep1922. +[43] X.H. Wang, J.G. Li, H. Kamiyama, M. Katada, N. Ohashi, Y. Moriyoshi, T. J. Ishigaki, +Pyrogenic iron (III)-doped TiO2 nanopowders synthesized in RF thermal plasma: phase formation, +defect structure, band gap, and magnetic properties, J. Am. Chem. Soc. 127 (2005) 10982–10990, +https://doi.org/10.1021/ja051240n. +[44] I. Nakamura, N. Negishi, S. Kutsuna, T. Ihara, S. Sugihara, K.J. Takeuchi, Role of oxygen +vacancy in the plasma-treated TiO2 photocatalyst with visible light activity for NO removal, J. +Mol. Catal. A 161 (2000) 205–212. https://doi.org/10.1016/S1381-1169(00)00362-9. +[45] M. Li, X. He, Y. Zeng, M. Chen, Z. Zhang, H. Yang, P. Fang, X. Lu, Y. Tong, Solar-microbial +hybrid device based on oxygen-deficient niobium pentoxide anodes for sustainable hydrogen +production, Chem. Sci. 6 (2015) 6799. https://doi.org/10.1039/C5SC03249K. +[46] Y. Wang, Y. Chen, Y. Zuo, F. Wang, J. Yao, B. Li, S. Kang, X. Li, L. Cui, Hierarchically +mesostructured TiO2/graphitic carbon composite as a new efficient photocatalyst for the reduction +of CO2 under simulated solar irradiation, Catal. Sci. Technol. 3 (2013) 3286-3291. +https://doi.org/10.1039/C3CY00524K. +[47] Z. He, L. Wen, D. Wang, Y. Xue, Q. Lu, C. Wu, J. Chen, S. Song, Photocatalytic reduction +of CO2 in aqueous solution on surface-fluorinated anatase TiO2 nanosheets with exposed {001} +facets, Energy Fuels. 28 (2014) 3982-3993. https://doi.org/10.1021/ef500648k. +[48] Y. Li, C. Wang, M. Song, D. Li, X. Zhang, Y. Liu, TiO2-x/CoOx photocatalyst sparkles in +photothermocatalytic reduction of CO2 with H2O steam, Appl. Catal. B 243 (2019) 760–770. +https://doi.org/10.1016/j.apcatb.2018.11.022. +[49] J. Jiao, Y. Wei, Y. Zhao, Z. Zhao, A. Duan, J. Liu, Y. Pang, J. Li, G. Jiang, Y. Wang, +AuPd/3DOM-TiO2 catalysts for photocatalytic reduction of CO2: High efficient separation of +photogenerated +charge +carriers, +Appl. +Catal. +B +209 +(2017) +228-239. +https://doi.org/10.1016/j.apcatb.2017.02.076. +[50] E.A. Kozlova, M.N. Lyulyukin, D.V. Markovskaya, D.S. Selishchev, S.V. Cherepanova, D.V. +Kozlov, Synthesis of Cd1-xZnxS photocatalysts for gas-phase CO2 reduction under visible light, +Photochem. Photobiol. Sci. 18 (2019) 871-877. https://doi.org/10.1039/C8PP00332G. +[51] L. Ye, H. Wang, X. Jin, Y. Su, D. Wang, H. Xie, X. Liu, X. Liu, Synthesis of olive-green +fewlayered BiOI for efficient photoreduction of CO2 into solar fuels under visible/near-infrared +light, +Sol. +Energy +Mater. +Sol. +Cells +144 +(2016) +732-739. +https://doi.org/10.1016/j.solmat.2015.10.022. +[52] T. Ye, W. Huang, L. Zeng, M. Li, J. Shi, CeO2-x platelet from monometallic cerium layered +double hydroxides and its photocatalytic reduction of CO2, Appl. Catal. B 210 (2017) 141-148. +https://doi.org/10.1016/j.apcatb.2017.11.011. +[53] E. Pastor, F. Pesci, A. Reynal, A. Handoko, M. Guo, X. An, A. Cowan, D. Klug, J. Durrant, +J. Tang, Interfacial charge separation in Cu2O/RuOx as a visible light driven CO2 reduction +catalyst, Phys. Chem. Chem. Phys. 16 (2014) 5922-5926. https://doi.org/ 10.1039/C4CP00102H. +[54] K. Wang, J. Lu, Y. Lu, C.H. Lau, Y. Zheng, X. Fan, Unravelling the C-C coupling in CO2 +photocatalytic reduction with H2O on Au/TiO2-x: combination of plasmonic excitation and oxygen +vacancy, Appl. Catal. B 292 (2021), 120147. https://doi. org/10.1016/j.apcatb.2021.120147. +[55] L.Y. Lin, S. Kavadiya, X. He, W.N. Wang, B.B. Karakocak, Y.C. Lin, M.Y. Berezin, P. +Biswas, Engineering stable Pt nanoparticles and oxygen vacancies on defective TiO2 via + +24 + +introducing strong electronic metal-support interaction for efficient CO2 photoreduction, Chem. +Eng. J. 389 (2020), 123450. https://doi.org/10.1016/j. cej.2019.123450. +[56] S. Wang, X. Han, Y. Zhang, N. Tian, T. Ma, H. Huang, Inside-and-out semiconductor +engineering for CO2 photoreduction: from recent advances to new trends, Small Struct. 2 (2021) +2000061. https://doi.org/10.1002/sstr.202000061. +[57] S. Akrami, P. Edalati, K. Edalati, M. Fuji, High-entropy ceramics: review of principles, +production +and +applications, +Mater. +Sci. +Eng. +R +146 +(2021) +100644. +https://doi.org/10.1016/j.mser.2021.100644. +[58] F.Y. Liu, Y.M. Dai, F.H. Chen, C.C. Chen, Lead bismuth oxybromide/graphene oxide: +synthesis, characterization, and photocatalytic activity for removal of carbon dioxide, crystal violet +dye, and 2-hydroxybenzoic acid, J. Colloid. Interface Sci. 562 (2020) 112-124. +https://doi.org/10.1016/j.jcis.2019.12.006 +[59] H.L. Chen, F.Y. Liu, X. Xiao, J. Hu, B. Gao, D. Zou, C.C. Chen, Visible-light-driven +photocatalysis of carbon dioxide and organic pollutants by MFeO2 (M = Li, Na, or K), J. Colloid. +Interface Sci. 601 (2021) 758-772. https://doi.org/10.1016/j.jcis.2021.05.156. + diff --git a/kdE4T4oBgHgl3EQfTgyJ/content/tmp_files/load_file.txt b/kdE4T4oBgHgl3EQfTgyJ/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..986498768e177ec061a0be5207c06488d3c99050 --- /dev/null +++ b/kdE4T4oBgHgl3EQfTgyJ/content/tmp_files/load_file.txt @@ -0,0 +1,1500 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf,len=1499 +page_content='1 Applied Catalysis B, Volume 303, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 120896, 2022 https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='apcatb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='120896 Received on 24 August 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Revised on 22 October 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Accepted on:2 November 202;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Available online 8 November 2021 Defective high-entropy oxide photocatalyst with high activity for CO2 conversion Saeid Akrami1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Yasushi Murakami2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Monotori Watanabe3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Tatsumi Ishihara2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Makoto Arita4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Masayoshi Fuji1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='5,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='* and Kaveh Edalati3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='* 1 Department of Life Science and Applied Chemistry,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Nagoya Institute of Technology,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Tajimi 507-0071,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Japan 2 Department of Applied Chemistry,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Faculty of Engineering,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Kyushu University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Fukuoka 819- 0395,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Japan 3 WPI,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' International Institute for Carbon-Neutral Energy Research (WPI-I2CNER),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Kyushu University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Fukuoka 819-0395,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Japan 4 Department of Materials Science and Engineering,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Faculty of Engineering,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Kyushu University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Fukuoka 819-0395,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Japan 5 Advanced Ceramics Research Center,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Nagoya Institute of Technology,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Tajimi 507-0071,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Japan Abstract High-entropy oxides (HEOs),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' as a new family of materials with five or more principal cations,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' have shown promising properties for various applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' In this work and inspired by inherent defective and strained structure of HEOs, photocatalytic CO2 conversion is examined on a dual-phase TiZrNbHfTaO11 synthesized by a two-step high-pressure torsion mechanical alloying and high-temperature oxidation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' The HEO, which had various structural defects, showed simultaneous photocatalytic activity for CO2 to CO and H2O to H2 conversion without the addition of a co-catalyst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' The photocatalytic activity of this HEO for CO2 conversion was better than conventional photocatalysts such as anatase TiO2 and BiVO4 and similar to P25 TiO2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' The high activity of HEO was discussed in terms of lattice defects, lattice strain, light absorbance, band structure, photocurrent generation and charge carrier mobility to activation centers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' The current study confirms the high potential of HEOs as a new family of photocatalysts for CO2 conversion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Keywords: High-entropy alloys (HEAs);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' High-entropy oxide (HEO);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Photocatalyst, Photocatalytic CO2 conversion;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Oxygen vacancy Corresponding authors: Masayoshi Fuji (E-mail: fuji@ fuji@nitech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='jp;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Tel: +81-57-227-6811) Kaveh Edalati (E-mail: kaveh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='edalati@kyudai.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='jp;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Tel: +81-92-802-6744) 2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Introduction Carbon dioxide (CO2) is a stable molecule, which is produced mainly from human activities such as combustion of hydrocarbons and partly from natural sources such as decomposition of organisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Emission of CO2 from combustion of hydrocarbon fuels is considered as a main reason for the global warming on the earth [1,2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' There are currently significant attempts to explore effective strategies to reduce the human-activity-based CO2 emission or to convert CO2 to useful products [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Photocatalytic CO2 conversion is considered as a clean technology to reduce the amount of this stable gas in the atmosphere, although the research on photocatalytic CO2 conversion is still at the early stages and significant efforts are required to enhance its efficiency for practical applications [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' In photocatalytic CO2 conversion, following the light absorbance by a semiconductor which is known as photocatalyst, electrons are excited from the valence band to the conduction band and contribute to CO2 conversion [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Such a CO2 conversion occurs through different pathways including carbene pathway, formaldehyde pathway and glyoxal pathway [3,4], leading to different conversion products, as shown in Table 1 [5,6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Reactions in CO2 conversion with their standard potentials [5,6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Reaction Standard Potential vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' NHE (eV) at PH = 0 CO2 + 2H+ + 2e- → HCOOH 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='20 CO2 + 2H+ + 2e- → CO + H2O 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='11 CO2 + 4H+ + 4e- → HCHO + H2O 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='07 CO2 + 6H+ + 6e- → CH3OH + H2O 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='03 CO2 + 8H+ + 8e- → CH4 + 2H2O 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='17 For photocatalytic CO2 conversion, a photocatalyst should have appropriate bandgap to absorb light photons, appropriate band structure to satisfy the standard potentials for each reaction shown in Table 1, long exited electron lifetime and appropriate charge carrier mobility [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' TiO2 [8], C3N4-based catalysts [9], bismuth-based compounds such as BiVO4 [10], Cu-based semiconductors [11] and WO3 [12] are some popular photocatalysts for CO2 conversion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Although the improvement of existing photocatalysts by different strategies such as heterostructure generation [7], nanosheet production [8], surface defect introduction [9], oxygen vacancy generation [12], mesoporous structure formation [13] and strain engineering [14,15] is currently the major research activity, there are high demands to explore new family of materials as highly active photocatalysts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' High-entropy ceramics are a new type of materials which show high stability and promising structural and functional properties due to the so-called cocktail effect, lattice strain/defects, heterogenous valence electron distribution and high configurational entropy [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 1a, high-entropy ceramics are defined as multi-component materials with at least five principal elements and a configurational entropy higher than 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='5R (R: the gas constant) [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' These materials have a low Gibbs free energy due to their high entropy and this gives a high stability to these materials under different conditions [16] including catalytic reactions [18,19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Moreover, the presence of at least five cations with different atomic sizes in these materials results in the formation of inherent lattice strain and defects [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Since lattice strain and defects are effective to enhance photocatalytic CO2 conversion [9,12,14,15], the high-entropy ceramics are expected to 3 show good activity for such a conversion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' High-entropy oxides (HEOs) are the most popular high- entropy ceramics which have been investigated for various applications and properties such as thermal barrier coatings [20,21], magnetic components [22,23], dielectric components [24,25], Li- ion batteries [26,27], Li-S batteries [28], Zn-air batteries [29], catalysts [30,31], electrocatalysts [32], and photocatalytic hydrogen production [33,34].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Despite the inherent defective and strained structure of HEOs, there have been no attempts to employ these materials for photocatalytic CO2 conversion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' In this study, a HEO photocatalyst, TiZrNbHfTaO11, is synthesized and its activity for CO2 conversion is examined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' The transition elements titanium, zirconium, niobium, hafnium, and tantalum are selected simply because their binary oxides with the d0 electronic structure can act as photocatalysts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' This first application of HEOs for photocatalytic CO2 conversion confirms that the HEO photocatalyst shows higher activity compared to common binary or ternary photocatalysts such as TiO2 and BiVO4, suggesting HEOs as a new family of photocatalysts for CO2 conversion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Experimental 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Sample preparation Although various methods have been developed in recent years for the synthesis of HEO [16-34], a two-step high-pressure mechanical alloying and high-temperature oxidation which is available in the authors’ laboratory was used to synthesize the HEO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' In the first step, equiatomic amounts of Ti (99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='9%), Zr (95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='0%), Hf (99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='5%), Nb (99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='9%) and Ta (99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='9%) powders were mixed in acetone, treated by ultrasonic and then dried.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' The dried powder mixture was processed by high- pressure torsion (HPT), shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 1b, to fabricate TiZrNbHfTa high entropy alloy (HEA) with the body-centered cubic (BCC) structure (see the principles of HPT and its applications to oxides in [35,36]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' To produce the TiZrNbHfTa alloy, a 10 mm diameter and 1 mm thick disc was prepared by compacting the powder mixture under a pressure of 400 MPa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' The compacted disc was then compressed between two HPT anvils under a high pressure of 6 GPa at room temperature and simultaneously processed by rotating the lower HPT anvil with respect to the upper one for 100 turns with a rotation rate of one turn per minute.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' In the second step, the HPT-processed TiZrNbHfTa alloy was exposed to hot air at a temperature of 1373 K for 24 h to produce an oxide, with the appearance shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 1c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Examination of the mass of sample before and after oxidation suggested a composition of TiZrNbHfTaO11 for the produced oxide.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' The oxide was crushed after oxidation into the powder form using a mortar and examined by various characterization methods, as described below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Characterization To examine the crystal structure, X-ray diffraction (XRD) using the Cu Kα radiation with a wavelength of λ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1542 nm and micro-Raman spectroscopy using a laser source with a wavelength of λ = 532 nm were utilized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Examination of microstructure was conducted by (i) scanning electron microscopy (SEM) with energy dispersive X-ray spectroscopy (EDS) analysis under 15 keV,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' (ii) transmission electron microscopy (TEM) with selected area electron diffraction (SAED),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' bright-field (BF) images,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' dark- field (DF) images,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' high-resolution images and fast Fourier transform (FFT) analysis under 200 4 keV,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' and (iii) scanning-transmission electron microscopy (STEM) with high-angle annular dark- field (HAADF) images and EDS analysis under 200 keV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' (a) Relationship between number of elements and configurational entropy and definition of high-entropy ceramics with equiatomic fractions of elements, (b) schematic illustration of high- pressure torsion (HPT), and (c) appearance of high-entropy oxide synthesized in this study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' To investigate the presence of point defects such as oxygen vacancies, electron paramagnetic resonance (EPR) was performed at ambient temperature using a microwave source with a frequency of 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='4688 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' To study the oxidation states of different elements and to estimate the valence band top position, X-ray photoelectron spectroscopy (XPS) using the Al Kα radiation with a wavelength of λ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='989 nm was used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' The XPS energy position for each element was adjusted by considering the peak position of C 1s at 284.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='8 eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' After correction of the energy positions, the peaks for different elements were analyzed by peak deconvolution by considering the standard energy relations and differences reported in the handbook [37]: f7/2:f5/2 = 4:3, d5/2:d3/2 = 3:2, p3/2:p1/2 = 2:1, Ti 2p1/2 - Ti 2p3/2 = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='54 eV, Zr 3d3/2 - Zr 3d5/2 = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='43 eV, Hf 4f5/2 - Hf 4f7/2 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='71 eV, Nb 3d3/2 - Nb 3d5/2 = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='72 eV, Ta 4f5/2 - Ta 4f7/2 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='91 eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' (a) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='0R High-Entropy Ceramics 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='5R Medium-Entropy Ceramics 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='0R 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='5R 0 1 2 3 4 5 6 7 8 Number of Elements, N (b) Upper Anvil (c) Pressure Disc Sample 个 个 10 mm Pressure LowerAnvil Torsion5 To investigate the light absorbance and bandgap (Kubelka-Munk analysis), UV-vis diffuse reflectance spectroscopy was conducted, and the band structure was calculated by considering both XPS and UV-vis spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' To study the lifetime of exited electrons, steady-state photoluminescence (PL) emission spectroscopy with a 325 nm laser source and time-resolved photoluminescence decay (PL decay) with a 285 nm laser source were conducted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' The specific surface area of powder was examined by nitrogen gas adsorption and using the Brunauer-Emmett-Teller (BET) method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Photocurrent test Photocurrent generation was examined using a thin film of sample in a 1 M Na2SO4 electrolyte under the full arc of Xe lamp (without using any filter), as described in detail earlier [38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' The thin film was prepared by deposition of HEO powder on FTO (fluorine-doped tin oxide) glass with 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='25 mm thickness and 15×25 mm2 surface area.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' about 5 mg of sample was crushed in 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='2 mL ethanol and carefully dispersed on the FTO glass using a drop and annealed at 473 K for 24 h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' The average thickness of HEO on FTO glass was about 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='04 mm, which was estimated by measuring the thickness of glass before and after deposition of HEO using a micrometer with 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='01 mm accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Photocurrent generation was examined by an electrochemical analyzer in the potentiostatic amperometry mode during time (30 s light ON and 60 s light OFF), while the counter electrode was Pt wire, the reference electrode was Ag/AgCl, and the external potential was 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='7 V vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Ag/AgCl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Photocatalytic test Photocatalytic CO2 conversion was conducted using the powder of HEO in a continuous flow quartz photoreactor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' The photoreactor, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 2a, had a cylindrical shape with a total inner volume of 858 mL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' The reactor had an inner space to insert the light source.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' There were two holes on the top of photoreactor: one for the inlet of CO2 flow, which was connected to a gas cylinder;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' and another one for the outlet of gas and sampling the reaction products for analysis, which was connected to a vent and gas chromatograph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' For the photocatalytic reaction, 120 mg of HEO was mixed with 500 mL of deionized water and NaHCO3 with 1 M concentration and then bubbled with CO2 with a flow rate of 3 mL/min.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' The temperature was controlled as 288 K using a water chiller and the suspension was continuously stirred using a magnetic stirrer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' The process was first conducted for 2 h without light irradiation, and after confirmation that no reaction products appear, the photocatalytic test was conducted under irradiation with a high-pressure Hg light source (Sen Lights Corporation, HL400BH-8, 400 W, with the spectral composition shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 2b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' The light intensity irradiated on the photocatalysts was 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='5 W/cm2 and no filter was used during the irradiation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' The reaction products were analyzed by a gas chromatograph (Shimadzu GC-8A, Ar Carrier).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' A flame ionization detector equipped with a methanizer (Shimadzu MTN-1) was used to measure the CO and CH4 production rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' A thermal conductivity detector also was utilized to evaluate the H2 and O2 production.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' To be sure about the absence of CO from other sources such as contamination, blank tests were conducted (i) under irradiation in the presence of CO2, NaHCO3 and H2O and without the photocatalyst addition and (ii) under irradiation in the presence of Ar, NaHCO3 and H2O and with photocatalyst addition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 6 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' (a) Description of experimental setting for photocatalytic CO2 conversion including photograph of photoreactor, and (b) spectroscopy of light source used for photocatalytic test.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Results 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Crystal structure and microstructure Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 3 shows the SEM images of HEO in various scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Particle size measured by SEM is 25 µm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' The HEO contains particles with different sizes, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 3, and its specific surface area, achieved by the BET method, is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='66 m2/g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Although big size of some particles can have negative effect on photocatalytic activity due to decreasing the active surface area, this issue can be addressed in the future by using other synthesis method or advanced crushing techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' The presence of numerous nanograins in each particle is obvious in higher magnification images in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 3b, c and d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' The average grain size for this material is estimated to be 192 nm, while some pores are also visible within the particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Here, it should be noted that low specific surface area and small grain size are characteristics of materials which are synthesized/processed by the HPT method [33-36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' To confirm the successful oxidation of the material, electronic states of each element in the HEO are presented in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 4 using the XPS analysis and corresponding peak deconvolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 4 shows that the main cations in the sample are Ti4+, Zr4+, Nb5+, Hf4+ and Ta5+, suggesting that the material is successfully oxidized to a d0 electronic configuration during the high-temperature oxidation [37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' However, it should be noted that the peaks for Ti, Zr, Nb, Hf and Ta have some shoulders to the lower energy sides, suggesting that some oxygen-deficient regions with lower oxidation states should exist within the material, as confirmed by the peak deconvolution analysis (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=', some oxygen vacancies present).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' The presence of vacancies is not surprising as similar issue can be observed in other HPT-processed materials due to the strain effect [35,36] and in other HEOs due to the atomic size mismatch effect [16,17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' MassFlow Gas (a) (q) Chromatograph High-Pressure Hg Lamp Controller Relative Intensity 00 0 a Vent CO2 Lamp 300 400 500 600 Stirring Photoreactor Wavelength (nm)7 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Morphology of high-entropy oxide examined by SEM at different magnifications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' To confirm the distribution of elements in the material, Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 5a and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 5b illustrate the elemental distribution mappings in the micrometer and nanometer scales, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 5 shows that the elements distribute appropriately in both micrometer and nanometer scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' It is confirmed that the elements are successfully mixed by high-pressure mechanical alloying and their distribution remains reasonably homogeneous even after high-temperature oxidation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' SEM-EDS analysis suggests that the material should have a general composition of TiZrNbHfTaO11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Uniform distribution of elements is a general requirement of high-entropy materials [16-32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 100um 500mm 200 nm8 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Electronic states and relevant peak deconvolution of (a) Ti, (b) Zr, (c) Nb, (d) Hf, (e) Ta and (f) O in high-entropy oxide examined by XPS analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' (a) TiZrNbHfTaO11 (b) TiZrNbHfTaO11 Ti2p1/2 T: 41 2p1/2 r 4+ 3d3/2 Intensity (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=') .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Ti2p3/2 T:4 41 2p3/2 (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=') 0- Sum T:o 2p1/2 Zr3d3/2 Ti3*2p3/2 Intensity ---Zr 3d5/2 o-Sum 456 458 460 462 464 466 178 180 182 184 186 188 Binding Energy (eV) Binding Energy (eV) (c) TiZrNbHfTaO11 (d) TiZrNbHfTaO11 Intensity (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=') Intensity (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=') Nb3*3d3/2 — Hf 4f 5/2 --- Hf 4f7/2 —Nb 3d3/2 o-Sum ---Nb 3d5/2 0-Sum 202 204206208210212214 1314 15 17 18 19 20 21 Binding Energy (eV) Binding Energy (eV) (e) 5+ TiZrNbHfTaO11 (f) TiZrNbHfTaO11 Ta 5+ Intensity (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=') Intensity (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=') o-Sum 3+ —Ta 4f5/2 --.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Ta 4f712 o-Sum 22 24 26 28 30 524 526 528 530 532 534 536 BindingEnergy(ev) BindingEnergy(ev)9 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Distribution of elements in high-entropy oxide examined at (a) micrometer scale using SEM-EDS and (b) nanometer scale using STEM-EDS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Crystal structure of HEO was examined using XRD analysis, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 6a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' The material contains two phases with the monoclinic and orthorhombic structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Based on the Rietveld analysis, the HEO consists of 40 wt% of monoclinic phase (A2/m space group, a = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='193 nm, b = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='381 nm, c = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='044 nm, α = 90°, β = 120.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='16°, γ = 90°) and 60 wt% of orthorhombic phase (Ima2 space group, a = 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='092 nm, b = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='493 nm, c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='527 nm, α = β = γ = 90°).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Raman spectra, shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 6b from three different positions, illustrate similar patterns in different positions, suggesting the size of phases should be smaller than the spatial resolution of micro-Raman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Taken altogether, a combination of XPS, EDS and XRD confirms that a dual-phase HEO could be successfully produced in this study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Examination of microstructural/nanostructural features of this dual-phase HEO is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 7, where a is a BF image, b is a corresponding SAED pattern, c is a DF image, d and e are HR images, and f is a magnified lattice image of the selected squared region in e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 7 reveals several important points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' (i) A ring pattern of SAED image confirms the presence of many nanocrystals with random orientation in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 7a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' (ii) The BF and DF images confirm that the grain (b) 100um 100 μm 20 nm 20 nm BF HAADF SM 100 μm 20 nm 100 μm 20 nm Ti Zr Nb 100 μm 100 μm 20 nm 20 nm Nb Hf Hf 100 μm 20nm 20 nm Ta10 sizes are quite small and less than 100 nm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' This indicates that there are still smaller crystals within the grain-like regions observed in the SEM images of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' (iii) The HR images confirm the co- existence of two monoclinic and orthorhombic phases at the nanoscale and large fraction of interphase boundaries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' It was shown that the presence of interphases as charge heterojunctions can improve the photocatalytic activity through enhanced charge carrier separation and mobility [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' (iv) The lattice images are quite distorted and close examination of the lattice confirms the presence of many dislocation defects within the grains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Since it was reported that the dislocations can enhance the light absorbance and photocatalytic activity at least in some semiconductors [39], the presence of dislocations in this HEO may positively act for enhancement of photocatalytic activity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Dual-phase structure of high-entropy oxide examined by (a) XRD profile and (b) micro- Raman spectra at three different positions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' (a) TiZrNbHfTaO11 Oxidation: T= 1373 K, t = 24 h Intensity (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=') 800888 8 880 Monoclinic MMMM W V Orthorhombic 20 30 40 50 60 70 80 Diffraction Angle, 20 (deg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=') (b) TiZrNbHfTaO11 Normalized Intensity Position 3 Position 2 Position 1 200 400 600 800 Raman Shift, o (cm11 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Presence of nanoscaled dual phases with large fraction of interfaces and dislocations in high-entropy oxide examined by TEM (a) BF image, (b) SAED analysis, (c) DF image and (d-f) HR images, where (c) was taken with diffracted beams indicated by arrow in (a), and (f) is a magnified view of squared region in (e).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Electronic structure and defect states Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 8 shows (a) UV-vis absorbance spectrum, (b) Kubelka-Munk plot, (c) XPS spectrum of top of valence band and (d) electronic structure determined by a combination of UV-vis and (a) (b) (c) 20 nm 20 nm BF DF (d) Orthorhombic Monoclinic [122] [311] 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='nmm (e) [310] 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' (602] Monoclinic[133] 2nm uu12 XPS analyses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 8a indicates that the HEO can absorb light in both ultraviolet and visible light regions, although the quantity of absorbed light in the ultraviolet region is higher than that in the visible light region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Such a visible light absorbance is not detected in binary oxides such as TiO2, ZrO2, HfO2, Nb2O5 and Ta2O5 [38,39].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Based on the Kubelka-Munk analysis, there are two apparent bandgaps of 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='0 and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='3 eV for this HEO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' The first energy gap should be related to the energy difference between the valence band and conduction band which is reasonably similar to the bandgap of TiO2 and smaller than the bandgap of other binary oxides in the Ti-Zr-Hf-Nb-Ta- O system (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1-5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='7 eV) [40,41], and the second gap should be due to the defect level between the valence band and conduction band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' The presence of defects (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=', oxygen vacancies or color centers), which can be confirmed from the low energy shoulders in XPS spectra of cations, should be a main reason for the orange color of sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' The top of valence band calculated by XPS is 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='8 eV vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' NHE, which is shown by an arrow in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 8c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' The bottom of conduction band is calculated as -1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='2 vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' NHE by considering an indirect bandgap of 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='0 eV and the defect state is estimated as 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='5 eV vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' NHE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' As summarized in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 8d, the potential of reactions for CO2 conversion and water splitting (see Table 1) are between the energy levels for the top of valence band and the bottom of conduction band, and thus, this HEO can basically satisfy the requirements for photocatalytic reactions [5-7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Appropriate electronic structure of high-entropy oxide for photocatalytic CO2 conversion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=" (a) UV-vis light absorbance spectrum, (b) Kubelka-Munk plot to calculate indirect bandgap (α: light absorption, h: Planck's constant, ν: light frequency), (c) XPS spectrum to estimate top of valence band, and (d) electronic band structure in comparison with potentials for photocatalytic CO2 conversion." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' (a) Uv IR (b) TiZrNbHfTaO11 TiZrNbHfTaO11, 14 (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=') 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='8 12 (ahu) (eV/cm) 0 10 rbance, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='6 8 2 6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='4 Absor 4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='2 2 0 200 400 600 800 2 3 4 5 Wavelength (nm) Photon Energy, hv(eV) (c) (d) TiZrNbHfTaO11 Conduction Band Intensity (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=') CO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='/HCOOH Defect State CO2/CO CO2/CH20 :2H/H2 1 CO,/CHOH CO2/CH4 Valence Band O,/H,0 2 0 2 4 8 10 12 Binding Energy (eV)13 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Charge-carrier dynamics Charge-carrier dynamics were examined by (a) steady-state PL spectroscopy, (b) PL decay spectroscopy, (c) EPR spectroscopy and (d) photocurrent measurement, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' The PL spectrum in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 9a shows a peak at 580 nm which is equivalent to an energy level of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='14 eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Since this energy level is close to the energy gap of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='3 eV, calculated using the Kubelka-Munk analysis for the defect states, it can be concluded that this peak corresponds to the recombination of excited electrons at the defect state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' To have an insight into the significance of these electron- hole recombination, Table 2 compares the PL intensity and PL wavelength of the HEO with those measured by the current authors for anatase TiO2 and BiVO4 (as two popular photocatalysts for CO2 conversion [2-5]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' It is obvious that the PL intensity of HEO is lower than that of anatase TiO2 and BiVO2, despite its high light absorbance which is an indication of large electron-hole production.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' The lower PL intensity suggests that the recombination in this HEO is not higher than TiO2 and BiVO2, provided that the heat energy generation through the electron-hole recombination is considered identical for the three oxides.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Evaluation of PL decay intensity versus time, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 9b, indicates that the PL decay of the HEO follows an exponential equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 𝐼(𝑡) = 𝐴1 exp (− 𝑡 𝜏1 ) + 𝐴2 exp (− 𝑡 𝜏2 ) (1) where, I(t), 𝐴1, 𝐴2, 𝜏1 and 𝜏2 are PL decay intensity at time t, amplitude of the first exponential function, amplitude of the second exponential function, fast decay time and slow decay time, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Analysis of data in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 9b suggests the values of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='53 and 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='39 ns for 𝜏1 and 𝜏2, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Here, the following equation can be used to estimate the average lifetime, 𝜏𝑎𝑣𝑒 [42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 𝜏𝑎𝑣𝑒 = 𝐴1𝜏1 2 + 𝐴2𝜏2 2 𝐴1𝜏1 + 𝐴1𝜏1 (2) Table 2 compares the average lifetime for the HEO with those for anatase TiO2 and BiVO4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' The average lifetime for the HEO is 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='5 ns which is close to the lifetime of TiO2 anatase (10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='7 ns).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Low recombination intensity of the HEO, measured by steady-state PL spectroscopy, and an appropriate electron lifetime close to TiO2 anatase, show that the exited electrons on the surface of this material can be active for appropriate time to take part in photocatalytic reaction before recombination with holes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' One reason for the appropriate charge carrier lifetime and low-intensity recombination for this HEO can be the presence of oxygen vacancies on the surface [43,44].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Prescence of oxygen vacancies, which was suggested by the orange color of sample in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 1c, XPS spectroscopy in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 4 and UV-vis spectroscopy in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 8a, was examined further by EPR spectroscopy, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 9c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Two symmetric hump peaks with a g factor of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='15 appear which may be due to the oxygen vacancies, as reported in some oxides such as Nb2O5 [45].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' It should be noted that the oxygen vacancies on the surface can act as active sites for electron-hole separation and photocatalytic reaction [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Moreover, it was shown that the surface oxygen vacancies have a direct effect on photocatalytic CO production rate: surface oxygen vacancies can absorb CO2 and contribute to breaking the C=O bonds to produce CO [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 14 Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' PL wavelength and intensity, fitted parameters of PL decay spectra and photocurrent density for high-entropy oxide in comparison with anatase TiO2 and BiVO4 photocatalysts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' PL Wavelength (nm) Intensity (cps) TiZrNbHfTaO11 580 190 Anatase TiO2 510 12300 BiVO4 640 300 PL Decay τ1 (ns) τ2 (ns) A1 A2 τ ave (ns) TiZrNbHfTaO11 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='53 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='39 42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='34 57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='66 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='5 Anatase TiO2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='24 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='46 41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='98 58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='02 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='7 BiVO4 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='17 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='90 56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='56 43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='44 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='9 Photocurrent (mA/m2) Cycle 1 Cycle 2 Cycle 3 Cycle 4 TiZrNbHfTaO11 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='6 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='9 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='4 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='2 Anatase TiO2 43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='5 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='2 27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='9 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='2 BiVO4 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='6 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='0 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='7 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' (a) Steady-state PL emission, (b) time-resolved PL decay, (c) EPR spectra and (d) photocurrent generation for high-entropy oxide.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' (a) (b) 200 TiZrNbHfTaO11 TiZrNbHfTaO11 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='0 (cps) Intensity (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=') 150 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='8 Intensity 100 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='4 50 PL 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='2 0 400 500 600 700 800 0 2 4 6 8 10 Wavelength(nm) Time (ns) (c) (d) TiZrNbHfTaO11 2 Current Density (mA/m TiZrNbHfTaO11 10 Vo LightON Intensity (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=') 8 9 4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='8 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='4 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='6 0 300 600 900 1200 1500 Time (s) g Factor15 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 9d shows photocurrent measurement on HEO thin film.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' The material successfully generates photocurrent, although its photocurrent density decreases during the time due to the accumulation of holes with positive charge on the surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Table 2 compares the photocurrent density of the HEO with that of reference anatase TiO2 and BiVO4 for the first four cycles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' It should be noted that the quantitative comparison of the photocurrent density of these three materials should be conducted by care due to the technical limits in making dense films with good FTO-oxide bonding by annealing at 473 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' The photocurrent density of HEO is apparently lower than that of the reference oxides.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Despite the low photocurrent density of HEO, photocurrent generation on this material indicates that the exited electrons can have enough lifetime to separate from the surface of material and take part in the photocurrent generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' The generation of photocurrent is a positive sign for possible photocatalytic activity of this HEO, as discussed earlier for other photocatalysts [38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Photocatalytic activity Photocatalytic activity of HEO for CO2 conversion is summarized in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 10a and b, the HEO could successfully produce both CO and H2 under the full arc emission of high-pressure Hg lamp without any co-catalyst addition, despite its low specific surface area as 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='66 m2/g (the error bar of gas amount measurement for three repeated tests was lower than 10%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Independent synthesis of the HEO material and repeating the photocatalytic test, as indicated as Sample #2 in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 10a, also confirm the high activity of this material for photocatalytic CO2 conversion with a reasonably constant CO and H2 production rate within an extended irradiation time of 10 h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' The amount of CO production is higher and the amount of H2 production is lower for Sample #2 compared to Sample #1, suggesting that the activity of this HEO can be still improved by modification of the synthesis method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Two points should be noted here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' First, CO and H2 were the only reaction products within the detection limits of analyses and no other products including methane could be detected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Second, blank tests confirmed that no CO and H2 are produced by (i) CO2 injection in the presence of HEO under the dark condition for 2 h, (ii) Ar injection in the presence of HEO under the light irradiation for 1 h, and (iii) CO2 injection without the presence of HEO under the light irradiation for 5 h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' The stability of HEO, examined by XRD analysis after the photocatalytic test, is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 10c, indicating that the crystal structure of the HEO is stable after photocatalytic test.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' The stability of HEOs, which was also reported for other applications such thermal barrier coatings [20,21], magnetic components [22,23], dielectric components [24,25], Li-ion batteries [26,27], Li-S batteries [28], Zn-air batteries [29], catalysts [30,31] and electrocatalysts [32], is usually due to their low Gibbs free energy resulting from their high entropy [16,17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 16 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Photocatalytic activity of high-entropy oxide for CO2 conversion and H2O decomposition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' (a) CO production rate versus time, (b) H2 production rate versus time, and (c) XRD pattern before and after photocatalytic test.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Discussion Three issues need to be discussed in detail here: (i) comparison of photocatalytic activity of the HEO with available photocatalysts, (ii) factors influencing the photocatalytic activity of the HEO, and (iii) mechanism of CO2 conversion on the HEO photocatalyst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' (a) TiZrNbHfTaO11 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='5 Sample#2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='4 Sample#1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1 co 0 0 1 2 3 4 5 6 7 8 9 10 Time (h) (b) 5 TiZrNbHfTaO11 4 Sample#1 3 Sample#2 2 0 0 1 2 3 4 5 6 7 8 9 10 Time (h) (c) TiZrNbHfTaO11 Normalized Intensity 80088 8 880 Monoclinic WV Orthorhombic AfterPhotocatalysis BeforePhotocatalysis L w 20 30 40 50 60 70 80 Diffraction Angle, 20(deg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' )17 Although the current results confirm the potential of HEOs as a new family of photocatalysts for CO2 conversion, their activity should be compared with other photocatalysts to have an insight into their significance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' To understand this issue, photocatalytic CO2 conversion activity of the HEO with a specific surface area of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='66 m2/g was compared with anatase TiO2 (99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='8%), BiVO4 (99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='9%) and P25 TiO2 (99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='5%) with the surface areas of 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='2, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='3 and 38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='7 m2/g, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Since various parameter such as catalyst concentration, temperature, reactor type, light source type and light intensity can influence the CO production rate, photocatalytic activity of these materials were compared in the same conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 11 shows the activity of these materials per 1 g of catalyst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' The CO production rate for HEO is significantly higher than anatase TiO2 and BiVO4 which are some of the most popular photocatalysts for photocatalytic CO2 conversion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Moreover, the CO and H2 production rate on this HEO is comparable with P25 TiO2 as a benchmark photocatalyst, although the surface area of current HEO is 60 times smaller than that of P25 TiO2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' It should be noted that the quantity of H2 production on anatase TiO2 and BiVO4 was not within the detection limits of gas chromatograph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' To get more insight on the significance of photocatalytic CO2 conversion on this HEO, its activity was compared with some reported data in the literature [8,9,11,46-53].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Although the experiments in the literature are not conducted under a consistent and standard condition, it is still useful to have a comparison.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' As given in Table 3, the amount of CO production rate varies in a wide range of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='12-10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='16 μmolh-1 g-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' The average CO production for HEO is 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='64±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='30 μmolh-1g-1 which is higher than many of the reported values in Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' The reason for high CO production rate on current HEO can be attributed to various factors: the presence of lattice defects such as oxygen vacancies which can act as activation sites [9,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='12],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' the presence of five cations which can enhance the activity by straining effect [14,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='15],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' appropriate electronic structure which satisfy most of the reactions for CO2 conversion and water splitting [5,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='6],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' and appropriate lifetime of charge carriers to participate in photocatalytic reaction due to the defective nature of HEOs [43,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='44].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Moreover, the presence of two phases can improve the charge carrier separation through interfaces and enhance the photocatalytic activity [7,38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' The presence of several cations in the HEO can also produce hybridized orbitals with higher activity for chemical reactions [16,17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' To further enhance the efficiency of current HEO for photocatalytic CO2 conversion, future works are required to enhance its specific surface area by improving the synthesis or crushing techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Regarding the third issue, three main mechanisms for photocatalytic CO2 reduction have been suggested, as summarized in Table 4: carbene pathway, formaldehyde pathway and glyoxal pathway [3,4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' The behavior of current HEO is similar to P25 TiO2, suggesting that both materials probably follow the same pathway.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Although even for TiO2 with different impurities and lattice defects, there are still significant arguments regarding the CO2 reduction pathways, it is still possible to discuss about the possible mechanisms for current HEO photocatalyst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' The nonappearance of HCOOH, CH3OH and CH4 in the gas and liquid phases within the detection limits of analyses suggests that the formaldehyde pathway may not be the major mechanism [3,4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' The nonappearance of HCOOH and CH4 also indicates that the glyoxal pathway may not be the major mechanism [3,4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' The production of CO suggests that the carbene pathway is probably the major mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' However, the absence of CH4 and the presence of H2, which is similar to the behavior of P25 TiO2 in this study, indicates that the carbene pathway possibly stops at some intermediate stages due to the formation of H2 gas [54].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' The absence of CH4 can also be explained by the defective structure of HEO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Since the HEO material has oxygen vacancies as surface defects, CO2 in connection with H2O as a Lewis acid tends to adsorb on oxygen vacancies [54].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 18 This adsorption degrades C=O bonding and produce •CO radicals and consequently generates CO gas [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Compared with CO2, the generated CO has lower tendency to be adsorbed on the surface defects [54], and thus, the carbene pathway does no continue to produce detectable quantity of CH4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' For TiO2, it was also reported that although the CH4 formation in the carbene pathway is thermodynamically more favorable than CO and H2 formation, the formation of CH4 is kinetically more difficult because it needs higher numbers of electrons and protons [55].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Taken altogether, this study introduces HEOs as active photocatalysts for CO2 conversion, and this opens a path to explore numerous photocatalysts by considering the state-of-art on engineering of catalysts for CO2 photoreduction [56].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Despite high activity of current HEO, future studies are required to clarify the exact CO2 conversion mechanism on this new family of materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' It should be noted that although the material in this study was synthesized by a two-step high- pressure mechanical alloying and high-temperature oxidation, other methods developed earlier for the synthesis of high-entropy ceramics [57] can be used in the future to synthesize powders with high specific surface area and low economical cost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Moreover, since earlier studies showed that the semiconductor photocatalysts with CO2 conversion capability can have good activity for degradation of organic pollutants as well [58,59], it is expected that the photocatalytic activity of HEOs is not limited to CO and H2 production.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' High efficiency of high-entropy oxide compared with TiO2 and BiVO4 for photocatalytic CO2 conversion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' (a) CO production rate and (b) H2 production rate versus time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' (a) 5 P25TiO2 COProduction 4 TiZrNbHfTaO11 (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' yown) 3 BivO4 2 Anatase TiO2 1 Blank 0 Y 0 1 2 3 4 5 Time (h) (b) P25TiO2 30 25 (umolh"g" TiZrNbHfTaO11 20 15 10 5 Blank BivO4 AnataseTiO, 0 1 2 3 4 5 Time (h)19 Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Summary of some reported photocatalytic CO2 conversion rates in literature in comparison with results of current study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Photocatalyst Light Source CO Production (µmolh-1g-1) References TiO2 Nanosheet -CN 150 W Xe lamp 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='04 [8] TiO2- Graphitic carbon 300 W Xe lamp 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='16 [46] TiO2 nanosheets exposed {001} facet 2 *18W Hg lamps 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='12 [47] TiO2 - Hydrogenated CoOx 150W UV lamp 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='24 [48] TiO2 3D Ordered Microporous - Pd 300 W Xe lamp 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='9 [49] C3N4 by Thermal Condensation 350 W Xe lamp 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='83 [9] Cd1−xZnxS 100 W LED plate 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='9 [50] BiOI 300 W Xe lamp 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1 [51] xCu2O-Zn2−2xCr 200-W Hg-Xe lamp 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='5 [11] CeO2-x 300 W Xe lamp 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='65 [52] Cu2O/RuOx 150 W Xe lamp 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='88 [53] TiO2 Anatase 400 W Hg Lamp 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='58±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='12 This Work BiVO4 400 W Hg Lamp 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='16±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='21 This Work TiO2 P25 400 W Hg Lamp 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='63±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='33 This Work TiZrNbHfTaO11 400 W Hg Lamp 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='64±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='30 This Work Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Main mechanisms for CO2 photocatalytic reduction pathway [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='Carbene Pathway ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='Formaldehyde Pathway ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='Glyoxal Pathway ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='(1) CO2 + e− → CO2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='− ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='(1) CO2 + e− → CO2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='− ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='(1) CO2 + e− → CO2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='− ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='(2) CO2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='− + e− + H+ → CO + OH− (2) CO2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='− + H+ → •COOH ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='(2) CO2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='− + e− + H+ → CHOO− ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='(3) CO + e− → CO•− ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='(3) •COOH + e− + H+ → HCOOH ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='(3) CHOO− + H+ → HCOOH ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='(4) CO•− + e− + H+ → C + OH− ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='(4) HCOOH + e− + H+ → H3OOC• ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='(4) HCOOH + e− → HOC• ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='(5) C + e− + H+ → CH• ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='(5) HCOOH2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='+ e− + H+ → HCOH+ H2O ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='(5) HOC• + OH− → C2H2O2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='(6) CH• + e− + H+ → CH2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='(6) HCOH + e− → H2C•O− ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='(6) C2H2O2 + e− + H+ → H3O2C2 (7) CH2 + e− + H+ → CH3 (7) H2C•O− + H+ → H2OHC• ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='(7) H3O2C2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='+ e− + H+ → C2H4O2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='(8) CH3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='+ e− + H+ → CH4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='(8) H2OHC• + e− + H+ → CH3OH ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='(8) C2H4O2 + e− + H+ → H3OC2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='+ H2O ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='(9) CH3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='+ OH− → CH3OH ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='(9) CH3OH + e− + H+ → •CH3 + ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='H2O ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='(9) H3OC2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='+ e− + H+ → C2H4O ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='(10) •CH3 + e− + H+ → CH4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='(10) C2H4O + h+ → H3OC2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='+ H+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='(11) H3OC2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='→ CH3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='CO ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='(12) CH3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='+ e− + H+ → CH4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Conclusion A high-entropy oxide with a general composition of TiZrNbHfTaO11 was synthesized and used for photocatalytic CO2 conversion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Due to appropriate electronic band structure, good charge carrier lifetime and a defective and strained dual-phase structure, the material acted as a photocatalyst for CO2 to CO conversion and H2O to H2 production without addition of any co- catalyst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' The photocatalytic activity of this oxide was better than well-known anatase TiO2 and BiVO4 photocatalysts and comparable with P25 TiO2 as a benchmark photocatalyst, suggesting high-entropy oxides as a new family of photocatalysts for CO2 conversion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 20 Acknowledgments This work is supported in part by the WPI-I2CNER, Japan, and in part by Grants-in-Aid for Scientific Research on Innovative Areas from the MEXT, Japan (19H05176 & 21H00150).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' References [1] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Forkel, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Carvalhais, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Rödenbeck, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Keeling, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Heimann, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Thonicke, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Zaehle, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Reichstein, Enhanced seasonal CO2 exchange caused by amplified plant productivity in northern ecosystems, Science 351 (2016) 696-699.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1126/science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='aac4971.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' [2] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Morris, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Meyer, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Fujita, Molecular approaches to the photocatalytic reduction of carbon dioxide for solar fuels, Acc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 42 (2009) 1983-1994.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1021/ar9001679.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' [3] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Habisreutinger, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Schmidt-Mende, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Stolarczyk, Photocatalytic reduction of CO2 on TiO2 and other semiconductors, Angew.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 52 (2013) 7372-7408.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1002/anie.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='201207199.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' [4] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Wang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Lu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Lu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Lau, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Zheng, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Fan, Unravelling the C-C coupling in CO2 photocatalytic reduction with H2O on Au/TiO2-x: combination of plasmonic excitation and oxygen vacancy, Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Catal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' B 292 (2021) 120147.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='apcatb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='120147.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' [5] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Li, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Yu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Jaroniec, Hierarchical photocatalysts, Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 45 (2016) 2603-2636.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1039/C5CS00838G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' [6] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Kalamaras, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Maroto-Valer, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Shao, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Xuan, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Wang, Solar carbon fuel via photoelectrochemistry, Catal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Today 317 (2018) 56-75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='cattod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='02.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='045.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' [7] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Li, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Peng, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Peng, Recent advances in heterogeneous photocatalytic CO2 conversion to solar fuels, ACS Catal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 6 (2016) 7485-7527.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1021/acscatal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='6b02089.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' [8] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Crake, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Christoforidis, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Godin, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Moss, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Kafizas, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Zafeiratos, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Durrant, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Petit, Titanium dioxide/carbon nitride nanosheet nanocomposites for gas phase CO2 photoreduction under UV-visible irradiation, Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Catal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' B 242 (2019) 369-378.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='apcatb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' [9] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Xia, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Antonietti, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Zhu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Heil, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Yu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Cao, Designing defective crystalline carbon nitride to enable selective CO2 photoreduction in the gas phase, Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Funct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Mater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 29 (2019) 1900093.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1002/adfm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='201900093.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' [10] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Bian, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Feng, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Zhang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Li, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Zhang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Liu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Ali, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Qu, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Bai, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Xie, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Tang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Li, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Bai, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Tang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Jing, Dimension-matched zinc phthalocyanine/BiVO4 ultrathin nanocomposites for CO2 reduction as efficient wide-visible-light-driven photocatalysts via a cascade charge transfer, Angew.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 131 (2019) 10989-10994.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1002/ange.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='201905274.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' [11] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Jiang, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Katsumata, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Hong, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Yamaguchi, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Nakata, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Terashima, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Matsushita, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Miyauchi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Fujishima, Photocatalytic reduction of CO2 on Cu2O-loaded Zn-Cr layered double hydroxides, Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Catal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' B 224 (2018) 783-790.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='apcatb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' [12] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Li, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Zhang, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Weng, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Chen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Chen, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Jia, Oxygen vacancies mediated charge separation and collection in Pt/WO3 nanosheets for enhanced photocatalytic performance, Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Surf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 507 (2020) 145133.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='apsusc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='145133.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 21 [13] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Li, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Wang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Zhan, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Woo, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Wu, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Biswas, Photocatalytic reduction of CO2 with H2O on mesoporous silica supported Cu/TiO2 catalysts, Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Catal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' B 100 (2010) 386-392.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='apcatb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='08.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' [14] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Liu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Menéndez, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Shenoy, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Hart, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Sorrell, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Cazorl, Strain engineering of oxide thin films for photocatalytic applications, Nano Energy 72 (2020) 104732.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='nanoen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='104732.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' [15] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Di, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Song, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Zhu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Chen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Xiong, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Duan, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Long, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Zhou, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Xu, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Kang, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Lin, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Liu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Chen, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Liu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Li, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Zhao, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Li, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Yan, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Song, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Liu, Strain-engineering of Bi2O17Br2 nanotubes for boosting photocatalytic CO2 reduction, ACS Mater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 2 (2020)1025– 1032.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1021/acsmaterialslett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='0c00306.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' [16] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Oses, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Toher, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Curtarolo, High-entropy ceramics, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Mater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 5 (2020) 295-309.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1038/s41578-019-0170-8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' [17] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Wright, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Wang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Huang, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Nieto, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Chen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Luo, From high-entropy ceramics to compositionally-complex ceramics: a case study of fluorite oxides, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Ceram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 40 (2020) 2120-2129.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='jeurceramsoc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='01.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' [18] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Chen, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Jie, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Jafta, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Yang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Yao, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Liu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Zhang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Liu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Chi, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Fu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Dai, An ultrastable heterostructured oxide catalyst based on high-entropy materials: a new strategy toward catalyst stabilization via synergistic interfacial interaction, Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Catal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' B 276 (2020) 119155.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='apcatb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='119155.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' [19] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Chen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Fu, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Zhang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Peng, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Abney, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Jie, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Liu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Chi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Dai, Entropy- stabilized metal oxide solid solutions as CO oxidation catalysts with high-temperature stability, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Mater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' A 6 (2018) 11129-11133.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1039/C8TA01772G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' [20] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Braun, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Rost, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Lim, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Giri, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Olson, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Kotsonis, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Stan, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Brenner, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Maria, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Hopkins, Charge‐induced disorder controls the thermal conductivity of entropy‐ stabilized oxides, Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Mater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 30 (2018) 1805004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1002/adma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='201805004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' [21] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Wright, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Huang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Walock, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Ghoshal, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Murugan, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Luo, Sand corrosion, thermal expansion, and ablation of medium‐and high‐entropy compositionally complex fluorite oxides, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Am.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Ceram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 104 (2021) 448-462.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1111/jace.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='17448.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' [22] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Witte, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Sarkar, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Kruk, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Eggert, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Brand, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Wende, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Hahn, High-entropy oxides: an emerging prospect for magnetic rare-earth transition metal perovskites, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Mater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 3 (2019) 034406.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1103/PhysRevMaterials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='034406.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' [23] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Mao, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Xiang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Zhang, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Kuramoto, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Zhang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Jia, A new class of spinel high- entropy oxides with controllable magnetic properties, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Magn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Magn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Mater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 497 (2020) 165884.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='jmmm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='165884.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' [24] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Radoń, Ł.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Hawełek, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Łukowiec, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Kubacki, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Włodarczyk, Dielectric and electromagnetic interference shielding properties of high entropy (Zn,Fe,Ni,Mg,Cd)Fe2O4 ferrite, Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 9 (2019) 20078.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1038/s41598-019-56586-6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' [25] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Zhou, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Pu, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Zhang, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Shi, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Guo, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Wang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Ji, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Wei, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Ouyang, Microstructure and dielectric properties of high entropy Ba(Zr0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='2Ti0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='2Sn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='2Hf0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='2Me0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='2)O3 perovskite oxides, Ceram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 46 (2020) 7430-7437.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='ceramint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='239.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' [26] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Sarkar, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Velasco, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Wang, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Wang, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Talasila, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' de Biasi, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Kübel, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Brezesinski, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Bhattacharya, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Hahn, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Breitung, High entropy oxides for reversible energy storage, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 9 (2018) 3400.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1038/s41467-018-05774-5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 22 [27] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Nguyen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Patra, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Chang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Ting, High entropy spinel oxide nanoparticles for superior lithiation-delithiation performance, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Mater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' A 8 (2020) 18963-18973.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1039/D0TA04844E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' [28] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Zheng, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Yi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Fan, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Liu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Li, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Zhang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Li, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='-A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Qiao, A high-entropy metal oxide as chemical anchor of polysulfide for lithium-sulfur batteries, Energy Storage Mater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 23 (2019) 678-683.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='ensm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='02.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='030.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' [29] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Fang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Gao, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Lv, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Jia, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Li, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Liu, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Xie, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Chen, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Huang, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Yuan,X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Liu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Lin, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Sun, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Qiu, Multi-component nanoporous alloy/(oxy) hydroxide for bifunctional oxygen electrocatalysis and rechargeable Zn-air batteries, Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Catal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' B 268 (2020) 118431.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='apcatb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='118431.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' [30] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Chen, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Lin, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Zhang, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Jie, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Mullins, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Sang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='-Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Yang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Jafta, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Bridges, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Hu, Mechanochemical synthesis of high entropy oxide materials under ambient conditions: dispersion of catalysts via entropy maximization, ACS Mater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 1 (2019) 83-88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1021/acsmaterialslett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='9b00064.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' [31] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Lal, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Sundara, High entropy oxides - a cost-effective catalyst for the growth of high yield carbon nanotubes and their energy applications, ACS Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Mater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Interfaces 11 (2019) 30846-30857.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1021/acsami.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='9b08794.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' [32] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Nguyen, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Liao, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Lin, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Su, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Ting, Advanced high entropy perovskite oxide electrocatalyst for oxygen evolution reaction, Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Funct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Mater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 31 (2021) 2101632.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1002/adfm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='202101632 [33] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Edalati, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Wang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Razavi-Khosroshahi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Fuji, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Ishihara, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Edalati, Photocatalytic hydrogen evolution on a high-entropy oxide, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Mater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' A 8 (2020) 3814-3821.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1039/C9TA12846H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' [34] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Edalati, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Shen, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Watanabe, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Ishihara, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Arita, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Fuji, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Edalati, High-entropy oxynitride as a low-bandgap and stable photocatalyst for hydrogen production, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Mater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' A 9 (2021) 15076-15086.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1039/D1TA03861C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' [35] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Edalati, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Horita, A review on high-pressure torsion (HPT) from 1935 to 1988, Mater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Eng.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' A 652 (2016) 325–352.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='msea.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='074.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' [36] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Edalati, Review on recent advancements in severe plastic deformation of oxides by high- pressure torsion (HPT), Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Eng.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Mater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 21 (2019) 1800272.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1002/adem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='201800272.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' [37] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Chastain, Handbook of X-ray Photoelectron Spectroscopy, Perkin-Elmer Corporation, Eden Prairie, MN, USA, 1992.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' [38] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Akrami, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Watanabe, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Ling, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Ishihara, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Arita, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Fuji, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Edalati, High-pressure TiO2-II polymorph as an active photocatalyst for CO2 to CO conversion, Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Catal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' B 298 (2021) 120566.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='apcatb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='120566.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' [39] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Ran, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Hou, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Cao, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Li, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Zhang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Wu, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Zhang, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Zhai, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Sun, Defect engineering of photocatalysts for solar energy conversion, Sol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' RRL 4 (2020) 1900487.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1002/solr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='201900487.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' [40] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Hoffmann, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Martin, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Choi and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Bahnemann, Environmental applications of semiconductor photocatalysis, Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 95 (1995) 69–96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1021/cr00033a004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' [41] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Maeda and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Domen, New non-oxide photocatalysts designed for overall water splitting under visible light, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' C, 111 (2007) 7851–7861.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1021/jp070911w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 23 [42] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Zhang, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Liu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Feng, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Bao, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Dong, Hierarchical sheet-on-sheet ZnIn2S4/g-C3N4 heterostructure with highly efficient photocatalytic H2 production based on photoinduced interfacial charge transfer, Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 6 (2016) 19221.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1038/srep1922.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' [43] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Wang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Li, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Kamiyama, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Katada, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Ohashi, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Moriyoshi, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Ishigaki, Pyrogenic iron (III)-doped TiO2 nanopowders synthesized in RF thermal plasma: phase formation, defect structure, band gap, and magnetic properties, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Am.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 127 (2005) 10982–10990, https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1021/ja051240n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' [44] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Nakamura, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Negishi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Kutsuna, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Ihara, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Sugihara, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Takeuchi, Role of oxygen vacancy in the plasma-treated TiO2 photocatalyst with visible light activity for NO removal, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Catal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' A 161 (2000) 205–212.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1016/S1381-1169(00)00362-9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' [45] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Li, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' He, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Zeng, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Chen, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Zhang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Yang, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Fang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Lu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Tong, Solar-microbial hybrid device based on oxygen-deficient niobium pentoxide anodes for sustainable hydrogen production, Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 6 (2015) 6799.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1039/C5SC03249K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' [46] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Wang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Chen, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Zuo, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Wang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Yao, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Li, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Kang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Li, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Cui, Hierarchically mesostructured TiO2/graphitic carbon composite as a new efficient photocatalyst for the reduction of CO2 under simulated solar irradiation, Catal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Technol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 3 (2013) 3286-3291.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1039/C3CY00524K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' [47] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' He, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Wen, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Wang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Xue, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Lu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Wu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Chen, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Song, Photocatalytic reduction of CO2 in aqueous solution on surface-fluorinated anatase TiO2 nanosheets with exposed {001} facets, Energy Fuels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 28 (2014) 3982-3993.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1021/ef500648k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' [48] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Li, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Wang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Song, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Li, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Zhang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Liu, TiO2-x/CoOx photocatalyst sparkles in photothermocatalytic reduction of CO2 with H2O steam, Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Catal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' B 243 (2019) 760–770.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='apcatb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' [49] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Jiao, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Wei, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Zhao, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Zhao, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Duan, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Liu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Pang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Li, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Jiang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Wang, AuPd/3DOM-TiO2 catalysts for photocatalytic reduction of CO2: High efficient separation of photogenerated charge carriers, Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Catal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' B 209 (2017) 228-239.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='apcatb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='02.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='076.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' [50] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Kozlova, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Lyulyukin, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Markovskaya, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Selishchev, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Cherepanova, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Kozlov, Synthesis of Cd1-xZnxS photocatalysts for gas-phase CO2 reduction under visible light, Photochem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Photobiol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 18 (2019) 871-877.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1039/C8PP00332G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' [51] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Ye, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Wang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Jin, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Su, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Wang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Xie, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Liu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Liu, Synthesis of olive-green fewlayered BiOI for efficient photoreduction of CO2 into solar fuels under visible/near-infrared light, Sol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Energy Mater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Sol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Cells 144 (2016) 732-739.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='solmat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' [52] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Ye, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Huang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Zeng, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Li, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Shi, CeO2-x platelet from monometallic cerium layered double hydroxides and its photocatalytic reduction of CO2, Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Catal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' B 210 (2017) 141-148.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='apcatb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' [53] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Pastor, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Pesci, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Reynal, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Handoko, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Guo, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' An, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Cowan, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Klug, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Durrant, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Tang, Interfacial charge separation in Cu2O/RuOx as a visible light driven CO2 reduction catalyst, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 16 (2014) 5922-5926.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='org/ 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1039/C4CP00102H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' [54] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Wang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Lu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Lu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Lau, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Zheng, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Fan, Unravelling the C-C coupling in CO2 photocatalytic reduction with H2O on Au/TiO2-x: combination of plasmonic excitation and oxygen vacancy, Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Catal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' B 292 (2021), 120147.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='apcatb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='120147.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' [55] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Lin, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Kavadiya, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' He, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Wang, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Karakocak, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Lin, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Berezin, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Biswas, Engineering stable Pt nanoparticles and oxygen vacancies on defective TiO2 via 24 introducing strong electronic metal-support interaction for efficient CO2 photoreduction, Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Eng.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 389 (2020), 123450.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' cej.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='123450.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' [56] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Wang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Han, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Zhang, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Tian, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Ma, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Huang, Inside-and-out semiconductor engineering for CO2 photoreduction: from recent advances to new trends, Small Struct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 2 (2021) 2000061.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1002/sstr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='202000061.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' [57] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Akrami, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Edalati, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Edalati, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Fuji, High-entropy ceramics: review of principles, production and applications, Mater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Eng.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' R 146 (2021) 100644.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='mser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='100644.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' [58] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Liu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Dai, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Chen, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Chen, Lead bismuth oxybromide/graphene oxide: synthesis, characterization, and photocatalytic activity for removal of carbon dioxide, crystal violet dye, and 2-hydroxybenzoic acid, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Colloid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Interface Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 562 (2020) 112-124.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='jcis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='006 [59] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Chen, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Liu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Xiao, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Hu, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Gao, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Zou, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Chen, Visible-light-driven photocatalysis of carbon dioxide and organic pollutants by MFeO2 (M = Li, Na, or K), J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Colloid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' Interface Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' 601 (2021) 758-772.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE4T4oBgHgl3EQfTgyJ/content/2301.05008v1.pdf'} +page_content='jcis.' 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Bakhshipour1, Alireza koochali1,2,3, Ulrich Dittmer1, Ali Haghighi4, S. +Ahmad1,3, A. Dengel1,3 +1 TU Kaiserslautern, Kaiserslautern, Germany +2 Ingenieurgesellschaft Auto und Verkehr(IAV) GmbH, Berlin,Germany +3 German Research Center for Artificial Intelligence (DFKI), Kaiserslautern, Germany +4 Shahid Chamran University of Ahvaz, Ahvaz, Iran +1 + 0000-0002-6921-2381, amin.bakhshipour@bauing-uni.kl.de, 2 + 0000-0001-7370-9369, +alireza.koochali@iav.de, 3 + 0000-0003-1723-3356, ulrich.dittmer@bauing.uni-kl.de, 4 + 0000-0002- +2765-6929, a.haghighi@scu.ac.ir, 5 + 0000-0002-4239-6520, sheraz.ahmed@dfki.de, 6 + 0000-0002- +6100-8255, andreas.dengel@dfki.de +Abstract +Despite various breakthroughs of machine learning and data analysis techniques for +improving smart operation and management of urban water infrastructures, some key +limitations obstruct this progress. Among these shortcomings, the absence of freely available +data due to data privacy or high costs of data gathering and the nonexistence of adequate rare +or extreme events in the available data plays a crucial role. Here, the Generative Adversarial +Networks (GANs) can help overcome these challenges. In machine learning, generative models +are a class of methods capable of learning data distribution to generate artificial data. In this +study, we developed a GAN model to generate synthetic time series to balance our limited +recorded time series data and improve the accuracy of a data-driven model for combined +sewer flow prediction. We considered the sewer system of a small town in Germany as the test +case. Precipitation and inflow to the storage tanks are used for the Data-Driven model +development. The aim is to predict the flow using precipitation data and examine the impact +of data augmentation using synthetic data in model performance. Results show that GAN can +successfully generate synthetic time series from real data distribution, which helps more +accurate peak flow prediction. However, the model without data augmentation works better +for dry weather prediction. Therefore, an ensemble model is suggested to combine the +advantages of both models. +Keywords +Machine Learning, Urban Water Infrastructures, Generative Adversarial Networks, Time Series Prediction, +synthetic time series generation, Combined Sewer Flow Prediction +1 +INTRODUCTION +Nowadays, many industry sectors such as health care, automation, financial markets, aerospace, +water resources management, and weather forecasts deal with time-series data in their +operations and development. Improving the data availability can increase the efficiency of existing +infrastructures and foster research for environmental sustainability. Data analysis and mining +would facilitate a shift from pure infrastructure development to smart operation and management +of our highly interconnected systems with environmental challenges. In recent years, we have +witnessed numerous breakthroughs in machine learning techniques in various domains, such as +computer vision, language processing, reinforcement learning, and many more [1]. +However, still, some fundamental shortcomings hinder progress in environmental management. +They include (1) lack of freely available data (e.g., due to data privacy or high expenses of data + +WDSA CCWI2022BY +NC +SAA Bayesian Generative Adversarial Network (GAN) to Generate Synthetic Time-Series Data, Application in Combined Sewer Flow +Prediction + +2022, Universitat Politècnica de València +2nd WDSA/CCWI Joint Conference + + +gathering) for an extended period as well as lack of rare or extreme events in the training data, +(2) lack of robust methods for anomaly detection, particularly for drift detection, (3) absence of +probabilistic time series forecasting data-driven methods to consider different sources of +uncertainty for optimal and robust operation of critical urban water infrastructures, (4) lack of +benchmark cases and (5) various sources of uncertainty affecting the data and the resulting +models. +Generative algorithms are powerful approaches in data science that can help us overcome the +challenges mentioned above in various domains of water and environmental management. GANs +are a deep learning architecture for training powerful generator models. The main goal of GANs +is to learn from a set of training data and generate new data with the same characteristics as the +training data. Initially, they were applied to domains where their results are intuitively assessable, +e.g., images. However, GANs have been successfully used to generate time series sequences in the +health care, finance, and energy industry and outperform state-of-the-art benchmarks. +Nevertheless, GANs' potential in Urban Water Management (UWM) problems are not yet +discovered to our knowledge. +In this study, as a proof of concept, we test one primary application of GANs, i.e., data +augmentation to urban drainage systems. We use GANs to generate synthetic time series to +balance our data set and improve the accuracy of a data-driven combined sewer flow prediction +model. As relevant events are relatively rare in the historical data, pure data-driven rainfall-runoff +models often underestimate the runoff when predicting these events. The optimal operation of +the sewer system during these events, which result in the most critical states for the urban area +and environment, depends highly on accurate flow predictions. We used GANs to generate +synthetic time series from approximately the same statistical distribution of our data set to +overcome these challenges. The generator model enables us to balance our training data with +extreme synthetic events. To evaluate the performance of the proposed approach, we train a +specific deep neural network model with and without synthetic data and test their performance +using a similar test data set. The remainder of this manuscript is structured as follows: +2 +MATERIALS AND METHODS +2.1 +Case Study +In this study, the sewer system of a small town in Baden-Württemberg state in Germany is +considered to evaluate the performance of the proposed model. Precipitation (mm), temperature +(°C), and inflow to the storage tanks are the data set used for the model development. All data are +measured from the beginning of June 2017 to the end of January 2018 at a 5-min time resolution +[2]. Figure 1 summarizes our data set. It also depicts an example of our measured time series. The +aim is to build a black-box simulator to predict combined sewer flow in the system using historical +and synthetic data. The model then can be employed for optimal operation, e.g., to minimize the +volume and duration of combined sewer overflows (CSOs) of the system using RTC. + +BY +NC +SAEbrahim Bakhshipour et al. (2022) + +2022, Universitat Politècnica de València +2nd WDSA/CCWI Joint Conference + + + +Figure 1. Case study + +2.2 +Problem Description +The release of untreated sewerage into receiving water bodies during rain events can be reduced +by dynamically controlling sewer flow and retention volume with sensor networks and automated +valves [1]. MPC is an advanced RTC technique in which the optimization is based not only on the +knowledge of the system's current state but also on its forecast state. Thus, MPC allows us to +improve the monitoring process and optimally utilize the storage capacities of rainwater +reservoirs, detention ponds, and in-sewer storage volumes by considering anticipated rainfall, +thus, e.g., reducing CSOs [1]. As relevant events are relatively rare in the historical data, pure data- +driven rainfall-runoff models often underestimate the runoff when predicting these events. The +optimal operation of the sewer system during extreme events, which result in the most critical +states for the urban area and environment, depends highly on accurate flow predictions. +2.3 +Generative Adversarial Networks (GANs) +Generative models are a class of algorithms that aim to generate realistic artificial data. These +models approximate the probability distribution of a given data set as closely as possible. Then, +we can fabricate new data samples from the approximated distribution. To put it in more concrete +terms, assume data set 𝒟 , which is consists of N i.i.d samples (𝑥 ) from a probability distribution +i.e., 𝒟  =  {𝑥1,   …  ,  𝑥𝑛}. We denote these samples as real data and their probability distribution as +𝑃𝑟𝑒𝑎𝑙. The goal of a generative model is to accurately approximate 𝑃𝑟𝑒𝑎𝑙 given samples from this +distribution i.e., real data. Once we have a good approximation of data distribution, we can sample +from this distribution and generate artificial data that follow the real data distribution. +The GAN [3] approach to achieving this goal is to define a mapping function 𝑓 that transforms +samples from a latent space (𝑃𝑧) to the samples in the data space (𝑃𝑟𝑒𝑎𝑙). In other words, our goal +is to define 𝑓 as: +𝑓(𝑧)  =  𝑥, +where 𝑧 ∼ 𝑃𝑙𝑎𝑡𝑒𝑛𝑡 and 𝑥 ∼ 𝑃𝑟𝑒𝑎𝑙 . Conventionally, GAN utilizes a Gaussian distribution as the latent +space. This latent space is also referred to as Noise space in the GAN domain. GAN employs a + +BY +NC +SAYear +Month +Precipitation(Average of +Min of +Max of +Average of +Max of +Average +Max of V(m/s) +mm) +T(coC) +T(ooC) +T(ooC) +Q(l/s) +Q(l/s) +of V(m/s) +2017June +1.70 +19.87 +18.20 +21.00 +10.02 +78.80 +0.31 +0.78 +K3500 +2017July +22.90 +20.36 +15.50 +23.60 +14.98 +890.00 +0.32 +1.37 +2017 August +9.20 +20.40 +16.80 +23.20 +8.95 +617.00 +EEO +1.09 +Gondelsheim +2017 +September +4.20 +19.03 +0.00 +21.40 +18.46 +855.00 +0.32 +1.39 +2017October +9.30 +16.46 +11.90 +18.50 +9.51 +781.00 +1.05 +MARTINSHOF +Gondelshei +2017 November +11.50 +12.19 +6.40 +16.80 +15.04 +295.00 +0.34 +0.91 +2017 +December +17.10 +10.19 +5.40 +13.30 +11.28 +403.00 +0.38 +1.00 +2018January +8.00 +10.38 +6.90 +12.40 +17.08 +565.00 +0.35 +1.05 +Total +93.90 +15.78 +0.00 +23.60 +12.92 +890.00 +0.34 +1.39 +Precipitation(mm) +Q(/s) +1.0 +400 +Precipitation (mm) +300 +0.5 +200 +100 +0.0 +0 +Jul25,12AM +Jul 25,12PM +Jul 26,12AM +Jul26,12PM +8 +TimeA Bayesian Generative Adversarial Network (GAN) to Generate Synthetic Time-Series Data, Application in Combined Sewer Flow +Prediction + +2022, Universitat Politècnica de València +2nd WDSA/CCWI Joint Conference + + + +Figure 2. The abstract representation of GAN architecture +neural network called Generator (𝐺) to approximate 𝑓. To train 𝐺 , GAN uses another neural +network called Discriminator (𝐷 ). The Discriminator is a classifier trained to differentiate +between data from the data set (real data) and generated from the generator (fake data). By +learning to discriminate between real and fake data, the Discriminator can provide generator +feedback regarding how realistic the fake data is. Figure 2 illustrates GAN's structure. First, we +sample vector z from latent space 𝑃𝑧. Then, generator takes the vector z and maps it to a data +sample. Finally, the Discriminator assesses the authenticity of generated with having access to +both fake data and generated. +During the training of the GAN, the Generator and Discriminator are trained interchangeably in +an adversarial fashion. We first train Discriminator to classify real and fake data as accurately as +possible in one training step. Then, we train the Generator to fabricate the data sample to be +identified as real by the Discriminator. In other words, the Generator tries to fool the +Discriminator by generating realistic data points while the Discriminator tries not to be fooled by +learning the classification between real and fake data. This two-player minimax game is set in +motion by optimizing the following value function: +min +𝐺 max +𝐷 +𝑉(𝐷, 𝐺) = 𝔼𝑥∼𝑃𝑟𝑒𝑎𝑙[log(𝐷(𝑥))] + 𝔼𝑧∼𝑃𝑧 [log (1 − 𝐷(𝐺(𝑧)))]. +If both models have enough capacity, the Generator will learn the probability distribution data +and 𝐷(𝑥) = +1 +2 for all x. +The original GAN proposal is quite challenging to train since the divergences which GANs typically +minimize are potentially not continuous with respect to the Generator's parameters [4]. +Therefore, various methods have been suggested to improve GAN's training stability. In this work, +we adopt the Wasserstein GAN gradient penalty (WGAN-gp) to improve the training process. In +WGAN, the training process minimizes the Wasserstein distance between a real distribution and +fake distribution, i.e., 𝑊(𝑃𝑟𝑒𝑎𝑙 ,  𝑃𝑓𝑎𝑘𝑒) which continues under mild assumptions. Using +Kantorovich-Rubinstein duality [5], the value function of WGAN is defined as: +min +𝐺 max +𝐷 ∈ℒ =  𝔼𝑥∼𝑃𝑟𝑒𝑎𝑙[𝐷(𝑥)]  −  𝔼𝑥∼𝑃𝑓𝑎𝑘𝑒[𝐷(𝑥)], + + + + + + + + + + + +BY +NC +SAEbrahim Bakhshipour et al. (2022) + +2022, Universitat Politècnica de València +2nd WDSA/CCWI Joint Conference + + +where, ℒ is the set of 1-Lipschitz functions and 𝑃𝑓𝑎𝑘𝑒 is the distribution learned by the Generator +implicitly. In this case, the discriminator network is replaced with the critic network. The critic +aims to assess the authenticity of its input and assigns a numerical score based on the similarity +of the input to real data. The WGAN-gp [6] imposes a penalty on gradient norm to enforce the +Lipschitz constraint. Hence, the final objective function is: +𝐿  =  𝐸𝑥∼𝑃𝑓𝑎𝑘𝑒[𝐷(𝑥)]  −  𝐸𝑥∼𝑃𝑟𝑒𝑎𝑙[𝐷(𝑥)] +  𝜆 𝔼 𝑥̂ ∼𝑃𝑥̂ [(|∇𝑥̂ 𝐷(𝑥̂)|{2}  − 1) +2] +where 𝜆 is the penalty coefficient and 𝑃𝑥̂ is implicitly defined by sampling uniformly on lines +between patis of points sampled from 𝑃𝑟𝑒𝑎𝑙 and 𝑃𝑓𝑎𝑘𝑒 . +2.4 +GAN Architecture +Figure 3 and 4 illustrate the Generator and Discriminator structures, respectively. The Generator +receives the start token and the noise vector from latent space. The start token is the mean value +of each data channel and serves as a common starting point for our generation. Note that the start +token is not part of the final generation. The Generator uses the start token as input of a GRU layer +and employs the noise vector as an initial hidden state of the GRU layer. Then, the output of GRU +passes through a fully connected layer to produce the first step of our fabricated time series. Next, +we feed the generated time-step back to the generator to fabricate the next time step. This auto- +regressive process continues until we generate the desired number of time-step (24 time steps in +this scenario). The Discriminator receives a time frame from the generator or dataset and passes +it through a GRU layer. Then, the output of the GRU layer is fed to a fully connected layer to obtain +the final output of Discriminator. +Figure 3. The architecture of critic + +Figure 4. The architecture of generator + + + + + + + + + + + + + + + + + + + + + +BY +NC +SAA Bayesian Generative Adversarial Network (GAN) to Generate Synthetic Time-Series Data, Application in Combined Sewer Flow +Prediction + +2022, Universitat Politècnica de València +2nd WDSA/CCWI Joint Conference + + +3 +RESULTS AND DISCUSSION +3.1 +Pre-processing pipeline +In this paper, we aim to generate artificial data to enhance the size of the dataset at hand, +especially for rare situations where data sample scarcity makes it difficult for any model to learn +the data pattern. Figure 5 illustrates our data preprocessing pipeline. Since the flow channel had +a skewed distribution toward zero value (Figure ), first, we applied log transform on this channel +to obtain a less skewed distribution. Then, we standardized data distribution by a linear +transformation to have mean=0 and standard deviation = 1. The next step of preprocessing the +data turned into a series of time-frames using the rolling window technique with windows size = +24. +Figure 5: The preprocessing pipeline +The rain channel data consists of long periods of dry days (low variation section) and a few short +periods of rainy days (high variations). Our goal is to generate more rare cases (rainy days) to +augment our data set. Therefore, we discard those data frames which did not have any variation +in their time frame. + a) Original data distribution b) Preprocessed data distribution +Figure 6: The data distribution before and after preprocessing + + + + + + + + + + + +BY +NC +SA100 +2.0 +80 +1.5 +60 +1.0 +40 +0.5 +20 +0.0 +0 +-1.0 +0.5 +0.0 +0.5 +1.0 +0.0 +0.2 +0.4 +0.6 +0.8 +1.0 +Preprocessed Rain +Rain (mm) +0.5 +0.08 +0.4 +0.06 +0.3 +0.04 +0.2 +0.1 +0.02 +0.0 +-4 +-2 +0 +4 +6 +0.00 +0 +200 +400 +600 +800 +Preprocessedflow +Flow (I/s)Ebrahim Bakhshipour et al. (2022) + +2022, Universitat Politècnica de València +2nd WDSA/CCWI Joint Conference + + +3.2 +Experiment Set-up +In order to train a GAN successfully, we need to select the Discriminator and the Generator +hyperparameters carefully. If one of the networks improves substantially faster than the other +network during training, it is likely that training stops before reaching equilibrium. Hence, we +perform a hyperparameter tuning for the Generator and the Discriminator. Table x presents the +list of hyperparameters we tuned alongside the search space for each hyperparameter and the +final value we select for the corresponding hyperparameter. +During training, the value function of GAN informs us about the performance of the Generator +against the current Discriminator for a given batch. It does not provide any information regarding +the performance of the Generator in general. Hence, we need a secondary assessment method to +determine the best-performing model during the hyperparameter tuning process. The task of +assessing a generative model in the time-series domain is a problem, and there is not any suitable +Table 1: This table presents the list of GAN's hyperparameters alongside the search of space of each +hyperparameter and the best hyperparameter we found during hyperparameter tuning +Hyperparameter +Search space +Best hyperparameter +GRU Layers in G +[1,4] +3 +GRU layers in D +[1,4] +3 +GRU hidden size in G +[32, 512] +450 +GRU hidden size in D +[32, 512] +120 + + + +measurement method for this task currently. For this work, we employed Jensen-Shannon +Divergence (JSD) between the batch of real points from the dataset and the batch of fake points +from the Generator. +𝐽𝑆𝐷(𝑃𝑟𝑒𝑎𝑙||𝑃𝑓𝑎𝑘𝑒) = +1 +2 𝐾𝐿𝐷(𝑃𝑟𝑒𝑎𝑙||𝑀) + +1 +2 𝐾𝐿𝐷(𝑃𝑓𝑎𝑘𝑒||𝑀), +where 𝑀 = +1 +2 (𝑃𝑟𝑒𝑎𝑙 + 𝑃𝑓𝑎𝑘𝑒) and KLD is Kullback–Leibler divergence: +𝐾𝐿𝐷(𝑃||𝑄) = ∑ 𝑃(𝑥) log (𝑃(𝑥) +𝑄(𝑥)) , +𝑥∈𝜒 + +where 𝜒 is the probability space. JSD does not consider the auto-correlation between the +consecutive point in time series or the channels' correlation. However, it provides us with an easy +to compute assessment method that can weakly measure the performance of GAN during the +training and allows us to prune poor-performing configurations in the early stages. Then, we can +select the best model based on the improvement of downstream tasks (in this case, forecasting) +from the set of good-performing candidates. + For hyperparameter tuning, we utilized Bayesian Optimization Hyper Band Algorithm (BOHB) +[7]. For implementing the networks, we used Pytorch [8] and for performing hyperparameter +tuning, we employed RayTune package [9]. All experiments were executed on two Nvidia RTX +1080Ti graphic cards. + + + +BY +NC +SAA Bayesian Generative Adversarial Network (GAN) to Generate Synthetic Time-Series Data, Application in Combined Sewer Flow +Prediction + +2022, Universitat Politècnica de València +2nd WDSA/CCWI Joint Conference + + +3.3 +Data Augmentation with GAN +The best model that is obtained during hyperparameter tuning has JSD equal to 0.33. Figure 7 +shows the generated time series. + + +Figure 7: Synthetic time series represented in different resolutions + +3.4 +Data-Driven Forecasting Model +For training the data-driven forecasting model, we transformed the time series prediction +problem into a supervised learning problem. We split the rainfall time series into 24-time steps +(120 minutes) windows. The aim is to predict flow using these windows, as depicted in figure 8. + + +Figure 8: Splitting rainfall time series into 24-time steps windows for supervised learning +We trained two different models to solve this problem, one with synthetic data and one without. +8000 windows generated from the synthetic data set are used to balance the training data for the +first model. We also balance the second model using the oversampling method for better +comparison. The train data set for both models consist of 38000 windows from the real dataset. +The test data set has 13000 windows only from the real data set. We built two sequential models +in TensorFlow with some LSTM layers connecting to some Dense layers. ADAM method is used as +an optimizer and means average error (MAE) as the cost function. A simple grid search is used to +tune the hyperparameters, including the number of LSTM and Dense layers and their neurons and +batch size. The results show that the model without synthetic data performs slightly better than +the model with synthetic data. The MAE for the model without synthetic data is 5.01, while this + +BY +NC +SARt-120 +Rt-115 +Qt ++...... +Rt●Rain(mm) +Flow (l/s) +1.0 +2.000 Q +1,500 +Rain (mm) +(S/I) MO +0.5 +1,000 +500 +00.0 +OK +5K +10K +15K +20K +Time (5 min intervals) +●Rain (mm) +Flow (l/s) +1.0 +400 +300 +Rain (mm) +Flow (I/s) +0.5 +200 +100 +00.0 +21000 +21050 +21100 +21150 +21200 +21250 +21300 +21350 +8 +Time (5 min intervalsEbrahim Bakhshipour et al. (2022) + +2022, Universitat Politècnica de València +2nd WDSA/CCWI Joint Conference + + +value is 5.40 for the model with synthetic data. However, a closer look at the results reveals that +the model with synthetic data has higher accuracy in predicting peak values which are the main +concerns of this study. Figure 9 presents the results of both models for the test dataset. As it can +be seen, the model with synthetic data predicts the peak values with higher accuracy for all +extreme events. Still, the other model has better accuracy for dry weather conditions. + +(a) +(b) +Figure 9: comparing flow predictions with observations for models with and without synthetic data + +BY +NC +SAObservation(/s)Predicted (/s)Predicted usingdataaugmentation(/s) +300 +200 +100 +100 +200 +300 +400 +500 +600 +Time (5 min intervals) +600 +400 +200 +1300 +1400 +1500 +1600 +1700 +1800 +).: +Time (5 min intervals)Observation (/s)Predicted (/s)Predicted withSyntheticData (//s) +400 +300 +200 +100 +0 +2500 +2550 +2600 +2650 +Time (5 min intervals) +Q 600 +400 +200 +0 +2160 +2180 +2200 +2220 +2240 +O +Time (5 min intervals)A Bayesian Generative Adversarial Network (GAN) to Generate Synthetic Time-Series Data, Application in Combined Sewer Flow +Prediction + +2022, Universitat Politècnica de València +2nd WDSA/CCWI Joint Conference + + +4 +CONCLUSION +As moderate or extreme rain events are relatively rare in the historical data, pure data-driven +rainfall-runoff models often underestimate the runoff when predicting these events. The optimal +operation of the sewer system during extreme events, which result in the most critical states for +the urban area and environment, depends highly on accurate flow predictions. To overcome these +challenges, we used Generative Adversarial Networks (GANs). GANs are a class of methods +capable of learning data distribution to generate artificial data. We developed a GAN model to +generate synthetic time series to balance our limited and imbalanced recorded time series data to +improve the accuracy of a data-driven model for combined sewer flow prediction using historical +rainfall and measured flow data. +Results show that balancing the training dataset using the synthetic data generated by the +developed GAN improves the accuracy of the data-driven model in peak flow prediction. However, +this data augmentation method reduces the model performance in dry weather conditions. Some +potential research themes to complement, expand, and build upon the presented study are given +in the following. +• +Clustering time series into dry and wet weather series and using different data-driven +models for each series +• +Using more complicated models like physic-informed ML +• +Ensemble learning +• +In the future, GANs can be applied for probabilistic anomaly detection and missing data +imputation in urban water management [10] +• +GANs can be used also for Probabilistic rainfall-runoff modeling for model predictive +combines sewer overflow control [11] + + + + + +BY +NC +SAEbrahim Bakhshipour et al. (2022) + +2022, Universitat Politècnica de València +2nd WDSA/CCWI Joint Conference + + +REFERENCES +[1] S. Eggimann et al., “The Potential of Knowing More: A Review of Data-Driven Urban Water +Management,” Environmental science & technology, vol. 51, no. 5, pp. 2538–2553, 2017, doi: +10.1021/acs.est.6b04267. +[2] Z. Ayazpour, A. E. Bakhshipour, and U. Dittmer, “Combined Sewer Flow Prediction Using +Hybrid Wavelet Artificial Neural Network Model,” in Green Energy and Technology, New +trends in urban drainage modelling, G. Mannina, Ed., New York NY: Springer Berlin +Heidelberg, 2018, pp. 693–698. +[3] I. Goodfellow et al., “Generative adversarial nets,” Advances in neural information processing +systems, vol. 27, 2014. +[4] M. Arjovsky, S. Chintala, and L. Bottou, “Wasserstein generative adversarial networks,” in +International conference on machine learning, 2017, pp. 214–223. +[5] C. Villani, Optimal transport: old and new: Springer, 2009. +[6] I. Gulrajani, F. Ahmed, M. Arjovsky, V. Dumoulin, and A. C. Courville, “Improved training of +wasserstein gans,” Advances in neural information processing systems, vol. 30, 2017. +[7] A. Klein, S. Falkner, S. Bartels, P. Hennig, and F. Hutter, “Fast bayesian optimization of +machine learning hyperparameters on large datasets,” in Artificial intelligence and statistics, +2017, pp. 528–536. +[8] A. Paszke et al., “Pytorch: An imperative style, high-performance deep learning library,” +Advances in neural information processing systems, vol. 32, 2019. +[9] R. Liaw, E. Liang, R. Nishihara, P. Moritz, J. E. Gonzalez, and I. Stoica, “Tune: A Research +Platform for Distributed Model Selection and Training,” arXiv preprint arXiv:1807.05118, +2018. +[10] A. Koochali, P. Schichtel, A. Dengel, and S. Ahmed, “Probabilistic Forecasting of Sensory Data +With Generative Adversarial Networks – ForGAN,” IEEE Access, vol. 7, pp. 63868–63880, +2019, doi: 10.1109/ACCESS.2019.2915544. +[11] A. Koochali, A. Dengel, and S. Ahmed, “If You Like It, GAN It—Probabilistic Multivariate +Times Series Forecast with GAN,” in The 7th International conference on Time Series and +Forecasting, p. 40. + + +BY +NC +SA \ No newline at end of file diff --git a/ltFST4oBgHgl3EQfJjg5/content/tmp_files/load_file.txt b/ltFST4oBgHgl3EQfJjg5/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..d574eb6c9044d20765e1da8b41e0e520f927eddc --- /dev/null +++ b/ltFST4oBgHgl3EQfJjg5/content/tmp_files/load_file.txt @@ -0,0 +1,396 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf,len=395 +page_content='2nd International Joint Conference on Water Distribution Systems Analysis & Computing and Control in the Water Industry Valencia (Spain), 18-22 July 2022 doi: https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='org/10.' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Dengel1,3 1 TU Kaiserslautern, Kaiserslautern, Germany 2 Ingenieurgesellschaft Auto und Verkehr(IAV) GmbH, Berlin,Germany 3 German Research Center for Artificial Intelligence (DFKI), Kaiserslautern, Germany 4 Shahid Chamran University of Ahvaz, Ahvaz, Iran 1 0000-0002-6921-2381, amin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='bakhshipour@bauing-uni.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='kl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='de, 2 0000-0001-7370-9369, alireza.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='koochali@iav.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='de, 3 0000-0003-1723-3356, ulrich.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='dittmer@bauing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='uni-kl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='de, 4 0000-0002- 2765-6929, a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='haghighi@scu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='ir, 5 0000-0002-4239-6520, sheraz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='ahmed@dfki.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='de, 6 0000-0002- 6100-8255, andreas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='dengel@dfki.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='de Abstract Despite various breakthroughs of machine learning and data analysis techniques for improving smart operation and management of urban water infrastructures, some key limitations obstruct this progress.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Among these shortcomings, the absence of freely available data due to data privacy or high costs of data gathering and the nonexistence of adequate rare or extreme events in the available data plays a crucial role.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Here, the Generative Adversarial Networks (GANs) can help overcome these challenges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' In machine learning, generative models are a class of methods capable of learning data distribution to generate artificial data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' In this study, we developed a GAN model to generate synthetic time series to balance our limited recorded time series data and improve the accuracy of a data-driven model for combined sewer flow prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' We considered the sewer system of a small town in Germany as the test case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Precipitation and inflow to the storage tanks are used for the Data-Driven model development.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' The aim is to predict the flow using precipitation data and examine the impact of data augmentation using synthetic data in model performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Results show that GAN can successfully generate synthetic time series from real data distribution, which helps more accurate peak flow prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' However, the model without data augmentation works better for dry weather prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Therefore, an ensemble model is suggested to combine the advantages of both models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Keywords Machine Learning, Urban Water Infrastructures, Generative Adversarial Networks, Time Series Prediction, synthetic time series generation, Combined Sewer Flow Prediction 1 INTRODUCTION Nowadays, many industry sectors such as health care, automation, financial markets, aerospace, water resources management, and weather forecasts deal with time-series data in their operations and development.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Improving the data availability can increase the efficiency of existing infrastructures and foster research for environmental sustainability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Data analysis and mining would facilitate a shift from pure infrastructure development to smart operation and management of our highly interconnected systems with environmental challenges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' In recent years, we have witnessed numerous breakthroughs in machine learning techniques in various domains, such as computer vision, language processing, reinforcement learning, and many more [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' However, still, some fundamental shortcomings hinder progress in environmental management.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' They include (1) lack of freely available data (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=',' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' due to data privacy or high expenses of data WDSA CCWI2022BY NC SAA Bayesian Generative Adversarial Network (GAN) to Generate Synthetic Time-Series Data,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Application in Combined Sewer Flow Prediction 2022,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Universitat Politècnica de València 2nd WDSA/CCWI Joint Conference gathering) for an extended period as well as lack of rare or extreme events in the training data,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' (2) lack of robust methods for anomaly detection,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' particularly for drift detection,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' (3) absence of probabilistic time series forecasting data-driven methods to consider different sources of uncertainty for optimal and robust operation of critical urban water infrastructures,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' (4) lack of benchmark cases and (5) various sources of uncertainty affecting the data and the resulting models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Generative algorithms are powerful approaches in data science that can help us overcome the challenges mentioned above in various domains of water and environmental management.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' GANs are a deep learning architecture for training powerful generator models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' The main goal of GANs is to learn from a set of training data and generate new data with the same characteristics as the training data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Initially, they were applied to domains where their results are intuitively assessable, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=', images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' However, GANs have been successfully used to generate time series sequences in the health care, finance, and energy industry and outperform state-of-the-art benchmarks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=" Nevertheless, GANs' potential in Urban Water Management (UWM) problems are not yet discovered to our knowledge." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' In this study, as a proof of concept, we test one primary application of GANs, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=', data augmentation to urban drainage systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' We use GANs to generate synthetic time series to balance our data set and improve the accuracy of a data-driven combined sewer flow prediction model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' As relevant events are relatively rare in the historical data, pure data-driven rainfall-runoff models often underestimate the runoff when predicting these events.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' The optimal operation of the sewer system during these events, which result in the most critical states for the urban area and environment, depends highly on accurate flow predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' We used GANs to generate synthetic time series from approximately the same statistical distribution of our data set to overcome these challenges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' The generator model enables us to balance our training data with extreme synthetic events.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' To evaluate the performance of the proposed approach, we train a specific deep neural network model with and without synthetic data and test their performance using a similar test data set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' The remainder of this manuscript is structured as follows: 2 MATERIALS AND METHODS 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='1 Case Study In this study, the sewer system of a small town in Baden-Württemberg state in Germany is considered to evaluate the performance of the proposed model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Precipitation (mm), temperature (°C), and inflow to the storage tanks are the data set used for the model development.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' All data are measured from the beginning of June 2017 to the end of January 2018 at a 5-min time resolution [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Figure 1 summarizes our data set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' It also depicts an example of our measured time series.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' The aim is to build a black-box simulator to predict combined sewer flow in the system using historical and synthetic data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' The model then can be employed for optimal operation, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=', to minimize the volume and duration of combined sewer overflows (CSOs) of the system using RTC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' BY NC SAEbrahim Bakhshipour et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' (2022) 2022, Universitat Politècnica de València 2nd WDSA/CCWI Joint Conference Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Case study 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='2 Problem Description The release of untreated sewerage into receiving water bodies during rain events can be reduced by dynamically controlling sewer flow and retention volume with sensor networks and automated valves [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=" MPC is an advanced RTC technique in which the optimization is based not only on the knowledge of the system's current state but also on its forecast state." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Thus, MPC allows us to improve the monitoring process and optimally utilize the storage capacities of rainwater reservoirs, detention ponds, and in-sewer storage volumes by considering anticipated rainfall, thus, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=', reducing CSOs [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' As relevant events are relatively rare in the historical data, pure data- driven rainfall-runoff models often underestimate the runoff when predicting these events.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' The optimal operation of the sewer system during extreme events, which result in the most critical states for the urban area and environment, depends highly on accurate flow predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='3 Generative Adversarial Networks (GANs) Generative models are a class of algorithms that aim to generate realistic artificial data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' These models approximate the probability distribution of a given data set as closely as possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Then, we can fabricate new data samples from the approximated distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' To put it in more concrete terms, assume data set 𝒟 , which is consists of N i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='d samples (𝑥 ) from a probability distribution i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=', 𝒟 = {𝑥1, … , 𝑥𝑛}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' We denote these samples as real data and their probability distribution as 𝑃𝑟𝑒𝑎𝑙.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' The goal of a generative model is to accurately approximate 𝑃𝑟𝑒𝑎𝑙 given samples from this distribution i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=', real data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Once we have a good approximation of data distribution, we can sample from this distribution and generate artificial data that follow the real data distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' The GAN [3] approach to achieving this goal is to define a mapping function 𝑓 that transforms samples from a latent space (𝑃𝑧) to the samples in the data space (𝑃𝑟𝑒𝑎𝑙).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' In other words, our goal is to define 𝑓 as: 𝑓(𝑧) = 𝑥, where 𝑧 ∼ 𝑃𝑙𝑎𝑡𝑒𝑛𝑡 and 𝑥 ∼ 𝑃𝑟𝑒𝑎𝑙 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Conventionally, GAN utilizes a Gaussian distribution as the latent space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' This latent space is also referred to as Noise space in the GAN domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' GAN employs a BY NC SAYear Month Precipitation(Average of Min of Max of Average of Max of Average Max of V(m/s) mm) T(coC) T(ooC) T(ooC) Q(l/s) Q(l/s) of V(m/s) 2017June 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='70 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='87 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='20 21.' 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2017October 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='30 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='46 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='90 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='50 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='51 781.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='00 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='05 MARTINSHOF Gondelshei 2017 November 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='50 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='19 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='40 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='80 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='04 295.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} 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+page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='38 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='00 2018January 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='00 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='38 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='90 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='40 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} 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+page_content='60 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='92 890.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='34 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='39 Precipitation(mm) Q(/s) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='0 400 Precipitation (mm) 300 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='5 200 100 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='0 0 Jul25,12AM Jul 25,12PM Jul 26,12AM Jul26,12PM 8 TimeA Bayesian Generative Adversarial Network (GAN) to Generate Synthetic Time-Series Data, Application in Combined Sewer Flow Prediction 2022, Universitat Politècnica de València 2nd WDSA/CCWI Joint Conference Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' The abstract representation of GAN architecture neural network called Generator (𝐺) to approximate 𝑓.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' To train 𝐺 , GAN uses another neural network called Discriminator (𝐷 ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' The Discriminator is a classifier trained to differentiate between data from the data set (real data) and generated from the generator (fake data).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' By learning to discriminate between real and fake data, the Discriminator can provide generator feedback regarding how realistic the fake data is.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=" Figure 2 illustrates GAN's structure." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' First, we sample vector z from latent space 𝑃𝑧.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Then, generator takes the vector z and maps it to a data sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Finally, the Discriminator assesses the authenticity of generated with having access to both fake data and generated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' During the training of the GAN, the Generator and Discriminator are trained interchangeably in an adversarial fashion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' We first train Discriminator to classify real and fake data as accurately as possible in one training step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Then, we train the Generator to fabricate the data sample to be identified as real by the Discriminator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' In other words, the Generator tries to fool the Discriminator by generating realistic data points while the Discriminator tries not to be fooled by learning the classification between real and fake data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' This two-player minimax game is set in motion by optimizing the following value function: min 𝐺 max 𝐷 𝑉(𝐷, 𝐺) = 𝔼𝑥∼𝑃𝑟𝑒𝑎𝑙[log(𝐷(𝑥))] + 𝔼𝑧∼𝑃𝑧 [log (1 − 𝐷(𝐺(𝑧)))].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' If both models have enough capacity, the Generator will learn the probability distribution data and 𝐷(𝑥) = 1 2 for all x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=" The original GAN proposal is quite challenging to train since the divergences which GANs typically minimize are potentially not continuous with respect to the Generator's parameters [4]." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=" Therefore, various methods have been suggested to improve GAN's training stability." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' In this work, we adopt the Wasserstein GAN gradient penalty (WGAN-gp) to improve the training process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' In WGAN, the training process minimizes the Wasserstein distance between a real distribution and fake distribution, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=', 𝑊(𝑃𝑟𝑒𝑎𝑙 , 𝑃𝑓𝑎𝑘𝑒) which continues under mild assumptions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Using Kantorovich-Rubinstein duality [5], the value function of WGAN is defined as: min 𝐺 max 𝐷 ∈ℒ = 𝔼𝑥∼𝑃𝑟𝑒𝑎𝑙[𝐷(𝑥)] − 𝔼𝑥∼𝑃𝑓𝑎𝑘𝑒[𝐷(𝑥)], BY NC SAEbrahim Bakhshipour et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' (2022) 2022, Universitat Politècnica de València 2nd WDSA/CCWI Joint Conference where, ℒ is the set of 1-Lipschitz functions and 𝑃𝑓𝑎𝑘𝑒 is the distribution learned by the Generator implicitly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' In this case, the discriminator network is replaced with the critic network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' The critic aims to assess the authenticity of its input and assigns a numerical score based on the similarity of the input to real data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' The WGAN-gp [6] imposes a penalty on gradient norm to enforce the Lipschitz constraint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Hence, the final objective function is: 𝐿 = 𝐸𝑥∼𝑃𝑓𝑎𝑘𝑒[𝐷(𝑥)] − 𝐸𝑥∼𝑃𝑟𝑒𝑎𝑙[𝐷(𝑥)] + 𝜆 𝔼 𝑥̂ ∼𝑃𝑥̂ [(|∇𝑥̂ 𝐷(𝑥̂)|{2} − 1) 2] where 𝜆 is the penalty coefficient and 𝑃𝑥̂ is implicitly defined by sampling uniformly on lines between patis of points sampled from 𝑃𝑟𝑒𝑎𝑙 and 𝑃𝑓𝑎𝑘𝑒 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='4 GAN Architecture Figure 3 and 4 illustrate the Generator and Discriminator structures, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' The Generator receives the start token and the noise vector from latent space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' The start token is the mean value of each data channel and serves as a common starting point for our generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Note that the start token is not part of the final generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' The Generator uses the start token as input of a GRU layer and employs the noise vector as an initial hidden state of the GRU layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Then, the output of GRU passes through a fully connected layer to produce the first step of our fabricated time series.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Next, we feed the generated time-step back to the generator to fabricate the next time step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' This auto- regressive process continues until we generate the desired number of time-step (24 time steps in this scenario).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' The Discriminator receives a time frame from the generator or dataset and passes it through a GRU layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Then, the output of the GRU layer is fed to a fully connected layer to obtain the final output of Discriminator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' The architecture of critic Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' The architecture of generator BY NC SAA Bayesian Generative Adversarial Network (GAN) to Generate Synthetic Time-Series Data, Application in Combined Sewer Flow Prediction 2022, Universitat Politècnica de València 2nd WDSA/CCWI Joint Conference 3 RESULTS AND DISCUSSION 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='1 Pre-processing pipeline In this paper, we aim to generate artificial data to enhance the size of the dataset at hand, especially for rare situations where data sample scarcity makes it difficult for any model to learn the data pattern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Figure 5 illustrates our data preprocessing pipeline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Since the flow channel had a skewed distribution toward zero value (Figure ), first, we applied log transform on this channel to obtain a less skewed distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Then, we standardized data distribution by a linear transformation to have mean=0 and standard deviation = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' The next step of preprocessing the data turned into a series of time-frames using the rolling window technique with windows size = 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Figure 5: The preprocessing pipeline The rain channel data consists of long periods of dry days (low variation section) and a few short periods of rainy days (high variations).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Our goal is to generate more rare cases (rainy days) to augment our data set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Therefore, we discard those data frames which did not have any variation in their time frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' a) Original data distribution b) Preprocessed data distribution Figure 6: The data distribution before and after preprocessing BY NC SA100 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='0 80 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='5 60 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='0 40 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='5 20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='0 0 -1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='0 Preprocessed Rain Rain (mm) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='08 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='06 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='04 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='02 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='0 -4 -2 0 4 6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='00 0 200 400 600 800 Preprocessedflow Flow (I/s)Ebrahim Bakhshipour et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' (2022) 2022, Universitat Politècnica de València 2nd WDSA/CCWI Joint Conference 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='2 Experiment Set-up In order to train a GAN successfully, we need to select the Discriminator and the Generator hyperparameters carefully.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' If one of the networks improves substantially faster than the other network during training, it is likely that training stops before reaching equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Hence, we perform a hyperparameter tuning for the Generator and the Discriminator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Table x presents the list of hyperparameters we tuned alongside the search space for each hyperparameter and the final value we select for the corresponding hyperparameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' During training, the value function of GAN informs us about the performance of the Generator against the current Discriminator for a given batch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' It does not provide any information regarding the performance of the Generator in general.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Hence, we need a secondary assessment method to determine the best-performing model during the hyperparameter tuning process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' The task of assessing a generative model in the time-series domain is a problem,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=" and there is not any suitable Table 1: This table presents the list of GAN's hyperparameters alongside the search of space of each hyperparameter and the best hyperparameter we found during hyperparameter tuning Hyperparameter Search space Best hyperparameter GRU Layers in G [1," metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='4] 3 GRU layers in D [1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='4] 3 GRU hidden size in G [32,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' 512] 450 GRU hidden size in D [32,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' 512] 120 measurement method for this task currently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' For this work, we employed Jensen-Shannon Divergence (JSD) between the batch of real points from the dataset and the batch of fake points from the Generator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' 𝐽𝑆𝐷(𝑃𝑟𝑒𝑎𝑙||𝑃𝑓𝑎𝑘𝑒) = 1 2 𝐾𝐿𝐷(𝑃𝑟𝑒𝑎𝑙||𝑀) + 1 2 𝐾𝐿𝐷(𝑃𝑓𝑎𝑘𝑒||𝑀), where 𝑀 = 1 2 (𝑃𝑟𝑒𝑎𝑙 + 𝑃𝑓𝑎𝑘𝑒) and KLD is Kullback–Leibler divergence: 𝐾𝐿𝐷(𝑃||𝑄) = ∑ 𝑃(𝑥) log (𝑃(𝑥) 𝑄(𝑥)) , 𝑥∈𝜒 where 𝜒 is the probability space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=" JSD does not consider the auto-correlation between the consecutive point in time series or the channels' correlation." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' However, it provides us with an easy to compute assessment method that can weakly measure the performance of GAN during the training and allows us to prune poor-performing configurations in the early stages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Then, we can select the best model based on the improvement of downstream tasks (in this case, forecasting) from the set of good-performing candidates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' For hyperparameter tuning, we utilized Bayesian Optimization Hyper Band Algorithm (BOHB) [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' For implementing the networks, we used Pytorch [8] and for performing hyperparameter tuning, we employed RayTune package [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' All experiments were executed on two Nvidia RTX 1080Ti graphic cards.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' BY NC SAA Bayesian Generative Adversarial Network (GAN) to Generate Synthetic Time-Series Data, Application in Combined Sewer Flow Prediction 2022, Universitat Politècnica de València 2nd WDSA/CCWI Joint Conference 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='3 Data Augmentation with GAN The best model that is obtained during hyperparameter tuning has JSD equal to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Figure 7 shows the generated time series.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Figure 7: Synthetic time series represented in different resolutions 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='4 Data-Driven Forecasting Model For training the data-driven forecasting model, we transformed the time series prediction problem into a supervised learning problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' We split the rainfall time series into 24-time steps (120 minutes) windows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' The aim is to predict flow using these windows, as depicted in figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Figure 8: Splitting rainfall time series into 24-time steps windows for supervised learning We trained two different models to solve this problem, one with synthetic data and one without.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' 8000 windows generated from the synthetic data set are used to balance the training data for the first model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' We also balance the second model using the oversampling method for better comparison.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' The train data set for both models consist of 38000 windows from the real dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' The test data set has 13000 windows only from the real data set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' We built two sequential models in TensorFlow with some LSTM layers connecting to some Dense layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' ADAM method is used as an optimizer and means average error (MAE) as the cost function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' A simple grid search is used to tune the hyperparameters, including the number of LSTM and Dense layers and their neurons and batch size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' The results show that the model without synthetic data performs slightly better than the model with synthetic data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' The MAE for the model without synthetic data is 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='01, while this BY NC SARt-120 Rt-115 Qt +.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='. Rt●Rain(mm) Flow (l/s) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='000 Q 1,500 Rain (mm) (S/I) MO 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='5 1,000 500 00.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='0 OK 5K 10K 15K 20K Time (5 min intervals) ●Rain (mm) Flow (l/s) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='0 400 300 Rain (mm) Flow (I/s) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='5 200 100 00.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='0 21000 21050 21100 21150 21200 21250 21300 21350 8 Time (5 min intervalsEbrahim Bakhshipour et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' (2022) 2022, Universitat Politècnica de València 2nd WDSA/CCWI Joint Conference value is 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='40 for the model with synthetic data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' However, a closer look at the results reveals that the model with synthetic data has higher accuracy in predicting peak values which are the main concerns of this study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Figure 9 presents the results of both models for the test dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' As it can be seen, the model with synthetic data predicts the peak values with higher accuracy for all extreme events.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Still, the other model has better accuracy for dry weather conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' (a) (b) Figure 9: comparing flow predictions with observations for models with and without synthetic data BY NC SAObservation(/s)Predicted (/s)Predicted usingdataaugmentation(/s) 300 200 100 100 200 300 400 500 600 Time (5 min intervals) 600 400 200 1300 1400 1500 1600 1700 1800 ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' : Time (5 min intervals)Observation (/s)Predicted (/s)Predicted withSyntheticData (//s) 400 300 200 100 0 2500 2550 2600 2650 Time (5 min intervals) Q 600 400 200 0 2160 2180 2200 2220 2240 O Time (5 min intervals)A Bayesian Generative Adversarial Network (GAN) to Generate Synthetic Time-Series Data,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Application in Combined Sewer Flow Prediction 2022,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Universitat Politècnica de València 2nd WDSA/CCWI Joint Conference 4 CONCLUSION As moderate or extreme rain events are relatively rare in the historical data,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' pure data-driven rainfall-runoff models often underestimate the runoff when predicting these events.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' The optimal operation of the sewer system during extreme events, which result in the most critical states for the urban area and environment, depends highly on accurate flow predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' To overcome these challenges, we used Generative Adversarial Networks (GANs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' GANs are a class of methods capable of learning data distribution to generate artificial data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' We developed a GAN model to generate synthetic time series to balance our limited and imbalanced recorded time series data to improve the accuracy of a data-driven model for combined sewer flow prediction using historical rainfall and measured flow data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Results show that balancing the training dataset using the synthetic data generated by the developed GAN improves the accuracy of the data-driven model in peak flow prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' However, this data augmentation method reduces the model performance in dry weather conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Some potential research themes to complement, expand, and build upon the presented study are given in the following.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Clustering time series into dry and wet weather series and using different data-driven models for each series • Using more complicated models like physic-informed ML • Ensemble learning • In the future, GANs can be applied for probabilistic anomaly detection and missing data imputation in urban water management [10] • GANs can be used also for Probabilistic rainfall-runoff modeling for model predictive combines sewer overflow control [11] BY NC SAEbrahim Bakhshipour et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' (2022) 2022, Universitat Politècnica de València 2nd WDSA/CCWI Joint Conference REFERENCES [1] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Eggimann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=', “The Potential of Knowing More: A Review of Data-Driven Urban Water Management,” Environmental science & technology, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' 51, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' 5, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' 2538–2553, 2017, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='1021/acs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='est.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='6b04267.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' [2] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Ayazpour, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Bakhshipour, and U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Dittmer, “Combined Sewer Flow Prediction Using Hybrid Wavelet Artificial Neural Network Model,” in Green Energy and Technology, New trends in urban drainage modelling, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Mannina, Ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=', New York NY: Springer Berlin Heidelberg, 2018, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' 693–698.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' [3] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Goodfellow et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=', “Generative adversarial nets,” Advances in neural information processing systems, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' 27, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' [4] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Arjovsky, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Chintala, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Bottou, “Wasserstein generative adversarial networks,” in International conference on machine learning, 2017, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' 214–223.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' [5] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Villani, Optimal transport: old and new: Springer, 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' [6] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Gulrajani, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Ahmed, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Arjovsky, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Dumoulin, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Courville, “Improved training of wasserstein gans,” Advances in neural information processing systems, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' 30, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' [7] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Klein, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Falkner, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Bartels, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Hennig, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Hutter, “Fast bayesian optimization of machine learning hyperparameters on large datasets,” in Artificial intelligence and statistics, 2017, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' 528–536.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' [8] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Paszke et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=', “Pytorch: An imperative style, high-performance deep learning library,” Advances in neural information processing systems, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' 32, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' [9] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Liaw, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Liang, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Nishihara, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Moritz, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Gonzalez, and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Stoica, “Tune: A Research Platform for Distributed Model Selection and Training,” arXiv preprint arXiv:1807.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='05118, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' [10] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Koochali, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Schichtel, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Dengel, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Ahmed, “Probabilistic Forecasting of Sensory Data With Generative Adversarial Networks – ForGAN,” IEEE Access, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' 7, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' 63868–63880, 2019, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='1109/ACCESS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content='2915544.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' [11] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Koochali, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Dengel, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' Ahmed, “If You Like It, GAN It—Probabilistic Multivariate Times Series Forecast with GAN,” in The 7th International conference on Time Series and Forecasting, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' 40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} +page_content=' BY NC SA' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltFST4oBgHgl3EQfJjg5/content/2301.13733v1.pdf'} diff --git 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100644 index 0000000000000000000000000000000000000000..27a8bcb6639c25f22b48ea1e5e6d41f25e22b994 --- /dev/null +++ b/udE4T4oBgHgl3EQfWgxs/content/tmp_files/2301.05033v1.pdf.txt @@ -0,0 +1,1038 @@ +Sim2real Transfer Learning for Point Cloud Segmentation: An Industrial +Application Case on Autonomous Disassembly +Chengzhi Wu1, Xuelei Bi1, Julius Pfrommer2,3, +Alexander Cebulla1, Simon Mangold4, and J¨urgen Beyerer2 +1Institute for Anthropomatics and Robotics, Karlsruhe Institute of Technology, Germany +2Fraunhofer Institute of Optronics, System Technologies and Image Exploitation IOSB, Germany +3Fraunhofer Center for Machine Learning, Germany +4wbk Institute of Production Science, Karlsruhe Institute of Technology, Germany +chengzhi.wu@kit.edu +xuelei.bi@student.kit.edu +julius.pfrommer@iosb.fraunhofer.de +alexander.cebulla@kit.edu +simon.mangold@kit.edu +juergen.beyerer@iosb.fraunhofer.de +Abstract +On robotics computer vision tasks, generating and an- +notating large amounts of data from real-world for the use +of deep learning-based approaches is often difficult or even +impossible. A common strategy for solving this problem is +to apply simulation-to-reality (sim2real) approaches with +the help of simulated scenes. While the majority of cur- +rent robotics vision sim2real work focuses on image data, +we present an industrial application case that uses sim2real +transfer learning for point cloud data. We provide insights +on how to generate and process synthetic point cloud data +in order to achieve better performance when the learned +model is transferred to real-world data. The issue of imbal- +anced learning is investigated using multiple strategies. A +novel patch-based attention network is proposed addition- +ally to tackle this problem. +1. Introduction +Due to the rapid development of neural network algo- +rithms, an increasing number of industrial companies and +factories have started using deep learning (DL) methods for +a variety of manufacturing and remanufacturing tasks in the +past decade. In general, neural networks require a substan- +tial amount of data in order to be trained, whereas for practi- +cal industrial applications, allocating and annotating a large +amount of data is difficult or even impossible, especially +when robots are involved. In the field of robotics, when +the robot or manipulator directly interacts and samples with +the real-world environment, there will be problems of low +sampling efficiency and safety problems. +One possible solution to this problem is to apply +simulation-to-reality (sim2real) method, which learns with +simulated data and transfers the learned knowledge to real- +world application. +This is a common strategy used in +robotics for learning robot movement controls [2, 33] and +robotic-related vision tasks [42, 24, 29]. +In those com- +puter vision tasks, simulated scenes are usually rendered +into RGB images with possible auxiliary depth, thermal, +or even flow images. Then, DL-based neural networks are +pre-trained with the synthetic data and subsequently trans- +ferred to real-world use cases via domain adaption. How- +ever, most current sim2real work focuses on image data. +Few researches apply sim2real methods on point cloud data. +In this paper, we show a full pipeline of how to perform +sim2real transfer learning on point clouds for a robotics use +case as a part of a practical remanufactoring application. +We consider the automated disassembly of different vari- +ants of actuators which are commonly used in vehicle man- +ufacturing, e.g., as seat adjuster motors, window lift motors +or rear door motors. Several example motors are shown in +Figure 1(a). The ultimate goal of this project is to use robots +to perform automatic disassembly of motors, not only for +the known motor types, but also for future variants with +unseen specifications. In this case, generating a synthetic +dataset with motor variants in simulated scenes for sim2real +transfer learning [55] is a good solution. By learning the in- +ternal structure on part level, (e.g. gear container, pole pot, +electrical connection), processes on unseen variants which +have similarities to the known population of actuators be- +come feasible. This paper focuses on the first step of getting +precise screw positions and orientations on motor covers for +robots as one of the most important tasks for disassembly. +arXiv:2301.05033v1 [cs.CV] 12 Jan 2023 + +(a) +(b) +(c) +Figure 1: Real-world motors and generated demo motors. +(b) Upper row: no textures added; bottom row: textures +added and rendered. (c) An explosion figure of a generated +motor. The original assembled motor model is also shown +at the right most. +Generating a synthetic point cloud dataset for sim2real +transfer learning has following advantages in our project: (i) +a large synthetic dataset can be easily created, segmentation +ground truth labels are given in the simulation, no manual +annotation needed; (ii) motor variants with unseen specifi- +cations may be generated, which will strengthen the gen- +eralization ability of the trained network model; (iii) point +cloud data contain richer 3D information for the learning. +Using point cloud data avoids some problems that may oc- +cur when using image data, e.g., colors of the simulated im- +ages are far from realistic since it is hard to get the perfect +textures for scene objects or to render the scene with perfect +lighting conditions. When using the point cloud dataset, we +use point coordinates information other than colors. +The remainder of this paper is structured as follows: +Section 2 summarizes the state-of-the-art of 3D synthetic +dataset creation, sim2real transfer learning, and point cloud +segmentation. Section 3 shows a general pipeline of cre- +ating a synthetic dataset with simulated scenes. Section 4 +describes the whole sim2real learning framework and gives +experimental results. Section 5 additionally explores sev- +eral strategies for imbalanced learning, including a novel +patch-based attention network module. Finally, Section 6 +summarizes presented results and discusses future work. +2. Related Work +3D synthetic dataset. Generating synthetic datasets as +training data for machine learning purposes has already +been widely discussed and used as a learning approach for +various computer vision applications. In the past decade, +many synthetic datasets of 3D models have been created, +including the Princeton Shape Benchmark [38], ModelNet +[50], ShapeNet [6], PartNet [28], etc. They collect large +amounts of 3D models of different categories. +A large +dataset of 3D-printing models is provided in Thingi10K +[54], while a more recent ABC dataset [19] collects over +1 million CAD models including many mechanical compo- +nents. Regarding 3D scenes, [45], [36] and [18] generate +synthetic datasets for the segmentation and detection of ob- +jects in virtual urban scenes. [22] generates images from +virtual garden scenes, while [43] creates a dataset for pose +estimation. There are also works that generate synthetic +point clouds. SynthCity [12] generates point clouds of ur- +ban scenes using Blender, while [30] also uses Blender but +for the generation of point clouds of historical objects. +Sim2real transfer learning. By allowing faster, more scal- +able, and lower-cost data collection than is possible in real- +world, sim2real approaches show great impact on machine +learning and have been applied in many fields including +robotics and classic machine vision tasks. [42], [24] and +[44] train neural network models on synthetic RGB images +with domain randomization or domain adaption then trans- +fer it to real-world, while Pachevish et al. [29] work with +synthetic depth images. Also working with synthetic im- +age data, Du et al. [9] propose a method for automatically +tuning simulator system parameters to match the real world. +With the help of deep reinforcement learning [27], robotics +policies are directly used as training data for sim2real learn- +ing in some works [25, 2]. A more detailed survey is given +in [53]. Apart from robotics tasks, sim2real methods have +also been widely used in other fields including autonomous +driving [51, 34], medical diagnosis [1], or even the control +of atmospheric pressure plasma jets [48]. +Point cloud segmentation. Before the appearance of Point- +Net [31], deep learning-based methods for point cloud seg- +mentation are usually multi-view based [20, 5, 3, 40] or +volumetric-based [26, 17, 21]. PointNet [31] is the first DL- +based method that learns directly on points. It uses point- +wise multi-layer perceptrons to extract global features. Its +subsequent work of PointNet++ [32] further considers lo- +cal information. PointConv[49] and KPConv [41] propose +point-wise convolution operators with which points are con- +voluted with neighbor points. Similar ideas are proposed in +[46, 16]. Simonovsky et al. [39] takes each point as a graph +vertex and applies graph convolution. +In DGCNN [47], +EdgeConv blocks update the neighbor information dynami- +cally. RandLA-Net [15] learns attention scores for points as +a soft mask to replace the original pooling layer. GAPNet +[7] and Liang et al. [23] propose graph-attention operations +with neighbor points to learn coefficients. More recently, +transformer-based methods are starting to trend. PCT [14] + +(a) +(b) +(c) +Figure 2: Synthetic dataset generation: (a) simulated scene +built in Blender; (b) synthetic image data generated with +BlenderProc; (c) synthetic point cloud data generated with +BlenSor. +pioneers on this direction by replacing the encoder layers +in the original PointNet [31] framework with self-attention +layers, while PT [52] is based on U-Net [35]. SortNet is +proposed in [10] to learn sub-point clouds, with which at- +tention operations are applied on their latent features and +the global feature to perform local-global attention. +3. Synthetic Dataset Generation +3.1. Synthetic Mesh Model Generation +To easily generate motor mesh models of a variety of +specifications, we create a Blender addon based on the mo- +tor types we have. As an open source software, Blender +[4] is a proven tool that performs well in modeling shapes +and creating highly customizable addons. Our addon is able +to generate motor mesh models with various specifications +and save them in desired file formats. Each component of a +generated motor can also be saved separately. +The generated models contain the following compo- +nents: (i) Pole Pot; (ii) Electric Connection; (iii) Gear Con- +tainer; (iv) Cover and (v) Screws. Those are the five main +categories we need perform segmentation on. Additionally, +following inner components have also been generated : (vi) +Magnets; (vii) Armature; (viii) Lower Gear and (ix) Upper +Gear as presented in 1(c). However, since we only focus +on the first step of unscrewing process in this paper, inner +parts will not be investigated. To generate motors with vari- +ous specifications, we provide lots of parameter options that +control the type, size, position and rotation of different parts +of motor, e.g. screw position, gear size, or pole pot length. +Figure 1(b) shows ten generated demo motors with different +parameters and an exploded view of a demo motor. All the +individual components mentioned above are modeled sepa- +rately as illustrated. +3.2. Synthetic Point Cloud Generation +The generated mesh models are further used to create +synthetic image and point cloud datasets. +A simulated +scene is built in Blender for it. Apart from the lights and +cameras, the Blender scene also contains the model of the +real-world clamping system and a background panel. The +camera rotates randomly on top of the scene within a cer- +tain range yet always towards the motor. To create image +dataset, apart from the scene images rendered by Blender +directly, BlenderProc [8] can be used to generate corre- +sponding depth images, normal images, and segmentation +ground truth images as shown in Figure 2(b). Or in our +case, BlenSor [13] is used to simulate the sensors to create +point cloud dataset. Figure 2(c) gives a demo of generated +point cloud colored in the material color or its segmentation +ground truth. +3.3. Data Pre-processing and Augmentation +The generated point clouds are of relatively large size. +Each point cloud contains around 1.2 million points. How- +ever, neural networks have a limitation of point number per +batch, common choices are 1024/2048/4096 points. Direct +downsampling makes the sub-point clouds contain too less +points for tail categories (e.g., screws in our case) thus does +not work. To deal with large point clouds, common indus- +trial applications use sliding voxels to voxelize the point +cloud space and perform prediction voxel-wise. In our case, +we want to perform the point cloud segmentation fast and +precisely to prevent the robot from being idle for a too long +time. Using the prior knowledge that motors are always +clamped in a relatively fixed position in the clamping sys- +tem and only the area around the motor is of our interest, +we restrict the sampling region by cropping a cuboid area +around that location and use it as input to the segmenta- +tion neural network. All other residual points are labeled as +background points directly. The size of the cropped point +cuboid is of only around 10% of the raw point cloud. By +doing so, direct downsampling the point cuboid into sub- +point clouds of 2048 points makes the tail categories still +have enough points for learning. A cropped point cuboid +demo is given in Figure 2(c). +Apart from pre-processing, augmentation is also an im- +portant part to improve the generalization ability of the +models. Common augmentation methods include random +rotation and random jittering over the whole point cloud. + +旺Figure 3: Sim2real transfer learning piepline for the point cloud segmentation task in our industrial application. +In our case, we additionally introduce other augmentation +methods of (i) random cuboid size along all three axes; (ii) +random mild translation and rotation of motors; and (iii) +adding random size and random position hovering tiles over +the clamping system as scene masks, which is similar to +the masking augmentation on images. An detailed ablation +study regarding the augmentations is given in Section 4.5. +4. Sim2real Point Cloud Learning +As illustrated in Figure 3, apart from the synthetic point +cloud dataset generation, the whole pipeline consists fol- +lowing other steps: pre-train the network model on syn- +thetic data, fine-tune the network model on real-world data, +and post-processing for screw information. +4.1. Pre-training on Simulated Scenes +As reviewed in Section 2, there are a variety of neural +network models that can be used for the point cloud seg- +mentation task. Since the backbone itself is not of our main +focus, balancing the performance and the computation time, +we use DGCNN [47] as our backbone network for the seg- +mentation task. To better deal with the camera perspective +variance, a spatial transform network (STN) [31] is intro- +duced at the beginning. +In the previous step, a dataset of 1000 random scenes +with 1000 random motors is generated. We use 80% of it +for training and 20% for test. In the pre-training process, the +training takes 100 epochs and the batch size is 16. We use an +initial learning rate of 0.01, and a cos decay scheduler with +a final learning rate of 0.00001. The optimization method is +stochastic gradient descent (SGD). We use the widely used +cross entropy for the segmentation loss Lseg. An auxiliary +STN rotation loss Lrot which describes the L2 difference +between the learned rotation matrix and the ground truth +(saved during the augmentation) is additionally applied with +a small weight α. The total loss is defined as: +Ltotal = Lseg + αLrot +(1) +Table 1: Numerical results of models with different settings. +The second column indicates whether the model is pre- +trained on the synthetic dataset or not. Both results in the +pre-training step (Simulation) and the fine-tuning step (Re- +ality) are given. Note that the results in Simulation columns +are the test results on synthetic test dataset, other than real- +world test dataset. Same below. +STN +Pre-train +Simulation +Reality +mIoU +screw IoU +mIoU +screw IoU +- +- +- +- +0.8707 +0.4884 +✓ +- +- +- +0.9030 +0.6272 +- +✓ +0.9202 +0.7120 +0.9187 +0.6830 +✓ +✓ +0.9675 +0.8875 +0.9375 +0.7842 +We set α = 0.01. During the training, the common segmen- +tation metric, mean intersection over union (mIoU), is used +to measure the model performance. The IoU of screw cate- +gory is used as an additional metric since screws are of our +main focus. During both pre-training and fine-tuning pro- +cesses, we save the model that performs best on the screw +IoU metric. +4.2. Fine-tuning on Real-world Scenes +During the fine-tuning step, we load the network parame- +ters from the pre-training step and perform transfer learning, +i.e., adapting the network model from simulated scenes to +real-world scenes. We took 26 real-world point clouds with +Zivid camera and manually labeled them. 20 scenes are +used for fine-tuning and 6 scenes are used for test. Note that +this is not a small dataset since the point cloud cuboid from +each scene contains around 200,000 points and can be sam- +pled to around 100 sub-point clouds of 2048 points. In the +fine-tuning process, the training takes 300 epochs and the +batch size is 16. We use an initial learning rate of 0.001, and +a cos decay scheduler with a final learning rate of 0.00001. +The optimizer, loss, evaluation metrics are identical to that +in the pre-training step. + +Scan +Zivid Camera +Real-World +Real-world point cloud +objects +Fine-tune/test +Render +Blensor +Pre-training +Segmentation +Output +Post-processing +Network +Synthetic +Synthetic +Segmented +Screw location +Simulated scene +mesh model +point cloud +result +and orientationinput +GT +w/o pre-train +only pre-train +fine-tuned +Figure 4: Segmentation result visualization on real-world test data. Without pre-train means the network is trained on real- +world data directly. Only pre-train means the network is trained only on synthetic dataset and directly used for the testing on +real-world data. Fine-tuned means the network is both pre-trained and fine-tuned. +Table 2: Ablation study on augmentation methods. Aug 1: random rotation and random jittering over the cuboid point cloud. +Aug 2: random cuboid size along all three axes. Aug 3: random mild translation and rotation of motors. Aug 4: adding +random position hovering tiles over the clamping system as scene masks. +Dataset +Augmentations +Simulation +Reality +aug 1 +aug 2 +aug 3 +aug 4 +mIoU +screw IoU +mIoU +screw IoU +dataset 1 +✓ +0.9751 +0.9141 +0.9280 +0.7518 +dataset 2 +✓ +✓ +0.9801 +0.9372 +0.9368 +0.7799 +dataset 3 +✓ +✓ +✓ +0.9742 +0.9161 +0.9370 +0.7815 +dataset 4 +✓ +✓ +✓ +✓ +0.9675 +0.8875 +0.9375 +0.7842 +Note that after the model is trained, the dataloader for the +test process is different from that for the training process. +When training the network, each input point cuboid splits +into sub-point clouds of 2048 points as much as it can, and +the residual points are discarded. When testing the trained +model, the residual points are not discarded but completed +into a sub-point cloud of 2048 points with other random +points resampled from the original input. +4.3. Quantitative and Qualitative Results +Numerical results over the metrics of mIoU and screw +IoU are given in Table 1. From it, we can observe that using +the STN module improves the performance drastically. On +the other hand, using the sim2real transfer learning with two +steps of pre-training and fine-tuning also boosts the perfor- +mance. Combining both gets even better performance. +Some qualitative results are given in Figure 4. From it, +we can observe that direct training on the real-world data +performs decent on most points but not so good on tail cat- +egories. With pre-training on the simulated scenes and fine- +tune the model on real-world scenes can achieve a much +better segmentation result, especially for the tail categories. +4.4. Post-processing for Screw Information +After the network model is fine-tuned, given a real-world +point cloud as input, the network outputs the segmenta- +tion result. The post-processing step aims at getting screw +locations and orientations with the screw points that have +been segmented out. To get screw locations, clustering al- +gorithms are firstly used to group segmented screw points. +In our case, we use the Density-Based Spatial Clustering +of Applications with Noise (DBSCAN) [11, 37] algorithm +for clustering. With appropriate parameter settings, each +cluster is one screw. Using the prior knowledge that the +bottom most screw is always the side screw, all the clusters +above are cover screws that need to be unscrewed in this +process. The cover screw locations are obtained by com- +puting the center of each cluster. For the screw orientations, +processing on the screw points directly is problematic since +screws have uneven surfaces. Using the prior knowledge +that all cover screws are having the same orientation as the +flat cover, the screw orientation is actually identical to the + +Figure 5: Post-processing for screw information. +(a) +(b) +(c) +Figure 6: Patch-based attention network. (a) Full architecture. (b) Proposed patch module, has an additional defined kernel +loss, outputs patch feature. (c) Cross attention module. +normal of the cover flat part in our case. We hence apply +DBSCAN on the points that are segmented as the cover cat- +egory but with their estimated normals other than coordi- +nates. With appropriate parameter settings, we can make the +cluster number to be only one, which means all the points +whose normal vectors are similar to the cover flat part are +clustered together. Then the cover normal, or the screw ori- +entation, is obtained by averaging all the normal vectors of +those points. The process is illustrated in Figure 5. +4.5. Ablation Study on Data Augmentation +A variety of augmentation methods have been used on +our synthetic dataset. +To validate their effectiveness, an +ablation study is performed by generating several differ- +ent datasets and using a same network architecture for the +pre-training and fine-tuning processes. The numerical re- +sults are given in Table 2. In the used four augmentation +methods, the former two methods are augmentations per- +formed during the data pre-processing, and the latter two +methods are augmentations performed during the data gen- +eration. From Table 2, we can observe that randomly chang- +ing the cuboid size improves the segmentation performance +on both pre-training and fine-tuning steps. On the other +hand, while the latter two augmentation methods decreases +the pre-training performance, they both improves the fine- +tuning performance when the model is transferred to real- +world point cloud data. In this paper, we use dataset 4 for +most other experiments. +5. Imbalanced Learning +Imbalanced learning, also referred as long-tail learning +in the classification tasks, is a problem where the distri- +bution of examples across the known categories is biased +or skewed. In our case, original synthetic point clouds are +mostly occupied with background points (around 96%) and +have extremely less screw points (around 0.1%). After ap- +plying the sample region restriction, i.e., the cuboid crop +strategy as illustrated in Figure 2(c) and described in sub- +section 3.3, in each point cuboid, background points take +up around 64% while screw points take up around 1%. The +imbalanced problem has been alleviated. Meanwhile, it is +still worth investigating to further improve the performance. +Several additional strategies are proposed to deal with the +imbalanced learning problem in this paper. They are pro- +posed from the perspectives of data augmentation, weight- +ing loss, and extra network block respectively. +5.1. Focused Sampling for Tail Categories +One common strategy to deal with the long-tail problem +in classification tasks is resampling like manually adding +samples of the tail categories. In our case, the key cate- +gory of screw only occupies a extreme small portion of the +whole point cloud compared to other components, hence it +is possible to increase the number of screw points by den- +sifying them. The strategy is as follows. For each point +p1 belongs to the screw category, get its nearest same cat- +egory point p2. (a) If the nearest same category point of + +48 x 512 +Nx 512 +Patch +Cross +Module +Attention +maxpool +repeat +dw +dw +1024 +N × 1024 +1728 +djw +192 +2 +3 +3 +Sequential +5 +102 +6 +X +STN +X +Edgeconvs +XN +XN +XN +1x +XN +Z +Z +DGCNN BackboneNx 3 +(after STN) +Patch Module +* mlp +N x 256 +Nx 3 +self-attention +(before STN) +Nx 256 ++ mlp +N x 48 +top1 +top32 +set +1x 48 +32 x48 +goals + get coords +get feature +48 x 3 +48x1x3 +48x32x256 +,conv +48 x 480 +Kernel +concate +Loss +48x 512(point feature) +(patch feature) +Nx 512 +48x512 +Q +K +V +N x 256 +48 x 256 +48x 256 +★ transpose +multiply +256x48 +& softmax +N x 48 +multiply +N x 256 +, mlp +Cross +Nx512 +residual +Attention +N x512Table 3: Ablation study on proposed strategies for imbalanced learning. +Sample region +restriction +Focused +sampling +Weighting +loss +Patch-based +attention +Simulation +Reality +mIoU +screw IoU +mIoU +screw IoU +✓ +- +- +- +0.9675 +0.8875 +0.9375 +0.7842 +✓ +✓ +- +- +0.9627 +0.8661 +0.9376 +0.7570 +✓ +- +✓ +- +0.9668 +0.8862 +0.9409 +0.7717 +✓ +- +- +✓ +0.9693 +0.9063 +0.9462 +0.7968 +✓ +✓ +- +✓ +0.9644 +0.8850 +0.9389 +0.7622 +✓ +- +✓ +✓ +0.9729 +0.9165 +0.9412 +0.7794 +✓ +✓ +✓ +✓ +0.9680 +0.8972 +0.9401 +0.7683 +Figure 7: Visualizing learned patches on sub-point clouds of 2048 points. +p2 is also p1, this means both points are not at the cluster +boundary, hence a new point is added with the coordinate +of padd = p1 + 1 +3(p2 − p1). (b) If the nearest same category +point of p2 is not p1, this means p1 is likely to be an outlier +point or at the cluster boundary, hence a new point is added +with the coordinate of padd = p1 + 2 +3(p2 − p1). Above op- +eration doubles the point number of the tail category in the +training dataset. +5.2. Weighting Category Loss +Adding additional weights to each category when com- +puting the cross entropy loss is another widely used strat- +egy. Most current DL packages provide such an optional +argument in their in-built loss functions. +However, it is +an unsolved question that what is the best way to compute +and set the category weights. In this paper, we propose a +following method. Assume the point cloud has M cate- +gories and N points in total. For each category that has +ni(i = 1, 2, . . . , M) points, its ratio is given as ri = ni/N. +Then a scaled ratio sri is computed by decreasing the orig- +inal ratio difference with a cubic root operation as sri = +ti/(�M +i=1 ti), where ti = (max(r1, r2, . . . , rM)/ri) +1 +3 . In +this case, smaller ri means the corresponding category gets +a larger sri. However, using sri directly leads to a huge +decrease on the loss magnitude. To eliminate the possible +problem caused by it, an additional factor is computed as +f = �M +i=1 ri × sri and multiplied. Hence the final cate- +gory weight is given as ωi = sri × f for each category. +5.3. Patch-based Attention Network +Additionally, we propose a novel patch-based attention +network to deal with the imbalanced learning problem. The +key idea is to force the network to learn a same number +of kernel points for all categories by using an additional +kernel loss. In our task, we have 6 categories in total and +we select 8 kernel points per category. For each category, +the ground truth kernel points are obtained by performing +K-means algorithm on all points of this category. After 8 +clusters are grouped, cluster centers are computed and their +nearest neighbor points that belong to this category are de- +fined as kernel points. The kernel loss is a L2 loss between +the goal kernels and learned kernels. Hence the total loss in +this case is defined as: +Ltotal = Lseg + αLrot + βLker +(2) +where β is a loss weight. We set β = 0.05. Apart from the +obtained kernel points, their 32 neighbor points are grouped +to form a patch and a convolution layer is used to get patch- +wise features. The patch-wise features are further used to +perform cross attention with the point-wise features learned +from the DGCNN backbone (lower branch in Figure 6(a)). +This is a patch-to-point cross attention, i.e., using patch fea- +tures to represent point features. The output is concatenated +back to the lower branch for final segmentation. Detailed +network designs are given in Figure 6. +5.4. Experimental results +All the experiments are conducted with the same dataset +on which all augmentation methods are applied (dataset 4 + +in Table 2). Numerical results of them are presented in Ta- +ble 3. From it, we can observe that the focused sampling +strategy always leads to a worse performance. One possible +reason is that this operation is only performed during train- +ing. For test cases, labels are segmentation goals and are not +provided hence the focused sampling operation is not appli- +cable. This causes data distribution difference between the +training set and the test set thus leads to bad performance. +The loss weighting strategy improves the performance on +synthetic data but degrades the performance on real-world +data slightly. This indicates the strategy contributes to a +better pre-training yet not performing well on transfer learn- +ing. On the other hand, our proposed patch-based attention +module improves the performance on both steps. To give +better insights of our proposed module, learned patches of +some sub-point clouds are visualized in Figure 7. It shows +that our method forces the network to learn patches around +boundaries or other informative places. +6. Conclusion +In this paper, we adopt sim2real transfer learning method +for an industrial application on point cloud data. Follow- +ing the pipeline, synthetic dataset are generated in simulated +scenes. The network model is firstly pre-trained on the syn- +thetic data and then fine-tuned on the real-world data. Both +quantitative and qualitative results show that this achieves +better performance. To deal with the imbalanced learning +problem, several strategies have been tested. The proposed +patch-based attention module shows its effectiveness by im- +proving the performance drastically. For future directions, +we would like to try more backbones, as well as investigate +more attention-based learning methods for point cloud data. +Acknowledgements +The project AgiProbot is funded by the Carl Zeiss Foun- +dation. +References +[1] Juan Felipe Perez-Juste Abascal, Nicolas Ducros, Va- +leriya Pronina, Simon Rit, Pierre-Antoine Rodesch, Thomas +Broussaud, Suzanne Bussod, Philippe Douek, Andreas +Hauptmann, Simon Robert Arridge, and Franc¸oise Peyrin. +Material decomposition in spectral ct using deep learning: A +sim2real transfer approach. IEEE Access, 9:25632–25647, +2021. +[2] Karol Arndt, Murtaza Hazara, Ali Ghadirzadeh, and Ville +Kyrki. Meta reinforcement learning for sim-to-real domain +adaptation. 2020 IEEE International Conference on Robotics +and Automation (ICRA), pages 2725–2731, 2020. +[3] Nicolas Audebert, Bertrand Le Saux, and S´ebastien Lef`evre. +Semantic segmentation of earth observation data using mul- +timodal and multi-scale deep networks. In Asian conference +on computer vision, pages 180–196. Springer, 2016. +[4] Christian Bonatti, Sylvain Crovisier, Lorenzo Diaz, and +Amie Wilkinson. +What is... a blender? +arXiv preprint +arXiv:1608.02848, 2016. +[5] Alexandre Boulch, Bertrand Le Saux, and Nicolas Audebert. +Unstructured point cloud semantic labeling using deep seg- +mentation networks. 3DOR@ Eurographics, 3, 2017. +[6] Angel X. Chang, T. Funkhouser, L. Guibas, P. Hanra- +han, Qixing Huang, Zimo Li, S. Savarese, M. Savva, +Shuran Song, +Hao Su, +J. Xiao, +L. Yi, +and F. Yu. +Shapenet: An information-rich 3d model repository. ArXiv, +abs/1512.03012, 2015. +[7] Can Chen, Luca Zanotti Fragonara, and Antonios Tsour- +dos. Gapnet: Graph attention based point neural network +for exploiting local feature of point cloud. Neurocomputing, +438:122–132, 2021. +[8] Maximilian Denninger, +Martin Sundermeyer, +Dominik +Winkelbauer, Youssef Zidan, Dmitry Olefir, Mohamad El- +badrawy, Ahsan Lodhi, and Harinandan Katam. +Blender- +proc. arXiv preprint arXiv:1911.01911, 2019. +[9] Yuqing Du, Olivia Watkins, Trevor Darrell, P. Abbeel, and +Deepak Pathak. +Auto-tuned sim-to-real transfer. +2021 +IEEE International Conference on Robotics and Automation +(ICRA), pages 1290–1296, 2021. +[10] Nico Engel, Vasileios Belagiannis, and Klaus C. J. Diet- +mayer. Point transformer. IEEE Access, 9:134826–134840, +2021. +[11] Martin Ester, Hans-Peter Kriegel, J¨org Sander, and Xiaowei +Xu. A density-based algorithm for discovering clusters in +large spatial databases with noise. In KDD, 1996. +[12] David Griffiths and Jan Boehm. Synthcity: A large scale +synthetic point cloud. ArXiv, abs/1907.04758, 2019. +[13] Michael Gschwandtner, R. Kwitt, A. Uhl, and W. Pree. +Blensor: Blender sensor simulation toolbox. In ISVC, 2011. +[14] Meng-Hao Guo, Junxiong Cai, Zheng-Ning Liu, Tai-Jiang +Mu, Ralph Robert Martin, and Shimin Hu. Pct: Point cloud +transformer. Comput. Vis. Media, 7:187–199, 2021. +[15] Qingyong Hu, Bo Yang, Linhai Xie, Stefano Rosa, Yu- +lan Guo, Zhihua Wang, Agathoniki Trigoni, and Andrew +Markham. Randla-net: Efficient semantic segmentation of +large-scale point clouds. +2020 IEEE/CVF Conference on +Computer Vision and Pattern Recognition (CVPR), pages +11105–11114, 2020. +[16] Binh-Son Hua, Minh-Khoi Tran, and Sai-Kit Yeung. Point- +wise convolutional neural networks. In Proceedings of the +IEEE Conference on Computer Vision and Pattern Recogni- +tion, pages 984–993, 2018. +[17] Mingyang Jiang, Yiran Wu, Tianqi Zhao, Zelin Zhao, and +Cewu Lu. +Pointsift: +A sift-like network module for +3d point cloud semantic segmentation. +arXiv preprint +arXiv:1807.00652, 2018. +[18] Samin Khan, Buu Phan, Rick Salay, and Krzysztof Czar- +necki. Procsy: Procedural synthetic dataset generation to- +wards influence factor studies of semantic segmentation net- +works. In CVPRW, pages 88–96, 2019. +[19] Sebastian Koch, Albert Matveev, Zhongshi Jiang, Francis +Williams, A. Artemov, Evgeny Burnaev, M. Alexa, D. Zorin, +and Daniele Panozzo. Abc: A big cad model dataset for ge- +ometric deep learning. CVPR, pages 9593–9603, 2019. + +[20] Felix J¨aremo Lawin, Martin Danelljan, Patrik Tosteberg, +Goutam Bhat, Fahad Shahbaz Khan, and Michael Felsberg. +Deep projective 3d semantic segmentation. In International +Conference on Computer Analysis of Images and Patterns, +pages 95–107. Springer, 2017. +[21] Truc Le and Ye Duan. Pointgrid: A deep network for 3d +shape understanding. In Proceedings of the IEEE conference +on computer vision and pattern recognition, pages 9204– +9214, 2018. +[22] Le Hoang-An, +Thomas Mensink, +Partha Das, +Sezer +Karaoglu, and Theo Gevers. Eden: Multimodal synthetic +dataset of enclosed garden scenes. 2021 IEEE Winter Con- +ference on Applications of Computer Vision (WACV), pages +1578–1588, 2021. +[23] Zhidong Liang, Ming Yang, Hao Li, and Chunxiang Wang. +3d instance embedding learning with a structure-aware loss +function for point cloud segmentation. IEEE Robotics and +Automation Letters, 5:4915–4922, 2020. +[24] Nai Qing Liu, Yinghao Cai, Tao Lu, Rui Wang, and Shuo +Wang. Real–sim–real transfer for real-world robot control +policy learning with deep reinforcement learning. Applied +Sciences, 2020. +[25] Mohammadhossein Malmir, Josip Josifovski, Noah Klar- +mann, and Alois Knoll. Robust sim2real transfer by learning +inverse dynamics of simulated systems. 2020. +[26] Daniel Maturana and Sebastian Scherer. Voxnet: A 3d con- +volutional neural network for real-time object recognition. +In 2015 IEEE/RSJ International Conference on Intelligent +Robots and Systems (IROS), pages 922–928. IEEE, 2015. +[27] Volodymyr Mnih, Koray Kavukcuoglu, David Silver, An- +drei A. Rusu, Joel Veness, Marc G. Bellemare, Alex Graves, +Martin A. Riedmiller, Andreas Fidjeland, Georg Ostro- +vski, Stig Petersen, Charlie Beattie, Amir Sadik, Ioannis +Antonoglou, Helen King, Dharshan Kumaran, Daan Wier- +stra, Shane Legg, and Demis Hassabis. Human-level control +through deep reinforcement learning. Nature, 518:529–533, +2015. +[28] Kaichun Mo, Shilin Zhu, Angel Chang, Li Yi, Subarna Tri- +pathi, Leonidas Guibas, and Hao Su. PartNet: A large-scale +benchmark for fine-grained and hierarchical part-level 3D +object understanding. 2019. +[29] Alexander Pashevich, Robin Strudel, Igor Kalevatykh, Ivan +Laptev, and Cordelia Schmid. Learning to augment synthetic +images for sim2real policy transfer. 2019 IEEE/RSJ Interna- +tional Conference on Intelligent Robots and Systems (IROS), +pages 2651–2657, 2019. +[30] R. Pierdicca, M. Mameli, E. Malinverni, M. Paolanti, and +E. Frontoni. Automatic generation of point cloud synthetic +dataset for historical building representation. In AVR, pages +203–219, 2019. +[31] C. Qi, Hao Su, Kaichun Mo, and L. Guibas. Pointnet: Deep +learning on point sets for 3d classification and segmentation. +CVPR, pages 77–85, 2017. +[32] Charles R Qi, Li Yi, Hao Su, and Leonidas J Guibas. Point- +Net++: Deep hierarchical feature learning on point sets in a +metric space. arXiv preprint arXiv:1706.02413, 2017. +[33] Aravind Rajeswaran, Vikash Kumar, Abhishek Gupta, John +Schulman, Emanuel Todorov, and Sergey Levine. Learning +complex dexterous manipulation with deep reinforcement +learning and demonstrations. ArXiv, abs/1709.10087, 2018. +[34] Jacob Revell, Dominic Welch, and James M. Hereford. +Sim2real: Issues in transferring autonomous driving model +from simulation to real world. SoutheastCon 2022, pages +296–301, 2022. +[35] Olaf Ronneberger, Philipp Fischer, and Thomas Brox. U-net: +Convolutional networks for biomedical image segmentation. +ArXiv, abs/1505.04597, 2015. +[36] G. Ros, Laura Sellart, Joanna Materzynska, David V´azquez, +and Antonio M. L´opez. The synthia dataset: A large collec- +tion of synthetic images for semantic segmentation of urban +scenes. CVPR, pages 3234–3243, 2016. +[37] Erich Schubert, J¨org Sander, Martin Ester, Hans Peter +Kriegel, and Xiaowei Xu. Dbscan revisited, revisited: why +and how you should (still) use dbscan. ACM Transactions on +Database Systems (TODS), 42(3):1–21, 2017. +[38] Philip Shilane, P. Min, M. Kazhdan, and T. Funkhouser. The +princeton shape benchmark. Proceedings Shape Modeling +Applications, 2004., pages 167–178, 2004. +[39] Martin Simonovsky and Nikos Komodakis. Dynamic edge- +conditioned filters in convolutional neural networks on +graphs. In Proceedings of the IEEE conference on computer +vision and pattern recognition, pages 3693–3702, 2017. +[40] Maxim Tatarchenko, Jaesik Park, Vladlen Koltun, and Qian- +Yi Zhou. Tangent convolutions for dense prediction in 3d. +In Proceedings of the IEEE Conference on Computer Vision +and Pattern Recognition, pages 3887–3896, 2018. +[41] Hugues Thomas, Charles R Qi, Jean-Emmanuel Deschaud, +Beatriz Marcotegui, Franc¸ois Goulette, and Leonidas J +Guibas. Kpconv: Flexible and deformable convolution for +point clouds. In Proceedings of the IEEE/CVF international +conference on computer vision, pages 6411–6420, 2019. +[42] Joshua Tobin, Rachel Fong, Alex Ray, Jonas Schneider, Wo- +jciech Zaremba, and P. Abbeel. Domain randomization for +transferring deep neural networks from simulation to the real +world. 2017 IEEE/RSJ International Conference on Intelli- +gent Robots and Systems (IROS), pages 23–30, 2017. +[43] Jonathan Tremblay, Thang To, and Stan Birchfield. Falling +things: A synthetic dataset for 3d object detection and pose +estimation. CVPRW, pages 2119–21193, 2018. +[44] Juliano Vacaro, Guilherme Marques, Bruna Oliveira, Gabriel +Paz, Thomas S. Paula, Wagston Staehler, and David Murphy. +Sim-to-real in reinforcement learning for everyone. +2019 +Latin American Robotics Symposium (LARS), 2019 Brazil- +ian Symposium on Robotics (SBR) and 2019 Workshop on +Robotics in Education (WRE), pages 305–310, 2019. +[45] G¨ul Varol, Javier Romero, Xavier Martin, Naureen Mah- +mood, Michael J. Black, Ivan Laptev, and Cordelia Schmid. +Learning from synthetic humans. CVPR, pages 4627–4635, +2017. +[46] Shenlong Wang, +Simon Suo, +Wei-Chiu Ma, +Andrei +Pokrovsky, and Raquel Urtasun. Deep parametric continu- +ous convolutional neural networks. In Proceedings of the +IEEE Conference on Computer Vision and Pattern Recogni- +tion, pages 2589–2597, 2018. +[47] Yue Wang, Yongbin Sun, Ziwei Liu, Sanjay E Sarma, +Michael M Bronstein, and Justin M Solomon. +Dynamic + +graph cnn for learning on point clouds. Acm Transactions +On Graphics (tog), 38(5):1–12, 2019. +[48] Matthew Witman, Dogan Gidon, David B. Graves, Berend +Smit, and Ali Mesbah. Sim-to-real transfer reinforcement +learning for control of thermal effects of an atmospheric +pressure plasma jet. Plasma Sources Science and Technol- +ogy, 2019. +[49] Wenxuan Wu, Zhongang Qi, and Fuxin Li. Pointconv: Deep +convolutional networks on 3d point clouds. 2019 IEEE/CVF +Conference on Computer Vision and Pattern Recognition +(CVPR), pages 9613–9622, 2019. +[50] Zhirong Wu, Shuran Song, A. Khosla, F. Yu, Linguang +Zhang, Xiaoou Tang, and J. Xiao. 3d shapenets: A deep rep- +resentation for volumetric shapes. CVPR, pages 1912–1920, +2015. +[51] Xiangyu Yue, Yang Zhang, Sicheng Zhao, Alberto L. +Sangiovanni-Vincentelli, +Kurt +Keutzer, +and +Boqing +Gong. +Domain randomization and pyramid consistency: +Simulation-to-real generalization without accessing target +domain data. 2019 IEEE/CVF International Conference on +Computer Vision (ICCV), pages 2100–2110, 2019. +[52] Hengshuang Zhao, Li Jiang, Jiaya Jia, Philip H. S. Torr, and +Vladlen Koltun. Point transformer. ArXiv, abs/2012.09164, +2020. +[53] Wenshuai Zhao, Jorge Pe˜na Queralta, and Tomi Wester- +lund. Sim-to-real transfer in deep reinforcement learning for +robotics: a survey. 2020 IEEE Symposium Series on Compu- +tational Intelligence (SSCI), pages 737–744, 2020. +[54] Qingnan Zhou and A. Jacobson. Thingi10k: A dataset of 10, +000 3d-printing models. ArXiv, abs/1605.04797, 2016. +[55] Fuzhen Zhuang, Zhiyuan Qi, Keyu Duan, Dongbo Xi, +Yongchun Zhu, Hengshu Zhu, Hui Xiong, and Qing He. A +comprehensive survey on transfer learning. Proceedings of +the IEEE, 109:43–76, 2021. + diff --git a/udE4T4oBgHgl3EQfWgxs/content/tmp_files/load_file.txt b/udE4T4oBgHgl3EQfWgxs/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..f7a8f328e9f909907567179f5276fedce88e9bdf --- /dev/null +++ b/udE4T4oBgHgl3EQfWgxs/content/tmp_files/load_file.txt @@ -0,0 +1,624 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf,len=623 +page_content='Sim2real Transfer Learning for Point Cloud Segmentation: An Industrial Application Case on Autonomous Disassembly Chengzhi Wu1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Xuelei Bi1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Julius Pfrommer2,' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' System Technologies and Image Exploitation IOSB,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Germany 3Fraunhofer Center for Machine Learning,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Germany 4wbk Institute of Production Science,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Karlsruhe Institute of Technology,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Germany chengzhi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='wu@kit.' 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alexander.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='cebulla@kit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='edu simon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='mangold@kit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='edu juergen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='beyerer@iosb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='fraunhofer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='de Abstract On robotics computer vision tasks, generating and an- notating large amounts of data from real-world for the use of deep learning-based approaches is often difficult or even impossible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' A common strategy for solving this problem is to apply simulation-to-reality (sim2real) approaches with the help of simulated scenes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' While the majority of cur- rent robotics vision sim2real work focuses on image data, we present an industrial application case that uses sim2real transfer learning for point cloud data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' We provide insights on how to generate and process synthetic point cloud data in order to achieve better performance when the learned model is transferred to real-world data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' The issue of imbal- anced learning is investigated using multiple strategies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' A novel patch-based attention network is proposed addition- ally to tackle this problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Introduction Due to the rapid development of neural network algo- rithms, an increasing number of industrial companies and factories have started using deep learning (DL) methods for a variety of manufacturing and remanufacturing tasks in the past decade.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' In general, neural networks require a substan- tial amount of data in order to be trained, whereas for practi- cal industrial applications, allocating and annotating a large amount of data is difficult or even impossible, especially when robots are involved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' In the field of robotics, when the robot or manipulator directly interacts and samples with the real-world environment, there will be problems of low sampling efficiency and safety problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' One possible solution to this problem is to apply simulation-to-reality (sim2real) method, which learns with simulated data and transfers the learned knowledge to real- world application.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' This is a common strategy used in robotics for learning robot movement controls [2, 33] and robotic-related vision tasks [42, 24, 29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' In those com- puter vision tasks, simulated scenes are usually rendered into RGB images with possible auxiliary depth, thermal, or even flow images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Then, DL-based neural networks are pre-trained with the synthetic data and subsequently trans- ferred to real-world use cases via domain adaption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' How- ever, most current sim2real work focuses on image data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Few researches apply sim2real methods on point cloud data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' In this paper, we show a full pipeline of how to perform sim2real transfer learning on point clouds for a robotics use case as a part of a practical remanufactoring application.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' We consider the automated disassembly of different vari- ants of actuators which are commonly used in vehicle man- ufacturing, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=', as seat adjuster motors, window lift motors or rear door motors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Several example motors are shown in Figure 1(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' The ultimate goal of this project is to use robots to perform automatic disassembly of motors, not only for the known motor types, but also for future variants with unseen specifications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' In this case, generating a synthetic dataset with motor variants in simulated scenes for sim2real transfer learning [55] is a good solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' By learning the in- ternal structure on part level, (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' gear container, pole pot, electrical connection), processes on unseen variants which have similarities to the known population of actuators be- come feasible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' This paper focuses on the first step of getting precise screw positions and orientations on motor covers for robots as one of the most important tasks for disassembly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='05033v1 [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='CV] 12 Jan 2023 (a) (b) (c) Figure 1: Real-world motors and generated demo motors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' (b) Upper row: no textures added;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' bottom row: textures added and rendered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' (c) An explosion figure of a generated motor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' The original assembled motor model is also shown at the right most.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Generating a synthetic point cloud dataset for sim2real transfer learning has following advantages in our project: (i) a large synthetic dataset can be easily created, segmentation ground truth labels are given in the simulation, no manual annotation needed;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' (ii) motor variants with unseen specifi- cations may be generated, which will strengthen the gen- eralization ability of the trained network model;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' (iii) point cloud data contain richer 3D information for the learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Using point cloud data avoids some problems that may oc- cur when using image data, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=', colors of the simulated im- ages are far from realistic since it is hard to get the perfect textures for scene objects or to render the scene with perfect lighting conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' When using the point cloud dataset, we use point coordinates information other than colors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' The remainder of this paper is structured as follows: Section 2 summarizes the state-of-the-art of 3D synthetic dataset creation, sim2real transfer learning, and point cloud segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Section 3 shows a general pipeline of cre- ating a synthetic dataset with simulated scenes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Section 4 describes the whole sim2real learning framework and gives experimental results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Section 5 additionally explores sev- eral strategies for imbalanced learning, including a novel patch-based attention network module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Finally, Section 6 summarizes presented results and discusses future work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Related Work 3D synthetic dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Generating synthetic datasets as training data for machine learning purposes has already been widely discussed and used as a learning approach for various computer vision applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' In the past decade, many synthetic datasets of 3D models have been created, including the Princeton Shape Benchmark [38], ModelNet [50], ShapeNet [6], PartNet [28], etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' They collect large amounts of 3D models of different categories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' A large dataset of 3D-printing models is provided in Thingi10K [54], while a more recent ABC dataset [19] collects over 1 million CAD models including many mechanical compo- nents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Regarding 3D scenes, [45], [36] and [18] generate synthetic datasets for the segmentation and detection of ob- jects in virtual urban scenes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' [22] generates images from virtual garden scenes, while [43] creates a dataset for pose estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' There are also works that generate synthetic point clouds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' SynthCity [12] generates point clouds of ur- ban scenes using Blender, while [30] also uses Blender but for the generation of point clouds of historical objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Sim2real transfer learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' By allowing faster, more scal- able, and lower-cost data collection than is possible in real- world, sim2real approaches show great impact on machine learning and have been applied in many fields including robotics and classic machine vision tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' [42], [24] and [44] train neural network models on synthetic RGB images with domain randomization or domain adaption then trans- fer it to real-world, while Pachevish et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' [29] work with synthetic depth images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Also working with synthetic im- age data, Du et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' [9] propose a method for automatically tuning simulator system parameters to match the real world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' With the help of deep reinforcement learning [27], robotics policies are directly used as training data for sim2real learn- ing in some works [25, 2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' A more detailed survey is given in [53].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Apart from robotics tasks, sim2real methods have also been widely used in other fields including autonomous driving [51, 34], medical diagnosis [1], or even the control of atmospheric pressure plasma jets [48].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Point cloud segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Before the appearance of Point- Net [31], deep learning-based methods for point cloud seg- mentation are usually multi-view based [20, 5, 3, 40] or volumetric-based [26, 17, 21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' PointNet [31] is the first DL- based method that learns directly on points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' It uses point- wise multi-layer perceptrons to extract global features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Its subsequent work of PointNet++ [32] further considers lo- cal information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' PointConv[49] and KPConv [41] propose point-wise convolution operators with which points are con- voluted with neighbor points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Similar ideas are proposed in [46, 16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Simonovsky et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' [39] takes each point as a graph vertex and applies graph convolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' In DGCNN [47], EdgeConv blocks update the neighbor information dynami- cally.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' RandLA-Net [15] learns attention scores for points as a soft mask to replace the original pooling layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' GAPNet [7] and Liang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' [23] propose graph-attention operations with neighbor points to learn coefficients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' More recently, transformer-based methods are starting to trend.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' PCT [14] (a) (b) (c) Figure 2: Synthetic dataset generation: (a) simulated scene built in Blender;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' (b) synthetic image data generated with BlenderProc;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' (c) synthetic point cloud data generated with BlenSor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' pioneers on this direction by replacing the encoder layers in the original PointNet [31] framework with self-attention layers, while PT [52] is based on U-Net [35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' SortNet is proposed in [10] to learn sub-point clouds, with which at- tention operations are applied on their latent features and the global feature to perform local-global attention.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Synthetic Dataset Generation 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Synthetic Mesh Model Generation To easily generate motor mesh models of a variety of specifications, we create a Blender addon based on the mo- tor types we have.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' As an open source software, Blender [4] is a proven tool that performs well in modeling shapes and creating highly customizable addons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Our addon is able to generate motor mesh models with various specifications and save them in desired file formats.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Each component of a generated motor can also be saved separately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' The generated models contain the following compo- nents: (i) Pole Pot;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' (ii) Electric Connection;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' (iii) Gear Con- tainer;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' (iv) Cover and (v) Screws.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Those are the five main categories we need perform segmentation on.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Additionally, following inner components have also been generated : (vi) Magnets;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' (vii) Armature;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' (viii) Lower Gear and (ix) Upper Gear as presented in 1(c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' However, since we only focus on the first step of unscrewing process in this paper, inner parts will not be investigated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' To generate motors with vari- ous specifications, we provide lots of parameter options that control the type, size, position and rotation of different parts of motor, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' screw position, gear size, or pole pot length.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Figure 1(b) shows ten generated demo motors with different parameters and an exploded view of a demo motor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' All the individual components mentioned above are modeled sepa- rately as illustrated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Synthetic Point Cloud Generation The generated mesh models are further used to create synthetic image and point cloud datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' A simulated scene is built in Blender for it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Apart from the lights and cameras, the Blender scene also contains the model of the real-world clamping system and a background panel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' The camera rotates randomly on top of the scene within a cer- tain range yet always towards the motor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' To create image dataset, apart from the scene images rendered by Blender directly, BlenderProc [8] can be used to generate corre- sponding depth images, normal images, and segmentation ground truth images as shown in Figure 2(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Or in our case, BlenSor [13] is used to simulate the sensors to create point cloud dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Figure 2(c) gives a demo of generated point cloud colored in the material color or its segmentation ground truth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Data Pre-processing and Augmentation The generated point clouds are of relatively large size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Each point cloud contains around 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='2 million points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' How- ever, neural networks have a limitation of point number per batch, common choices are 1024/2048/4096 points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Direct downsampling makes the sub-point clouds contain too less points for tail categories (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=', screws in our case) thus does not work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' To deal with large point clouds, common indus- trial applications use sliding voxels to voxelize the point cloud space and perform prediction voxel-wise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' In our case, we want to perform the point cloud segmentation fast and precisely to prevent the robot from being idle for a too long time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Using the prior knowledge that motors are always clamped in a relatively fixed position in the clamping sys- tem and only the area around the motor is of our interest, we restrict the sampling region by cropping a cuboid area around that location and use it as input to the segmenta- tion neural network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' All other residual points are labeled as background points directly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' The size of the cropped point cuboid is of only around 10% of the raw point cloud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' By doing so, direct downsampling the point cuboid into sub- point clouds of 2048 points makes the tail categories still have enough points for learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' A cropped point cuboid demo is given in Figure 2(c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Apart from pre-processing, augmentation is also an im- portant part to improve the generalization ability of the models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Common augmentation methods include random rotation and random jittering over the whole point cloud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' 旺Figure 3: Sim2real transfer learning piepline for the point cloud segmentation task in our industrial application.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' In our case, we additionally introduce other augmentation methods of (i) random cuboid size along all three axes;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' (ii) random mild translation and rotation of motors;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' and (iii) adding random size and random position hovering tiles over the clamping system as scene masks, which is similar to the masking augmentation on images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' An detailed ablation study regarding the augmentations is given in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Sim2real Point Cloud Learning As illustrated in Figure 3, apart from the synthetic point cloud dataset generation, the whole pipeline consists fol- lowing other steps: pre-train the network model on syn- thetic data, fine-tune the network model on real-world data, and post-processing for screw information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Pre-training on Simulated Scenes As reviewed in Section 2, there are a variety of neural network models that can be used for the point cloud seg- mentation task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Since the backbone itself is not of our main focus, balancing the performance and the computation time, we use DGCNN [47] as our backbone network for the seg- mentation task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' To better deal with the camera perspective variance, a spatial transform network (STN) [31] is intro- duced at the beginning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' In the previous step, a dataset of 1000 random scenes with 1000 random motors is generated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' We use 80% of it for training and 20% for test.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' In the pre-training process, the training takes 100 epochs and the batch size is 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' We use an initial learning rate of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='01, and a cos decay scheduler with a final learning rate of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='00001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' The optimization method is stochastic gradient descent (SGD).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' We use the widely used cross entropy for the segmentation loss Lseg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' An auxiliary STN rotation loss Lrot which describes the L2 difference between the learned rotation matrix and the ground truth (saved during the augmentation) is additionally applied with a small weight α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' The total loss is defined as: Ltotal = Lseg + αLrot (1) Table 1: Numerical results of models with different settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' The second column indicates whether the model is pre- trained on the synthetic dataset or not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Both results in the pre-training step (Simulation) and the fine-tuning step (Re- ality) are given.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Note that the results in Simulation columns are the test results on synthetic test dataset, other than real- world test dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Same below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' STN Pre-train Simulation Reality mIoU screw IoU mIoU screw IoU 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='8707 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='4884 ✓ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='9030 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='6272 ✓ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='9202 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='7120 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='9187 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='6830 ✓ ✓ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='9675 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='8875 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='9375 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='7842 We set α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='01.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' During the training, the common segmen- tation metric, mean intersection over union (mIoU), is used to measure the model performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' The IoU of screw cate- gory is used as an additional metric since screws are of our main focus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' During both pre-training and fine-tuning pro- cesses, we save the model that performs best on the screw IoU metric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Fine-tuning on Real-world Scenes During the fine-tuning step, we load the network parame- ters from the pre-training step and perform transfer learning, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=', adapting the network model from simulated scenes to real-world scenes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' We took 26 real-world point clouds with Zivid camera and manually labeled them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' 20 scenes are used for fine-tuning and 6 scenes are used for test.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Note that this is not a small dataset since the point cloud cuboid from each scene contains around 200,000 points and can be sam- pled to around 100 sub-point clouds of 2048 points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' In the fine-tuning process, the training takes 300 epochs and the batch size is 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' We use an initial learning rate of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='001, and a cos decay scheduler with a final learning rate of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='00001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' The optimizer, loss, evaluation metrics are identical to that in the pre-training step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Scan Zivid Camera Real-World Real-world point cloud objects Fine-tune/test Render Blensor Pre-training Segmentation Output Post-processing Network Synthetic Synthetic Segmented Screw location Simulated scene mesh model point cloud result and orientationinput GT w/o pre-train only pre-train fine-tuned Figure 4: Segmentation result visualization on real-world test data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Without pre-train means the network is trained on real- world data directly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Only pre-train means the network is trained only on synthetic dataset and directly used for the testing on real-world data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Fine-tuned means the network is both pre-trained and fine-tuned.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Table 2: Ablation study on augmentation methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Aug 1: random rotation and random jittering over the cuboid point cloud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Aug 2: random cuboid size along all three axes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Aug 3: random mild translation and rotation of motors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Aug 4: adding random position hovering tiles over the clamping system as scene masks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Dataset Augmentations Simulation Reality aug 1 aug 2 aug 3 aug 4 mIoU screw IoU mIoU screw IoU dataset 1 ✓ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='9751 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='9141 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='9280 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='7518 dataset 2 ✓ ✓ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='9801 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='9372 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='9368 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='7799 dataset 3 ✓ ✓ ✓ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='9742 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='9161 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='9370 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='7815 dataset 4 ✓ ✓ ✓ ✓ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='9675 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='8875 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='9375 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='7842 Note that after the model is trained, the dataloader for the test process is different from that for the training process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' When training the network, each input point cuboid splits into sub-point clouds of 2048 points as much as it can, and the residual points are discarded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' When testing the trained model, the residual points are not discarded but completed into a sub-point cloud of 2048 points with other random points resampled from the original input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Quantitative and Qualitative Results Numerical results over the metrics of mIoU and screw IoU are given in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' From it, we can observe that using the STN module improves the performance drastically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' On the other hand, using the sim2real transfer learning with two steps of pre-training and fine-tuning also boosts the perfor- mance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Combining both gets even better performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Some qualitative results are given in Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' From it, we can observe that direct training on the real-world data performs decent on most points but not so good on tail cat- egories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' With pre-training on the simulated scenes and fine- tune the model on real-world scenes can achieve a much better segmentation result, especially for the tail categories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Post-processing for Screw Information After the network model is fine-tuned, given a real-world point cloud as input, the network outputs the segmenta- tion result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' The post-processing step aims at getting screw locations and orientations with the screw points that have been segmented out.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' To get screw locations, clustering al- gorithms are firstly used to group segmented screw points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' In our case, we use the Density-Based Spatial Clustering of Applications with Noise (DBSCAN) [11, 37] algorithm for clustering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' With appropriate parameter settings, each cluster is one screw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Using the prior knowledge that the bottom most screw is always the side screw, all the clusters above are cover screws that need to be unscrewed in this process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' The cover screw locations are obtained by com- puting the center of each cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' For the screw orientations, processing on the screw points directly is problematic since screws have uneven surfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Using the prior knowledge that all cover screws are having the same orientation as the flat cover, the screw orientation is actually identical to the Figure 5: Post-processing for screw information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' (a) (b) (c) Figure 6: Patch-based attention network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' (a) Full architecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' (b) Proposed patch module, has an additional defined kernel loss, outputs patch feature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' (c) Cross attention module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' normal of the cover flat part in our case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' We hence apply DBSCAN on the points that are segmented as the cover cat- egory but with their estimated normals other than coordi- nates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' With appropriate parameter settings, we can make the cluster number to be only one, which means all the points whose normal vectors are similar to the cover flat part are clustered together.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Then the cover normal, or the screw ori- entation, is obtained by averaging all the normal vectors of those points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' The process is illustrated in Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Ablation Study on Data Augmentation A variety of augmentation methods have been used on our synthetic dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' To validate their effectiveness, an ablation study is performed by generating several differ- ent datasets and using a same network architecture for the pre-training and fine-tuning processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' The numerical re- sults are given in Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' In the used four augmentation methods, the former two methods are augmentations per- formed during the data pre-processing, and the latter two methods are augmentations performed during the data gen- eration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' From Table 2, we can observe that randomly chang- ing the cuboid size improves the segmentation performance on both pre-training and fine-tuning steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' On the other hand, while the latter two augmentation methods decreases the pre-training performance, they both improves the fine- tuning performance when the model is transferred to real- world point cloud data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' In this paper, we use dataset 4 for most other experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Imbalanced Learning Imbalanced learning, also referred as long-tail learning in the classification tasks, is a problem where the distri- bution of examples across the known categories is biased or skewed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' In our case, original synthetic point clouds are mostly occupied with background points (around 96%) and have extremely less screw points (around 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='1%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' After ap- plying the sample region restriction, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=', the cuboid crop strategy as illustrated in Figure 2(c) and described in sub- section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='3, in each point cuboid, background points take up around 64% while screw points take up around 1%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' The imbalanced problem has been alleviated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Meanwhile, it is still worth investigating to further improve the performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Several additional strategies are proposed to deal with the imbalanced learning problem in this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' They are pro- posed from the perspectives of data augmentation, weight- ing loss, and extra network block respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Focused Sampling for Tail Categories One common strategy to deal with the long-tail problem in classification tasks is resampling like manually adding samples of the tail categories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' In our case, the key cate- gory of screw only occupies a extreme small portion of the whole point cloud compared to other components, hence it is possible to increase the number of screw points by den- sifying them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' The strategy is as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' For each point p1 belongs to the screw category, get its nearest same cat- egory point p2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' (a) If the nearest same category point of 48 x 512 Nx 512 Patch Cross Module Attention maxpool repeat dw dw 1024 N × 1024 1728 djw 192 2 3 3 Sequential 5 102 6 X STN X Edgeconvs XN XN XN 1x XN Z Z DGCNN BackboneNx 3 (after STN) Patch Module mlp N x 256 Nx 3 self-attention (before STN) Nx 256 + mlp N x 48 top1 top32 set 1x 48 32 x48 goals get coords get feature 48 x 3 48x1x3 48x32x256 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='conv 48 x 480 Kernel concate Loss 48x 512(point feature) (patch feature) Nx 512 48x512 Q K V N x 256 48 x 256 48x 256 ★ transpose multiply 256x48 & softmax N x 48 multiply N x 256 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='8972 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='9401 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='7683 Figure 7: Visualizing learned patches on sub-point clouds of 2048 points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' p2 is also p1, this means both points are not at the cluster boundary, hence a new point is added with the coordinate of padd = p1 + 1 3(p2 − p1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' (b) If the nearest same category point of p2 is not p1, this means p1 is likely to be an outlier point or at the cluster boundary, hence a new point is added with the coordinate of padd = p1 + 2 3(p2 − p1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Above op- eration doubles the point number of the tail category in the training dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Weighting Category Loss Adding additional weights to each category when com- puting the cross entropy loss is another widely used strat- egy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Most current DL packages provide such an optional argument in their in-built loss functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' However, it is an unsolved question that what is the best way to compute and set the category weights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' In this paper, we propose a following method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Assume the point cloud has M cate- gories and N points in total.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' For each category that has ni(i = 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' , M) points, its ratio is given as ri = ni/N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Then a scaled ratio sri is computed by decreasing the orig- inal ratio difference with a cubic root operation as sri = ti/(�M i=1 ti), where ti = (max(r1, r2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' , rM)/ri) 1 3 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' In this case, smaller ri means the corresponding category gets a larger sri.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' However, using sri directly leads to a huge decrease on the loss magnitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' To eliminate the possible problem caused by it, an additional factor is computed as f = �M i=1 ri × sri and multiplied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Hence the final cate- gory weight is given as ωi = sri × f for each category.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Patch-based Attention Network Additionally, we propose a novel patch-based attention network to deal with the imbalanced learning problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' The key idea is to force the network to learn a same number of kernel points for all categories by using an additional kernel loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' In our task, we have 6 categories in total and we select 8 kernel points per category.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' For each category, the ground truth kernel points are obtained by performing K-means algorithm on all points of this category.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' After 8 clusters are grouped, cluster centers are computed and their nearest neighbor points that belong to this category are de- fined as kernel points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' The kernel loss is a L2 loss between the goal kernels and learned kernels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Hence the total loss in this case is defined as: Ltotal = Lseg + αLrot + βLker (2) where β is a loss weight.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' We set β = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Apart from the obtained kernel points, their 32 neighbor points are grouped to form a patch and a convolution layer is used to get patch- wise features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' The patch-wise features are further used to perform cross attention with the point-wise features learned from the DGCNN backbone (lower branch in Figure 6(a)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' This is a patch-to-point cross attention, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=', using patch fea- tures to represent point features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' The output is concatenated back to the lower branch for final segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Detailed network designs are given in Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Experimental results All the experiments are conducted with the same dataset on which all augmentation methods are applied (dataset 4 in Table 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Numerical results of them are presented in Ta- ble 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' From it, we can observe that the focused sampling strategy always leads to a worse performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' One possible reason is that this operation is only performed during train- ing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' For test cases, labels are segmentation goals and are not provided hence the focused sampling operation is not appli- cable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' This causes data distribution difference between the training set and the test set thus leads to bad performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' The loss weighting strategy improves the performance on synthetic data but degrades the performance on real-world data slightly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' This indicates the strategy contributes to a better pre-training yet not performing well on transfer learn- ing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' On the other hand, our proposed patch-based attention module improves the performance on both steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' To give better insights of our proposed module, learned patches of some sub-point clouds are visualized in Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' It shows that our method forces the network to learn patches around boundaries or other informative places.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Conclusion In this paper, we adopt sim2real transfer learning method for an industrial application on point cloud data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Follow- ing the pipeline, synthetic dataset are generated in simulated scenes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' The network model is firstly pre-trained on the syn- thetic data and then fine-tuned on the real-world data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Both quantitative and qualitative results show that this achieves better performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' To deal with the imbalanced learning problem, several strategies have been tested.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' The proposed patch-based attention module shows its effectiveness by im- proving the performance drastically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' For future directions, we would like to try more backbones, as well as investigate more attention-based learning methods for point cloud data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Acknowledgements The project AgiProbot is funded by the Carl Zeiss Foun- dation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' References [1] Juan Felipe Perez-Juste Abascal, Nicolas Ducros, Va- leriya Pronina, Simon Rit, Pierre-Antoine Rodesch, Thomas Broussaud, Suzanne Bussod, Philippe Douek, Andreas Hauptmann, Simon Robert Arridge, and Franc¸oise Peyrin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Material decomposition in spectral ct using deep learning: A sim2real transfer approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' IEEE Access, 9:25632–25647, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' [2] Karol Arndt, Murtaza Hazara, Ali Ghadirzadeh, and Ville Kyrki.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Meta reinforcement learning for sim-to-real domain adaptation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' 2020 IEEE International Conference on Robotics and Automation (ICRA), pages 2725–2731, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' [3] Nicolas Audebert, Bertrand Le Saux, and S´ebastien Lef`evre.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Semantic segmentation of earth observation data using mul- timodal and multi-scale deep networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' In Asian conference on computer vision, pages 180–196.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Springer, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' [4] Christian Bonatti, Sylvain Crovisier, Lorenzo Diaz, and Amie Wilkinson.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' What is.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' a blender?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' arXiv preprint arXiv:1608.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='02848, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' [5] Alexandre Boulch, Bertrand Le Saux, and Nicolas Audebert.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Unstructured point cloud semantic labeling using deep seg- mentation networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' 3DOR@ Eurographics, 3, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' [6] Angel X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Chang, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Funkhouser, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Guibas, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Hanra- han, Qixing Huang, Zimo Li, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Savarese, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Savva, Shuran Song, Hao Su, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Xiao, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Yi, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Yu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Shapenet: An information-rich 3d model repository.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' ArXiv, abs/1512.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='03012, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' [7] Can Chen, Luca Zanotti Fragonara, and Antonios Tsour- dos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Gapnet: Graph attention based point neural network for exploiting local feature of point cloud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Neurocomputing, 438:122–132, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' [8] Maximilian Denninger, Martin Sundermeyer, Dominik Winkelbauer, Youssef Zidan, Dmitry Olefir, Mohamad El- badrawy, Ahsan Lodhi, and Harinandan Katam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Blender- proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' arXiv preprint arXiv:1911.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='01911, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' [9] Yuqing Du, Olivia Watkins, Trevor Darrell, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Abbeel, and Deepak Pathak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Auto-tuned sim-to-real transfer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' 2021 IEEE International Conference on Robotics and Automation (ICRA), pages 1290–1296, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' [10] Nico Engel, Vasileios Belagiannis, and Klaus C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Diet- mayer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Point transformer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' IEEE Access, 9:134826–134840, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' [11] Martin Ester, Hans-Peter Kriegel, J¨org Sander, and Xiaowei Xu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' A density-based algorithm for discovering clusters in large spatial databases with noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' In KDD, 1996.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' [12] David Griffiths and Jan Boehm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Synthcity: A large scale synthetic point cloud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' ArXiv, abs/1907.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='04758, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' [13] Michael Gschwandtner, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Kwitt, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Uhl, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Pree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Blensor: Blender sensor simulation toolbox.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' In ISVC, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' [14] Meng-Hao Guo, Junxiong Cai, Zheng-Ning Liu, Tai-Jiang Mu, Ralph Robert Martin, and Shimin Hu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Pct: Point cloud transformer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Vis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Media, 7:187–199, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' [15] Qingyong Hu, Bo Yang, Linhai Xie, Stefano Rosa, Yu- lan Guo, Zhihua Wang, Agathoniki Trigoni, and Andrew Markham.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Randla-net: Efficient semantic segmentation of large-scale point clouds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 11105–11114, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' [16] Binh-Son Hua, Minh-Khoi Tran, and Sai-Kit Yeung.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Point- wise convolutional neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' In Proceedings of the IEEE Conference on Computer Vision and Pattern Recogni- tion, pages 984–993, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' [17] Mingyang Jiang, Yiran Wu, Tianqi Zhao, Zelin Zhao, and Cewu Lu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Pointsift: A sift-like network module for 3d point cloud semantic segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' arXiv preprint arXiv:1807.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='00652, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' [18] Samin Khan, Buu Phan, Rick Salay, and Krzysztof Czar- necki.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Procsy: Procedural synthetic dataset generation to- wards influence factor studies of semantic segmentation net- works.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' In CVPRW, pages 88–96, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' [19] Sebastian Koch, Albert Matveev, Zhongshi Jiang, Francis Williams, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Artemov, Evgeny Burnaev, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Alexa, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Zorin, and Daniele Panozzo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Abc: A big cad model dataset for ge- ometric deep learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' CVPR, pages 9593–9603, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' [20] Felix J¨aremo Lawin, Martin Danelljan, Patrik Tosteberg, Goutam Bhat, Fahad Shahbaz Khan, and Michael Felsberg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Deep projective 3d semantic segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' In International Conference on Computer Analysis of Images and Patterns, pages 95–107.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Springer, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' [21] Truc Le and Ye Duan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Pointgrid: A deep network for 3d shape understanding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 9204– 9214, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' [22] Le Hoang-An, Thomas Mensink, Partha Das, Sezer Karaoglu, and Theo Gevers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Eden: Multimodal synthetic dataset of enclosed garden scenes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' 2021 IEEE Winter Con- ference on Applications of Computer Vision (WACV), pages 1578–1588, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' [23] Zhidong Liang, Ming Yang, Hao Li, and Chunxiang Wang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' 3d instance embedding learning with a structure-aware loss function for point cloud segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' IEEE Robotics and Automation Letters, 5:4915–4922, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' [24] Nai Qing Liu, Yinghao Cai, Tao Lu, Rui Wang, and Shuo Wang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Real–sim–real transfer for real-world robot control policy learning with deep reinforcement learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Applied Sciences, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' [25] Mohammadhossein Malmir, Josip Josifovski, Noah Klar- mann, and Alois Knoll.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Robust sim2real transfer by learning inverse dynamics of simulated systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' [26] Daniel Maturana and Sebastian Scherer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Voxnet: A 3d con- volutional neural network for real-time object recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' In 2015 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pages 922–928.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' IEEE, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' [27] Volodymyr Mnih, Koray Kavukcuoglu, David Silver, An- drei A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Rusu, Joel Veness, Marc G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Bellemare, Alex Graves, Martin A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Riedmiller, Andreas Fidjeland, Georg Ostro- vski, Stig Petersen, Charlie Beattie, Amir Sadik, Ioannis Antonoglou, Helen King, Dharshan Kumaran, Daan Wier- stra, Shane Legg, and Demis Hassabis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Human-level control through deep reinforcement learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Nature, 518:529–533, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' [28] Kaichun Mo, Shilin Zhu, Angel Chang, Li Yi, Subarna Tri- pathi, Leonidas Guibas, and Hao Su.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' PartNet: A large-scale benchmark for fine-grained and hierarchical part-level 3D object understanding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' [29] Alexander Pashevich, Robin Strudel, Igor Kalevatykh, Ivan Laptev, and Cordelia Schmid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Learning to augment synthetic images for sim2real policy transfer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' 2019 IEEE/RSJ Interna- tional Conference on Intelligent Robots and Systems (IROS), pages 2651–2657, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' [30] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Pierdicca, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Mameli, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Malinverni, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Paolanti, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Frontoni.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Automatic generation of point cloud synthetic dataset for historical building representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' In AVR, pages 203–219, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' [31] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Qi, Hao Su, Kaichun Mo, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Guibas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Pointnet: Deep learning on point sets for 3d classification and segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' CVPR, pages 77–85, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' [32] Charles R Qi, Li Yi, Hao Su, and Leonidas J Guibas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Point- Net++: Deep hierarchical feature learning on point sets in a metric space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' arXiv preprint arXiv:1706.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='02413, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' [33] Aravind Rajeswaran, Vikash Kumar, Abhishek Gupta, John Schulman, Emanuel Todorov, and Sergey Levine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Learning complex dexterous manipulation with deep reinforcement learning and demonstrations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' ArXiv, abs/1709.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='10087, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' [34] Jacob Revell, Dominic Welch, and James M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Hereford.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Sim2real: Issues in transferring autonomous driving model from simulation to real world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' SoutheastCon 2022, pages 296–301, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' [35] Olaf Ronneberger, Philipp Fischer, and Thomas Brox.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' U-net: Convolutional networks for biomedical image segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' ArXiv, abs/1505.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='04597, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' [36] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Ros, Laura Sellart, Joanna Materzynska, David V´azquez, and Antonio M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' L´opez.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' The synthia dataset: A large collec- tion of synthetic images for semantic segmentation of urban scenes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' CVPR, pages 3234–3243, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' [37] Erich Schubert, J¨org Sander, Martin Ester, Hans Peter Kriegel, and Xiaowei Xu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Dbscan revisited, revisited: why and how you should (still) use dbscan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' ACM Transactions on Database Systems (TODS), 42(3):1–21, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' [38] Philip Shilane, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Min, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Kazhdan, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Funkhouser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' The princeton shape benchmark.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Proceedings Shape Modeling Applications, 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=', pages 167–178, 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' [39] Martin Simonovsky and Nikos Komodakis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Dynamic edge- conditioned filters in convolutional neural networks on graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 3693–3702, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' [40] Maxim Tatarchenko, Jaesik Park, Vladlen Koltun, and Qian- Yi Zhou.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Tangent convolutions for dense prediction in 3d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 3887–3896, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' [41] Hugues Thomas, Charles R Qi, Jean-Emmanuel Deschaud, Beatriz Marcotegui, Franc¸ois Goulette, and Leonidas J Guibas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Kpconv: Flexible and deformable convolution for point clouds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' In Proceedings of the IEEE/CVF international conference on computer vision, pages 6411–6420, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' [42] Joshua Tobin, Rachel Fong, Alex Ray, Jonas Schneider, Wo- jciech Zaremba, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Abbeel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Domain randomization for transferring deep neural networks from simulation to the real world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' 2017 IEEE/RSJ International Conference on Intelli- gent Robots and Systems (IROS), pages 23–30, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' [43] Jonathan Tremblay, Thang To, and Stan Birchfield.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Falling things: A synthetic dataset for 3d object detection and pose estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' CVPRW, pages 2119–21193, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' [44] Juliano Vacaro, Guilherme Marques, Bruna Oliveira, Gabriel Paz, Thomas S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Paula, Wagston Staehler, and David Murphy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Sim-to-real in reinforcement learning for everyone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' 2019 Latin American Robotics Symposium (LARS), 2019 Brazil- ian Symposium on Robotics (SBR) and 2019 Workshop on Robotics in Education (WRE), pages 305–310, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' [45] G¨ul Varol, Javier Romero, Xavier Martin, Naureen Mah- mood, Michael J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Black, Ivan Laptev, and Cordelia Schmid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Learning from synthetic humans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' CVPR, pages 4627–4635, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' [46] Shenlong Wang, Simon Suo, Wei-Chiu Ma, Andrei Pokrovsky, and Raquel Urtasun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Deep parametric continu- ous convolutional neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' In Proceedings of the IEEE Conference on Computer Vision and Pattern Recogni- tion, pages 2589–2597, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' [47] Yue Wang, Yongbin Sun, Ziwei Liu, Sanjay E Sarma, Michael M Bronstein, and Justin M Solomon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Dynamic graph cnn for learning on point clouds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Acm Transactions On Graphics (tog), 38(5):1–12, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' [48] Matthew Witman, Dogan Gidon, David B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Graves, Berend Smit, and Ali Mesbah.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Sim-to-real transfer reinforcement learning for control of thermal effects of an atmospheric pressure plasma jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Plasma Sources Science and Technol- ogy, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' [49] Wenxuan Wu, Zhongang Qi, and Fuxin Li.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Pointconv: Deep convolutional networks on 3d point clouds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 9613–9622, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' [50] Zhirong Wu, Shuran Song, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Khosla, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Yu, Linguang Zhang, Xiaoou Tang, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Xiao.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' 3d shapenets: A deep rep- resentation for volumetric shapes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' CVPR, pages 1912–1920, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' [51] Xiangyu Yue, Yang Zhang, Sicheng Zhao, Alberto L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Sangiovanni-Vincentelli, Kurt Keutzer, and Boqing Gong.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Domain randomization and pyramid consistency: Simulation-to-real generalization without accessing target domain data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' 2019 IEEE/CVF International Conference on Computer Vision (ICCV), pages 2100–2110, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' [52] Hengshuang Zhao, Li Jiang, Jiaya Jia, Philip H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Torr, and Vladlen Koltun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Point transformer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' ArXiv, abs/2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='09164, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' [53] Wenshuai Zhao, Jorge Pe˜na Queralta, and Tomi Wester- lund.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Sim-to-real transfer in deep reinforcement learning for robotics: a survey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' 2020 IEEE Symposium Series on Compu- tational Intelligence (SSCI), pages 737–744, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' [54] Qingnan Zhou and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Jacobson.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Thingi10k: A dataset of 10, 000 3d-printing models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' ArXiv, abs/1605.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content='04797, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' [55] Fuzhen Zhuang, Zhiyuan Qi, Keyu Duan, Dongbo Xi, Yongchun Zhu, Hengshu Zhu, Hui Xiong, and Qing He.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' A comprehensive survey on transfer learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} +page_content=' Proceedings of the IEEE, 109:43–76, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE4T4oBgHgl3EQfWgxs/content/2301.05033v1.pdf'} diff --git 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mode 100644 index 0000000000000000000000000000000000000000..3025b0f92d42cb1c06be1fd94fb7628e511df71d --- /dev/null +++ b/wNE3T4oBgHgl3EQfOQnS/content/tmp_files/2301.04392v1.pdf.txt @@ -0,0 +1,1568 @@ +Adaptive Data Path Selection for Durable +Transaction in GPU Persistent Memory +1st Xinjian Long, +State Key Laboratory of Networking and Switching Technologies +Beijing University of Posts and Telecommunications +Beijing, China +barbiel origin@bupt.edu.cn +Abstract—The new non-volatile memory technology relies on +data recoverability to achieve the promise of byte-addressable +persistence in computer applications. The durable transaction +(e.g. logging) is one of the major persistency programming models +to provide recoverable data structures. To achieve performant +failure-atomic transactional updates to PM, multi-data-path ar- +chitectures that separate the data paths for persists are recently +explored for CPUs. Considering the importance of GPU as a key +computing platform for many application domains, we investigate +the multi-data-path architecture for durable transactions to PM +in GPU. Our solution, AGPM, exploits an adaptative data-path- +selection strategy for the log updates to PM. AGPM reduces the +GPU kernels’ execution time by at least 24.37% (at most 66.44%) +compared to the state-of-the-art designs. +Index Terms—Graphics Processing Unit, Persistent Memory, +Durable Transaction +I. INTRODUCTION +Persistent memory (PM) or non-volatile memory (NVM) +technologies have received significant attention from both +academia [1, 2, 3, 4, 5, 6, 7] and industry [8, 9, 10, 11]. +PM is expected to provide high integration density compara- +ble to disk storage at latencies comparable to DRAM [12] +while supporting byte-grained addressability and durability +[13]. The recent commercialization of PM is Intel’s Optane +NVM [14]. Years of PM research on the CPU have been +stacked [6, 15, 16, 17, 18, 19, 20], but the corresponding +exploration on the GPU is surprisingly limited, let alone the +hardware implementation of PM onboard the modern GPU. +However, features of PM (increased memory capacity, high +access speed, data recoverability, etc.) are proven beneficial +for GPU workloads [21]. Thus, it is necessary for GPU to +support PM, and there is a lot of potential for GPU-specific +PM design that yields high performance. +Data recoverability is one of the key reasons why GPU +applications are benefited from the PM. For instance, long- +running GPU applications (deep neural network training, +proof-of-work algorithms in blockchain applications, etc.) can +obtain performance improvement by relying on recoverable +data structures residing in the main memory instead of con- +ducting costly system checkpointing [22, 23]. Persistency +model [6, 7, 16, 24, 25] is necessary for the implementation +of the recoverable data structure. This is because the commit +order of the PM updates could be different from the order they +reach the PM due to the existence of the volatile write-back +caches. Besides, persistency models can provide transaction- +like semantics [6, 8, 26], which enables a part of the program, +delineated by durable transaction, to be recoverable with all +the data persisted therein all or nothing. Durable transactions +could apply separate data paths to move data to PM for +durability and consistency as needed. On the one hand, a +store followed by a clwb instruction can be used to persist a +specific line from the volatile cache hierarchy to PM (temporal +path). On the other hand, applications can also use non- +temporal instructions to bypass the cache and write directly to +the PM (non-temporal path). Upon analysis of different GPU +workloads, we observe that the inappropriate selection of the +data path further deteriorates the performance problem. Most +of the current persistency models are designed to statically use +a single-data-path architecture, which risks the applications +using PM experiencing unnecessary performance loss. +Recently, Shahri et al. [27] proposed an extension to the x86 +memory persistency model to exploit the differences in speeds +of requests sent along the temporal and the non-temporal paths +to reduce the reliance on using sfence instruction. Jeong et +al. [28] proposed a hardware/software co-design scheme that +leverages the separate FIFO data paths to enforce persisting +orders. These designs decided to only consider the types of +PM requests (load, store, etc.) as the key factor to selecting +the data path. For example, when using undo logging, the log +updates must persist before the corresponding data updates. In +this case, logs are intuitively updated using the non-temporal +path instead of the temporal one [13, 29]. This is because +the non-temporal path is commonly faster than the temporal +one by skipping the multiple levels of caches between the +processor and the persistent domain. In addition, logs are +expected to never be read during failure-free execution, and +the usage of the temporal data path’s write-no-allocate policy +can avoid polluting the volatile caches while reducing the undo +logging’s overhead. In contrast with this intuition, we observe +that the performance of using different data paths varies +across GPU applications due to their different memory access +behaviors. In some cases, we observe that log updates using +the slow temporal path can be more beneficial than using the +fast non-temporal path. On the other hand, the temporal path is +not always more beneficial for data updates with temporal and +arXiv:2301.04392v1 [cs.AR] 11 Jan 2023 + +spatial localities. Specifically, the non-temporal path is more +recommended compared to the temporal one when the data +locality is too strong and the reuse distances are too long to +help the cached data be reused before eviction. Overall, our +observation manifests that it is not amenable to handling GPU +PM requests using a static path selection strategy, and there +is a lot of potential for the multi-path architecture to achieve +better performance for GPU workloads’ persist ordering. +Building on our observations, we propose an adaptive +approach (AGPM) to select the data path for the durable +transactions in GPU. This approach adds AGPM buffers in +the GPU memory hierarchy to record the data locality between +the PM log updates and the subsequent data updates, as well +as the locality among the log updates, within the GPU L1D +caches and the shared L2 cache. Periodically, statistics in the +AGPM buffers are fed to an added path selector in each SM +and are translated to 8 reasons/patterns. Such translation is +conducted upon the temporal and spatial locality of the PM +logging data in the L1D and the L2 caches, the GPU kernel’s +usage of the shared memory, and the number of log updates. +Reasons/patterns are exploited to help derive the data path +selection decision for undo logging. Overall, this paper makes +the following contributions: +1) We analyze the L1D and L2 data localities for GPU +kernels’ transactional interaction with PM (undo log- +ging) and their resulting performance in different types +of GPU workloads. +2) We propose an adaptive approach for PM requests’ data +path selection in GPU referred to as AGPM, such that +the PM log updates’ data paths are selected according +to the kernel accesses’ data locality and characteristics. +3) Experimental results show that AGPM achieves signifi- +cant performance improvement over the static data path +selection methods. Meanwhile, AGPM outperforms the +state-of-the-art (SOTA) multi-data-path architectures to +PM. Compared to the SOTA designs, AGPM reduces +the GPU kernels’ execution time by at least 24.37% (at +most 66.44%). +The remainder of this paper is organized as follows. Sec- +tion II presents the background. Section III discusses the +motivation of this study. Section IV describes the design of +the proposed AGPM. Section V compares the results of our +proposed AGPM with the other methods. Section VI discusses +the related works, before providing concluding remarks in +Section VII. +II. BACKGROUND +In this section, we review the current persistency models +on CPUs and GPUs. We also introduce the GPU architecture +and the programming model following the NVIDIA/CUDA +terminology. It is worth noting that the techniques mentioned +in this section, as well as our design described in the following +sections, are adaptable to other GPU architecture besides +NVIDIA. +A. Memory persistency models +Byte-addressable persistent memory provides a promising +future for high-performance in-memory computing with re- +coverable data structures (RDS). However, due to the volatile +write-back caches, the order of load and store requests +arriving at the persistent memory can be different from their +commit order. This breaks the rule of RDS. For example, +assuming that p is a persistent structure. ’p → data’ and ’p +→ state’ reside in different cache lines and the update to ’p +→ data’ precedes the update to ’p → state’ in the program. +However, the ’p → state’ in memory may be updated before ’p +→ data’ due to the caches. In this case, if a fault (e.g., a power +failure) happens, the persistent memory state becomes incor- +rect after power is restored. To deal with this issue and support +correct implementations of RDS, memory persistency models +[6, 7, 16, 24, 25, 30] are proposed to formally specify the order +of writes to PM. These models can be broadly characterized +as the strict and the relaxed models, which are distinct in +the levels of concurrency. In the strict persistency model, the +order of the volatile memory operations is identical to the +order of the PM operations. This model is easy to implement, +but it limits the program’s concurrency which leads to the +most serious performance degradation. The relaxed persistency +model is more performant by breaking the tie between the +volatile memory operations and the PM operations. A higher +level of PM writes concurrency is supported at the cost of +program annotation and hardware complexities. +The memory persistency models mentioned above specify +the durability order of stores but ordering alone does not +guarantee data recoverability. For example, assume that with +either a strict or relaxed persistency model, ’p → data’ and +’p → state’ in PM are updated in the program order. But +it is still possible that a fault happens after ’p → data’ is +updated but before ’p → state’ is updated. In this case, the +memory state in PM is still not correct for data recovery. To +handle this issue, durable transactions [6, 8, 26] (e.g. undo +logging), which provide all-or-nothing guarantees by undoing +changes from an aborted transaction, are required. To be able +to roll back changes, an undo log entry will be created prior +to every update performed within the transaction. The undo +log entry contains the current value of the persistent structure +that is to be updated. Once the log entry has been created and +persisted, only then is the actual value updated. If a transaction +succeeds, a commit message is atomically sent to invalidate +the log entries belonging to the transaction. If a transaction +fails, the recovery process uses all the persisted log entries to +roll back partial changes from that transaction. +Currently, memory persistency models, as well as durable +transactions, are designed for the CPU. These models need to +be re-architected for GPUs due to the differences in both the +workloads and the processors’ architectures. Lin et al. [31] +explore the implementation of different levels (kernel-level, +CTA-level, and loop-level) of memory persistency models in +GPU. We exploit their implementation, especially the CTA- +level undo logging for GPU, in this study. Figure 1 shows + +an example of CTA-level undo logging. First, undo logs are +created for the output elements (Loc1 and Loc2) that are to be +updated by the CTA. After ensuring all the threads persist their +log using the sfence followed by the CUDA +syncthreads +function, a flag for the log is set to be inTx and is made +durable. The values (p→data and p→state) of the output +elements are updated iteratively by the CTA. At the end of the +CTA, all the outputs are ensured to be persisted using another +syncthread function, and the flag is set to be complete. +Note that all the undo logging described in the following +sections in this study refers to CTA-level undo logging. +Fig. 1. An example of CTA-level undo logging of a GPU kernel. +B. GPU with PM +Today, there is no hardware with PM onboard the GPU. If a +GPU application wishes to leverage PM’s persistence, it would +typically perform computations on the GPU and ensure the +persistence of the results on the CPU. The computation results +need to be transferred from the GPU’s memory to the CPU’s +memory and rely on the CPU to guarantee data recoverability. +Alternatively, one could leverage the file system, since only +the file systems atop block-storage devices could guarantee +persistence before the advent of NVM technologies. After +the computation results from the GPU are transferred to +the CPU’s memory, the CPU writes the results to a PM- +resident file and then guarantees persistence using the fsync +function. Furthermore, a PM resident file can be memory- +mapped onto the CPU’s address space, and the GPU’s results +can be transferred to the memory-mapped file residing in the +CPU memory using cudaMemcpy. +Pandey et al. proposed GPM [21] to use NVIDIA’s uniform +virtual addressing (UVA) technique [32] to map PM to GPU’s +address space, and system-scoped fence with selective dis- +abling of the data direct IO (DDIO) feature to enable GPUs to +access and persist data in PM with no CPU involvement. GPM +leverage the fact that the modern PM (Intel Optane [14]) is +placed alongside the DRAM, as in a typical Intel Xeon server, +and can be accessed by a GPU over the PCI-e interconnect. In +this case, UVA can be used to map desired portions of NVM +onto the virtual address space of a GPU kernel. Then, GPU +kernels can directly access and manipulate PM-resident data +structures at byte granularity using loads and stores without +the CPU’s assistance. +III. MOTIVATION +This section discussed the impetus of this study. For sim- +plicity, we assume a discrete GPU system equipped with +persistent memory (Figure 2). This assumption enables us to +focus on the GPU memory hierarchy without considering the +potential effects of the host-side memory system as well as +the costly data transfers between the system and GPU device +memory. We further assume that the PM controller supports +the asynchronous DRAM refresh (ADR) [33] feature and is +in the persistent domain. All updates to PM will be durable +once they reach the PM controller. Intel recently announced +an enhanced ADR (eADR) [34] feature. eADR drains the +entire contents of CPU caches to PM on power failures, which +obviates the need to flush cache blocks from the CPU’s caches +in order to guarantee persistence in future processors. Besides, +the fence is still needed to maintain the ordering of writes to +PM [35]. This study can be projected on a future system with +eADR, since the data path selection of data persisting takes +place before the cache line flushes. We focus on GPUs’ durable +transactions (undo logging) in this study. Note that there are +other persistency memory models for persist ordering in GPU, +these models are beyond the scope of this study. +TABLE I +DIFFERENT TYPES OF BENCHMARKS ARE CATEGORIZED BY THE +PERFORMANCE DIFFERENCE USING THE TEMPORAL AND THE +NON-TEMPORAL PATH FOR UNDO LOGGING. +Type +Metric +Benchmark +I +perfT > perfNT , diff > 5% +SAD1, GRID1, GRID2, +2DCONV, Backprop1, +Pathfinder, 2MM1, +3MM1, GEMM +II +perfT < perfNT , diff > 5% +SGEMM, Backprop2, +ATAX1, ATAX2, NW, +SSSP2, MVT1, +GESUMMV, RA +III +diff ≤ 5% +Stencil1, SSSP1, +StreamTriad, BFS +Figure 3 shows the experimental results of 22 GPU bench- +mark kernels using a static data path selection for undo- +logging. Figure 3 reveals several important observations. First, + +device_ woid CTA_ log_example(..) +1 +Locl[tid] = p->data[tid] +Loc2[tid] = p->state[tid]; +Wp is initialzed +1og (Locl[tid]),clwb;sfence; +1og (Loc2[tid]),clwb ;sfence; +/logsforp +synchthreads(0. +/logs are persisted +if(tid==0)K +flag=inIx. +1og(flag);clwb,sfenc2; +/flag is pers isted +1 +for (iterations ) +W/p is upd ated +Locl [tid] = p->data[tid]; +clwb,sfence; +Loc2[tid] = p->state[tid]; +clwb,sfence: +1 +synchthreads(O: +/CTA completes +if(Gd =0) +flag=complete: +1og(flag);clwb,sfence; +/flag is pers isted +1Fig. 2. Overviews of the assumed GPU system equipped with NVM/PM. $ +denotes cache. MC denotes the memory controller. NVMC denotes the non- +volatile memory controller. +data recoverability enabled by undo logging introduces +different levels of performance overheads to different +GPU benchmark kernels. For instance, the PM operations +invoking the nt-store instructions expand the execution time +of the SAD1 kernel to 325.5% compared to the execution +time without undo logging, while nt-store expands SGEMM’s +execution time to 102.7%. Furthermore, we can see that +store+clwb delivers a shorter execution time than nt-store +among several benchmark kernels (SAD1, GRID1, GRID2, +2DCONV, Pathfinder, 2MM1, 3MM1, GEMM). These results +lead to our second observation: the presumption that nt- +store is more beneficial for undo logging is not applicable +to all GPU applications. According to Figure 3, we broadly +categorized 22 benchmark kernels into three types according +to two metrics (perf and diff) as described in Table I. +perf T denotes the benchmark performance (execution time, +etc.) using the temporal path (store+clwb) for undo logging, +and perf NT denotes the performance using the non-temporal +path (nt-store). diff denotes the absolute difference between +perf T and perf NT . +Due to the similarity between this study and the cache +bypassing problem [36, 37] in GPU, we try to explain +the benchmark kernels’ performance difference following the +cache bypassing logic. One of the most important ideas in +this area is to perform cache bypassing according to GPU +kernels’ memory coalescing behaviors [36]. These studies +conclude that the un-coalesced loads/stores should bypass +the volatile caches because such requests generate massive +memory accesses compared to the other memory instructions. +Besides, data fetched by these requests is likely to possess +poor locality, which is not worthy of consuming the scarce +cache resources in the GPU architecture. Figure 4 shows the +distribution of the loads/stores (including the undo loggings +and the other memory updates) with different numbers of +memory accesses. We can see that the performance difference +shown in Figure 3 is not coherent with the benchmark kernels’ +coalescing behaviors. For example, StreamTriad, ATAX2, and +3MM1 are perfectly memory coalesced, whose memory un- +coalescing degrees are within [1, 2]. However, these kernels +vary from type I to III as described in Table I. Thus, we can +see that this study is not essentially identical to the cache +bypassing problem in GPU, and a new design is required. +In order to explain the performance difference using differ- +ent data paths, we define 10 variables to characterize the GPU +kernels’ temporal and spatial localities as described in Table +II. For example, l1d t all denotes the number of cache hits +with the temporal locality in the L1D cache, and these accesses +are generated by both the log and the other data updates. This +goes the same for the other 7 variables (l1d(l2) t(s) all(log)). +Since we are focusing on durable transactions in GPU PM, we +believe that the statistics of both the log updates (log) and the +non-log updates (all) are required. We define that the non- +log updates’ temporal locality in the L1D cache means the +re-hits of a specific byte by a log update followed by a non- +log data update, and the log updates’ temporal locality in the +L1D cache means the re-hits of a specific byte by a log update +followed by another log update. Similarly, we define that the +non-log updates’ spatial locality in the L1D cache means the +re-hits of a specific aligned 128-byte segment (cache block) +by a log update followed by a non-log data update, and the +log updates’ spatial locality in the L1D cache means the re- +hits of a specific byte by a log update followed by another +log update. These go the same for the statistics of the L2 +cache. Note that Maxwell, Pascal, and Volta GPU architectures +use demand-fetch caches to fetch only the chunks that are +requested instead of fetching a full cache line to handle the +data over-fetch problem [38]. Thus, the number of accesses in +the GPU caches with the temporal locality is not necessarily +identical to the one with the spatial locality. According to Table +II, we conclude 8 reasons to explain Figure 3’s performance +difference as described in Table III. +Intuitively, the nt-store instruction is considered profitable +for log updates [13, 29]. This is because logs are considered +only necessary for crash consistency and never read in failure- +free execution. In this case, the nt-store’s write-no-allocate +policy, which writes data blocks directly to memory without +adding to the cache, provides more benefits for logging and +reduces cache pollution. On the other hand, introducing the +frequently reused data blocks into the volatile caches by +the store+clwb’s write-allocate policy help save a lot of +expensive memory transactions. Thus, a simple idea for the +undo logging’s data path selection is to rely on the locality be- +tween the log updates and the subsequent data updates. More +specifically, the stronger locality is observed the more likely +to use the temporal path (store+clwb). Otherwise, the non- +temporal path (nt-store) should be selected. However, Table +II shows different patterns compared to this intuition. And +this leads to our third observation: store+clwb do not always +provide more benefits than nt-store for data updates with +good localities in GPU caches. For reasons a, b, and d, the +major differences come from whether the values of l1d t log + +SM +SM +SM +SIMD +SIMD +SIMD +core +core +core +L1 $ +L1 $ +L1 $ +Interconnect +partition +partition +partition +partition +MC +MC +NVMC +NVMC +GDDR +GDDR +NVM +NVM +Persistent domainFig. 3. Normalized execution time of 22 GPU benchmark kernels using separate data paths for undo-logging. ATAX1 and ATAX2 indicate the first and the +second kernel of the ATAX benchmark. This goes the same for the other benchmarks. base denotes the benchmarks that are executed using NVM without +persistency support. nt-store denotes the implementation follows the description in [27, 28], which uses the non-temporal path to persist the log updates to +PM and uses the temporal path for the subsequent data updates. store+clwb denotes that both the log and the corresponding data updates use the temporal +path. All the results are normalized by the execution time running with base. +TABLE II +TEMPORAL AND SPATIAL LOCALITY OF 22 GPU BENCHMARK KERNELS’ MEMORY ACCESSES IN GPU’S L1D AND L2 CACHE. l1d DENOTES THE L1D +CACHE. l2 DENOTES THE L2 CACHE. t DENOTES TEMPORAL. s DENOTES SPATIAL. all DENOTES THE MEMORY ACCESS GENERATED BY BOTH THE LOG +AND THE OTHER DATA UPDATES. log DENOTES THE MEMORY ACCESS GENERATED BY THE LOG UPDATES. type DENOTES THE KERNELS’ TYPE AS +DESCRIBED IN TABLE I. reason DENOTES THE REASON WHY THE CERTAIN KERNEL BELONGS TO A CERTAIN TYPE AS DESCRIBED IN TABLE III. +Benchmark +l1d t all +l1d t log +l1d s all +l1d s log +l2 t all +l2 t log +l2 s all +l2 s log +all +log +type +reason +SAD1 +0 +0 +0 +0 +289160 +157652 +300509 +167001 +2288857 +324803 +I +c +Stencil1 +0 +0 +0 +0 +0 +0 +0 +0 +131871 +33849 +III +f +SGEMM +0 +0 +0 +0 +0 +0 +0 +0 +3191435 +133274 +II +h +GRID1 +2398 +0 +3126 +0 +7495 +3483 +9588 +3930 +1047435 +662069 +I +a +GRID2 +47898 +0 +47898 +0 +140745 +64156 +140745 +64156 +591011 +200163 +I +a +2DCONV +0 +0 +0 +0 +0 +0 +0 +0 +79334 +17060 +III +f +Backprop1 +0 +0 +7 +6 +0 +0 +153 +147 +88412 +65076 +I +g +Backprop2 +8764 +2671 +9476 +2987 +8958 +6330 +9707 +6920 +280763 +118159 +II +b +Pathfinder +1221 +97 +1225 +101 +35000 +26646 +35843 +27229 +806640 +382582 +I +d +StreamTriad +0 +0 +0 +0 +0 +0 +0 +0 +36000 +17476 +III +f +RA +1 +1 +2 +2 +2 +1 +4 +2 +6644 +2676 +II +b +ATAX1 +45460 +45460 +45460 +45460 +135526 +89964 +135526 +89964 +1926411 +180170 +II +b +ATAX2 +89032 +45562 +134032 +45562 +135770 +90000 +135770 +90000 +545022 +180170 +II +b +NW +82 +40 +154 +84 +204 +88 +426 +156 +3195 +1392 +II +h +BFS +5 +0 +5 +0 +2 +1 +2 +1 +9528 +79 +III +e +SSSP1 +0 +0 +0 +0 +1 +0 +1 +0 +1007 +17 +III +e +SSSP2 +1028 +771 +1028 +771 +2570 +1285 +2570 +1285 +9509 +6168 +II +b +MVT +63720 +63720 +63720 +63720 +196227 +130846 +196227 +130846 +9444863 +341037 +II +b +GESUMMV +60929 +60929 +60929 +60929 +193639 +129104 +193639 +129104 +15752038 +281725 +II +b +2MM1 +1639464 +0 +2809772 +0 +5608094 +4905025 +6369854 +5416431 +95599514 +51796409 +I +a +3MM1 +28360 +0 +28608 +0 +441916 +411072 +449205 +418361 +7281497 +4458165 +I +a +GEMM +33545 +2031 +34045 +2031 +1533475 +1501161 +1559512 +1527197 +7332760 +4503201 +I +d +and l1d s log are equal to 0 or not. l1d t log and l1d s log +reveal whether the identical cache chunk or the identical cache +line is repeatedly referenced by the log updates. When these +two variables are equal to 0 (reason a) or only occupy a small +fraction (≤ 0.25) of all the memory accesses with the locality +(reason d), the experimental results follow the aforementioned +intuition that using the store+clwb instructions achieve better +performance than using the nt-store (type I). However, when +too-strong localities are observed in the L1D cache accesses +caused by the log updates (reason b), we can see that nt-store +provides more benefits compared to store+clwb in this case. +This is because the cache thrashing between the L1D cache +and the L2 cache through the slow interconnected network +impedes the performance advantage of using the caches for +the data with good localities. Figure 5 shows the normalized +mean transmitted bytes of the kernels belonging to a certain +reason using the temporal (store+clwb) and the non-temporal +(nt-store) data path. When the data localities in volatile +caches increase, the memory traffic as well as the pipeline +utilization grow due to the less warp stall and the fewer +expensive memory transactions. However, when such localities +become too strong and the reuse distances are too long to +help the cached data be reused before eviction, the invalidation +frequency of the GPU volatile caches will grow dramatically + +base +nt-store +μ storetclwbFig. 4. +Distribution of loads/stores with different memory un-coalescing +degrees. N denotes the number of memory accesses for a load/store +belonging to the same warp after memory coalescing. +TABLE III +STATISTICS-BASED REASONING. +Reason +Metrics +Type +a +l1d t all ̸= 0 and l1d s all ̸= 0 and +I +l1d t log = 0 and l1d s log = 0 +b +l1d t all ̸= 0 and l1d s all ̸= 0 and +II +l1d t log ̸= 0 and l1d s log ̸= 0 and +l1d t(s) log / l1d t(s) all > 0.25 +c +l1d t all = 0 and l1d s all = 0 and +I +l1d t log = 0 and l1d s log = 0 and +l2 t all ̸= 0 and l2 s all ̸= 0 and +l2 t log ̸= 0 and l2 s log ̸= 0 +d +l1d t all ̸= 0 and l1d s all ̸= 0 and +I +l1d t log ̸= 0 and l1d s log ̸= 0 and +l1d t(s) log / l1d t(s) all ≤ 0.25 +e +log ≤ 100 +III +f +l1d t all = 0 and l1d s all = 0 and +II, III +l1d t log = 0 and l1d s log = 0 and +l2 t all = 0 and l2 s all = 0 and +l2 t log = 0 and l2 s log = 0 +g +l1d t all = 0 and l1d s all ̸= 0 and +I +l1d t log = 0 and l1d s log ̸= 0 +h +usage of shared memory +II +which finally turns into cache contention and thrashing. For +kernels belonging to reason c, since no locality is observed in +the L1D cache, there is no risk of experiencing serious thrash- +ing while enjoying the benefit provided by store+clwb, these +kernels are categorized as type I. For reason f, kernels have +no data locality in either the L1D cache or the L2 cache. nt- +store is intuitively considered suitable for this pattern because +of the write-no-allocate policy. However, these GPU kernels +show interesting behavior in that the performance of using the +store+clwb and the nt-store are similar (type III). We believe +that this is because of GPU’s massive multi-threading which +effectively hides the cache allocation overhead, and this results +in average performance using either the temporal path or the +non-temporal path for persistency. For reason g, moderate +localities are observed in both the L1D cache and the L2 cache, +thus kernels belonging to this category are type I. For reason +e and reason h, these are two special cases that can not be +explained by the adaptability between the log and the non- +log updates’ localities and the temporal or the non-temporal +data path. For reason e, the number of the log updates is too +small (<100) and this makes a negligible difference between +the usage of the store+clwb and the nt-store (type III). For +reason h, these kernels use the shared memory to communicate +and synchronize for the threads within the same CTA(TB). In +this case, most of the data fetched in the volatile cache will not +be reused, and using the nt-store instruction becomes more +beneficial than using the store+clwb instructions (type II). +Fig. 5. Normalized mean transmitted bytes comparison between the GPU L1D +cache and the L2 cache using the store+clwb and the nt-store instructions. +s2m denotes the transmission from the L1D cache to the L2 cache, and m2s +denotes the transmission from the L2 cache to the L1D cache. +IV. OUR SOLUTION +As discussed in Section III, we leverage 10 variables and 8 +reasons to explain the performance difference of GPU’ undo +logging using the store+clwb and the nt-store instructions. +Based on these observations, we propose adaptive data path +selection for durable transactions in GPU PM (AGPM). The +key idea is to alter the log updates’ data path adaptively +according to statistics tracking the localities between the +log and the non-log updates within the GPU L1D and the +L2 caches. The temporal data path (store+clwb) should be +selected for log updates when moderate localities are presented +between the L1D and the L2 cache, or there are no risks of +contention among different levels of volatile caches through +the GPU interconnected network. The non-temporal path +should be selected for log updates when too-strong localities +are simultaneously presented in more than one GPU cache. +For cases when no localities are presented inside the GPU +memory hierarchy, the selection of the path is flexible and the +non-temporal path is recommended to use to reserve the scarce +cache resources for other data with high localities. For special +cases when the shared memory is used or the number of log +updates is too small, the non-temporal path is recommended +to avoid wasting the volatile caches. +A. Period-based strategy +Although we want to leverage observations described in +Section III to achieve adaptive data path selection, results in +Table II are not amenable for direct use in runtime execution +since they are recorded when the kernels are completed. In +order to enable undo logging’s adaptive path selection by +capturing the patterns revealed in Table II, we collect statistics +in periods during kernel execution and we use these statistics + +100% +90% +80% +70% +60% +50% +40% +30% +20% +10% +0% +NE [1,2]N E (2,16] +N E (16.32)1.8 +1.6 +1.4 +1.2 +0.8 +0.6 +0.4 +0.2 +0 +reason c +reason freason areason d +reasongreasonb +reason e +reason h +(clwb s2m)/(nt-store s2m) + (clwb_m2s) (nt-store_m2s)to feed a path selector as shown in Figure 6. This is further +discussed in Section IV-B. +It is challenging to determine a cycle-based period for all +types of GPU kernels. This is because the execution time +of different GPU kernels or different CTAs belonging to +the same kernel may vary vastly, and this leads to different +levels (kernel-level, CTA-level, iteration-level, etc.) of memory +persistency models in GPU [31]. In this study, a period is +defined as a thresholded number of log updates to PM. When +the number of logs exceeds the threshold, all the AGPM +buffers will be flushed and data localities will be re-captured +in the new period. According to Table II, we initialize this +threshold as 10000. We define a metric, cycles-waited-per-PM- +request (CWPPR), to update the threshold. CWPPR denotes +the average number of cycles that each PM request finishes +servicing. We exploit this metric and apply a sampling method +that updates the threshold every time one period is completed. +We define the current period (P1) as the sampling period. If +the CWPPR of the sampling period (P1) is bigger than the +previous period (P0), we consider the length of the threshold +is not long enough to capture the right pattern. In this case, the +threshold is increased by 10% of the previous threshold. For +instance, if the previous threshold is 10000, then the updated +threshold is 11000. Otherwise, the threshold is decreased by +10% of the previous threshold. Finally, the updated threshold +is stored and used in the next sampling period. In some cases +when the number of log updates to PM of the entire GPU +kernel is less than 10000, the threshold will be initialized with +a smaller value. +B. AGPM architecture +Figure 6 shows the overall architecture of AGPM. The gray +rhombus between the SIMD core and the L1 cache inside +the GPU SM denotes the path selector which determines the +memory requests from a PM log updates to use a specific data +path to reach the persistent domain (NVMC in this study). +The gray blocks attached to the L1 cache and the L2 cache +partition denote the AGPM buffers which are used to capture +the localities between the log updates and the subsequent data +updates. The gray blocks attached to the non-volatile memory +denote the reservation buffers which are used to keep the +information flushed from the AGPM buffer. The blue and the +red solid lines denote the temporal and the non-temporal data +path respectively. The green dashed line denotes the control +signals to instruct the selector which path should be selected +for undo logging. Note that Figure 6 demonstrates the AGPM- +related memory transactions between one SM and one memory +partition, and these transactions can be performed among +different SMs and different non-volatile memory partitions in +the GPU. +After coalescing in LD/ST, PM requests from a memory +instruction may need to access the L1D cache. In AGPM, +these requests are first sent to a path selector. According to the +requested addresses and the corresponding statistics recorded +in the AGPM buffers extended in the L1D and the L2 cache, +if patterns that are identical to the reason a, c, d, and g as +described in Table III are observed, the requests from the same +warp which execute the PM instructions will access the GPU’s +volatile caches. Since ADR is assumed to be supported in +the non-volatile memory controller (NVMC), data is persisted +when the dirty cache lines are sent to the NVMC from the +L2 cache partition. Otherwise, if patterns that are identical to +the reason b, e, f, g, and h are observed, the requests will +bypass the caches and they will be directly inserted into the +write-pending queue (WPQ) residing in the NVMC. In this +case, data becomes persisted once they reach NVMC without +taking extra actions. +The structure of the AGPM buffer is similar to a 2-way set- +associative cache (depicted in Figure 6). One way is for the +statistics of the exclusive PM log updates (log way), and the +other way is for the statistics of all kinds of memory requests +(all way). In each way, every entry in the set-associative cache +has two fields: tag and data. The tag is an aligned 128-byte +cache block address and the data is a counter vector, which +records the number of references to each byte in a cache +block. Besides the byte counters, two extra counters are used +in the data field. One extra counter is used to record the +number of references to the specific cache block. Another extra +counter is used as a mark for the change of the data path. If +a certain log update’s data path is changed from the temporal +one to the non-temporal one, then the original clwb should +be dropped since the data is sent directly to the persistent +memory controller. Otherwise, if the data path is changed +from the non-temporal one to the temporal one, then a clwb- +like operation needs to be added after the temporal store +to guarantee the data persistence. When a new PM request +is made, an associated entry will be initialized with 0 and +added in both ways in the AGPM buffer. The counters of the +requested bytes are increased by 1. Then, for a subsequent +memory request (both the PM requests and the others), the +page table walker (PTW) begins a walk. Once the walker +knows the request is a hit, it notifies the AGPM buffer with +the byte address. Then the cache block address and the offset +are calculated. The AGPM buffer searches the entries with +the cache block address. If there is a miss in the AGPM +buffer and the request is not from a PM instruction, then +no actions will be taken. If there is a hit, according to the +offset, if the corresponding byte counter is 0, then only the +cache block counter will be increased. If the byte counter is +larger than 0, then both the byte and the cache block counters +will be increased. If the subsequent request belongs to a PM +instruction, counters in both ways of the AGPM buffer will +be updated. Otherwise, only the counters in the all way will +be updated. When the AGPM buffers are enquired for path +selection, variables described in Table III are calculated using +the recorded counters. For example, l1d t all is calculated as +the sum of all the byte counters whose values are larger than 1 +in the all way of the AGPM buffers at the L1 cache level, and +l1d s all is calculated as the sum of both the byte counters +whose values are larger than 1 and the cache block counters +in the all way of the AGPM buffers at the L1 cache level. +These go the same for the other variables described in Table + +Fig. 6. Overview of AGPM’s architecture. +III. +When a cache block is flushed to a lower memory hierarchy, +the associated AGPM entry will also be flushed to a lower- +level AGPM buffer. When a cache block recorded in the +AGPM buffer is eventually written back either due to a +regular replacement or due to a clwb-like instruction, the +associated content in the AGPM buffer will be first placed +in the reservation buffer residing in the GPU memory, and +then flushed from the AGPM buffer. Once this cache block is +fetched in the volatile caches again before the current period +or the kernel is completed, the reserved information in the +GPU memory will be re-filled into the AGPM buffer. When a +period ends or the kernel execution completes, all the contents +in the AGPM buffer and the reservation buffer will be flushed. +C. Overheads analysis +We used a 2-way AGPM buffer with 1024 entries to record +the localities between the log updates and the subsequent +data updates. Each entry has a tag and a data field. Assume +the system is 64-bit wide, then the tag is 57 bits. The data +has 128+2=130 counters, and a 5-bit counter can meet the +requirement in most cases. Thus, the data field needs 650 bits +in total. An entry needs 707 bits (about 89 B), and 1024 entries +translate to 89 KB storage cost. As the memory access patterns +are nearly the same among different SMs, optimistically only +1 AGPM buffer is needed to be implemented to track the +L1-level data localities. Another AGPM buffer is required to +be shared among all the L2 partitions. The total cost will be +89*2=178 KB. +V. EVALUATION +We evaluate AGPM by comparing it against the conven- +tional memory persistency models which use a static path +strategy for undo logging. We further compare the bench- +marks’ normalized execution time using AGPM against using +the other state-of-the-art multi-data-path architectures to PM +and cache bypassing methods to verify the proposed solution’s +feasibility for the GPU PM applications. +A. Evaluation methodology +We use a GPGPU-Sim extension implemented by [31]. This +extension provides functional and timing simulation support +for memory persistency models which are re-architected for +GPUs. These models are adapted and optimized according to +GPU workloads’ characteristics, GPU’s bandwidth-sensitive +feature, and GPU’s memory hierarchy. To leverage this ex- +tension, the compiler uses inline assembly to insert the PM +instructions such as clwb and sfence, and the simulator is +modified to support the semantics of these instructions. In our +experiments, durable transactions are supported by software- +based undo logging. More specifically, before a transaction +starts, an undo log is created by making a copy of the data +to be updated and this log is persisted. A flag is set and +persisted to indicate that the transaction is in process. During +this transaction, data are updated and persisted. The flag is +updated when the transaction completes, and the undo log will +be released. With undo logging, the recovery code checks the +flag to find out the status of a transaction. If the transaction is +interrupted before its completion, the undo log will be applied +to restore the data. +Our experiments use a set of regular and irregular appli- +cations from Rodinia [39], Lonestar [40], Polybench [41], +and Parboil [42] GPU benchmark suites. These benchmarks +are modified to use the PM instructions to construct durable +transactions, which are similar to the implementation of [31]. +The simulation configurations of GPGPU-Sim are shown in +Table IV. +B. Performance comparison +Figure 7 shows the performance comparison of 22 GPU +benchmark kernels using different data path selection strate- +gies for undo logging. nt-store and store+clwb indicate +that using a static strategy of using the non-temporal and +the temporal data path for all the log updates. Themis [27] +presents a multi-data-path architecture to PM that differentiates +temporal and non-temporal stores. Themis uses a non-temporal +store path as a fast store path to PM, while temporal stores + +SM +SM +SM +All way +Log way +SIMD +SIMD +SIMD +Tag +Data +Tag +Data +core +core +core +PTW +L1 $ +PTWH +L1 $ +L1 $ +0xc0000000 +0xc0000000 +Interconnect +shared +L2 $ +L2 $ +L2 $ +L2 $ +PTW +partition +partition +partition +- +partition +MC +MC +NVMC +NVMC +Control +Temporal +Non-temporal +AGPM +GDDR +GDDR +NVM +NVM +signals +data path +data path +modifi cationFig. 7. Normalized execution time of 22 GPU benchmark kernels using different strategies for undo-logging’s data path selection. All the results are normalized +by the execution time running with base. +TABLE IV +CONFIGURATION PARAMETERS OF GPGPU-SIM. +GPU cores +20 SMs, SIMD width=32, 1.8GHz +Shader Core Config +Max 2048 threads and 64 warps and 32 CTAs +per SM, 32 threads per warp, 4 GTO scheduler +Per-SM L1D-cache +24KB, 128B line, 6-way associativity, +256 MSHRs +Per-SM SMEM +96KB, 32 banks +Shared L2 cache +2048KB, 128KB/partition, 128B line, +16-way associativity, 256 MSHRs +L1D/L2 policies +XOR-indexing, allocate-on-miss, LRU, +L1D:WEWN, L2:WBWA +Interconnect +16*16 crossbar, 32B flit size, 1.4GHz +Memory Controller +8 channels, 2 L2 banks/channel, +FR-FCFS scheduler, 1.2GHz, BW:307GB/s +NVM latency +Read: 160ns, Write: 480ns +DRAM latency +Read: 160ns, Write: 160ns +use a slow data path. Due to paths’ latency difference, Themis +can eliminate almost all persist-barriers, leading to higher +performance of persistent applications. PM-spec [28] also +presents a multi-data-path architecture to PM. In contrast to +Themis, PM-spec allows the PM controller to receive PM load +and store with separate data paths respectively. Specifically, +PM loads go to the temporal data path while PM stores +through the non-temporal data path. BUCL [36] is a GPU +cache bypassing scheme for un-coalesced loads. If the number +of un-coalesced memory access is bigger than the threshold of +coalescing degree, the non-temporal data path will be selected. +Otherwise, the temporal data path will be used. +According to Figure 7, the average normalized execution +time of using different strategies for undo logging is nt- +store: 203.39%, store+clwb: 198.43%, Themis: 165.22%, +PM-spec: 207.29%, BUCL: 185.60%, and AGPM: 140.85%. +We can see that PM-spec achieves the longest normalized +execution time even compared to the experimental results of +the static strategies (nt-store, store+clwb). This is because +the majority of the memory accesses generated from the PM +log updates are store operations. In this case, separating +the data paths according to load and store is not suitable +for undo logging. And this leads to the result that the +performance of using PM-spec (207.29%) is close to nt- +store (203.39%). Except for the static strategies and PM- +spec, BUCL achieves the second-longest normalized execution +time. One of the reasons is that the bypassing logic of BUCL +mainly relies on the coalescing degree of the GPU workloads. +According to Figure 4 and Table I, we can see that the +GPU workloads’ coalescing degrees do not always match +their corresponding type. For example, according to BUCL’s +criteria and the coalescing degrees shown in Figure 4, SAD1, +Stencil1, GRID1, GRID2, 2DCONV, Backprop1, Backprop2, +Pathfinder, ATAX1, MVT1, and GESUMMV belong to the +memory un-coalesced applications. However, SAD1, GRID1, +GRID2, Backprop1, and Pathfinder belong type I. Stencil1 and +2DCONV belong to type II. Backprop2, ATAX1, MVT1, and +GESUMMV belong to type III. In this case, using BUCL +for data path selection can not provide equal performance +improvement to PM log updates when it serves for GPU cache +bypassing. Besides, BUCL is not designed for PM applications +and this may lead to its incompatibility with undo logging +transaction routine that a log update reaches persistence before +the corresponding data updates. Whereas, BUCL delivers the +best performance for some of the benchmarks (StreamTriad, +SSSP1). This is because BUCL sends a memory request to +the cache bypassing logic when there is a reservation fail +after this request accesses the volatile caches. This feature +prevents the interconnect network and the GPU memory +hierarchy from being underutilized due to congested or stalled +caches. Themis achieves the second-best performance among +all the strategies. Themis delivers data path selection decisions +relying on store’s temporal locality, and this is similar to +AGPM. In this case, Themis achieves a comparatively shorter +normalized execution time for most of the benchmarks except +for Backprop2, ATAX1, ATAX2, MVT1, and GESUMMV. +These benchmarks belong to reason b described in Table III, +and Themis does not aware of the potential cache thrashing +due to the too-strong data locality. In this case, temporal +and non-temporal data paths are not differentiated and this +leads to negatively affected performance using Themis. Note +that one of the key advantages provided by Themis is to + +3 +2 +base +nt-store +storetclwb +Thems +PM-spec +BUCL +■AGPMeliminate almost all persist-barriers of the persistency model. +This feature achieves significant performance improvement +for CPU workloads because the sfence instruction precludes +buffering, reordering of memory accesses, and out-of-order +execution due to its ordering semantics. However, in the case +of GPU where threads are highly overlapped and their memory +latency could be hidden through massive multi-threading, the +impact of removing the persist-barriers in GPU kernels is not +as significant as it does in CPU workloads (1.5% on average +[31]). +VI. RELATED WORKS +Intel provides PMDK [8], a library to leverage Optane NVM +[14]. Haria et al. [17] propose a C++ library to allow multiple +updates to one or more data structures to be atomic with +respect to failure. Hsu et al. [18] propose a programming +model and runtime that adds persistence to existing multi- +threaded C/C++ programs. Liu et al. [43] propose Janus, a +hardware-software co-design that parallelizes and pre-executes +backend memory operations in an NVM system. Mnemosyne +[6], NV-Heaps [16], and NVRAM transactions [26] explored +techniques for transactional interactions with PM. Check- +pointing is often used for fault tolerance. Previous works +[22, 23] for checkpointing on NVM focused on minimizing +the checkpointing latency and bandwidth. +Lin et al. [31] adapt existing CPU persistency models for +GPUs. DRAGON [44] exploits NVM’s capability for GPU +through unified memory. GPM [21] exploits UVA to map PM +to GPU’s address space to support fine-grain persistence to +GPU kernels without the CPU’s help. +Nalli et al [13] propose WHISPER, a PM benchmark suite, +and HOPS, a hands-off persistence system. HOPS tracks +updates to PM in hardware and provides high-level ISA +primitives for applications to express durability and ordering +constraints separately. Themis [27] exploits separate data paths +to provide implicit ordering guarantees without using interven- +ing fence instructions. DPO [45] and PMEM-spec [28] exploit +a dedicated persist-path for PM stores and a regular path for +PM loads. +VII. CONCLUSION +In this paper, we propose an adaptive approach (AGPM) +for PM log updates’ data path selection in the GPU. We +first describe the observations we found in the comparison +of the experimental results of the GPU kernels using a static +data path selection strategy. We observe the presumption that +it is more beneficial to use a non-temporal path for undo +logging does not fit the GPU workloads. Besides, we also +observe that the log updates possessing strong locality with +the subsequent data updates are not always appropriate to use +the temporal data path. We analyze the data locality among the +GPU kernels’ log updates and the subsequent data updates, as +well as the data locality among the exclusive log updates, in +the GPU’s L1D and L2 caches. We translate these analyses into +8 reasons and use these reasons to guide the data path selection +in our proposed solution. We implement L1- and L2-level +AGPM buffers to record the statistics in GPU kernels’ runtime +execution, and we feed the statistic to the AGPM path selector +in each SM to match with the reasons we concluded. Upon the +matching results, AGPM adaptatively changes the data path +for the log updates to PM. According to the experimental +results, AGPM outperforms the state-of-the-art multi-data-path +architecture to PM for different types of GPU workloads. +ACKNOWLEDGMENT +TBD +REFERENCES +[1] J. Arulraj, A. Pavlo, S. R. Dulloor, +Let’s talk about +storage & recovery methods for non-volatile memory +database systems, +in: Proceedings of the 2015 ACM +SIGMOD International Conference on Management of +Data, 2015, pp. 707–722. +[2] J. Condit, E. B. Nightingale, C. Frost, E. Ipek, B. Lee, +D. Burger, D. Coetzee, +Better i/o through byte- +addressable, persistent memory, in: Proceedings of the +ACM SIGOPS 22nd symposium on Operating systems +principles, 2009, pp. 133–146. +[3] S. R. Dulloor, S. Kumar, A. Keshavamurthy, P. Lantz, +D. Reddy, R. Sankaran, J. Jackson, +System software +for persistent memory, +in: Proceedings of the Ninth +European Conference on Computer Systems, 2014, pp. +1–15. +[4] A. Joshi, V. Nagarajan, M. Cintra, S. Viglas, Efficient +persist barriers for multicores, in: Proceedings of the 48th +International Symposium on Microarchitecture, 2015, pp. +660–671. +[5] J. Ren, J. Zhao, S. Khan, J. Choi, Y. Wu, O. Mutlu, +Thynvm: Enabling software-transparent crash consis- +tency in persistent memory systems, in: Proceedings of +the 48th International Symposium on Microarchitecture, +2015, pp. 672–685. +[6] H. Volos, A. J. Tack, M. M. Swift, +Mnemosyne: +Lightweight persistent memory, ACM SIGARCH Com- +puter Architecture News 39 (2011) 91–104. +[7] J. Zhao, S. Li, D. H. Yoon, Y. Xie, N. P. Jouppi, Kiln: +Closing the performance gap between systems with and +without persistence support, +in: Proceedings of the +46th Annual IEEE/ACM International Symposium on +Microarchitecture, 2013, pp. 421–432. +[8] N. L. T. at Intel, 2023, Persistent memory programming +blog, URL: pmem.io. +[9] H. P. Enterprise, 2023, Persistent memory, URL: hpe. +com/us/en/servers/persistent-memory.html. +[10] I. +Newsroom, +2015, +Intel +and +micron +produce +breakthrough memory technology, +URL: newsroom. +intel.com/community/intel newsroom/blog/2015/07/28/ +intel-and-micron-produce-breakthrough-memory-technology. +[11] SNIA, 2023, Nvm programming technical work group, +URL: snia.org/forums/sssi/nvmp. +[12] I. B. Peng, M. B. Gokhale, E. W. Green, +System +evaluation of the intel optane byte-addressable nvm, in: + +Proceedings of the International Symposium on Memory +Systems, 2019, pp. 304–315. +[13] S. Nalli, S. Haria, M. D. Hill, M. M. Swift, H. Volos, +K. Keeton, An analysis of persistent memory use with +whisper, ACM SIGPLAN Notices 52 (2017) 135–148. +[14] Intel, +2023, +Intel +optane +persistent +mem- +ory, +URL: +https://www.intel.in/content/ +www/in/en/architecture-and-technology/ +optane-dc-persistent-memory.html. +[15] V. Chidambaram, T. S. Pillai, A. C. Arpaci-Dusseau, +R. H. Arpaci-Dusseau, Optimistic crash consistency, in: +Proceedings of the Twenty-Fourth ACM Symposium on +Operating Systems Principles, 2013, pp. 228–243. +[16] J. Coburn, A. M. Caulfield, A. Akel, L. M. Grupp, +R. K. Gupta, R. Jhala, S. Swanson, Nv-heaps: Making +persistent objects fast and safe with next-generation, non- +volatile memories, ACM SIGARCH Computer Architec- +ture News 39 (2011) 105–118. +[17] S. Haria, M. D. Hill, M. M. Swift, +Mod: Minimally +ordered durable data structures for persistent memory, +in: Proceedings of the Twenty-Fifth International Con- +ference on Architectural Support for Programming Lan- +guages and Operating Systems, 2020, pp. 775–788. +[18] T. C.-H. Hsu, H. Br¨ugner, I. Roy, K. Keeton, P. Eug- +ster, Nvthreads: Practical persistence for multi-threaded +applications, in: Proceedings of the Twelfth European +Conference on Computer Systems, 2017, pp. 468–482. +[19] R. Kadekodi, S. K. Lee, S. Kashyap, T. Kim, A. Kolli, +V. Chidambaram, Splitfs: Reducing software overhead in +file systems for persistent memory, in: Proceedings of the +27th ACM Symposium on Operating Systems Principles, +2019, pp. 494–508. +[20] S. K. Lee, J. Mohan, S. Kashyap, T. Kim, V. Chi- +dambaram, Recipe: Converting concurrent dram indexes +to persistent-memory indexes, +in: Proceedings of the +27th ACM Symposium on Operating Systems Principles, +2019, pp. 462–477. +[21] S. Pandey, A. K. Kamath, A. Basu, Gpm: leveraging per- +sistent memory from a gpu, in: Proceedings of the 27th +ACM International Conference on Architectural Support +for Programming Languages and Operating Systems, +2022, pp. 142–156. +[22] H. Elnawawy, M. Alshboul, J. Tuck, Y. Solihin, Efficient +checkpointing of loop-based codes for non-volatile main +memory, in: 2017 26th International Conference on Par- +allel Architectures and Compilation Techniques (PACT), +IEEE, 2017, pp. 318–329. +[23] M. Alshboul, J. Tuck, Y. Solihin, Lazy persistency: A +high-performing and write-efficient software persistency +technique, +in: 2018 ACM/IEEE 45th Annual Interna- +tional Symposium on Computer Architecture (ISCA), +IEEE, 2018, pp. 439–451. +[24] R.-S. Liu, D.-Y. Shen, C.-L. Yang, S.-C. Yu, C.-Y. M. +Wang, +Nvm duet: Unified working memory and per- +sistent store architecture, +ACM SIGARCH Computer +Architecture News 42 (2014) 455–470. +[25] J. Ren, J. Zhao, S. Khan, J. Choi, Y. Wu, O. Mutlu, +Thynvm: Enabling software-transparent crash consis- +tency in persistent memory systems, in: Proceedings of +the 48th International Symposium on Microarchitecture, +2015, pp. 672–685. +[26] A. Kolli, S. Pelley, A. Saidi, P. M. Chen, T. F. Wenisch, +High-performance transactions for persistent memories, +in: Proceedings of the Twenty-First International Con- +ference on Architectural Support for Programming Lan- +guages and Operating Systems, 2016, pp. 399–411. +[27] S. M. Shahri, S. A. V. Ghahani, A. Kolli, +(almost) +fence-less persist ordering, +in: 2020 53rd Annual +IEEE/ACM International Symposium on Microarchitec- +ture (MICRO), IEEE, 2020, pp. 539–554. +[28] J. Jeong, C. Jung, +Pmem-spec: persistent memory +speculation (strict persistency can trump relaxed persis- +tency), in: Proceedings of the 26th ACM International +Conference on Architectural Support for Programming +Languages and Operating Systems, 2021, pp. 517–529. +[29] A. Joshi, V. Nagarajan, S. Viglas, M. Cintra, +Atom: +Atomic durability in non-volatile memory through hard- +ware logging, in: 2017 IEEE International Symposium +on High Performance Computer Architecture (HPCA), +IEEE, 2017, pp. 361–372. +[30] S. Pelley, P. M. Chen, T. F. Wenisch, Memory persis- +tency: Semantics for byte-addressable nonvolatile mem- +ory technologies, IEEE Micro 35 (2015) 125–131. +[31] Z. Lin, M. Alshboul, Y. Solihin, H. Zhou, +Exploring +memory persistency models for gpus, +in: 2019 28th +International Conference on Parallel Architectures and +Compilation Techniques (PACT), IEEE, 2019, pp. 311– +323. +[32] C. webinar, 2011, Peer-to-peer & unified virtual ad- +dressing, +URL: https://developer.download.nvidia.com/ +CUDA/training/cuda webinars GPUDirect uva.pdf. +[33] A. M. R. [n.d.], 2016, Deprecating the pcommit instruc- +tion, URL: https://software.intel.com/blogs/2016/09/12/ +deprecate-pcommit-instruction. +[34] Intel, +2021, +eadr: +New +opportunities +for +persistent +memory +applications, +URL: +https: +//software.intel.com/content/www/us/en/develop/articles/ +eadr-new-opportunities-for-persistent-memory-applications. +html. +[35] Intel, +2021, +Persistent +memory +learn +more +series +part +2, +URL: +https://software.intel.com/ +content/www/us/en/developer/articles/training/ +pmem-learn-more-series-part-2.html. +[36] C. Zhao, F. Wang, Z. Lin, H. Zhou, N. Zheng, Selectively +gpu cache bypassing for un-coalesced loads, in: 2016 +IEEE 22nd International Conference on Parallel and +Distributed Systems (ICPADS), IEEE, 2016, pp. 908– +915. +[37] X. Xie, Y. Liang, Y. Wang, G. Sun, T. Wang, Coordinated +static and dynamic cache bypassing for gpus, in: 2015 +IEEE 21st International Symposium on High Perfor- +mance Computer Architecture (HPCA), IEEE, 2015, pp. + +76–88. +[38] W. Jia, K. A. Shaw, M. Martonosi, Characterizing and +improving the use of demand-fetched caches in gpus, in: +Proceedings of the 26th ACM international conference +on Supercomputing, 2012, pp. 15–24. +[39] S. Che, M. Boyer, J. Meng, D. Tarjan, J. W. Sheaffer, +S.-H. Lee, K. Skadron, Rodinia: A benchmark suite for +heterogeneous computing, in: 2009 IEEE international +symposium on workload characterization (IISWC), Ieee, +2009, pp. 44–54. +[40] M. Kulkarni, M. Burtscher, C. Casc¸aval, K. Pingali, +Lonestar: A suite of parallel irregular programs, in: 2009 +IEEE International Symposium on Performance Analysis +of Systems and Software, IEEE, 2009, pp. 65–76. +[41] J. Karimov, T. Rabl, V. Markl, +Polybench: The first +benchmark for polystores, +in: Technology Conference +on Performance Evaluation and Benchmarking, Springer, +2019, pp. 24–41. +[42] J. A. Stratton, C. Rodrigues, I.-J. Sung, N. Obeid, L.-W. +Chang, N. Anssari, G. D. Liu, W.-m. W. Hwu, Parboil: +A revised benchmark suite for scientific and commercial +throughput computing, +Center for Reliable and High- +Performance Computing 127 (2012) 27. +[43] S. Liu, K. Seemakhupt, G. Pekhimenko, A. Kolli, +S. Khan, Janus: Optimizing memory and storage support +for non-volatile memory systems, in: 2019 ACM/IEEE +46th Annual International Symposium on Computer Ar- +chitecture (ISCA), IEEE, 2019, pp. 143–156. +[44] P. Markthub, M. E. Belviranli, S. Lee, J. S. Vetter, +S. Matsuoka, +Dragon: breaking gpu memory capacity +limits with direct nvm access, in: SC18: International +Conference for High Performance Computing, Network- +ing, Storage and Analysis, IEEE, 2018, pp. 414–426. +[45] A. Kolli, J. Rosen, S. Diestelhorst, A. Saidi, S. Pelley, +S. Liu, P. M. Chen, T. F. Wenisch, +Delegated persist +ordering, in: 2016 49th Annual IEEE/ACM International +Symposium on Microarchitecture (MICRO), IEEE, 2016, +pp. 1–13. + diff --git a/wNE3T4oBgHgl3EQfOQnS/content/tmp_files/load_file.txt b/wNE3T4oBgHgl3EQfOQnS/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..a6c8823df4e1a01070e2b30592328564109ac3f3 --- /dev/null +++ b/wNE3T4oBgHgl3EQfOQnS/content/tmp_files/load_file.txt @@ -0,0 +1,1067 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf,len=1066 +page_content='Adaptive Data Path Selection for Durable Transaction in GPU Persistent Memory 1st Xinjian Long, State Key Laboratory of Networking and Switching Technologies Beijing University of Posts and Telecommunications Beijing, China barbiel origin@bupt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='cn Abstract—The new non-volatile memory technology relies on data recoverability to achieve the promise of byte-addressable persistence in computer applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' The durable transaction (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' logging) is one of the major persistency programming models to provide recoverable data structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' To achieve performant failure-atomic transactional updates to PM, multi-data-path ar- chitectures that separate the data paths for persists are recently explored for CPUs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Considering the importance of GPU as a key computing platform for many application domains, we investigate the multi-data-path architecture for durable transactions to PM in GPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Our solution, AGPM, exploits an adaptative data-path- selection strategy for the log updates to PM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' AGPM reduces the GPU kernels’ execution time by at least 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='37% (at most 66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='44%) compared to the state-of-the-art designs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Index Terms—Graphics Processing Unit, Persistent Memory, Durable Transaction I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' INTRODUCTION Persistent memory (PM) or non-volatile memory (NVM) technologies have received significant attention from both academia [1, 2, 3, 4, 5, 6, 7] and industry [8, 9, 10, 11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' PM is expected to provide high integration density compara- ble to disk storage at latencies comparable to DRAM [12] while supporting byte-grained addressability and durability [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' The recent commercialization of PM is Intel’s Optane NVM [14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Years of PM research on the CPU have been stacked [6, 15, 16, 17, 18, 19, 20], but the corresponding exploration on the GPU is surprisingly limited, let alone the hardware implementation of PM onboard the modern GPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' However, features of PM (increased memory capacity, high access speed, data recoverability, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=') are proven beneficial for GPU workloads [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Thus, it is necessary for GPU to support PM, and there is a lot of potential for GPU-specific PM design that yields high performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Data recoverability is one of the key reasons why GPU applications are benefited from the PM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' For instance, long- running GPU applications (deep neural network training, proof-of-work algorithms in blockchain applications, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=') can obtain performance improvement by relying on recoverable data structures residing in the main memory instead of con- ducting costly system checkpointing [22, 23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Persistency model [6, 7, 16, 24, 25] is necessary for the implementation of the recoverable data structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' This is because the commit order of the PM updates could be different from the order they reach the PM due to the existence of the volatile write-back caches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Besides, persistency models can provide transaction- like semantics [6, 8, 26], which enables a part of the program, delineated by durable transaction, to be recoverable with all the data persisted therein all or nothing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Durable transactions could apply separate data paths to move data to PM for durability and consistency as needed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' On the one hand, a store followed by a clwb instruction can be used to persist a specific line from the volatile cache hierarchy to PM (temporal path).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' On the other hand, applications can also use non- temporal instructions to bypass the cache and write directly to the PM (non-temporal path).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Upon analysis of different GPU workloads, we observe that the inappropriate selection of the data path further deteriorates the performance problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Most of the current persistency models are designed to statically use a single-data-path architecture, which risks the applications using PM experiencing unnecessary performance loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Recently, Shahri et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' [27] proposed an extension to the x86 memory persistency model to exploit the differences in speeds of requests sent along the temporal and the non-temporal paths to reduce the reliance on using sfence instruction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Jeong et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' [28] proposed a hardware/software co-design scheme that leverages the separate FIFO data paths to enforce persisting orders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' These designs decided to only consider the types of PM requests (load, store, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=') as the key factor to selecting the data path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' For example, when using undo logging, the log updates must persist before the corresponding data updates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' In this case, logs are intuitively updated using the non-temporal path instead of the temporal one [13, 29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' This is because the non-temporal path is commonly faster than the temporal one by skipping the multiple levels of caches between the processor and the persistent domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' In addition, logs are expected to never be read during failure-free execution, and the usage of the temporal data path’s write-no-allocate policy can avoid polluting the volatile caches while reducing the undo logging’s overhead.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' In contrast with this intuition, we observe that the performance of using different data paths varies across GPU applications due to their different memory access behaviors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' In some cases, we observe that log updates using the slow temporal path can be more beneficial than using the fast non-temporal path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' On the other hand, the temporal path is not always more beneficial for data updates with temporal and arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='04392v1 [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='AR] 11 Jan 2023 spatial localities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Specifically, the non-temporal path is more recommended compared to the temporal one when the data locality is too strong and the reuse distances are too long to help the cached data be reused before eviction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Overall, our observation manifests that it is not amenable to handling GPU PM requests using a static path selection strategy, and there is a lot of potential for the multi-path architecture to achieve better performance for GPU workloads’ persist ordering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Building on our observations, we propose an adaptive approach (AGPM) to select the data path for the durable transactions in GPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' This approach adds AGPM buffers in the GPU memory hierarchy to record the data locality between the PM log updates and the subsequent data updates, as well as the locality among the log updates, within the GPU L1D caches and the shared L2 cache.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Periodically, statistics in the AGPM buffers are fed to an added path selector in each SM and are translated to 8 reasons/patterns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Such translation is conducted upon the temporal and spatial locality of the PM logging data in the L1D and the L2 caches, the GPU kernel’s usage of the shared memory, and the number of log updates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Reasons/patterns are exploited to help derive the data path selection decision for undo logging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Overall, this paper makes the following contributions: 1) We analyze the L1D and L2 data localities for GPU kernels’ transactional interaction with PM (undo log- ging) and their resulting performance in different types of GPU workloads.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' 2) We propose an adaptive approach for PM requests’ data path selection in GPU referred to as AGPM, such that the PM log updates’ data paths are selected according to the kernel accesses’ data locality and characteristics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' 3) Experimental results show that AGPM achieves signifi- cant performance improvement over the static data path selection methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Meanwhile, AGPM outperforms the state-of-the-art (SOTA) multi-data-path architectures to PM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Compared to the SOTA designs, AGPM reduces the GPU kernels’ execution time by at least 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='37% (at most 66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='44%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' The remainder of this paper is organized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Sec- tion II presents the background.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Section III discusses the motivation of this study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Section IV describes the design of the proposed AGPM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Section V compares the results of our proposed AGPM with the other methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Section VI discusses the related works, before providing concluding remarks in Section VII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' BACKGROUND In this section, we review the current persistency models on CPUs and GPUs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' We also introduce the GPU architecture and the programming model following the NVIDIA/CUDA terminology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' It is worth noting that the techniques mentioned in this section, as well as our design described in the following sections, are adaptable to other GPU architecture besides NVIDIA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Memory persistency models Byte-addressable persistent memory provides a promising future for high-performance in-memory computing with re- coverable data structures (RDS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' However, due to the volatile write-back caches, the order of load and store requests arriving at the persistent memory can be different from their commit order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' This breaks the rule of RDS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' For example, assuming that p is a persistent structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' ’p → data’ and ’p → state’ reside in different cache lines and the update to ’p → data’ precedes the update to ’p → state’ in the program.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' However, the ’p → state’ in memory may be updated before ’p → data’ due to the caches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' In this case, if a fault (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=', a power failure) happens, the persistent memory state becomes incor- rect after power is restored.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' To deal with this issue and support correct implementations of RDS, memory persistency models [6, 7, 16, 24, 25, 30] are proposed to formally specify the order of writes to PM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' These models can be broadly characterized as the strict and the relaxed models, which are distinct in the levels of concurrency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' In the strict persistency model, the order of the volatile memory operations is identical to the order of the PM operations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' This model is easy to implement, but it limits the program’s concurrency which leads to the most serious performance degradation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' The relaxed persistency model is more performant by breaking the tie between the volatile memory operations and the PM operations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' A higher level of PM writes concurrency is supported at the cost of program annotation and hardware complexities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' The memory persistency models mentioned above specify the durability order of stores but ordering alone does not guarantee data recoverability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' For example, assume that with either a strict or relaxed persistency model, ’p → data’ and ’p → state’ in PM are updated in the program order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' But it is still possible that a fault happens after ’p → data’ is updated but before ’p → state’ is updated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' In this case, the memory state in PM is still not correct for data recovery.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' To handle this issue, durable transactions [6, 8, 26] (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' undo logging), which provide all-or-nothing guarantees by undoing changes from an aborted transaction, are required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' To be able to roll back changes, an undo log entry will be created prior to every update performed within the transaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' The undo log entry contains the current value of the persistent structure that is to be updated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Once the log entry has been created and persisted, only then is the actual value updated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' If a transaction succeeds, a commit message is atomically sent to invalidate the log entries belonging to the transaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' If a transaction fails, the recovery process uses all the persisted log entries to roll back partial changes from that transaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Currently, memory persistency models, as well as durable transactions, are designed for the CPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' These models need to be re-architected for GPUs due to the differences in both the workloads and the processors’ architectures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Lin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' [31] explore the implementation of different levels (kernel-level, CTA-level, and loop-level) of memory persistency models in GPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' We exploit their implementation, especially the CTA- level undo logging for GPU, in this study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Figure 1 shows an example of CTA-level undo logging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' First, undo logs are created for the output elements (Loc1 and Loc2) that are to be updated by the CTA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' After ensuring all the threads persist their log using the sfence followed by the CUDA syncthreads function, a flag for the log is set to be inTx and is made durable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' The values (p→data and p→state) of the output elements are updated iteratively by the CTA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' At the end of the CTA, all the outputs are ensured to be persisted using another syncthread function, and the flag is set to be complete.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Note that all the undo logging described in the following sections in this study refers to CTA-level undo logging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' An example of CTA-level undo logging of a GPU kernel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' GPU with PM Today, there is no hardware with PM onboard the GPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' If a GPU application wishes to leverage PM’s persistence, it would typically perform computations on the GPU and ensure the persistence of the results on the CPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' The computation results need to be transferred from the GPU’s memory to the CPU’s memory and rely on the CPU to guarantee data recoverability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Alternatively, one could leverage the file system, since only the file systems atop block-storage devices could guarantee persistence before the advent of NVM technologies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' After the computation results from the GPU are transferred to the CPU’s memory, the CPU writes the results to a PM- resident file and then guarantees persistence using the fsync function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Furthermore, a PM resident file can be memory- mapped onto the CPU’s address space, and the GPU’s results can be transferred to the memory-mapped file residing in the CPU memory using cudaMemcpy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Pandey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' proposed GPM [21] to use NVIDIA’s uniform virtual addressing (UVA) technique [32] to map PM to GPU’s address space, and system-scoped fence with selective dis- abling of the data direct IO (DDIO) feature to enable GPUs to access and persist data in PM with no CPU involvement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' GPM leverage the fact that the modern PM (Intel Optane [14]) is placed alongside the DRAM, as in a typical Intel Xeon server, and can be accessed by a GPU over the PCI-e interconnect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' In this case, UVA can be used to map desired portions of NVM onto the virtual address space of a GPU kernel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Then, GPU kernels can directly access and manipulate PM-resident data structures at byte granularity using loads and stores without the CPU’s assistance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' MOTIVATION This section discussed the impetus of this study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' For sim- plicity, we assume a discrete GPU system equipped with persistent memory (Figure 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' This assumption enables us to focus on the GPU memory hierarchy without considering the potential effects of the host-side memory system as well as the costly data transfers between the system and GPU device memory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' We further assume that the PM controller supports the asynchronous DRAM refresh (ADR) [33] feature and is in the persistent domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' All updates to PM will be durable once they reach the PM controller.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Intel recently announced an enhanced ADR (eADR) [34] feature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' eADR drains the entire contents of CPU caches to PM on power failures, which obviates the need to flush cache blocks from the CPU’s caches in order to guarantee persistence in future processors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Besides, the fence is still needed to maintain the ordering of writes to PM [35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' This study can be projected on a future system with eADR, since the data path selection of data persisting takes place before the cache line flushes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' We focus on GPUs’ durable transactions (undo logging) in this study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Note that there are other persistency memory models for persist ordering in GPU, these models are beyond the scope of this study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' TABLE I DIFFERENT TYPES OF BENCHMARKS ARE CATEGORIZED BY THE PERFORMANCE DIFFERENCE USING THE TEMPORAL AND THE NON-TEMPORAL PATH FOR UNDO LOGGING.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Type Metric Benchmark I perfT > perfNT , diff > 5% SAD1, GRID1, GRID2, 2DCONV, Backprop1, Pathfinder, 2MM1, 3MM1, GEMM II perfT < perfNT , diff > 5% SGEMM, Backprop2, ATAX1, ATAX2, NW, SSSP2, MVT1, GESUMMV, RA III diff ≤ 5% Stencil1, SSSP1, StreamTriad, BFS Figure 3 shows the experimental results of 22 GPU bench- mark kernels using a static data path selection for undo- logging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Figure 3 reveals several important observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' First, device_ woid CTA_ log_example(.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='.) 1 Locl[tid] = p->data[tid] Loc2[tid] = p->state[tid];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Wp is initialzed 1og (Locl[tid]),clwb;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='sfence;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' 1og (Loc2[tid]),clwb ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='sfence;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' /logsforp synchthreads(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' /logs are persisted if(tid==0)K flag=inIx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' 1og(flag);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='clwb,sfenc2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' /flag is pers isted 1 for (iterations ) W/p is upd ated Locl [tid] = p->data[tid];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' clwb,sfence;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Loc2[tid] = p->state[tid];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' clwb,sfence: 1 synchthreads(O: /CTA completes if(Gd =0) flag=complete: 1og(flag);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='clwb,sfence;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' /flag is pers isted 1Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Overviews of the assumed GPU system equipped with NVM/PM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' $ denotes cache.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' MC denotes the memory controller.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' NVMC denotes the non- volatile memory controller.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' data recoverability enabled by undo logging introduces different levels of performance overheads to different GPU benchmark kernels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' For instance, the PM operations invoking the nt-store instructions expand the execution time of the SAD1 kernel to 325.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='5% compared to the execution time without undo logging, while nt-store expands SGEMM’s execution time to 102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='7%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Furthermore, we can see that store+clwb delivers a shorter execution time than nt-store among several benchmark kernels (SAD1, GRID1, GRID2, 2DCONV, Pathfinder, 2MM1, 3MM1, GEMM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' These results lead to our second observation: the presumption that nt- store is more beneficial for undo logging is not applicable to all GPU applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' According to Figure 3, we broadly categorized 22 benchmark kernels into three types according to two metrics (perf and diff) as described in Table I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' perf T denotes the benchmark performance (execution time, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=') using the temporal path (store+clwb) for undo logging, and perf NT denotes the performance using the non-temporal path (nt-store).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' diff denotes the absolute difference between perf T and perf NT .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Due to the similarity between this study and the cache bypassing problem [36, 37] in GPU, we try to explain the benchmark kernels’ performance difference following the cache bypassing logic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' One of the most important ideas in this area is to perform cache bypassing according to GPU kernels’ memory coalescing behaviors [36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' These studies conclude that the un-coalesced loads/stores should bypass the volatile caches because such requests generate massive memory accesses compared to the other memory instructions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Besides, data fetched by these requests is likely to possess poor locality, which is not worthy of consuming the scarce cache resources in the GPU architecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Figure 4 shows the distribution of the loads/stores (including the undo loggings and the other memory updates) with different numbers of memory accesses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' We can see that the performance difference shown in Figure 3 is not coherent with the benchmark kernels’ coalescing behaviors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' For example, StreamTriad, ATAX2, and 3MM1 are perfectly memory coalesced, whose memory un- coalescing degrees are within [1, 2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' However, these kernels vary from type I to III as described in Table I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Thus, we can see that this study is not essentially identical to the cache bypassing problem in GPU, and a new design is required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' In order to explain the performance difference using differ- ent data paths, we define 10 variables to characterize the GPU kernels’ temporal and spatial localities as described in Table II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' For example, l1d t all denotes the number of cache hits with the temporal locality in the L1D cache, and these accesses are generated by both the log and the other data updates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' This goes the same for the other 7 variables (l1d(l2) t(s) all(log)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Since we are focusing on durable transactions in GPU PM, we believe that the statistics of both the log updates (log) and the non-log updates (all) are required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' We define that the non- log updates’ temporal locality in the L1D cache means the re-hits of a specific byte by a log update followed by a non- log data update, and the log updates’ temporal locality in the L1D cache means the re-hits of a specific byte by a log update followed by another log update.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Similarly, we define that the non-log updates’ spatial locality in the L1D cache means the re-hits of a specific aligned 128-byte segment (cache block) by a log update followed by a non-log data update, and the log updates’ spatial locality in the L1D cache means the re- hits of a specific byte by a log update followed by another log update.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' These go the same for the statistics of the L2 cache.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Note that Maxwell, Pascal, and Volta GPU architectures use demand-fetch caches to fetch only the chunks that are requested instead of fetching a full cache line to handle the data over-fetch problem [38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Thus, the number of accesses in the GPU caches with the temporal locality is not necessarily identical to the one with the spatial locality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' According to Table II, we conclude 8 reasons to explain Figure 3’s performance difference as described in Table III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Intuitively, the nt-store instruction is considered profitable for log updates [13, 29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' This is because logs are considered only necessary for crash consistency and never read in failure- free execution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' In this case, the nt-store’s write-no-allocate policy, which writes data blocks directly to memory without adding to the cache, provides more benefits for logging and reduces cache pollution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' On the other hand, introducing the frequently reused data blocks into the volatile caches by the store+clwb’s write-allocate policy help save a lot of expensive memory transactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Thus, a simple idea for the undo logging’s data path selection is to rely on the locality be- tween the log updates and the subsequent data updates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' More specifically, the stronger locality is observed the more likely to use the temporal path (store+clwb).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Otherwise, the non- temporal path (nt-store) should be selected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' However, Table II shows different patterns compared to this intuition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' And this leads to our third observation: store+clwb do not always provide more benefits than nt-store for data updates with good localities in GPU caches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' For reasons a, b, and d, the major differences come from whether the values of l1d t log SM SM SM SIMD SIMD SIMD core core core L1 $ L1 $ L1 $ Interconnect partition partition partition partition MC MC NVMC NVMC GDDR GDDR NVM NVM Persistent domainFig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Normalized execution time of 22 GPU benchmark kernels using separate data paths for undo-logging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' ATAX1 and ATAX2 indicate the first and the second kernel of the ATAX benchmark.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' This goes the same for the other benchmarks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' base denotes the benchmarks that are executed using NVM without persistency support.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' nt-store denotes the implementation follows the description in [27, 28], which uses the non-temporal path to persist the log updates to PM and uses the temporal path for the subsequent data updates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' store+clwb denotes that both the log and the corresponding data updates use the temporal path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' All the results are normalized by the execution time running with base.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' TABLE II TEMPORAL AND SPATIAL LOCALITY OF 22 GPU BENCHMARK KERNELS’ MEMORY ACCESSES IN GPU’S L1D AND L2 CACHE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' l1d DENOTES THE L1D CACHE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' l2 DENOTES THE L2 CACHE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' t DENOTES TEMPORAL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' s DENOTES SPATIAL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' all DENOTES THE MEMORY ACCESS GENERATED BY BOTH THE LOG AND THE OTHER DATA UPDATES.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' log DENOTES THE MEMORY ACCESS GENERATED BY THE LOG UPDATES.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' type DENOTES THE KERNELS’ TYPE AS DESCRIBED IN TABLE I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' reason DENOTES THE REASON WHY THE CERTAIN KERNEL BELONGS TO A CERTAIN TYPE AS DESCRIBED IN TABLE III.' metadata={'source': 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metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' l1d t log and l1d s log reveal whether the identical cache chunk or the identical cache line is repeatedly referenced by the log updates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' When these two variables are equal to 0 (reason a) or only occupy a small fraction (≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='25) of all the memory accesses with the locality (reason d), the experimental results follow the aforementioned intuition that using the store+clwb instructions achieve better performance than using the nt-store (type I).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' However, when too-strong localities are observed in the L1D cache accesses caused by the log updates (reason b), we can see that nt-store provides more benefits compared to store+clwb in this case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' This is because the cache thrashing between the L1D cache and the L2 cache through the slow interconnected network impedes the performance advantage of using the caches for the data with good localities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Figure 5 shows the normalized mean transmitted bytes of the kernels belonging to a certain reason using the temporal (store+clwb) and the non-temporal (nt-store) data path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' When the data localities in volatile caches increase, the memory traffic as well as the pipeline utilization grow due to the less warp stall and the fewer expensive memory transactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' However, when such localities become too strong and the reuse distances are too long to help the cached data be reused before eviction, the invalidation frequency of the GPU volatile caches will grow dramatically base nt-store μ storetclwbFig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Distribution of loads/stores with different memory un-coalescing degrees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' N denotes the number of memory accesses for a load/store belonging to the same warp after memory coalescing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' TABLE III STATISTICS-BASED REASONING.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Reason Metrics Type a l1d t all ̸= 0 and l1d s all ̸= 0 and I l1d t log = 0 and l1d s log = 0 b l1d t all ̸= 0 and l1d s all ̸= 0 and II l1d t log ̸= 0 and l1d s log ̸= 0 and l1d t(s) log / l1d t(s) all > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='25 c l1d t all = 0 and l1d s all = 0 and I l1d t log = 0 and l1d s log = 0 and l2 t all ̸= 0 and l2 s all ̸= 0 and l2 t log ̸= 0 and l2 s log ̸= 0 d l1d t all ̸= 0 and l1d s all ̸= 0 and I l1d t log ̸= 0 and l1d s log ̸= 0 and l1d t(s) log / l1d t(s) all ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='25 e log ≤ 100 III f l1d t all = 0 and l1d s all = 0 and II, III l1d t log = 0 and l1d s log = 0 and l2 t all = 0 and l2 s all = 0 and l2 t log = 0 and l2 s log = 0 g l1d t all = 0 and l1d s all ̸= 0 and I l1d t log = 0 and l1d s log ̸= 0 h usage of shared memory II which finally turns into cache contention and thrashing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' For kernels belonging to reason c, since no locality is observed in the L1D cache, there is no risk of experiencing serious thrash- ing while enjoying the benefit provided by store+clwb, these kernels are categorized as type I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' For reason f, kernels have no data locality in either the L1D cache or the L2 cache.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' nt- store is intuitively considered suitable for this pattern because of the write-no-allocate policy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' However, these GPU kernels show interesting behavior in that the performance of using the store+clwb and the nt-store are similar (type III).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' We believe that this is because of GPU’s massive multi-threading which effectively hides the cache allocation overhead, and this results in average performance using either the temporal path or the non-temporal path for persistency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' For reason g, moderate localities are observed in both the L1D cache and the L2 cache, thus kernels belonging to this category are type I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' For reason e and reason h, these are two special cases that can not be explained by the adaptability between the log and the non- log updates’ localities and the temporal or the non-temporal data path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' For reason e, the number of the log updates is too small (<100) and this makes a negligible difference between the usage of the store+clwb and the nt-store (type III).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' For reason h, these kernels use the shared memory to communicate and synchronize for the threads within the same CTA(TB).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' In this case, most of the data fetched in the volatile cache will not be reused, and using the nt-store instruction becomes more beneficial than using the store+clwb instructions (type II).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Normalized mean transmitted bytes comparison between the GPU L1D cache and the L2 cache using the store+clwb and the nt-store instructions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' s2m denotes the transmission from the L1D cache to the L2 cache, and m2s denotes the transmission from the L2 cache to the L1D cache.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' OUR SOLUTION As discussed in Section III, we leverage 10 variables and 8 reasons to explain the performance difference of GPU’ undo logging using the store+clwb and the nt-store instructions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Based on these observations, we propose adaptive data path selection for durable transactions in GPU PM (AGPM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' The key idea is to alter the log updates’ data path adaptively according to statistics tracking the localities between the log and the non-log updates within the GPU L1D and the L2 caches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' The temporal data path (store+clwb) should be selected for log updates when moderate localities are presented between the L1D and the L2 cache, or there are no risks of contention among different levels of volatile caches through the GPU interconnected network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' The non-temporal path should be selected for log updates when too-strong localities are simultaneously presented in more than one GPU cache.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' For cases when no localities are presented inside the GPU memory hierarchy, the selection of the path is flexible and the non-temporal path is recommended to use to reserve the scarce cache resources for other data with high localities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' For special cases when the shared memory is used or the number of log updates is too small, the non-temporal path is recommended to avoid wasting the volatile caches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Period-based strategy Although we want to leverage observations described in Section III to achieve adaptive data path selection, results in Table II are not amenable for direct use in runtime execution since they are recorded when the kernels are completed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' In order to enable undo logging’s adaptive path selection by capturing the patterns revealed in Table II, we collect statistics in periods during kernel execution and we use these statistics 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% NE [1,2]N E (2,16] N E (16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='32)1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='2 0 reason c reason freason areason d reasongreasonb reason e reason h (clwb s2m)/(nt-store s2m) (clwb_m2s) (nt-store_m2s)to feed a path selector as shown in Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' This is further discussed in Section IV-B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' It is challenging to determine a cycle-based period for all types of GPU kernels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' This is because the execution time of different GPU kernels or different CTAs belonging to the same kernel may vary vastly, and this leads to different levels (kernel-level, CTA-level, iteration-level, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=') of memory persistency models in GPU [31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' In this study, a period is defined as a thresholded number of log updates to PM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' When the number of logs exceeds the threshold, all the AGPM buffers will be flushed and data localities will be re-captured in the new period.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' According to Table II, we initialize this threshold as 10000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' We define a metric, cycles-waited-per-PM- request (CWPPR), to update the threshold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' CWPPR denotes the average number of cycles that each PM request finishes servicing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' We exploit this metric and apply a sampling method that updates the threshold every time one period is completed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' We define the current period (P1) as the sampling period.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' If the CWPPR of the sampling period (P1) is bigger than the previous period (P0), we consider the length of the threshold is not long enough to capture the right pattern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' In this case, the threshold is increased by 10% of the previous threshold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' For instance, if the previous threshold is 10000, then the updated threshold is 11000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Otherwise, the threshold is decreased by 10% of the previous threshold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Finally, the updated threshold is stored and used in the next sampling period.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' In some cases when the number of log updates to PM of the entire GPU kernel is less than 10000, the threshold will be initialized with a smaller value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' AGPM architecture Figure 6 shows the overall architecture of AGPM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' The gray rhombus between the SIMD core and the L1 cache inside the GPU SM denotes the path selector which determines the memory requests from a PM log updates to use a specific data path to reach the persistent domain (NVMC in this study).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' The gray blocks attached to the L1 cache and the L2 cache partition denote the AGPM buffers which are used to capture the localities between the log updates and the subsequent data updates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' The gray blocks attached to the non-volatile memory denote the reservation buffers which are used to keep the information flushed from the AGPM buffer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' The blue and the red solid lines denote the temporal and the non-temporal data path respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' The green dashed line denotes the control signals to instruct the selector which path should be selected for undo logging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Note that Figure 6 demonstrates the AGPM- related memory transactions between one SM and one memory partition, and these transactions can be performed among different SMs and different non-volatile memory partitions in the GPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' After coalescing in LD/ST, PM requests from a memory instruction may need to access the L1D cache.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' In AGPM, these requests are first sent to a path selector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' According to the requested addresses and the corresponding statistics recorded in the AGPM buffers extended in the L1D and the L2 cache, if patterns that are identical to the reason a, c, d, and g as described in Table III are observed, the requests from the same warp which execute the PM instructions will access the GPU’s volatile caches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Since ADR is assumed to be supported in the non-volatile memory controller (NVMC), data is persisted when the dirty cache lines are sent to the NVMC from the L2 cache partition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Otherwise, if patterns that are identical to the reason b, e, f, g, and h are observed, the requests will bypass the caches and they will be directly inserted into the write-pending queue (WPQ) residing in the NVMC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' In this case, data becomes persisted once they reach NVMC without taking extra actions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' The structure of the AGPM buffer is similar to a 2-way set- associative cache (depicted in Figure 6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' One way is for the statistics of the exclusive PM log updates (log way), and the other way is for the statistics of all kinds of memory requests (all way).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' In each way, every entry in the set-associative cache has two fields: tag and data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' The tag is an aligned 128-byte cache block address and the data is a counter vector, which records the number of references to each byte in a cache block.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Besides the byte counters, two extra counters are used in the data field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' One extra counter is used to record the number of references to the specific cache block.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Another extra counter is used as a mark for the change of the data path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' If a certain log update’s data path is changed from the temporal one to the non-temporal one, then the original clwb should be dropped since the data is sent directly to the persistent memory controller.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Otherwise, if the data path is changed from the non-temporal one to the temporal one, then a clwb- like operation needs to be added after the temporal store to guarantee the data persistence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' When a new PM request is made, an associated entry will be initialized with 0 and added in both ways in the AGPM buffer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' The counters of the requested bytes are increased by 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Then, for a subsequent memory request (both the PM requests and the others), the page table walker (PTW) begins a walk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Once the walker knows the request is a hit, it notifies the AGPM buffer with the byte address.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Then the cache block address and the offset are calculated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' The AGPM buffer searches the entries with the cache block address.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' If there is a miss in the AGPM buffer and the request is not from a PM instruction, then no actions will be taken.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' If there is a hit, according to the offset, if the corresponding byte counter is 0, then only the cache block counter will be increased.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' If the byte counter is larger than 0, then both the byte and the cache block counters will be increased.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' If the subsequent request belongs to a PM instruction, counters in both ways of the AGPM buffer will be updated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Otherwise, only the counters in the all way will be updated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' When the AGPM buffers are enquired for path selection, variables described in Table III are calculated using the recorded counters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' For example, l1d t all is calculated as the sum of all the byte counters whose values are larger than 1 in the all way of the AGPM buffers at the L1 cache level, and l1d s all is calculated as the sum of both the byte counters whose values are larger than 1 and the cache block counters in the all way of the AGPM buffers at the L1 cache level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' These go the same for the other variables described in Table Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Overview of AGPM’s architecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' When a cache block is flushed to a lower memory hierarchy, the associated AGPM entry will also be flushed to a lower- level AGPM buffer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' When a cache block recorded in the AGPM buffer is eventually written back either due to a regular replacement or due to a clwb-like instruction, the associated content in the AGPM buffer will be first placed in the reservation buffer residing in the GPU memory, and then flushed from the AGPM buffer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Once this cache block is fetched in the volatile caches again before the current period or the kernel is completed, the reserved information in the GPU memory will be re-filled into the AGPM buffer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' When a period ends or the kernel execution completes, all the contents in the AGPM buffer and the reservation buffer will be flushed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Overheads analysis We used a 2-way AGPM buffer with 1024 entries to record the localities between the log updates and the subsequent data updates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Each entry has a tag and a data field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Assume the system is 64-bit wide, then the tag is 57 bits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' The data has 128+2=130 counters, and a 5-bit counter can meet the requirement in most cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Thus, the data field needs 650 bits in total.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' An entry needs 707 bits (about 89 B), and 1024 entries translate to 89 KB storage cost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' As the memory access patterns are nearly the same among different SMs, optimistically only 1 AGPM buffer is needed to be implemented to track the L1-level data localities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Another AGPM buffer is required to be shared among all the L2 partitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' The total cost will be 89*2=178 KB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' EVALUATION We evaluate AGPM by comparing it against the conven- tional memory persistency models which use a static path strategy for undo logging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' We further compare the bench- marks’ normalized execution time using AGPM against using the other state-of-the-art multi-data-path architectures to PM and cache bypassing methods to verify the proposed solution’s feasibility for the GPU PM applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Evaluation methodology We use a GPGPU-Sim extension implemented by [31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' This extension provides functional and timing simulation support for memory persistency models which are re-architected for GPUs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' These models are adapted and optimized according to GPU workloads’ characteristics, GPU’s bandwidth-sensitive feature, and GPU’s memory hierarchy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' To leverage this ex- tension, the compiler uses inline assembly to insert the PM instructions such as clwb and sfence, and the simulator is modified to support the semantics of these instructions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' In our experiments, durable transactions are supported by software- based undo logging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' More specifically, before a transaction starts, an undo log is created by making a copy of the data to be updated and this log is persisted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' A flag is set and persisted to indicate that the transaction is in process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' During this transaction, data are updated and persisted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' The flag is updated when the transaction completes, and the undo log will be released.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' With undo logging, the recovery code checks the flag to find out the status of a transaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' If the transaction is interrupted before its completion, the undo log will be applied to restore the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Our experiments use a set of regular and irregular appli- cations from Rodinia [39], Lonestar [40], Polybench [41], and Parboil [42] GPU benchmark suites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' These benchmarks are modified to use the PM instructions to construct durable transactions, which are similar to the implementation of [31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' The simulation configurations of GPGPU-Sim are shown in Table IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Performance comparison Figure 7 shows the performance comparison of 22 GPU benchmark kernels using different data path selection strate- gies for undo logging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' nt-store and store+clwb indicate that using a static strategy of using the non-temporal and the temporal data path for all the log updates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Themis [27] presents a multi-data-path architecture to PM that differentiates temporal and non-temporal stores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Themis uses a non-temporal store path as a fast store path to PM, while temporal stores SM SM SM All way Log way SIMD SIMD SIMD Tag Data Tag Data core core core PTW L1 $ PTWH L1 $ L1 $ 0xc0000000 0xc0000000 Interconnect shared L2 $ L2 $ L2 $ L2 $ PTW partition partition partition partition MC MC NVMC NVMC Control Temporal Non-temporal AGPM GDDR GDDR NVM NVM signals data path data path modifi cationFig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Normalized execution time of 22 GPU benchmark kernels using different strategies for undo-logging’s data path selection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' All the results are normalized by the execution time running with base.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' TABLE IV CONFIGURATION PARAMETERS OF GPGPU-SIM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' GPU cores 20 SMs, SIMD width=32, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='8GHz Shader Core Config Max 2048 threads and 64 warps and 32 CTAs per SM, 32 threads per warp, 4 GTO scheduler Per-SM L1D-cache 24KB, 128B line, 6-way associativity, 256 MSHRs Per-SM SMEM 96KB, 32 banks Shared L2 cache 2048KB, 128KB/partition, 128B line, 16-way associativity, 256 MSHRs L1D/L2 policies XOR-indexing, allocate-on-miss, LRU, L1D:WEWN, L2:WBWA Interconnect 16*16 crossbar, 32B flit size, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='4GHz Memory Controller 8 channels, 2 L2 banks/channel, FR-FCFS scheduler, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='2GHz, BW:307GB/s NVM latency Read: 160ns, Write: 480ns DRAM latency Read: 160ns, Write: 160ns use a slow data path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Due to paths’ latency difference, Themis can eliminate almost all persist-barriers, leading to higher performance of persistent applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' PM-spec [28] also presents a multi-data-path architecture to PM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' In contrast to Themis, PM-spec allows the PM controller to receive PM load and store with separate data paths respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Specifically, PM loads go to the temporal data path while PM stores through the non-temporal data path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' BUCL [36] is a GPU cache bypassing scheme for un-coalesced loads.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' If the number of un-coalesced memory access is bigger than the threshold of coalescing degree, the non-temporal data path will be selected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Otherwise, the temporal data path will be used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' According to Figure 7, the average normalized execution time of using different strategies for undo logging is nt- store: 203.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='39%, store+clwb: 198.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='43%, Themis: 165.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='22%, PM-spec: 207.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='29%, BUCL: 185.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='60%, and AGPM: 140.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='85%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' We can see that PM-spec achieves the longest normalized execution time even compared to the experimental results of the static strategies (nt-store, store+clwb).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' This is because the majority of the memory accesses generated from the PM log updates are store operations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' In this case, separating the data paths according to load and store is not suitable for undo logging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' And this leads to the result that the performance of using PM-spec (207.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='29%) is close to nt- store (203.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='39%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Except for the static strategies and PM- spec, BUCL achieves the second-longest normalized execution time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' One of the reasons is that the bypassing logic of BUCL mainly relies on the coalescing degree of the GPU workloads.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' According to Figure 4 and Table I, we can see that the GPU workloads’ coalescing degrees do not always match their corresponding type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' For example, according to BUCL’s criteria and the coalescing degrees shown in Figure 4, SAD1, Stencil1, GRID1, GRID2, 2DCONV, Backprop1, Backprop2, Pathfinder, ATAX1, MVT1, and GESUMMV belong to the memory un-coalesced applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' However, SAD1, GRID1, GRID2, Backprop1, and Pathfinder belong type I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Stencil1 and 2DCONV belong to type II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Backprop2, ATAX1, MVT1, and GESUMMV belong to type III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' In this case, using BUCL for data path selection can not provide equal performance improvement to PM log updates when it serves for GPU cache bypassing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Besides, BUCL is not designed for PM applications and this may lead to its incompatibility with undo logging transaction routine that a log update reaches persistence before the corresponding data updates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Whereas, BUCL delivers the best performance for some of the benchmarks (StreamTriad, SSSP1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' This is because BUCL sends a memory request to the cache bypassing logic when there is a reservation fail after this request accesses the volatile caches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' This feature prevents the interconnect network and the GPU memory hierarchy from being underutilized due to congested or stalled caches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Themis achieves the second-best performance among all the strategies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Themis delivers data path selection decisions relying on store’s temporal locality, and this is similar to AGPM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' In this case, Themis achieves a comparatively shorter normalized execution time for most of the benchmarks except for Backprop2, ATAX1, ATAX2, MVT1, and GESUMMV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' These benchmarks belong to reason b described in Table III, and Themis does not aware of the potential cache thrashing due to the too-strong data locality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' In this case, temporal and non-temporal data paths are not differentiated and this leads to negatively affected performance using Themis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Note that one of the key advantages provided by Themis is to 3 2 base nt-store storetclwb Thems PM-spec BUCL ■AGPMeliminate almost all persist-barriers of the persistency model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' This feature achieves significant performance improvement for CPU workloads because the sfence instruction precludes buffering, reordering of memory accesses, and out-of-order execution due to its ordering semantics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' However, in the case of GPU where threads are highly overlapped and their memory latency could be hidden through massive multi-threading, the impact of removing the persist-barriers in GPU kernels is not as significant as it does in CPU workloads (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='5% on average [31]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' RELATED WORKS Intel provides PMDK [8], a library to leverage Optane NVM [14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Haria et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' [17] propose a C++ library to allow multiple updates to one or more data structures to be atomic with respect to failure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Hsu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' [18] propose a programming model and runtime that adds persistence to existing multi- threaded C/C++ programs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' [43] propose Janus, a hardware-software co-design that parallelizes and pre-executes backend memory operations in an NVM system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Mnemosyne [6], NV-Heaps [16], and NVRAM transactions [26] explored techniques for transactional interactions with PM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Check- pointing is often used for fault tolerance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Previous works [22, 23] for checkpointing on NVM focused on minimizing the checkpointing latency and bandwidth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Lin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' [31] adapt existing CPU persistency models for GPUs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' DRAGON [44] exploits NVM’s capability for GPU through unified memory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' GPM [21] exploits UVA to map PM to GPU’s address space to support fine-grain persistence to GPU kernels without the CPU’s help.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Nalli et al [13] propose WHISPER, a PM benchmark suite, and HOPS, a hands-off persistence system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' HOPS tracks updates to PM in hardware and provides high-level ISA primitives for applications to express durability and ordering constraints separately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Themis [27] exploits separate data paths to provide implicit ordering guarantees without using interven- ing fence instructions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' DPO [45] and PMEM-spec [28] exploit a dedicated persist-path for PM stores and a regular path for PM loads.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' VII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' CONCLUSION In this paper, we propose an adaptive approach (AGPM) for PM log updates’ data path selection in the GPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' We first describe the observations we found in the comparison of the experimental results of the GPU kernels using a static data path selection strategy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' We observe the presumption that it is more beneficial to use a non-temporal path for undo logging does not fit the GPU workloads.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Besides, we also observe that the log updates possessing strong locality with the subsequent data updates are not always appropriate to use the temporal data path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' We analyze the data locality among the GPU kernels’ log updates and the subsequent data updates, as well as the data locality among the exclusive log updates, in the GPU’s L1D and L2 caches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' We translate these analyses into 8 reasons and use these reasons to guide the data path selection in our proposed solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' We implement L1- and L2-level AGPM buffers to record the statistics in GPU kernels’ runtime execution, and we feed the statistic to the AGPM path selector in each SM to match with the reasons we concluded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Upon the matching results, AGPM adaptatively changes the data path for the log updates to PM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' According to the experimental results, AGPM outperforms the state-of-the-art multi-data-path architecture to PM for different types of GPU workloads.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' ACKNOWLEDGMENT TBD REFERENCES [1] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Arulraj, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Pavlo, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Dulloor, Let’s talk about storage & recovery methods for non-volatile memory database systems, in: Proceedings of the 2015 ACM SIGMOD International Conference on Management of Data, 2015, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' 707–722.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' [2] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Condit, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Nightingale, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Frost, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Ipek, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Lee, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Burger, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Coetzee, Better i/o through byte- addressable, persistent memory, in: Proceedings of the ACM SIGOPS 22nd symposium on Operating systems principles, 2009, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' 133–146.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' [3] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Dulloor, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Kumar, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Keshavamurthy, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Lantz, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Reddy, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Sankaran, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Jackson, System software for persistent memory, in: Proceedings of the Ninth European Conference on Computer Systems, 2014, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' 1–15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' [4] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Joshi, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Nagarajan, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Cintra, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Viglas, Efficient persist barriers for multicores, in: Proceedings of the 48th International Symposium on Microarchitecture, 2015, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' 660–671.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' [5] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Ren, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Zhao, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Khan, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Choi, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Wu, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Mutlu, Thynvm: Enabling software-transparent crash consis- tency in persistent memory systems, in: Proceedings of the 48th International Symposium on Microarchitecture, 2015, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' 672–685.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' [6] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Volos, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Tack, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Swift, Mnemosyne: Lightweight persistent memory, ACM SIGARCH Com- puter Architecture News 39 (2011) 91–104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' [7] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Zhao, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Li, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Yoon, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Xie, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Jouppi, Kiln: Closing the performance gap between systems with and without persistence support, in: Proceedings of the 46th Annual IEEE/ACM International Symposium on Microarchitecture, 2013, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' 421–432.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' [8] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' at Intel, 2023, Persistent memory programming blog, URL: pmem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='io.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' [9] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Enterprise, 2023, Persistent memory, URL: hpe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' com/us/en/servers/persistent-memory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='html.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' [10] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Newsroom, 2015, Intel and micron produce breakthrough memory technology, URL: newsroom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' intel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='com/community/intel newsroom/blog/2015/07/28/ intel-and-micron-produce-breakthrough-memory-technology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' [11] SNIA, 2023, Nvm programming technical work group, URL: snia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='org/forums/sssi/nvmp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' [12] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Peng, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Gokhale, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Green, System evaluation of the intel optane byte-addressable nvm, in: Proceedings of the International Symposium on Memory Systems, 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' 304–315.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' [13] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Nalli, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Haria, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Hill, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Swift, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Volos, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Keeton, An analysis of persistent memory use with whisper, ACM SIGPLAN Notices 52 (2017) 135–148.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' [14] Intel, 2023, Intel optane persistent mem- ory, URL: https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='intel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='in/content/ www/in/en/architecture-and-technology/ optane-dc-persistent-memory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='html.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' [15] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Chidambaram, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Pillai, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Arpaci-Dusseau, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Arpaci-Dusseau, Optimistic crash consistency, in: Proceedings of the Twenty-Fourth ACM Symposium on Operating Systems Principles, 2013, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' 228–243.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' [16] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Coburn, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Caulfield, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Akel, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Grupp, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Gupta, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Jhala, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Swanson, Nv-heaps: Making persistent objects fast and safe with next-generation, non- volatile memories, ACM SIGARCH Computer Architec- ture News 39 (2011) 105–118.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' [17] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Haria, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Hill, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Swift, Mod: Minimally ordered durable data structures for persistent memory, in: Proceedings of the Twenty-Fifth International Con- ference on Architectural Support for Programming Lan- guages and Operating Systems, 2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' 775–788.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' [18] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Hsu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Br¨ugner, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Roy, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Keeton, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Eug- ster, Nvthreads: Practical persistence for multi-threaded applications, in: Proceedings of the Twelfth European Conference on Computer Systems, 2017, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' 468–482.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' [19] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Kadekodi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Lee, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Kashyap, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Kim, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Kolli, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Chidambaram, Splitfs: Reducing software overhead in file systems for persistent memory, in: Proceedings of the 27th ACM Symposium on Operating Systems Principles, 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' 494–508.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' [20] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Lee, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Mohan, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Kashyap, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Kim, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Chi- dambaram, Recipe: Converting concurrent dram indexes to persistent-memory indexes, in: Proceedings of the 27th ACM Symposium on Operating Systems Principles, 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' 462–477.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' [21] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Pandey, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Kamath, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Basu, Gpm: leveraging per- sistent memory from a gpu, in: Proceedings of the 27th ACM International Conference on Architectural Support for Programming Languages and Operating Systems, 2022, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' 142–156.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' [22] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Elnawawy, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Alshboul, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Tuck, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Solihin, Efficient checkpointing of loop-based codes for non-volatile main memory, in: 2017 26th International Conference on Par- allel Architectures and Compilation Techniques (PACT), IEEE, 2017, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' 318–329.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' [23] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Alshboul, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Tuck, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Solihin, Lazy persistency: A high-performing and write-efficient software persistency technique, in: 2018 ACM/IEEE 45th Annual Interna- tional Symposium on Computer Architecture (ISCA), IEEE, 2018, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' 439–451.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' [24] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Liu, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Shen, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Yang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Yu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Wang, Nvm duet: Unified working memory and per- sistent store architecture, ACM SIGARCH Computer Architecture News 42 (2014) 455–470.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' [25] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Ren, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Zhao, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Khan, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Choi, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Wu, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Mutlu, Thynvm: Enabling software-transparent crash consis- tency in persistent memory systems, in: Proceedings of the 48th International Symposium on Microarchitecture, 2015, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' 672–685.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' [26] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Kolli, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Pelley, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Saidi, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Chen, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Wenisch, High-performance transactions for persistent memories, in: Proceedings of the Twenty-First International Con- ference on Architectural Support for Programming Lan- guages and Operating Systems, 2016, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' 399–411.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' [27] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Shahri, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Ghahani, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Kolli, (almost) fence-less persist ordering, in: 2020 53rd Annual IEEE/ACM International Symposium on Microarchitec- ture (MICRO), IEEE, 2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' 539–554.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' [28] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Jeong, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Jung, Pmem-spec: persistent memory speculation (strict persistency can trump relaxed persis- tency), in: Proceedings of the 26th ACM International Conference on Architectural Support for Programming Languages and Operating Systems, 2021, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' 517–529.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' [29] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Joshi, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Nagarajan, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Viglas, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Cintra, Atom: Atomic durability in non-volatile memory through hard- ware logging, in: 2017 IEEE International Symposium on High Performance Computer Architecture (HPCA), IEEE, 2017, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' 361–372.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' [30] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Pelley, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Chen, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Wenisch, Memory persis- tency: Semantics for byte-addressable nonvolatile mem- ory technologies, IEEE Micro 35 (2015) 125–131.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' [31] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Lin, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Alshboul, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Solihin, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Zhou, Exploring memory persistency models for gpus, in: 2019 28th International Conference on Parallel Architectures and Compilation Techniques (PACT), IEEE, 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' 311– 323.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' [32] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' webinar, 2011, Peer-to-peer & unified virtual ad- dressing, URL: https://developer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='download.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='nvidia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='com/ CUDA/training/cuda webinars GPUDirect uva.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='pdf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' [33] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' [n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='], 2016, Deprecating the pcommit instruc- tion, URL: https://software.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='intel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='com/blogs/2016/09/12/ deprecate-pcommit-instruction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' [34] Intel, 2021, eadr: New opportunities for persistent memory applications, URL: https: //software.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='intel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='com/content/www/us/en/develop/articles/ eadr-new-opportunities-for-persistent-memory-applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' html.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' [35] Intel, 2021, Persistent memory learn more series part 2, URL: https://software.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='intel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='com/ content/www/us/en/developer/articles/training/ pmem-learn-more-series-part-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='html.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' [36] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Zhao, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Wang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Lin, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Zhou, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Zheng, Selectively gpu cache bypassing for un-coalesced loads, in: 2016 IEEE 22nd International Conference on Parallel and Distributed Systems (ICPADS), IEEE, 2016, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' 908– 915.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' [37] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Xie, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Liang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Wang, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Sun, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Wang, Coordinated static and dynamic cache bypassing for gpus, in: 2015 IEEE 21st International Symposium on High Perfor- mance Computer Architecture (HPCA), IEEE, 2015, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' 76–88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' [38] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Jia, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Shaw, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Martonosi, Characterizing and improving the use of demand-fetched caches in gpus, in: Proceedings of the 26th ACM international conference on Supercomputing, 2012, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' 15–24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' [39] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Che, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Boyer, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Meng, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Tarjan, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Sheaffer, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Lee, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Skadron, Rodinia: A benchmark suite for heterogeneous computing, in: 2009 IEEE international symposium on workload characterization (IISWC), Ieee, 2009, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' 44–54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' [40] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Kulkarni, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Burtscher, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Casc¸aval, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Pingali, Lonestar: A suite of parallel irregular programs, in: 2009 IEEE International Symposium on Performance Analysis of Systems and Software, IEEE, 2009, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' 65–76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' [41] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Karimov, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Rabl, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Markl, Polybench: The first benchmark for polystores, in: Technology Conference on Performance Evaluation and Benchmarking, Springer, 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' 24–41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' [42] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Stratton, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Rodrigues, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Sung, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Obeid, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='-W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Chang, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Anssari, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Liu, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content='-m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Hwu, Parboil: A revised benchmark suite for scientific and commercial throughput computing, Center for Reliable and High- Performance Computing 127 (2012) 27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' [43] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Liu, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Seemakhupt, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Pekhimenko, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Kolli, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Khan, Janus: Optimizing memory and storage support for non-volatile memory systems, in: 2019 ACM/IEEE 46th Annual International Symposium on Computer Ar- chitecture (ISCA), IEEE, 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' 143–156.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' [44] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Markthub, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Belviranli, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Lee, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Vetter, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Matsuoka, Dragon: breaking gpu memory capacity limits with direct nvm access, in: SC18: International Conference for High Performance Computing, Network- ing, Storage and Analysis, IEEE, 2018, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' 414–426.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' [45] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Kolli, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Rosen, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Diestelhorst, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Saidi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Pelley, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Liu, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Chen, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' Wenisch, Delegated persist ordering, in: 2016 49th Annual IEEE/ACM International Symposium on Microarchitecture (MICRO), IEEE, 2016, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} +page_content=' 1–13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQfOQnS/content/2301.04392v1.pdf'} diff --git a/xtE2T4oBgHgl3EQf3gi9/content/2301.04172v1.pdf b/xtE2T4oBgHgl3EQf3gi9/content/2301.04172v1.pdf new file mode 100644 index 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Barnes1, Pedram Hassanzadeh2,3 and Mike Pritchard4 +1Department of Atmospheric Science, Colorado State University, Fort Collins, CO +2Department of Mechanical Engineering, Rice University, Houston 77005 TX +3Department of Earth, Environmental and Planetary Sciences, Rice University, Houston +77005 TX +4Department of Earth System Science, University of California, Irvine, CA 92697, USA +January 3, 2023 +This manuscript has been submitted for consideration for publication in +Artificial Intelligence for the Earth Systems +1 +arXiv:2301.00496v1 [physics.ao-ph] 2 Jan 2023 + +Abstract +Two distinct features of anthropogenic climate change, warming in the tropical upper tro- +posphere and warming at the Arctic surface, have competing effects on the mid-latitude jet +stream’s latitudinal position, often referred to as a “tug-of-war”. Studies that investigate the +jet’s response to these thermal forcings show that it is sensitive to model type, season, initial +atmospheric conditions, and the shape and magnitude of the forcing. Much of this past work +focuses on studying a simulation’s response to external manipulation. In contrast, we explore +the potential to train a convolutional neural network (CNN) on internal variability alone and +then use it to examine possible nonlinear responses of the jet to tropospheric thermal forcing +that more closely resemble anthropogenic climate change. Our approach leverages the idea be- +hind the fluctuation-dissipation theorem, which relates the internal variability of a system to its +forced response but so far has been only used to quantify linear responses. We train a CNN on +data from a long control run of the CESM dry dynamical core and show that it is able to skill- +fully predict the nonlinear response of the jet to sustained external forcing. The trained CNN +provides a quick method for exploring the jet stream sensitivity to a wide range of tropospheric +temperature tendencies and, considering that this method can likely be applied to any model +with a long control run, could lend itself useful for early stage experiment design. +1 +Introduction +The eddy-driven jet stream drives much of the northern hemisphere mid-latitude weather (e.g. +Nakamura et al., 2004; Athanasiadis et al., 2010; Shaw et al., 2016; Madonna et al., 2017). Conse- +quently, changes in the jet stream position and strength can result in enormous societal impact by +impacting heat waves, droughts, and flooding events (Schubert et al., 2011; Coumou and Rahm- +storf, 2012; Bibi et al., 2020; Rousi et al., 2021, 2022), extreme weather across the mid-latitudes +(Mahlstein et al., 2012; R¨othlisberger et al., 2016), hurricane tracks (Mattingly et al., 2015), and +crop production (Kornhuber et al., 2019). Two robust features of anthropogenic climate change, +warming in the upper troposphere of the tropics and warming at the surface of the Arctic, have +been shown to independently force opposite responses in the mean jet location (e.g. Held, 1993; +Harvey et al., 2015; Stendel et al., 2021) These competing responses are driven by changes in the +pole to equator temperature gradient (Blackport and Screen, 2020; Stendel et al., 2021). Warming +in the tropical upper troposphere drives a poleward shift in the mean jet location by increasing +the upper tropospheric temperature gradient, while simultaneously, warming at the Arctic surface +drives an equatorward shift in the mean jet location by decreasing the surface temperature gradient +(Butler et al., 2010; Screen et al., 2013; Chen et al., 2020; Stendel et al., 2021), The competing jet +response stemming from these two thermal forcings is commonly referred to as the “tug-of-war” on +the jet stream. Current consensus across climate models is that the upper tropospheric warming +wins-out over the Arctic surface warming, causing a net poleward shift of the jet (Yin, 2005; Swart +and Fyfe, 2012; Barnes and Polvani, 2013; Harvey et al., 2015). However, there is still substantial +disagreement over the magnitude of the jet response due to uncertainty in the strength and spatial +extent of the regional heating anomalies (Grise and Polvani, 2016). +Warming in both the tropical upper troposphere and Arctic surface are caused by distinctly dif- +ferent dynamical processes that determine the characteristics of the thermal anomalies. The tropical +upper atmosphere warms more as a result of additional water vapor stored in the warmer tropical +tropospheric air (i.e. a reduction in the moist adiabatic lapse rate; (Sherwood and Nidhi Nishant, +2015). +The enhanced Arctic warming, commonly referred to as Arctic Amplification, is occur- +ring three times faster than elsewhere on the planet (Blunden and Arndt, 2012; Druckenmiller +et al., 2021) and is driven by multiple processes that include changes in poleward energy transport +(Hwang and Frierson, 2010; Graversen and Langen, 2019), surface ice-albedo feedbacks (Manabe +2 + +and Stouffer, 1980; Dai et al., 2019), cloud feedbacks (Abbot and Tziperman, 2008) and lapse- +rate feedbacks (Pithan and Mauritsen, 2014). To further increase the complexity of the processes +driving the regional warming, the two thermal forcings likely do not act entirely independently. +Research has shown that increased transient Rossby waves initiated in the tropics may drive in- +creased heat transport into the high latitudes and as a result drive further warming in the mid- +and upper-troposphere of the Arctic (Lee, 2014; Dunn-Sigouin et al., 2021). Uncertainties in the +processes that contribute to the magnitude and shape of warming in the tropical upper troposphere +and Arctic surface (Blackport and Screen, 2020; Stendel et al., 2021), in turn, make it even more +challenging to predict the magnitude of the jet response. +Despite the large body of work that investigates the response of the mid-latitude jet under +climate change, multiple challenges, such as the short observational record, isolating the jet’s forced +response from internal variability, and modeling ice and cloud feedbacks continue to make the +question difficult to answer (Tjernstr¨om et al., 2008; Kattsov et al., 2010; Cohen et al., 2014; +Pithan and Mauritsen, 2014; Vihma, 2014). The studies that have investigated the response of the +jet to a thermal forcing have shown that the jet is sensitive to the shape, location, and magnitude +of the thermal forcing (Butler et al., 2010), the season in which the forcing is imposed (McGraw +and Barnes, 2016), the current state of the atmosphere (i.e. position of the jet stream; (Gerber +et al., 2008; Barnes et al., 2010; Kidston and Gerber, 2010; Garfinkel et al., 2013), and the climate +models used for the study (Meehl et al., 2007; Barnes and Polvani, 2013). +In an attempt to explore circulation sensitivities to a wide range of possible thermal forcings, +Hassanzadeh and Kuang (2016b) used a control run from the GFDL dry dynamical core (Manabe +et al., 1974) and employed the fluctuation-dissipation theorem (FDT) to compute the linear response +function of the circulation to a number of external thermal and mechanical forcing. FDT relates +the mean linear response of a nonlinear system to a forcing through a linear operator created from +the internal variability of the system (e.g. Kraichnan, 1959; Leith, 1975; Marconi et al., 2008). +With the ability to explore a forced response from internal variability, FDT has been proposed as a +method to quickly estimate circulation sensitivities in climate models (Fuchs et al., 2015) and serve +as a useful tool for planning expensive climate model experiments (Leith, 1975). There have been +encouraging results using FDT to explore the circulation response to thermal forcings in general +circulation models (Gritsun and Branstator, 2007) as well as more complex coupled climate models +(Phipps, 2010) to estimate the response to realistic sea surface thermal forcings (Fuchs et al., 2015). +In order for the linear operator of FDT to accurately predict the mean response to a forcing, +the system must satisfy a number of conditions (Marconi et al., 2008). The first condition is that +the system must be in equilibrium, because FDT assumes that small changes in the system’s state +(internal variability) has a recovery back to equilibrium that is similar to the system’s response to +a small perturbation (Kraichnan, 1959; Leith, 1975). The second is that the perturbation must be +small enough so that the response is linear even though the system that the operator is created +from is not necessarily linear (Leith 1975). Lastly, the probability density function of the system +must be differentiable, and many applications of the FDT assume the system probability density +function is Gaussian (Majda et al., 2005), though work has been done to make versions of FDT +where the system can be quasi-Gaussian (Cooper and Haynes, 2011). In theory, a system that +satisfies these conditions can use FDT to compute the systems’ linear response to a forcing, though +there are practical challenges in applying FDT to high-dimensional systems, such as GCMs (Lutsko +et al., 2015; Hassanzadeh and Kuang, 2016b; Khodkar and Hassanzadeh, 2018). +Instead of using FDT to relate a forcing to a response, this study uses a convolutional neural +network (CNN) to learn the nonlinear relationship between a forcing and a response. Moreover, +using a CNN in place of the linear operator removes the need to make some of the FDT assumptions +(i.e. small forcing for a linear response, Gaussianity assumption). Training is performed on data +3 + +from a long control run with the CESM dry dynamical core. Once trained, the CNN is used to +explore the jet sensitivity to a variety of thermal forcings. Throughout this study, we evaluate +the CNN’s ability to quantify the CESM dry dynamical core’s jet sensitivity, placing particular +emphasis on the tug-of-war between the warming in the tropical upper troposphere and the Arctic +surface. Training a neural network on internal variability alone and then using it to predict a forced +response is, to our knowledge, a novel application of deep learning to climate analysis. Therefore, +we assess the strengths and weaknesses of this approach in multiple ways (see Section 3). +2 +Methods +We train a CNN to predict the jet stream response to zonally averaged regional temperature +perturbations. The goal is to investigate jet sensitivity to thermal features associated with anthro- +pogenic climate change. The CNN, detailed in Section 2.2, is trained on a long control run from a +dry dynamical core, which is documented to reproduce the majority of the northern hemisphere’s +jet response to heating perturbations along with simulating the correct sign of the jet shift (e.g. +Mbengue and Schneider, 2013; Hassanzadeh et al., 2014; McGraw and Barnes, 2016; Baker et al., +2017). Once trained, the CNN’s skill is examined by comparing to additional baseline prediction +methods and dry core experiments that include an imposed thermal forcing. Details on the dry +dynamical core setup, the CNN architecture and training, additional baseline prediction methods, +and additional dry core heating experiments are discussed in more detail in the following Sections. +2.1 +Training Data +We use output from the Community Earth System Model (CESM) Eulerian spectral-transform +dry dynamical core (Lauritzen et al., 2018). The model runs are completed with the Held-Suarez +configuration (Held and Suarez, 1994), such that friction exists at the surface and the temperature +is relaxed to a prescribed hemispherically symmetric temperature field. The relaxation temperature +field is set to equinoctial conditions and there is no absorption of solar energy by the atmosphere +(i.e. there are no seasons or diurnal cycles). All runs are performed at T42 resolution with 30 +vertical levels, 64 latitude bands, and 128 longitude bands. The simulation is run in the above +configuration for one million six hour time steps. +The first 20,000 time steps (13.7 years) are +thrown out to account for model spin up. +All data processing is performed to create efficient training data for a CNN (Section 2.2) to +predict the zonally-averaged jet response to a range of tropospheric temperature perturbations. +Two variables are used in this study, zonally averaged temperature and zonally averaged zonal +wind speed. The zonally-averaged temperature data is used to calculate the temperature tendency +field used as input to the CNN. The zonally-averaged zonal wind speed is used to calculate the +initial location of the jet and the subsequent shift of the jet, which are used as a CNN input and +the CNN prediction respectively. We exclude data from 200 hPa and above, effectively removing +the stratosphere which is not well resolved in this model without modification (Polvani, 2002) and +so focus can remain solely on the troposphere for both the forcing and the jet response. Given that +this study focuses on hemispheric jets, we take advantage of the hemispheric symmetry in the dry +core and use each hemisphere as a separate independent sample, doubling the amount of available +training data to two million. After zonally averaging, removing the stratosphere, and considering +each hemisphere as a separate sample, the resulting size of the temperature field is 25 vertical levels +by 32 latitude bands. +Backward differencing is used to calculate the temperature tendency which is then smoothed +using a backward running mean of 240 time steps (60 days) to remove higher frequency variability. +4 + +Removing the high frequency variability allows the network to focus on learning the response to a +forcing that more closely mimics continuous climate change forcing. This smoothing is also aligned +with FDT calculations, in which an integration over long time lags (often up to the decorrelation +timescale) is done; e.g., see Eq. (3) in Hassanzadeh and Kuang (2016b). Smoothing the data before +calculating the temperature tendency did not result in any changes in the CNN skill (not shown). +Following established methods (Woollings et al., 2010; McGraw and Barnes, 2016), the jet +location is defined as the latitude of the maximum wind speed at a pressure level near the surface. +Zonal wind speeds from the 850 hPa level are used here and are first smoothed with a 240 time +step (60 days) backward running mean. Then, a second order polynomial is fit to the peak of the +smoothed 850 hPa zonal wind profile and the jet location is defined as the latitude of the maximum +wind speeds. +Now that a smoothed zonal temperature tendency and a jet location are calculated, the data +are split into training, validation, and testing data. Splitting is completed by chunking the data +into three groups where training data is the first chunk, validation the second, and testing the last. +Lastly, the jet response to a given temperature tendency is defined by the change in jet latitude +from the time of input to 120 time steps later (i.e. the jet shift). A positive jet shift indicates a +poleward shift in jet location and a negative jet shift indicates an equatorward shift in jet location +relative to the jet’s latitude at the time of prediction. The jet shift is calculated within each dataset +(training, validation, and testing) by subtracting a 240 time step backward running mean of jet +stream locations from a 240 time step forward running mean of jet stream locations 120 time steps +into the future. This processing results in 359,280 training samples, 199,280 validation samples, +and 1,399,558 testing samples. Training the CNN required fewer samples than expected as adding +more samples to the training dataset did not improve the CNN skill, explaining why the testing +dataset is much larger than the training and validation datasets. +2.2 +Convolutional Neural Network +Figure 1: Schematic of the convolutional neural network with an example of an input and output. +CNNs are commonly used for image recognition and classification tasks as the convolutional +5 + +Standardized +Scaled +Jet Shift +Temperature Tendency +25x32x32 +12x16x64 +1.44 +200 +00m +500 +00 +Uncertainty +6x8x64 +12x16x32 +.86 +25x32 +500 500 500 500 500 500 +Convolutional Layer (same padding, (3x3) kernel) +Standardized +Jet Location +Average Pooling (2x2) +-0.66 +3073 +Fully Connected Layer +Dropout Layer (rate = .3)layers can extract spatial features in the input image that help the network learn the correlations +between the inputs and output (Fukushima, 1980; Yann et al., 1998; Zeiler and Fergus, 2014). While +a fully connected feedforward network (e.g. LeCun et al., 2015) has the ability to learn the same +features extracted by the convolutional layers within a CNN, it may require a larger network and +more training data to do so (Yann et al., 1998; Ingrosso and Goldt, 2022). In this study, we utilize +a CNN so that the network can efficiently learn the correlation between temperature tendencies +and the jet response while also trying to minimize the amount of training data required. +The CNN has two inputs: a smoothed temperature tendency field (K day−1) and an initial +jet location (degrees latitude). Including the temperature tendency as an input allows us to in- +vestigate the jet response to regional temperature tendencies and including the initial jet location +supplies the CNN with essential information about the current state of the jet at the prediction +time, an important factor for the jet response to forcing (Gerber et al., 2008; Barnes et al., 2010; +Kidston and Gerber, 2010; Garfinkel et al., 2013). Before the data is input into the CNN, the +smoothed temperature tendency field is multiplied by a factor of 10 and the initial jet location is +standardized using the standard deviation and mean jet location from the training data. Scaling +and standardizing are done so that both inputs have similar magnitudes (order of 1). +The network consists of four convolutional layers: two average pooling layers, three dense layers, +and three dropout layers (Fig. +1). +Convolutional and dense layers use the hyperbolic tangent +activation function. +Data are passed through the network as follows: the scaled temperature +tendency goes directly into the first convolutional layer with 32 filters of size 3 x 3 and a stride +of 1 followed by a second convolutional layer with the same attributes. The second convolutional +layer is then connected to an average pooling layer with a kernel size of 2 x 2. These three layers, +two convolutional and a single average pooling, are repeated with the same attributes with the +exception of containing 64 filters rather than 32 in the convolutional layers. The output from the +second average pooling layer is flattened and the standardized initial jet location is concatenated +to the end. This layer is then fed into the first dense layer with 500 nodes and then goes through a +dropout layer with a dropout rate of 30%. The data passes through a combination of dense layers +with 500 nodes followed by dropout layers with a dropout rate of 30% two more times. The data +from the final dropout layer then passes into the output layer consisting of two nodes. +The CNN outputs two values denoted as µ and σ, which represent a mean and standard deviation +of a Gaussian distribution where µ denotes the predicted jet shift and σ represents its uncertainty. +Predicting the parameters of a Gaussian distribution is commonly used to quantify uncertainty for +neural networks (Nix and Weigend, 1994, 1995), and Gordon and Barnes (2022) recently showed the +utility of incorporating uncertainty into a regression neural network for climate science applications. +The network learns to predict µ and σ through the implementation of the negative log-likelihood +loss function: +Li = −log(pi) +(1) +where p is a value of the predicted Gaussian distribution evaluated at the true jet shift for the +ith input sample. To ensure the network is calibrated we employ the probability integral transform +(PIT) probability calibration scheme (Gneiting et al., 2007; Nipen and Stull, 2011; Barnes et al., +2022). The PIT histogram for this CNN can be found in Supplementary. +To train the CNN, we use the Adam stochastic gradient descent optimization algorithm (Kingma +and Ba, 2014) with a learning rate of 10−7, a batch size of 256, and a random seed of 300. We +apply early stopping to halt the training process once the validation loss fails to decrease for 10 +consecutive epochs and restore the model weights to the version with the lowest validation loss +(Prechelt, 2012). +6 + +2.3 +Baselines +We establish two baselines in this study to assess the performance of the CNN and demonstrate +that the CNN has learned relationships between the jet response and the regional temperature +tendencies. The first baseline is called persistence, similar to “persistence forecasting” (MacDonald, +1992), where future conditions are predicted to be identical to the current conditions. In our case, +this translates to the jet’s future location being the same as its location at the time of prediction (i.e. +jet shift equal to zero). Comparing this baseline to the CNN ensures that the CNN is predicting +jet shifts that are more accurate than predicting a jet shift of zero. The second baseline is called +average evolution and describes the average movement of the jet based on its position at the time +of prediction. For this baseline calculation, the training data is separated into 100 different bins +according to the initial jet location, essentially grouping samples with similar initial jet locations +together. The average jet shift for each bin is calculated, resulting in an average jet response that +is solely dependent on the jet stream’s starting position. The average evolution baseline is not +sensitive to the number of bins or their exact spacing (not shown). This baseline ensures that the +CNN is not just predicting the average evolution of the jet based solely on the initial jet location +but is also using the temperature tendency input to make its prediction. +Every test sample is thus associated with three jet shift predictions, one from the CNN and +two from the additional persistence and average evolution baselines. Although comparing results +between the CNN and the two baselines is useful for placing the CNN’s predictions into context, +we highlight that the baselines make predictions based solely on information about the initial +location of the jet while the CNN is provided additional information in the form of the temperature +tendency. Thus, the CNN is able to explore the correlations between a temperature tendency and +a jet response. +2.4 +Heating Experiments +The main goal of this study is to investigate the jet stream sensitivity to thermal forcing driven +by anthropogenic climate warming. However, as we have designed it, the CNN only trains on data +from a long control run (i.e. internal variability), and thus, only provides insights into the forced +response if the idea of the FDT holds (Kraichnan, 1959; Leith, 1975; Marconi et al., 2008). To +investigate whether this assumption is valid, we run additional dry core simulations (referred to as +heating experiments) with zonally symmetric imposed thermal forcing (F) that take the form of a +two-dimensional Gaussian in the latitude/pressure plane (Equation 2): +F(Θ, p) = qoexp +� +(| Θ | −Θo)2 +Θ2w +− (| p | −po)2 +p2w +� +(2) +where Θo and po are the horizontal and vertical centers respectively, Θw and pw define the width +and height, and the magnitude of the forcing is given by qo. Gaussians that fall near the edge are +cut off and therefore not complete two-dimensional Gaussians. For all Gaussians created in this +study, Θ, Θw, p, pw, qo are reported in Appendix A. +Eighteen heating experiments with either one or two Gaussian thermal forcings imposed are run +out to equilibrium to quantify the true jet shift (see experiments #1-18 in Table A1). To perform a +direct comparison between the CNN-predicted jet responses and the dry core jet responses, the CNN +is given the same temperature tendency that is imposed in each of the dry core heating experiments. +For the CNN’s initial jet location input, the average jet location from the long control run is used +(42.4°). By comparing the true forced response from the dry core to the predicted forced response +7 + +by the CNN we are able to investigate the CNN’s ability to predict the jet response to thermal +forcing from training on internal variability alone. +Each heating experiment is initiated at the end of the long control run (time step one million; +684.9 years), and therefore, have the same initial conditions. The heating experiments are run for +an additional 20,000 time steps with the first 4,000 removed to ensure that the model has reached +its new equilibrium. The 850 hPa zonal winds are then used to compute the location of the jet +(see Section 3.1). Finally, the true response of the jet to an imposed thermal forcing is defined +as the average jet location during the long control run subtracted from the jet location in the +corresponding heating experiment. +3 +Results +3.1 +Evaluation of CNN skill +Figure 2: Predicted jet response (y-axis) versus the true jet response (x-axis) for the (a) CNN, +(b) average evolution baseline, and (c) persistence baseline using the testing data from the control +simulation. Panel (a) is a contoured by density and panels (b) and (c) are scatter plots. Mean +absolute errors are shown in the bottom right corner of each panel. Gray lines represent a perfect +prediction (one-to-one line). Green line in panel (a) represents the best-fit line from the CNN +predictions. +We begin our discussion of the results with a focus on the deterministic predictions by the CNN +(µ). The deterministic skill on the testing data, which we define as the mean absolute error between +the predicted jet shift and the true jet shift, reveals how well the CNN generalizes to unseen samples +within the control simulation. The first look at the entire testing dataset will appear to show a +modest difference; a closer look within the testing dataset will prove more interesting. Figure 2a +shows the relationship between the predicted jet shift and the true jet shift where predictions with +higher accuracy are closer to the gray diagonal line (one-to-one line). Using orthogonal distance +regression (Boggs and Rogers, 1990; Virtanen et al., 2020), which takes into account error in both +the x and y variables as well as the CNN-predicted uncertainties in y, we calculate the slope from +the testing data to be 0.5 deg. poleward / (deg. poleward). This positive slope demonstrates the +CNN has learned relationships between the jet shift and the inputs. However, the slope of the +CNN predictions is less than that of the one-to-one line implying that the CNN underestimates +the magnitude of the largest jet shifts. +This is likely a result of the imbalanced training data +8 + +a) CNN +b) Average Evolution +c) Persistence +10 +10+ +10 +5 +5 +5. +-5' +Best-fit Line +One-to-one Line +Mean Absolute Error = 2.220 +Mean Absolute Error = 1.770 +Mean Absolute Error = 1.860 +10 +101 +-5 +5 +0 +10 +0 +10 +10 +10 +-5 +0 +5 +10 +10 +5 +5 +True Jet Shift (deg. poleward)as it includes more samples with smaller jet shifts than larger ones (shown in Figure 2a by the +density contours). During training, the goal of the CNN is to minimize the negative log-likelihood +loss function (see Equation 1), but with an unbalanced dataset, the CNN may never predict the +most extreme cases. Applying methods to make the network predict extremes, such as balancing +the dataset, using samples weights, or creating custom loss functions (Ma et al., 2013; Krawczyk, +2016), either caused a severe decrease in skill or did not succeed in solving the problem (not shown). +Nonetheless, as we will show next, the CNN outperforms the two benchmark baselines and is an +effective tool for exploring jet sensitivity to external forcing. +Comparing the CNN’s skill on the testing data to that of the two baselines: average evolution +(Fig. 2b) and persistence (Fig. 2c), allows us to place the CNN’s skill into context against other +basic prediction methods. Persistence has the lowest performance with a mean absolute error of +2.22°. Average evolution performs only slightly worse than the CNN with mean absolute errors +of 1.86° and 1.77° respectively. Unlike persistence, which can only ever predict a jet shift of zero, +average evolution makes a prediction based on the average relationship between the initial jet loca- +tion and the jet shift of the training data, allowing it to capture the mean jet response. Regardless, +average evolution is limited to predicting one of the 100 jet shifts resulting from the methods used +to calculate it (see Methods), hence the stripes in Figure 2b. Based on the mean absolute error +alone, the CNN outperforms both the persistence and average evolution baselines for the testing +data from dry dynamical core long control run. +Figure 3: The mean absolute error from the three prediction methods, CNN (black line), average +evolution (cyan line), and persistence (orange line) grouped by initial jet locations. gray violin +plots show the density curves of the CNN’s error distribution where the width corresponds with +the frequency of the data. Numbers at the bottom of each bar indicate the number of samples +in each group and the average initial jet location from the training data is marked on the x-axis +(42.4°). +The mean absolute errors in Figure 2 represent the error over the entire testing set, which is +prone to obscuring interesting details hiding within the distribution. For a more comprehensive +analysis of the CNN’s skill, the testing data is thus separated into groups based on the initial +9 + +Error based on Initial Latitude +CNN +Average Evolution +6 +Persistence +5 +4 +3 +2 +1 - +228 +1105 +4586 +11110 +22930 +52756 +122598 +287502 +479843 +326308 +85180 +5412 +0 +25 +30 +35 +40 +Avg. +45 +50 +Initial Latitudejet location. The mean absolute error for each group is shown for the CNN and the baselines in +Figure 3 and describes how the CNN’s skill and the baselines’ skill depend on the initial state of +the jet. The gray violin plots behind each bar indicate the CNN’s mean absolute error distribution +within that bin (i.e. the data used to calculate the CNN mean absolute error in each group). The +violin plots are smoothed with a kernel estimator using Scott’s rule and 100 points, which are the +default parameters of the Matplotlib library (Hunter, 2007). The numbers at the bottom of each +bar denote the number of samples in that bin. For all bins in Figure 3, the CNN outperforms the +baselines as demonstrated by the CNN’s error (black line) falling below the baseline errors (cyan +and orange lines). When the initial jet location is equatorward of 42° (labeled as “Avg.” along the +x-axis of Fig. 3), the CNN does considerably better than the baselines, but when the jet location +is poleward of 42°, the CNN and average evolution achieve similar skill. That is, in the cases where +the initial jet is near the pole, it appears that the CNN does not learn more than average evolution +but instead learns this average behavior to make its prediction. +When the initial jet location is near this climatological average position (42.4°), the errors of +the CNN and baselines converge (Fig. 3). About 30% of the samples in the training data have +initial jet locations within 2° of the climatological average and 14% of these samples have a jet shift +between -0.5° and 0.5°. Since so many samples near the climatological average have small jet shifts +and because the persistence baseline can only predict a jet shift of zero, the mean absolute error +for persistence is at its lowest near the jet’s climatological average position. The average evolution +baseline converges to a near zero prediction when the initial jet location is near the climatological +average, resulting in persistence and average evolution exhibiting similar errors. +Although the +persistence and average evolution baselines have an advantage near the climatological average, the +CNN still outperforms both baselines, implying that the CNN is using the additional information +provided by the input temperature tendencies. +Figure 4: The thermal forcing with a magnitude of qo = 0.25 K day −1 is moved around the +latitude and pressure plane where the shading in (a) and (b) represent the CNN-predicted jet shift +and uncertainty respectively. +An example of a thermal forcing is seen in the gray contours in +both panels. The “x” marks the center as well as the predicted jet shift and predicted uncertainty +associated with that thermal forcing. Gaussian parameters are found in Table A1 experiment #19. +10 + +b) Predicted Uncertainty +a) Predicted Jet Shift +200 + +200 - +300 +300 +400 +400 - + (hPa) +500 - +500 - +X +600 +600 +700 - +700 - +800 +800 - + 006 +900 +20 +30 +40 +50 +60 +80 +10 +20 +30 +40 +50 +60 +70 +80 +Latitude (deg.) +Latitude (deg.) +-10 +10 +0.0 +0.5 +1.0 +1.5 +2.0 +2.5 +-5 +Jet Shift (deg. poleward) +Sigma (deg.)Next, we focus on evaluating CNN’s ability to predict a jet stream forced response from an ar- +tificially constructed idealized temperature tendency not encountered within its noisy training en- +vironment. These temperature tendency inputs contain a two-dimensional Gaussian (see Methods) +with a prescribed magnitude, size, and location (latitude and pressure). Outside of the Gaussian, +the temperature tendency field is filled with zeros. Although some of these thermal forcings have +magnitudes larger than any temperature tendencies found in the internal variability training data, +we will provide strong evidence to support the CNN’s ability to extrapolate in the coming sections. +CNN predictions made from a thermal forcing use an initial jet location defined by the average +jet location of the training data (42.4°). Therefore, differences in predicted jet shifts between tem- +perature tendency inputs are a response to the thermal forcing alone and not the presumed initial +state. +The shading in Figure 4 shows the CNN-learned jet sensitivity to the location of heating by +holding the magnitude and the shape of a thermal forcing constant and changing only its location +(Fig. +4; see experiment #19 in Table A1). +An example of a thermal forcing is shown in the +gray contours where the “x” denotes its center and the color of the shading beneath represents +the predicted jet shift (Fig. 4a) and the predicted uncertainty (Fig. 4b) from the temperature +tendency. +Figure 4a exhibits multiple known features of the jet response to tropospheric thermal forcings. +For example, thermal forcings located higher in the troposphere are known to be more effective at +perturbing the jet than thermal forcings located lower in the troposphere (Hassanzadeh and Kuang, +2016a; Kim et al., 2021). This feature is learned by the CNN and is shown in Figure 4a as darker +shading at higher pressure levels. In addition, warming in the tropical upper troposphere has been +previously shown to cause the jet to shift poleward (Chen et al., 2008; Lim and Simmonds, 2009; +Butler et al., 2010). This poleward jet shift is seen in Figure 4a as denoted by the red shading in +the tropical upper troposphere. Finally, heating at the polar surface has been shown to cause the +jet to shift equatorward (Butler et al., 2010; Deser et al., 2010; Screen et al., 2013) and this is seen +in Figure 4a by the blue shading, albeit weak, near the polar surface. These features indicate that +the CNN has learned the correct sign of the jet shift as supported by prior research. +Figure 4a also highlights how moving the center of the heating by a few degrees or pressure +levels can change the direction of the jet shift. Take for instance heating at the polar surface, where +moving the heating from 80° latitude to 75° latitude changes the jet response from an equatorward +shift to a poleward shift. Baker et al. (2017) investigates the jet sensitivity to the location of heating +by running 306 dry core experiments with an imposed Gaussian shaped temperature tendency that +is moved around the latitude-pressure plane, just as we have done here with a trained CNN. In +Baker et al. (2017), they show that changes in the latitude of the heating most strongly impact +the sign of the jet shift while changing the pressure level has very little impact. Similar behavior is +found here with the CNN, although with a few exceptions. A more in-depth discussion about the +failure of the CNN to capture the correct direction of the jet shift at the surface of the mid-latitudes +is found in Supplementary. +Recall that the CNN predicts both the jet shift (µ) as well as its uncertainty (σ). +Figure +4b displays the predicted uncertainty values and highlights three regions where the CNN is less +certain. The CNN is less certain when heating occurs around 10° latitude and 600 hPa (σ ≈ 4°) +and additionally has large uncertainty when the heating is centered near 85° latitude and 900 hPa +and the 60° latitude and 550 hPa (σ ≈ 1.5°). The reasons behind the greater uncertainty in these +regions require further investigation. +11 + +3.2 +Nonlinearities learned by the CNN +Ideally, a benefit of using a CNN is that it learns a nonlinear relationship between the temperature +tendency input and the jet shift output. The hyperbolic tangent activation functions in the convo- +lutional and dense layers of the CNN allow it to learn nonlinear relationships between the inputs +and outputs if nonlinearity is present in the data. However, this does not necessarily mean the CNN +has learned nonlinear relationships. To evaluate the nonlinearity learned by the CNN we complete +two analyses. The first analysis examines how the CNN-predicted jet shift varies as a function of +the thermal forcing magnitude. The second analysis looks at scenarios where two thermal forcings +are simultaneously present in the temperature tendency input and explores whether the CNN has +learned a nonlinear interaction between the two. Keep in mind that neither of these analyses has a +ground truth, and so we are exclusively exploring what the CNN has learned. In the next section, +we will then further test the accuracy of the CNN with additional dry core simulations. +Figure 5: The CNN learned nonlinear responses where panel (a) shows example thermal forcing +with magnitudes of 1 K day−1 at the five locations and panels (b) and (c) show the linear response +(dashed line) and the predicted response from the CNN (solid lines). Note the different y-axes in +panels (b) and (c). Gaussian parameters are found in Table A1 #20-24. +The first nonlinear analysis explores how the jet shift varies as a function of the thermal forcing +magnitude by separately inputting thermal forcings of different magnitudes in five different locations +(Fig. 5a; see experiments #20-24 in Table A1). We use ten different magnitudes that vary from +-1.0 K day−1 to 1.0 K day−1 in increments of 0.2 K day−1 for each location. For all cases, the +initial jet location input is fixed at the average jet location of the training data (42.4°). Figure +5b and 5c compare a linear relationship (dashed lines) and the CNN’s learned relationship (solid +lines) between the thermal forcing magnitude and the jet shift. The jet response to temperature +tendencies near the polar surface and the mid-tropospheric mid-latitudes are the most linear as +shown by the green line in Figure 5b and the blue line in Figure 5c. +In both of these cases, +the CNN-predicted jet shift is most similar to the linear dashed line. In contrast, temperature +tendencies in the tropics and the upper troposphere of the polar region have the largest nonlinear +response (yellow line in Figure 5b, pink, and red lines in Figure 5c) as these cases vary greatly from +the dashed linear line. +We next explore the nonlinearities learned by the CNN when two thermal forcings are present. +12 + +Nonlinear Response +b) +0 +400 - +Jet Shift (deg. poleward) +-0.8 +-0.6 +-0.4 +-0.2 +0.2 +0.4 +0.6 +0.8 +600 - +700 +0 +800 - +F 006 +-2 +c) +10 +30 +40 +20 +50 +60 +70 +-0.8 +-0.6 +-0.4 +-0.2 +0.2 +0.4 +0.6 +80 +0.8 +Latitude (deg.) +Temperature Tendency Magnitude (K/day)Figure 6: Panel (a) shows the CNN-predicted jet shift from when two thermal forcings vary with +magnitude. +One at the surface of the pole (x-axis) and the other in the upper troposphere of +the tropics (y-axis). Panel (b) shows the predicted uncertainty for the predictions of panel (a). +Panel (c) is similar to panel (a) but the CNN predicts the jet shift from the two thermal forcings +independently. Panel (d) is the difference between panel (a) minus panel (c) representing the CNN +learned nonlinearity. +The thermal forcings are centered on two key regions, the tropical upper troposphere and the polar +surface. As discussed previously, warming in the tropical upper troposphere forces the jet to shift +poleward (e.g. Chen et al., 2008; Lim and Simmonds, 2009; Butler et al., 2010) and warming at +the polar surface forces the jet to shift equatorward (e.g. Butler et al., 2010; Deser et al., 2010; +Screen et al., 2013). When they occur simultaneously, they force competing effects that can result +in a tug-of-war scenario on the jet stream (e.g. Harvey et al., 2015; Chen et al., 2020). To explore +the jet sensitivities to this climate change induced tug-of-war, the temperature tendency inputs are +composed of a Gaussian thermal forcing at the polar surface and another in the upper troposphere +of the tropics. Both vary independently in magnitude during the analyses (see experiment #25 in +Table A1) and Figure 6a shows the predicted jet shift (µ) and 6b shows the predicted uncertainty +(σ) for each forcing pattern. With regards to the tug-of-war, studies use a variety of atmospheric +models to show that despite opposite forced jet responses, the jet will likely shift poleward (Yin, +2005; Harvey et al., 2015). The upper right quadrant of Figure 6a depicts the situation where both +thermal forcings are positive (warming). In this scenario, the CNN predicts a poleward shift of the +jet in agreement with past work, however, the CNN is not equally certain for all predictions. As +shown in Figure 6b, the CNN is more confident with cooling at the pole and warming in the tropics +and less confident with warming in the pole combined with cooling in the tropics. Understanding +why these scenarios are more uncertain requires further investigation. +Figure 6a shows the CNN-predicted jet response when two thermal forcings are present in the +temperature tendency input. To test whether the CNN has learned a nonlinear impact on the jet +from two simultaneous forcings, we task the CNN to predict the jet shift from the two thermal +forcings independently (upper tropical troposphere and polar surface) and add the two predicted jet +shifts together subsequently. If the CNN exclusively learned a linear response between two forcings, +Figure 6a and Figure 6c would be identical, as predicting a jet shift from combined forcings would +be equal to predicting the jet shifts from individual forcing and adding the predictions together. +Instead, Figure 6d shows the difference in predicted jet shifts from these methods and provides +evidence of the nonlinearity learned by the CNN where inputs that contain stronger thermal forcings +(scenarios in the corners of 6d) have greater learned nonlinearity. +13 + +a) Predicted Jet Shift from Combined Forcing +b) Uncertainty from Combined Forcing +0.2 +0.2 +1.5 +0.1 +0.1 +F 0 +1.0 +0.0 +0.0 - +-0.1 +0.5 +-2 +-0.2 +L 0.0 +-2 +0.0 +0.5 +1.0 +0.5 +0.0 +0.5 +1.0 +Deg. +-0.5 +1.0 +.0 +Deg. +Poleward +Poleward +d) Difference between a) and c) +0.2 - +0.2 +0.5 + 2 +0.1 +Fo'0 +0 +0.0 +0.0 +-0.1 +-0.1 +-2 +-0.5 +-0.2 +0.2 +1.0 +-1.0 +-0.5 +Deg. +0.0 +0.5 +Deg. +0.5 +0.0 +.0 +Poleward +Poleward + Polar Forcing Magnitude (K/day) +Polar Forcing Magnitude (K/day)3.3 +Out-of-sample tests +Thus far we have compared the CNN-predicted jet shifts to our established baselines, true jet shifts +harvested from the internal variability of the control run, and past work. We next evaluate the +ability of the CNN to predict the explicit simulated jet response to an imposed idealized steady +thermal forcing outside the training set. The FDT states that the linear response of a nonlinear +system to external forcing can be related to the internal variability of the system. +Under the +assumption that FDT holds, our CNN trained on internal variability may also be able to predict +a forced response. We next explore this by comparing the true forced jet shift calculated from +additional dry core experiments to the predicted jet shift by the CNN. +We perform 14 additional forced heating experiments with the dry dynamical core (see Methods +and Table A1 experiments #1-14). These 14 heating experiments are motivated by the tug-of-war +on the jet resulting from anthropogenic climate change (Harvey et al., 2015; Chen et al., 2020; +Stendel et al., 2021). To mimic the tug-of-war, each experiment contains a thermal forcing in the +tropical upper troposphere and at the polar surface. The left side of Figure 7 includes the magnitude +of each Gaussian shaped thermal forcing. The forced jet response from the dry dynamical core +experiments and the CNN-predicted jet response from 14 heating experiments are shown on the +right side of Figure 7. Comparing the true forced jet shift simulated by the dry core (green dots) and +the predicted jet shift by the CNN trained on internal variability (black lines), we see that across +all experiments, the CNN accurately captures the sign of the jet shift. Experiments #1 through #7 +exhibit a negative jet shift and #8 through #14 exhibit a positive jet shift. Furthermore, nearly +all of the experiments (excluding #3, #4, and #14) have forced jet shifts that fall well within +the uncertainty bounds predicted by the CNN (±2σ; gray boxes). Additional discussion of other +heating experiments that do not focus on the tug-of-war on the jet can be found in Appendix C. +Heating experiments #6, #7, #8, and #9 contain only a thermal forcing at the polar surface +(no thermal forcing in the tropical upper troposphere) and are therefore useful for investigating +the difference in CNN-predicted uncertainty between polar warming and polar cooling. In heating +experiments #6 and #7, which contain polar warming, the CNN is less certain (larger σ), in +contrast to heating experiments #8 and #9, which contains polar cooling, where the CNN is more +certain (smaller σ). +The CNN’s uncertainty when there is a thermal forcing in the upper troposphere of the tropics is +more difficult to discern from Figure 7 because the CNN’s uncertainty is impacted considerably by +the thermal forcing at the polar surface. However, heating experiments #3 and #12 include only a +thermal forcing in the tropical upper troposphere, one cooling and one warming respectively. These +heating experiments suggest that the CNN is more certain when the upper tropical troposphere is +cooling rather than warming. +4 +Implications for Sensitivity Analysis +Given the CNN’s ability to replicate the sign of the jet stream’s forced response as validated +with the additional forced dry dynamical core experiments, we propose that our approach can be +deployed as a computationally efficient tool to aid in the design of forced model experiments. To +demonstrate this, we next revisit a historical study (Butler et al. 2010; afterward B10) and show +how the pre-trained CNN can be used to replicate the study’s results as well as document possible +sensitivities not included in the initial work. In B10, differences in dry core atmospheric circulations +due to variations in the location and shape of thermal forcings were identified and documented. +To test the atmospheric sensitivity, B10 ran multiple experiments with different imposed thermal +forcing patterns in the Colorado State University general circulation model (Ringler et al., 2000). +14 + +Figure 7: The 14 heating experiments, their resulting jet shift in the dry core, and the jet shift +as predicted by the CNN. The left side includes the magnitude of each Gaussian shaped thermal +forcing. The right side shows the true forced dry core jet shift (green dots), the predicted CNN jet +shift (black line), and the CNN-predicted uncertainty (gray boxes; ±2σ). +Although B10 did not quantify a shift of the jet stream the same way as we do here, the study +showed the zonal-mean zonal wind response and discussed which heating experiments resulted in a +stronger wind response. From this information, we are able to infer the relative magnitude of the +jet shift for each experiment. +Here, we focus on four specific heating experiments within B10 that aim to investigate how +sensitive the circulation response is to the height and shape of tropical upper tropospheric heating. +Examples of the thermal forcing patterns imposed in B10 are shown in Figure 8a-d and will be +referred to as heating experiments #26, #27, #28, and #29 for this discussion. In the original +study, B10 found that the jet shifts poleward in response to all heating experiments, but that +the magnitudes of the shifts varied. B10 shows that heating experiment #26 had the strongest +jet response and compressing the forcing vertically (heating experiment #27) or compressing the +forcing in the meridional direction (heating experiment #28) weakened the wind response. In the +last experiment (heating experiment #29), B10 showed that when the forcing was compressed +15 + +Polar +Tropical +Jet Shift (degrees poleward) +Heating +Magnitude +Magnitude +Experiment +-4 +-2 +(K/day) +(K/day) +2 +4 +#1 +1.0 +-0.1 +. +#2 +0.5 +-0.1 +#3 +0.0 +-0.1 +#4 +-0.5 +-0.1 +#5 +-1.0 +-0.1 +#6 +1.0 +0.0 +#7 +0.5 +0.0 +#8 +-0.5 +0.0 +#9 +-1.0 +0.0 +#10 +1.0 +0.1 +#11 +0.5 +0.1 +#12 +0.0 +0.1 +CNN Prediction +#13 +-0.5 +0.1 +CNN Uncertainty +Dry Core Output +#14 +-1.0 +0.1vertically and moved lower in the troposphere, the wind response was even weaker. +Figure 8: Panels (a) - (d) shows example thermal forcings of magnitude 0.5 K day−1 representing +the four heating experiments used in Butler et al. 2010, Gaussian parameters are found in Table +A1 #26-29. The panel outline corresponds to the predicted jet shifts (y-axis) in panel (e) which +are shown as a function of the magnitude of the temperate forcing (x-axis). The vertical gray line +at 0.5 K day−1 corresponds to the magnitude of the heating experiments used in Butler et al. 2010. +Following the same four heating experiments of B10, we recreated the thermal forcing patterns +(see experiments #26-29 in Table A1) and input them into the CNN with the initial jet location set +to the average jet location of the training data (42.4°). In addition to the magnitude of heating used +in B10 (qo = 0.5 K day −1), here the jet sensitivity to the magnitude of the thermal forcing is also +included since it is trivial to explore once the CNN is trained. Figure 8e shows the predicted jet shift +from the four heating experiments with varying magnitudes, and the vertical gray line indicates the +0.5 K day −1 magnitude used in B10. The CNN predicts the same relative relationship between +the heating experiments as found in B10, where heating experiment #26 exhibits the strongest +jet response and heating experiment #29 exhibits the weakest. Furthermore, by exploring the jet +sensitivity to the magnitude of heating, Figure 8e shows new information about jet sensitivity. For +example, as the magnitude of the thermal forcing increases, heating experiment #27 (compressed +vertically) and heating experiment #28 (compressed meridionally) converge to the same jet shift. +Alternatively, when the magnitude of the thermal forcing decreases, heating experiment #28 and +heating experiment #29 (compressed vertically and lower in the troposphere) converge to the same +jet shift. These two results could be confirmed with a few targeted forced dry core simulations (not +done here), though it was the ability provided by the CNN to quickly explore jet shifts in response +to thermal forcings that allowed us to discover these possible jet sensitivities. +16 + +Temperature Tendencies from Butler2010 +300 +300 +00m +400 +0.38 + 400 +400 +Pressure (hPa) +500 + 500 +0.25 +009 +700 +700 +0.2 +800 +008 +800 +300 +0.06 +b) heating experiment B +900 +00 +c) heating experiment C +d) heating experiment D +a) heating experiment A +0.00 +(K/day) +Latitude (deg.) +Jet Sensitivity +8 +6 +4 +0.1 +0.2 +0.3 +0.4 +0.5 +0.6 +0.7 +0.8 +0.9 +Temperature Tendency Magnitude (K/day)In this chapter, we show a successful example of using the CNN to explore the jet sensitivities +inside the dry dynamical core. The CNN is not perfect in its predictions which may be due to a lack +of predictability, non-optimal training of the CNN, a breakdown of the FDT, or a combination of +the three. However, as demonstrated throughout this paper, the comparisons in the CNN-predicted +jet shifts have the same sign and similar magnitudes to the forced jet shifts from the dry core in +response to a range of temperature tendencies and once trained, can make predictions quickly. We +wish to emphasize that this method should not replace the need to run designed climate model +experiments. Rather, training CNN on an existing long control run could provide the opportunity +to explore a large number of forcing experiments before any forced model runs are simulated and +be especially helpful for planning forced experiments in dynamic model simulations. +5 +Conclusions +We explore the jet stream’s response to external forcing by training a CNN on smoothed temper- +ature tendencies from a dry dynamical core long control run to predict a shift in the jet stream’s +location 30 days later. The main motivation of this work is to explore the potential for training +a CNN on internal variability alone and then using it to examine possible nonlinear responses of +the jet to tropospheric thermal forcing that more closely resemble anthropogenic climate change. +Since the CNN is trained entirely on data from a control simulation, it exclusively learns from +internal variability. Nevertheless, by comparing the CNN-predicted jet shifts to established base- +lines, peer reviewed literature, and additional dry core heating experiments, we show that the CNN +can predict the forced jet shift to sustained forcing. The trained CNN is then used to investi- +gate jet sensitivities to scenarios that mimic the tug-of-war between the tropics and poles under +anthropogenic climate change. +Given the CNN’s ability to predict the jet response to thermal +forcings, we propose training a CNN on long control runs that are increasingly becoming more +available to explore model sensitivities to various forcings as a tool to aid in early stage climate +model experiment design. Future work could include extending this method to evaluate whether it +generalizes to different experimental frameworks, including, but not limited to, evaluating it with +three-dimensional predictors, training on coupled climate model simulations, and learning complex +non-linear climate responses from forced simulations where FDT does not hold. +Acknowledgments +CC and EAB are supported, in part, by NSF CAREER AGS-1749261 under the Climate and Large- +scale Dynamics program. The authors thank Marybeth Arcodia for providing valuable support +during the writing process. +Data availability +The code used to prepare the data can be found on github https://github.com/connollyc152/ +DDC_jet_sensitivity and will be assigned a permanent doi on Zenodo upon publication. Data is +available upon request and will be made available on Zenodo and given a doi upon publication. +17 + +Appendix A +Table of two-dimensional Gaussians parameters +Table 1: Parameters for two-dimensional Gaussians for the forced dry core heating experiments +and CNN thermal forcings, ”V” indicates varying parameter. +18 + +Ow (degree +O。 (degree +Experiment +Po (hPa) +pw (hPa) +qo (K) +poleward) +poleward) +06 +16 +1000 +250 +1.0 +#1 +0 +27 +300 +125 +-0.1 +90 +16 +1000 +250 +0.5 +#2 +0 +27 +300 +125 +-0.1 +#3 +0 +27 +300 +125 +-0.1 +90 +16 +1000 +250 +-0.5 +#4 +0 +27 +300 +125 +-0.1 +90 +16 +1000 +250 +-1.0 +#5 +0 +27 +300 +125 +-0.1 +#6 +90 +16 +1000 +250 +1.0 +#7 +90 +16 +1000 +250 +0.5 +#8 +90 +16 +1000 +250 +-0.5 +#9 +90 +16 +1000 +250 +-1.0 +90 +16 +1000 +250 +1.0 +#10 +0 +27 +300 +125 +0.1 +90 +16 +1000 +250 +0.5 +#11 +0 +27 +300 +125 +0.1 +#12 +0 +27 +300 +125 +0.1 +90 +16 +1000 +250 +-0.5 +#13 +0 +27 +300 +125 +0.1 +90 +16 +1000 +250 +-1.0 +#14 +0 +27 +300 +125 +0.1 +#15 +60 +15 +1000 +200 +0.25 +#16 +60 +15 +700 +200 +0.25 +#17 +30 +15 +1000 +200 +0.25 +#18 +30 +15 +700 +200 +0.25 +#19 +10 +150 +1.0 +#20 +12 +15 +850 +200 +#21 +75 +15 +850 +200 +#22 +45 +15 +550 +200 +#23 +12 +15 +300 +200 +#24 +75 +15 +300 +200 +90 +16 +1000 +250 +#25 +0 +27 +300 +125 +v +#26 +27 +300 +125 +v +#27 +0 +27 +300 +75 +0 +13.5 +125 +#28 +300 +#29 +0 +27 +500 +125References +Abbot, D. S. and Tziperman, E. (2008). A high-latitude convective cloud feedback and equable +climates. Quart. J. Roy. Meteor. Soc., 134(630):165–185. +Athanasiadis, P. J., Wallace, J. M., and Wettstein, J. J. (2010). Patterns of wintertime jet stream +variability and their relation to the storm tracks. J. Atmos. Sci., 67(5):1361–1381. +Baker, H. S., Woollings, T., and Mbengue, C. (2017). +Eddy-Driven jet sensitivity to diabatic +heating in an idealized GCM. J. Clim., 30(16):6413–6431. +Barnes, E., Barnes, R., and DeMaria, M. (2022). Sinh-arcsinh-normal distributions to add uncer- +tainty to neural network regression tasks: applications to tropical cyclone intensity forecasts. +Barnes, E. A., Hartmann, D. L., Frierson, D. M. W., and Kidston, J. (2010). Effect of latitude on +the persistence of eddy-driven jets. Geophys. Res. Lett., 37(11). +Barnes, E. A. and Polvani, L. (2013). Response of the midlatitude jets, and of their variability, to +increased greenhouse gases in the CMIP5 models. J. Clim., 26(18):7117–7135. +Bibi, A., Ullah, K., Yushu, Z., Wang, Z., and Gao, S. (2020). Role of westerly jet in torrential +rainfall during monsoon over northern pakistan. Life Support Biosph. Sci., 7(2):e2019EA001022. +Blackport, R. and Screen, J. A. (2020). Insignificant effect of arctic amplification on the amplitude +of midlatitude atmospheric waves. Sci Adv, 6(8):eaay2880. +Blunden, J. and Arndt, D. S. (2012). State of the climate in 2011. Bull. Am. Meteorol. Soc., +93(7):S1–S282. +Boggs, P. T. and Rogers, J. E. (1990). Orthogonal distance regression. Contemporary Mathematics, +112:183–194. +Butler, A. H., Thompson, D. W. J., and Heikes, R. (2010). The Steady-State atmospheric circu- +lation response to climate change–like thermal forcings in a simple general circulation model. J. +Clim., 23(13):3474–3496. +Chen, G., Lu, J., and Frierson, D. M. W. (2008). Phase speed spectra and the latitude of surface +westerlies: Interannual variability and global warming trend. J. Clim., 21(22):5942–5959. +Chen, G., Zhang, P., and Lu, J. (2020). Sensitivity of the latitude of the westerly jet stream to +climate forcing. Geophys. Res. Lett., 47(4):345. +Cohen, J., Screen, J. A., Furtado, J. C., Barlow, M., Whittleston, D., Coumou, D., Francis, J., +Dethloff, K., Entekhabi, D., Overland, J., and Jones, J. (2014). Recent arctic amplification and +extreme mid-latitude weather. Nat. Geosci., 7(9):627–637. +Cooper, F. C. and Haynes, P. H. (2011). Climate sensitivity via a nonparametric Fluctuation– +Dissipation theorem. J. Atmos. Sci., 68(5):937–953. +Coumou, D. and Rahmstorf, S. (2012). A decade of weather extremes. Nat. Clim. Chang., 2(7):491– +496. +Dai, A., Luo, D., Song, M., and Liu, J. (2019). Arctic amplification is caused by sea-ice loss under +increasing CO2. Nat. Commun., 10(1):121. +19 + +Deser, C., Tomas, R., Alexander, M., and Lawrence, D. (2010). The seasonal atmospheric response +to projected arctic sea ice loss in the late Twenty-First century. J. Clim., 23(2):333–351. +Druckenmiller, M. L., Moon, T. A., Thoman, R. L., Ballinger, T. J., Berner, L. T., Bernhard, +G. H., Bhatt, U. S., Bjerke, J. W., and Box (2021). +The arctic. +Bull. Am. Meteorol. Soc., +102(8):S263–S316. +Dunn-Sigouin, E., Li, C., and Kushner, P. J. (2021). Limited influence of localized tropical sea- +surface temperatures on moisture transport into the arctic. Geophys. Res. Lett., 48(8). +Fuchs, D., Sherwood, S., and Hernandez, D. (2015). An exploration of multivariate fluctuation +dissipation operators and their response to sea surface temperature perturbations. J. Atmos. +Sci., 72(1):472–486. +Fukushima, K. (1980). Neocognitron: a self organizing neural network model for a mechanism of +pattern recognition unaffected by shift in position. Biol. Cybern., 36(4):193–202. +Garfinkel, C. I., Waugh, D. W., and Gerber, E. P. (2013). The effect of tropospheric jet latitude on +coupling between the stratospheric polar vortex and the troposphere. J. Clim., 26(6):2077–2095. +Gerber, E. P., Voronin, S., and Polvani, L. M. (2008). Testing the annular mode autocorrelation +time scale in simple atmospheric general circulation models. Mon. Weather Rev., 136(4):1523– +1536. +Gneiting, T., Balabdaoui, F., and Raftery, A. E. (2007). Probabilistic forecasts, calibration and +sharpness. J. R. Stat. Soc. Series B Stat. Methodol., 69(2):243–268. +Gordon, E. M. and Barnes, E. A. (2022). Incorporating uncertainty into a regression neural network +enables identification of decadal state-dependent predictability in CESM2. Geophys. Res. Lett., +49(15). +Graversen, R. G. and Langen, P. L. (2019). On the role of the atmospheric energy transport in 2 +× CO2–Induced polar amplification in CESM1. J. Clim., 32(13):3941–3956. +Grise, K. M. and Polvani, L. M. (2016). Is climate sensitivity related to dynamical sensitivity? J. +Geophys. Res., 121(10):5159–5176. +Gritsun, A. and Branstator, G. (2007). Climate response using a Three-Dimensional operator based +on the Fluctuation–Dissipation theorem. J. Atmos. Sci., 64(7):2558–2575. +Harvey, B. J., Shaffrey, L. C., and Woollings, T. J. (2015). Deconstructing the climate change +response of the northern hemisphere wintertime storm tracks. Clim. Dyn., 45(9):2847–2860. +Hassanzadeh, P. and Kuang, Z. (2016a). The linear response function of an idealized atmosphere. +part i: Construction using green’s functions and applications. J. Atmos. Sci., 73(9):3423–3439. +Hassanzadeh, P. and Kuang, Z. (2016b). The linear response function of an idealized atmosphere. +part II: Implications for the practical use of the Fluctuation–Dissipation theorem and the role of +operator’s nonnormality. J. Atmos. Sci., 73(9):3441–3452. +Hassanzadeh, P., Kuang, Z., and Farrell, B. F. (2014). Responses of midlatitude blocks and wave +amplitude to changes in the meridional temperature gradient in an idealized dry GCM. Geophys. +Res. Lett., 41(14):5223–5232. +20 + +Held, I. M. (1993). Large-Scale dynamics and global warming. Bull. Am. Meteorol. Soc., 74(2):228– +242. +Held, I. M. and Suarez, M. J. (1994). A proposal for the intercomparison of the dynamical cores +of atmospheric general circulation models. Bull. Am. Meteorol. Soc., 75(10):1825–1830. +Hunter, J. D. (2007). Matplotlib: A 2d graphics environment. Computing in Science & Engineering, +9(3):90–95. +Hwang, Y.-T. and Frierson, D. M. W. (2010). Increasing atmospheric poleward energy transport +with global warming. Geophys. Res. Lett., 37(24). +Ingrosso, A. and Goldt, S. (2022). +Data-driven emergence of convolutional structure in neural +networks. Proc. Natl. Acad. Sci. U. S. A., 119(40):e2201854119. +Kattsov, V. M., Ryabinin, V. E., Overland, J. E., Serreze, M. C., Visbeck, M., Walsh, J. E., Meier, +W., and Zhang, X. (2010). Arctic sea-ice change: a grand challenge of climate science. J. Glaciol., +56(200):1115–1121. +Khodkar, M. A. and Hassanzadeh, P. (2018). Data-driven reduced modelling of turbulent Rayleigh– +B´enard convection using DMD-enhanced fluctuation–dissipation theorem. +J. Fluid Mech., +852:R3. +Kidston, J. and Gerber, E. P. (2010). Intermodel variability of the poleward shift of the austral jet +stream in the CMIP3 integrations linked to biases in 20th century climatology. GEOPHYSICAL +RESEARCH LETTERS, 37(9). +Kim, D., Kang, S. M., Merlis, T. M., and Shin, Y. (2021). Atmospheric circulation sensitivity to +changes in the vertical structure of polar warming. Geophys. Res. Lett., 48(19). +Kingma, D. P. and Ba, J. (2014). Adam: A method for stochastic optimization. +Kornhuber, K., Coumou, D., Vogel, E., Lesk, C., Donges, J. F., Lehmann, J., and Horton, R. M. +(2019). +Amplified rossby waves enhance risk of concurrent heatwaves in major breadbasket +regions. Nat. Clim. Chang., 10(1):48–53. +Kraichnan, R. H. (1959). Classical Flucationation-Relaxation theorem. Institute of Mathematical +Sciences, 113(5). +Krawczyk, B. (2016). +Learning from imbalanced data: open challenges and future directions. +Progress in Artificial Intelligence, 5(4):221–232. +Lauritzen, P. H., Nair, R. D., Herrington, A. R., Callaghan, P., Goldhaber, S., Dennis, J. M., +Bacmeister, J. T., Eaton, B. E., Zarzycki, C. M., Taylor, M. A., Ullrich, P. A., Dubos, T., +Gettelman, A., Neale, R. B., Dobbins, B., Reed, K. A., Hannay, C., Medeiros, B., Benedict, +J. J., and Tribbia, J. J. (2018). NCAR release of CAM-SE in CESM2.0: A reformulation of the +spectral element dynamical core in dry-mass vertical coordinates with comprehensive treatment +of condensates and energy. J. Adv. Model. Earth Syst., 10(7):1537–1570. +LeCun, Y., Bengio, Y., and Hinton, G. (2015). Deep learning. Nature, 521(7553):436–444. +Lee, S. (2014). A theory for polar amplification from a general circulation perspective. Asia-Pacific +Journal of Atmospheric Sciences, 50(1):31–43. +21 + +Leith, C. E. (1975). Climate response and fluctuation dissipation. J. Atmos. Sci., 32(10):2022–2026. +Lim, E.-P. and Simmonds, I. (2009). Effect of tropospheric temperature change on the zonal mean +circulation and SH winter extratropical cyclones. Clim. Dyn., 33(1):19–32. +Lutsko, N. J., Held, I. M., and Zurita-Gotor, P. (2015). Applying the Fluctuation–Dissipation +theorem to a Two-Layer model of quasigeostrophic turbulence. J. Atmos. Sci., 72(8):3161–3177. +Ma, Y., He, H., He, H., and Ma, Y. (2013). Imbalanced Learning : Foundations, Algorithms, and +Applications. John Wiley & Sons, Incorporated, Somerset, UNITED STATES. +MacDonald, G. (1992). Persistence in climate. The MITRE Coporation, JSR–91–340:22102–3481. +Madonna, E., Li, C., Grams, C. M., and Woollings, T. (2017). The link between eddy-driven jet +variability and weather regimes in the north Atlantic-European sector. Quart. J. Roy. Meteor. +Soc., 143(708):2960–2972. +Mahlstein, I., Martius, O., Chevalier, C., and Ginsbourger, D. (2012). Changes in the odds of +extreme events in the atlantic basin depending on the position of the extratropical jet. Geophys. +Res. Lett., 39(22). +Majda, A., Abramov, R. V., and Grote, M. J. (2005). Information Theory and Stochastics for +Multiscale Nonlinear Systems, volume 25. American Mathematical Soc. +Manabe, S., Hahn, D. G., and Leith Holloway, J. (1974). The seasonal variation of the tropical +circulation as simulated by a global model of the atmosphere. J. Atmos. Sci., 31(1):43–83. +Manabe, S. and Stouffer, R. J. (1980). Sensitivity of a global climate model to an increase of +CO2concentration in the atmosphere. J. Geophys. Res., 85(C10):5529. +Marconi, U. M. B., Puglisi, A., Rondoni, L., and Vulpiani, A. (2008). Fluctuation–dissipation: +Response theory in statistical physics. Phys. Rep., 461(4):111–195. +Mattingly, K. S., McLeod, J. T., Knox, J. A., Shepherd, J. M., and Mote, T. L. (2015). +A +climatological assessment of greenland blocking conditions associated with the track of hurricane +sandy and historical north atlantic hurricanes. Int. J. Climatol., 35(5):746–760. +Mbengue, C. and Schneider, T. (2013). Storm track shifts under climate change: What can be +learned from Large-Scale dry dynamics. J. Clim., 26(24):9923–9930. +McGraw, M. C. and Barnes, E. A. (2016). Seasonal sensitivity of the Eddy-Driven jet to tropo- +spheric heating in an idealized AGCM. J. Clim., 29(14):5223–5240. +Meehl, G. A., Covey, C., Delworth, T., Latif, M., McAvaney, B., Mitchell, J. F. B., Stouffer, R. J., +and Taylor, K. E. (2007). THE WCRP CMIP3 multimodel dataset: A new era in climate change +research. Bull. Am. Meteorol. Soc., 88(9):1383–1394. +Nakamura, H., Sampe, T., Tanimoto, Y., and Shimpo, A. (2004). Observed associations among +storm tracks, jet streams and midlatitude oceanic fronts. +Earth’s Climate: +The Ocean– +Atmosphere Interaction, Geophys. Monogr, 147:329–345. +Nipen, T. and Stull, R. (2011). Calibrating probabilistic forecasts from an NWP ensemble. Tellus +Ser. A Dyn. Meteorol. Oceanogr., 63(5):858–875. +22 + +Nix, D. A. and Weigend, A. S. (1994). Estimating the mean and variance of the target proba- +bility distribution. In Proceedings of 1994 IEEE International Conference on Neural Networks +(ICNN’94), volume 1, pages 55–60 vol.1. +Nix, D. A. and Weigend, A. S. (1995). Learning local error bars for nonlinear regression. Advances +in Neural Information Processing Systems, 7((NIPS’94)):489–496. +Phipps, S. J. (2010). The CSIRO Mk3L climate system model v1.2. 4 121 pp. CRC Tech. rep. +Pithan, F. and Mauritsen, T. (2014). Arctic amplification dominated by temperature feedbacks in +contemporary climate models. Nat. Geosci., 7(3):181–184. +Polvani, L. M. (2002). Tropospheric response to stratospheric perturbations in a relatively simple +general circulation model. Geophys. Res. Lett., 29(7). +Prechelt, L. (2012). Early stopping — but when? In Montavon, G., Orr, G. B., and M¨uller, K.-R., +editors, Neural Networks: Tricks of the Trade: Second Edition, pages 53–67. Springer Berlin +Heidelberg, Berlin, Heidelberg. +Ringler, T. D., Heikes, R. P., and Randall, D. A. (2000). +Modeling the atmospheric general +circulation using a spherical geodesic grid: A new class of dynamical cores. Mon. Weather Rev., +128(7):2471–2490. +R¨othlisberger, M., Pfahl, S., and Martius, O. (2016). Regional-scale jet waviness modulates the +occurrence of midlatitude weather extremes. Geophys. Res. Lett., 43(20):10,989–10,997. +Rousi, E., Kornhuber, K., Beobide-Arsuaga, G., Luo, F., and Coumou, D. (2022). Accelerated west- +ern european heatwave trends linked to more-persistent double jets over eurasia. Nat. Commun., +13(1):3851. +Rousi, E., Selten, F., Rahmstorf, S., and Coumou, D. (2021). Changes in north atlantic atmospheric +circulation in a warmer climate favor winter flooding and summer drought over europe. J. Clim., +34(6):2277–2295. +Schubert, S., Wang, H., and Suarez, M. (2011). Warm season subseasonal variability and climate +extremes in the northern hemisphere: The role of stationary rossby waves. J. Clim., 24(18):4773– +4792. +Screen, J. A., Simmonds, I., Deser, C., and Tomas, R. (2013). The atmospheric response to three +decades of observed arctic sea ice loss. J. Clim., 26(4):1230–1248. +Shaw, T. A., Baldwin, M., Barnes, E. A., Caballero, R., Garfinkel, C. I., Hwang, Y.-T., Li, C., +O’Gorman, P. A., Rivi`ere, G., Simpson, I. R., and Voigt, A. (2016). Storm track processes and +the opposing influences of climate change. Nat. Geosci., 9:656–664. +Sherwood and Nidhi Nishant, S. (2015). Atmospheric changes through 2012 as shown by iteratively +homogenized radiosonde temperature and wind data (IUKv2). Environ. Res. Lett., 10(5):054007. +Stendel, M., Francis, J., White, R., Williams, P. D., and Woollings, T. (2021). Chapter 15 - the jet +stream and climate change. In Letcher, T. M., editor, Climate Change (Third Edition), pages +327–357. Elsevier. +Swart, N. C. and Fyfe, J. C. (2012). Observed and simulated changes in the southern hemisphere +surface westerly wind-stress. Geophys. Res. Lett., 39(16). +23 + +Tjernstr¨om, M., Sedlar, J., and Shupe, M. D. (2008). How well do regional climate models reproduce +radiation and clouds in the arctic? an evaluation of ARCMIP simulations. J. Appl. Meteorol. +Climatol., 47(9):2405–2422. +Vihma, T. (2014). Effects of arctic sea ice decline on weather and climate: A review. Surv. Geophys., +35(5):1175–1214. +Virtanen, P., Gommers, R., Oliphant, T. E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, +E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S. J., Brett, M., Wilson, J., Millman, +K. J., Mayorov, N., Nelson, A. R. J., Jones, E., Kern, R., Larson, E., Carey, C. J., Polat, ˙I., +Feng, Y., Moore, E. W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., +Quintero, E. A., Harris, C. R., Archibald, A. M., Ribeiro, A. H., Pedregosa, F., van Mulbregt, P., +and SciPy 1.0 Contributors (2020). SciPy 1.0: Fundamental Algorithms for Scientific Computing +in Python. Nature Methods, 17:261–272. +Woollings, T., Hannachi, A., and Hoskins, B. (2010). Variability of the north atlantic eddy-driven +jet stream. Quart. J. Roy. Meteor. Soc., 136(649):856–868. +Yann, L., Leon, B., Yoshia, B., and Haffner, P. (1998). Gradient-Based learning applied to document +recognition. Proceedings of the IEEE. +Yin, J. H. (2005). A consistent poleward shift of the storm tracks in simulations of 21st century +climate. Geophys. Res. Lett., 32(18). +Zeiler, M. D. and Fergus, R. (2014). Visualizing and understanding convolutional networks. In +European conference on computer vision, pages 818–833. Springer. +24 + diff --git a/ydAyT4oBgHgl3EQfnvjm/content/tmp_files/load_file.txt b/ydAyT4oBgHgl3EQfnvjm/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..5a1412d61467fb94a0cf217792adc4d8b10e245e --- /dev/null +++ b/ydAyT4oBgHgl3EQfnvjm/content/tmp_files/load_file.txt @@ -0,0 +1,1621 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf,len=1620 +page_content='Using Neural Networks to Learn the Jet Stream Forced Response from Natural Variability Charlotte Connolly1, Elizabeth A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Barnes1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Pedram Hassanzadeh2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='3 and Mike Pritchard4 1Department of Atmospheric Science,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Colorado State University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Fort Collins,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' CO 2Department of Mechanical Engineering,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Rice University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Houston 77005 TX 3Department of Earth,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Environmental and Planetary Sciences,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Rice University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Houston 77005 TX 4Department of Earth System Science,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' University of California,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Irvine,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' CA 92697,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' USA January 3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' 2023 This manuscript has been submitted for consideration for publication in Artificial Intelligence for the Earth Systems 1 arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='00496v1 [physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='ao-ph] 2 Jan 2023 Abstract Two distinct features of anthropogenic climate change, warming in the tropical upper tro- posphere and warming at the Arctic surface, have competing effects on the mid-latitude jet stream’s latitudinal position, often referred to as a “tug-of-war”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Studies that investigate the jet’s response to these thermal forcings show that it is sensitive to model type, season, initial atmospheric conditions, and the shape and magnitude of the forcing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Much of this past work focuses on studying a simulation’s response to external manipulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' In contrast, we explore the potential to train a convolutional neural network (CNN) on internal variability alone and then use it to examine possible nonlinear responses of the jet to tropospheric thermal forcing that more closely resemble anthropogenic climate change.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Our approach leverages the idea be- hind the fluctuation-dissipation theorem, which relates the internal variability of a system to its forced response but so far has been only used to quantify linear responses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' We train a CNN on data from a long control run of the CESM dry dynamical core and show that it is able to skill- fully predict the nonlinear response of the jet to sustained external forcing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The trained CNN provides a quick method for exploring the jet stream sensitivity to a wide range of tropospheric temperature tendencies and, considering that this method can likely be applied to any model with a long control run, could lend itself useful for early stage experiment design.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' 1 Introduction The eddy-driven jet stream drives much of the northern hemisphere mid-latitude weather (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Nakamura et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2004;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Athanasiadis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Shaw et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Madonna et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Conse- quently, changes in the jet stream position and strength can result in enormous societal impact by impacting heat waves, droughts, and flooding events (Schubert et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Coumou and Rahm- storf, 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Bibi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Rousi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2021, 2022), extreme weather across the mid-latitudes (Mahlstein et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' R¨othlisberger et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2016), hurricane tracks (Mattingly et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2015), and crop production (Kornhuber et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Two robust features of anthropogenic climate change, warming in the upper troposphere of the tropics and warming at the surface of the Arctic, have been shown to independently force opposite responses in the mean jet location (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Held, 1993;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Harvey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Stendel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2021) These competing responses are driven by changes in the pole to equator temperature gradient (Blackport and Screen, 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Stendel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Warming in the tropical upper troposphere drives a poleward shift in the mean jet location by increasing the upper tropospheric temperature gradient, while simultaneously, warming at the Arctic surface drives an equatorward shift in the mean jet location by decreasing the surface temperature gradient (Butler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Screen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Stendel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2021), The competing jet response stemming from these two thermal forcings is commonly referred to as the “tug-of-war” on the jet stream.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Current consensus across climate models is that the upper tropospheric warming wins-out over the Arctic surface warming, causing a net poleward shift of the jet (Yin, 2005;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Swart and Fyfe, 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Barnes and Polvani, 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Harvey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' However, there is still substantial disagreement over the magnitude of the jet response due to uncertainty in the strength and spatial extent of the regional heating anomalies (Grise and Polvani, 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Warming in both the tropical upper troposphere and Arctic surface are caused by distinctly dif- ferent dynamical processes that determine the characteristics of the thermal anomalies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The tropical upper atmosphere warms more as a result of additional water vapor stored in the warmer tropical tropospheric air (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' a reduction in the moist adiabatic lapse rate;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (Sherwood and Nidhi Nishant, 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The enhanced Arctic warming, commonly referred to as Arctic Amplification, is occur- ring three times faster than elsewhere on the planet (Blunden and Arndt, 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Druckenmiller et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2021) and is driven by multiple processes that include changes in poleward energy transport (Hwang and Frierson, 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Graversen and Langen, 2019), surface ice-albedo feedbacks (Manabe 2 and Stouffer, 1980;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Dai et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2019), cloud feedbacks (Abbot and Tziperman, 2008) and lapse- rate feedbacks (Pithan and Mauritsen, 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' To further increase the complexity of the processes driving the regional warming, the two thermal forcings likely do not act entirely independently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Research has shown that increased transient Rossby waves initiated in the tropics may drive in- creased heat transport into the high latitudes and as a result drive further warming in the mid- and upper-troposphere of the Arctic (Lee, 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Dunn-Sigouin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Uncertainties in the processes that contribute to the magnitude and shape of warming in the tropical upper troposphere and Arctic surface (Blackport and Screen, 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Stendel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2021), in turn, make it even more challenging to predict the magnitude of the jet response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Despite the large body of work that investigates the response of the mid-latitude jet under climate change, multiple challenges, such as the short observational record, isolating the jet’s forced response from internal variability, and modeling ice and cloud feedbacks continue to make the question difficult to answer (Tjernstr¨om et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2008;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Kattsov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Cohen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Pithan and Mauritsen, 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Vihma, 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The studies that have investigated the response of the jet to a thermal forcing have shown that the jet is sensitive to the shape, location, and magnitude of the thermal forcing (Butler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2010), the season in which the forcing is imposed (McGraw and Barnes, 2016), the current state of the atmosphere (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' position of the jet stream;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (Gerber et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2008;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Barnes et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Kidston and Gerber, 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Garfinkel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2013), and the climate models used for the study (Meehl et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2007;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Barnes and Polvani, 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' In an attempt to explore circulation sensitivities to a wide range of possible thermal forcings, Hassanzadeh and Kuang (2016b) used a control run from the GFDL dry dynamical core (Manabe et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 1974) and employed the fluctuation-dissipation theorem (FDT) to compute the linear response function of the circulation to a number of external thermal and mechanical forcing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' FDT relates the mean linear response of a nonlinear system to a forcing through a linear operator created from the internal variability of the system (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Kraichnan, 1959;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Leith, 1975;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Marconi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' With the ability to explore a forced response from internal variability, FDT has been proposed as a method to quickly estimate circulation sensitivities in climate models (Fuchs et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2015) and serve as a useful tool for planning expensive climate model experiments (Leith, 1975).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' There have been encouraging results using FDT to explore the circulation response to thermal forcings in general circulation models (Gritsun and Branstator, 2007) as well as more complex coupled climate models (Phipps, 2010) to estimate the response to realistic sea surface thermal forcings (Fuchs et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' In order for the linear operator of FDT to accurately predict the mean response to a forcing, the system must satisfy a number of conditions (Marconi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The first condition is that the system must be in equilibrium, because FDT assumes that small changes in the system’s state (internal variability) has a recovery back to equilibrium that is similar to the system’s response to a small perturbation (Kraichnan, 1959;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Leith, 1975).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The second is that the perturbation must be small enough so that the response is linear even though the system that the operator is created from is not necessarily linear (Leith 1975).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Lastly, the probability density function of the system must be differentiable, and many applications of the FDT assume the system probability density function is Gaussian (Majda et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2005), though work has been done to make versions of FDT where the system can be quasi-Gaussian (Cooper and Haynes, 2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' In theory, a system that satisfies these conditions can use FDT to compute the systems’ linear response to a forcing, though there are practical challenges in applying FDT to high-dimensional systems, such as GCMs (Lutsko et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Hassanzadeh and Kuang, 2016b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Khodkar and Hassanzadeh, 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Instead of using FDT to relate a forcing to a response, this study uses a convolutional neural network (CNN) to learn the nonlinear relationship between a forcing and a response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Moreover, using a CNN in place of the linear operator removes the need to make some of the FDT assumptions (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' small forcing for a linear response, Gaussianity assumption).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Training is performed on data 3 from a long control run with the CESM dry dynamical core.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Once trained, the CNN is used to explore the jet sensitivity to a variety of thermal forcings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Throughout this study, we evaluate the CNN’s ability to quantify the CESM dry dynamical core’s jet sensitivity, placing particular emphasis on the tug-of-war between the warming in the tropical upper troposphere and the Arctic surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Training a neural network on internal variability alone and then using it to predict a forced response is, to our knowledge, a novel application of deep learning to climate analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Therefore, we assess the strengths and weaknesses of this approach in multiple ways (see Section 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' 2 Methods We train a CNN to predict the jet stream response to zonally averaged regional temperature perturbations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The goal is to investigate jet sensitivity to thermal features associated with anthro- pogenic climate change.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The CNN, detailed in Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='2, is trained on a long control run from a dry dynamical core, which is documented to reproduce the majority of the northern hemisphere’s jet response to heating perturbations along with simulating the correct sign of the jet shift (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Mbengue and Schneider, 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Hassanzadeh et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' McGraw and Barnes, 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Baker et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Once trained, the CNN’s skill is examined by comparing to additional baseline prediction methods and dry core experiments that include an imposed thermal forcing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Details on the dry dynamical core setup, the CNN architecture and training, additional baseline prediction methods, and additional dry core heating experiments are discussed in more detail in the following Sections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='1 Training Data We use output from the Community Earth System Model (CESM) Eulerian spectral-transform dry dynamical core (Lauritzen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The model runs are completed with the Held-Suarez configuration (Held and Suarez, 1994), such that friction exists at the surface and the temperature is relaxed to a prescribed hemispherically symmetric temperature field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The relaxation temperature field is set to equinoctial conditions and there is no absorption of solar energy by the atmosphere (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' there are no seasons or diurnal cycles).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' All runs are performed at T42 resolution with 30 vertical levels, 64 latitude bands, and 128 longitude bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The simulation is run in the above configuration for one million six hour time steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The first 20,000 time steps (13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='7 years) are thrown out to account for model spin up.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' All data processing is performed to create efficient training data for a CNN (Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='2) to predict the zonally-averaged jet response to a range of tropospheric temperature perturbations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Two variables are used in this study, zonally averaged temperature and zonally averaged zonal wind speed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The zonally-averaged temperature data is used to calculate the temperature tendency field used as input to the CNN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The zonally-averaged zonal wind speed is used to calculate the initial location of the jet and the subsequent shift of the jet, which are used as a CNN input and the CNN prediction respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' We exclude data from 200 hPa and above, effectively removing the stratosphere which is not well resolved in this model without modification (Polvani, 2002) and so focus can remain solely on the troposphere for both the forcing and the jet response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Given that this study focuses on hemispheric jets, we take advantage of the hemispheric symmetry in the dry core and use each hemisphere as a separate independent sample, doubling the amount of available training data to two million.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' After zonally averaging, removing the stratosphere, and considering each hemisphere as a separate sample, the resulting size of the temperature field is 25 vertical levels by 32 latitude bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Backward differencing is used to calculate the temperature tendency which is then smoothed using a backward running mean of 240 time steps (60 days) to remove higher frequency variability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' 4 Removing the high frequency variability allows the network to focus on learning the response to a forcing that more closely mimics continuous climate change forcing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' This smoothing is also aligned with FDT calculations, in which an integration over long time lags (often up to the decorrelation timescale) is done;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (3) in Hassanzadeh and Kuang (2016b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Smoothing the data before calculating the temperature tendency did not result in any changes in the CNN skill (not shown).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Following established methods (Woollings et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' McGraw and Barnes, 2016), the jet location is defined as the latitude of the maximum wind speed at a pressure level near the surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Zonal wind speeds from the 850 hPa level are used here and are first smoothed with a 240 time step (60 days) backward running mean.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Then, a second order polynomial is fit to the peak of the smoothed 850 hPa zonal wind profile and the jet location is defined as the latitude of the maximum wind speeds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Now that a smoothed zonal temperature tendency and a jet location are calculated, the data are split into training, validation, and testing data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Splitting is completed by chunking the data into three groups where training data is the first chunk, validation the second, and testing the last.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Lastly, the jet response to a given temperature tendency is defined by the change in jet latitude from the time of input to 120 time steps later (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' the jet shift).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' A positive jet shift indicates a poleward shift in jet location and a negative jet shift indicates an equatorward shift in jet location relative to the jet’s latitude at the time of prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The jet shift is calculated within each dataset (training, validation, and testing) by subtracting a 240 time step backward running mean of jet stream locations from a 240 time step forward running mean of jet stream locations 120 time steps into the future.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' This processing results in 359,280 training samples, 199,280 validation samples, and 1,399,558 testing samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Training the CNN required fewer samples than expected as adding more samples to the training dataset did not improve the CNN skill, explaining why the testing dataset is much larger than the training and validation datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='2 Convolutional Neural Network Figure 1: Schematic of the convolutional neural network with an example of an input and output.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' CNNs are commonly used for image recognition and classification tasks as the convolutional 5 Standardized Scaled Jet Shift Temperature Tendency 25x32x32 12x16x64 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='44 200 00m 500 00 Uncertainty 6x8x64 12x16x32 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='86 25x32 500 500 500 500 500 500 Convolutional Layer (same padding, (3x3) kernel) Standardized Jet Location Average Pooling (2x2) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='66 3073 Fully Connected Layer Dropout Layer (rate = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='3)layers can extract spatial features in the input image that help the network learn the correlations between the inputs and output (Fukushima, 1980;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Yann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 1998;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Zeiler and Fergus, 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' While a fully connected feedforward network (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' LeCun et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2015) has the ability to learn the same features extracted by the convolutional layers within a CNN, it may require a larger network and more training data to do so (Yann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 1998;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Ingrosso and Goldt, 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' In this study, we utilize a CNN so that the network can efficiently learn the correlation between temperature tendencies and the jet response while also trying to minimize the amount of training data required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The CNN has two inputs: a smoothed temperature tendency field (K day−1) and an initial jet location (degrees latitude).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Including the temperature tendency as an input allows us to in- vestigate the jet response to regional temperature tendencies and including the initial jet location supplies the CNN with essential information about the current state of the jet at the prediction time, an important factor for the jet response to forcing (Gerber et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2008;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Barnes et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Kidston and Gerber, 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Garfinkel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Before the data is input into the CNN, the smoothed temperature tendency field is multiplied by a factor of 10 and the initial jet location is standardized using the standard deviation and mean jet location from the training data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Scaling and standardizing are done so that both inputs have similar magnitudes (order of 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The network consists of four convolutional layers: two average pooling layers, three dense layers, and three dropout layers (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Convolutional and dense layers use the hyperbolic tangent activation function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Data are passed through the network as follows: the scaled temperature tendency goes directly into the first convolutional layer with 32 filters of size 3 x 3 and a stride of 1 followed by a second convolutional layer with the same attributes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The second convolutional layer is then connected to an average pooling layer with a kernel size of 2 x 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' These three layers, two convolutional and a single average pooling, are repeated with the same attributes with the exception of containing 64 filters rather than 32 in the convolutional layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The output from the second average pooling layer is flattened and the standardized initial jet location is concatenated to the end.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' This layer is then fed into the first dense layer with 500 nodes and then goes through a dropout layer with a dropout rate of 30%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The data passes through a combination of dense layers with 500 nodes followed by dropout layers with a dropout rate of 30% two more times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The data from the final dropout layer then passes into the output layer consisting of two nodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The CNN outputs two values denoted as µ and σ, which represent a mean and standard deviation of a Gaussian distribution where µ denotes the predicted jet shift and σ represents its uncertainty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Predicting the parameters of a Gaussian distribution is commonly used to quantify uncertainty for neural networks (Nix and Weigend, 1994, 1995), and Gordon and Barnes (2022) recently showed the utility of incorporating uncertainty into a regression neural network for climate science applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The network learns to predict µ and σ through the implementation of the negative log-likelihood loss function: Li = −log(pi) (1) where p is a value of the predicted Gaussian distribution evaluated at the true jet shift for the ith input sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' To ensure the network is calibrated we employ the probability integral transform (PIT) probability calibration scheme (Gneiting et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2007;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Nipen and Stull, 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Barnes et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The PIT histogram for this CNN can be found in Supplementary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' To train the CNN, we use the Adam stochastic gradient descent optimization algorithm (Kingma and Ba, 2014) with a learning rate of 10−7, a batch size of 256, and a random seed of 300.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' We apply early stopping to halt the training process once the validation loss fails to decrease for 10 consecutive epochs and restore the model weights to the version with the lowest validation loss (Prechelt, 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' 6 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='3 Baselines We establish two baselines in this study to assess the performance of the CNN and demonstrate that the CNN has learned relationships between the jet response and the regional temperature tendencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The first baseline is called persistence, similar to “persistence forecasting” (MacDonald, 1992), where future conditions are predicted to be identical to the current conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' In our case, this translates to the jet’s future location being the same as its location at the time of prediction (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' jet shift equal to zero).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Comparing this baseline to the CNN ensures that the CNN is predicting jet shifts that are more accurate than predicting a jet shift of zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The second baseline is called average evolution and describes the average movement of the jet based on its position at the time of prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' For this baseline calculation, the training data is separated into 100 different bins according to the initial jet location, essentially grouping samples with similar initial jet locations together.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The average jet shift for each bin is calculated, resulting in an average jet response that is solely dependent on the jet stream’s starting position.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The average evolution baseline is not sensitive to the number of bins or their exact spacing (not shown).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' This baseline ensures that the CNN is not just predicting the average evolution of the jet based solely on the initial jet location but is also using the temperature tendency input to make its prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Every test sample is thus associated with three jet shift predictions, one from the CNN and two from the additional persistence and average evolution baselines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Although comparing results between the CNN and the two baselines is useful for placing the CNN’s predictions into context, we highlight that the baselines make predictions based solely on information about the initial location of the jet while the CNN is provided additional information in the form of the temperature tendency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Thus, the CNN is able to explore the correlations between a temperature tendency and a jet response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='4 Heating Experiments The main goal of this study is to investigate the jet stream sensitivity to thermal forcing driven by anthropogenic climate warming.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' However, as we have designed it, the CNN only trains on data from a long control run (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' internal variability), and thus, only provides insights into the forced response if the idea of the FDT holds (Kraichnan, 1959;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Leith, 1975;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Marconi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' To investigate whether this assumption is valid, we run additional dry core simulations (referred to as heating experiments) with zonally symmetric imposed thermal forcing (F) that take the form of a two-dimensional Gaussian in the latitude/pressure plane (Equation 2): F(Θ, p) = qoexp � (| Θ | −Θo)2 Θ2w − (| p | −po)2 p2w � (2) where Θo and po are the horizontal and vertical centers respectively, Θw and pw define the width and height, and the magnitude of the forcing is given by qo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Gaussians that fall near the edge are cut off and therefore not complete two-dimensional Gaussians.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' For all Gaussians created in this study, Θ, Θw, p, pw, qo are reported in Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Eighteen heating experiments with either one or two Gaussian thermal forcings imposed are run out to equilibrium to quantify the true jet shift (see experiments #1-18 in Table A1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' To perform a direct comparison between the CNN-predicted jet responses and the dry core jet responses, the CNN is given the same temperature tendency that is imposed in each of the dry core heating experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' For the CNN’s initial jet location input, the average jet location from the long control run is used (42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='4°).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' By comparing the true forced response from the dry core to the predicted forced response 7 by the CNN we are able to investigate the CNN’s ability to predict the jet response to thermal forcing from training on internal variability alone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Each heating experiment is initiated at the end of the long control run (time step one million;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' 684.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='9 years), and therefore, have the same initial conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The heating experiments are run for an additional 20,000 time steps with the first 4,000 removed to ensure that the model has reached its new equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The 850 hPa zonal winds are then used to compute the location of the jet (see Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Finally, the true response of the jet to an imposed thermal forcing is defined as the average jet location during the long control run subtracted from the jet location in the corresponding heating experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' 3 Results 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='1 Evaluation of CNN skill Figure 2: Predicted jet response (y-axis) versus the true jet response (x-axis) for the (a) CNN, (b) average evolution baseline, and (c) persistence baseline using the testing data from the control simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Panel (a) is a contoured by density and panels (b) and (c) are scatter plots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Mean absolute errors are shown in the bottom right corner of each panel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Gray lines represent a perfect prediction (one-to-one line).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Green line in panel (a) represents the best-fit line from the CNN predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' We begin our discussion of the results with a focus on the deterministic predictions by the CNN (µ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The deterministic skill on the testing data, which we define as the mean absolute error between the predicted jet shift and the true jet shift, reveals how well the CNN generalizes to unseen samples within the control simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The first look at the entire testing dataset will appear to show a modest difference;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' a closer look within the testing dataset will prove more interesting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Figure 2a shows the relationship between the predicted jet shift and the true jet shift where predictions with higher accuracy are closer to the gray diagonal line (one-to-one line).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Using orthogonal distance regression (Boggs and Rogers, 1990;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Virtanen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2020), which takes into account error in both the x and y variables as well as the CNN-predicted uncertainties in y, we calculate the slope from the testing data to be 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='5 deg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' poleward / (deg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' poleward).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' This positive slope demonstrates the CNN has learned relationships between the jet shift and the inputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' However, the slope of the CNN predictions is less than that of the one-to-one line implying that the CNN underestimates the magnitude of the largest jet shifts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' This is likely a result of the imbalanced training data 8 a) CNN b) Average Evolution c) Persistence 10 10+ 10 5 5 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=" 5' Best-fit Line One-to-one Line Mean Absolute Error = 2." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='220 Mean Absolute Error = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='770 Mean Absolute Error = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='860 10 101 5 5 0 10 0 10 10 10 5 0 5 10 10 5 5 True Jet Shift (deg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' poleward)as it includes more samples with smaller jet shifts than larger ones (shown in Figure 2a by the density contours).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' During training, the goal of the CNN is to minimize the negative log-likelihood loss function (see Equation 1), but with an unbalanced dataset, the CNN may never predict the most extreme cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Applying methods to make the network predict extremes, such as balancing the dataset, using samples weights, or creating custom loss functions (Ma et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Krawczyk, 2016), either caused a severe decrease in skill or did not succeed in solving the problem (not shown).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Nonetheless, as we will show next, the CNN outperforms the two benchmark baselines and is an effective tool for exploring jet sensitivity to external forcing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Comparing the CNN’s skill on the testing data to that of the two baselines: average evolution (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' 2b) and persistence (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' 2c), allows us to place the CNN’s skill into context against other basic prediction methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Persistence has the lowest performance with a mean absolute error of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='22°.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Average evolution performs only slightly worse than the CNN with mean absolute errors of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='86° and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='77° respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Unlike persistence, which can only ever predict a jet shift of zero, average evolution makes a prediction based on the average relationship between the initial jet loca- tion and the jet shift of the training data, allowing it to capture the mean jet response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Regardless, average evolution is limited to predicting one of the 100 jet shifts resulting from the methods used to calculate it (see Methods), hence the stripes in Figure 2b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Based on the mean absolute error alone, the CNN outperforms both the persistence and average evolution baselines for the testing data from dry dynamical core long control run.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Figure 3: The mean absolute error from the three prediction methods, CNN (black line), average evolution (cyan line), and persistence (orange line) grouped by initial jet locations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' gray violin plots show the density curves of the CNN’s error distribution where the width corresponds with the frequency of the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Numbers at the bottom of each bar indicate the number of samples in each group and the average initial jet location from the training data is marked on the x-axis (42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='4°).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The mean absolute errors in Figure 2 represent the error over the entire testing set, which is prone to obscuring interesting details hiding within the distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' For a more comprehensive analysis of the CNN’s skill, the testing data is thus separated into groups based on the initial 9 Error based on Initial Latitude CNN Average Evolution 6 Persistence 5 4 3 2 1 - 228 1105 4586 11110 22930 52756 122598 287502 479843 326308 85180 5412 0 25 30 35 40 Avg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' 45 50 Initial Latitudejet location.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The mean absolute error for each group is shown for the CNN and the baselines in Figure 3 and describes how the CNN’s skill and the baselines’ skill depend on the initial state of the jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The gray violin plots behind each bar indicate the CNN’s mean absolute error distribution within that bin (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' the data used to calculate the CNN mean absolute error in each group).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The violin plots are smoothed with a kernel estimator using Scott’s rule and 100 points, which are the default parameters of the Matplotlib library (Hunter, 2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The numbers at the bottom of each bar denote the number of samples in that bin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' For all bins in Figure 3, the CNN outperforms the baselines as demonstrated by the CNN’s error (black line) falling below the baseline errors (cyan and orange lines).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' When the initial jet location is equatorward of 42° (labeled as “Avg.” along the x-axis of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' 3), the CNN does considerably better than the baselines, but when the jet location is poleward of 42°, the CNN and average evolution achieve similar skill.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' That is, in the cases where the initial jet is near the pole, it appears that the CNN does not learn more than average evolution but instead learns this average behavior to make its prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' When the initial jet location is near this climatological average position (42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='4°), the errors of the CNN and baselines converge (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' About 30% of the samples in the training data have initial jet locations within 2° of the climatological average and 14% of these samples have a jet shift between -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='5° and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='5°.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Since so many samples near the climatological average have small jet shifts and because the persistence baseline can only predict a jet shift of zero, the mean absolute error for persistence is at its lowest near the jet’s climatological average position.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The average evolution baseline converges to a near zero prediction when the initial jet location is near the climatological average, resulting in persistence and average evolution exhibiting similar errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Although the persistence and average evolution baselines have an advantage near the climatological average, the CNN still outperforms both baselines, implying that the CNN is using the additional information provided by the input temperature tendencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Figure 4: The thermal forcing with a magnitude of qo = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='25 K day −1 is moved around the latitude and pressure plane where the shading in (a) and (b) represent the CNN-predicted jet shift and uncertainty respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' An example of a thermal forcing is seen in the gray contours in both panels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The “x” marks the center as well as the predicted jet shift and predicted uncertainty associated with that thermal forcing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Gaussian parameters are found in Table A1 experiment #19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' 10 b) Predicted Uncertainty a) Predicted Jet Shift 200 + 200 - 300 300 400 400 - (hPa) 500 - 500 - X 600 600 700 - 700 - 800 800 - 006 900 20 30 40 50 60 80 10 20 30 40 50 60 70 80 Latitude (deg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=') Latitude (deg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=') 10 10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='5 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='5 5 Jet Shift (deg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' poleward) Sigma (deg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' )Next, we focus on evaluating CNN’s ability to predict a jet stream forced response from an ar- tificially constructed idealized temperature tendency not encountered within its noisy training en- vironment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' These temperature tendency inputs contain a two-dimensional Gaussian (see Methods) with a prescribed magnitude, size, and location (latitude and pressure).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Outside of the Gaussian, the temperature tendency field is filled with zeros.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Although some of these thermal forcings have magnitudes larger than any temperature tendencies found in the internal variability training data, we will provide strong evidence to support the CNN’s ability to extrapolate in the coming sections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' CNN predictions made from a thermal forcing use an initial jet location defined by the average jet location of the training data (42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='4°).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Therefore, differences in predicted jet shifts between tem- perature tendency inputs are a response to the thermal forcing alone and not the presumed initial state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The shading in Figure 4 shows the CNN-learned jet sensitivity to the location of heating by holding the magnitude and the shape of a thermal forcing constant and changing only its location (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' 4;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' see experiment #19 in Table A1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' An example of a thermal forcing is shown in the gray contours where the “x” denotes its center and the color of the shading beneath represents the predicted jet shift (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' 4a) and the predicted uncertainty (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' 4b) from the temperature tendency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Figure 4a exhibits multiple known features of the jet response to tropospheric thermal forcings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' For example, thermal forcings located higher in the troposphere are known to be more effective at perturbing the jet than thermal forcings located lower in the troposphere (Hassanzadeh and Kuang, 2016a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Kim et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' This feature is learned by the CNN and is shown in Figure 4a as darker shading at higher pressure levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' In addition, warming in the tropical upper troposphere has been previously shown to cause the jet to shift poleward (Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2008;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Lim and Simmonds, 2009;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Butler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' This poleward jet shift is seen in Figure 4a as denoted by the red shading in the tropical upper troposphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Finally, heating at the polar surface has been shown to cause the jet to shift equatorward (Butler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Deser et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Screen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2013) and this is seen in Figure 4a by the blue shading, albeit weak, near the polar surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' These features indicate that the CNN has learned the correct sign of the jet shift as supported by prior research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Figure 4a also highlights how moving the center of the heating by a few degrees or pressure levels can change the direction of the jet shift.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Take for instance heating at the polar surface, where moving the heating from 80° latitude to 75° latitude changes the jet response from an equatorward shift to a poleward shift.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Baker et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2017) investigates the jet sensitivity to the location of heating by running 306 dry core experiments with an imposed Gaussian shaped temperature tendency that is moved around the latitude-pressure plane, just as we have done here with a trained CNN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' In Baker et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2017), they show that changes in the latitude of the heating most strongly impact the sign of the jet shift while changing the pressure level has very little impact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Similar behavior is found here with the CNN, although with a few exceptions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' A more in-depth discussion about the failure of the CNN to capture the correct direction of the jet shift at the surface of the mid-latitudes is found in Supplementary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Recall that the CNN predicts both the jet shift (µ) as well as its uncertainty (σ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Figure 4b displays the predicted uncertainty values and highlights three regions where the CNN is less certain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The CNN is less certain when heating occurs around 10° latitude and 600 hPa (σ ≈ 4°) and additionally has large uncertainty when the heating is centered near 85° latitude and 900 hPa and the 60° latitude and 550 hPa (σ ≈ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='5°).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The reasons behind the greater uncertainty in these regions require further investigation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' 11 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='2 Nonlinearities learned by the CNN Ideally, a benefit of using a CNN is that it learns a nonlinear relationship between the temperature tendency input and the jet shift output.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The hyperbolic tangent activation functions in the convo- lutional and dense layers of the CNN allow it to learn nonlinear relationships between the inputs and outputs if nonlinearity is present in the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' However, this does not necessarily mean the CNN has learned nonlinear relationships.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' To evaluate the nonlinearity learned by the CNN we complete two analyses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The first analysis examines how the CNN-predicted jet shift varies as a function of the thermal forcing magnitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The second analysis looks at scenarios where two thermal forcings are simultaneously present in the temperature tendency input and explores whether the CNN has learned a nonlinear interaction between the two.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Keep in mind that neither of these analyses has a ground truth, and so we are exclusively exploring what the CNN has learned.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' In the next section, we will then further test the accuracy of the CNN with additional dry core simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Figure 5: The CNN learned nonlinear responses where panel (a) shows example thermal forcing with magnitudes of 1 K day−1 at the five locations and panels (b) and (c) show the linear response (dashed line) and the predicted response from the CNN (solid lines).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Note the different y-axes in panels (b) and (c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Gaussian parameters are found in Table A1 #20-24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The first nonlinear analysis explores how the jet shift varies as a function of the thermal forcing magnitude by separately inputting thermal forcings of different magnitudes in five different locations (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' 5a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' see experiments #20-24 in Table A1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' We use ten different magnitudes that vary from 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='0 K day−1 to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='0 K day−1 in increments of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='2 K day−1 for each location.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' For all cases, the initial jet location input is fixed at the average jet location of the training data (42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='4°).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Figure 5b and 5c compare a linear relationship (dashed lines) and the CNN’s learned relationship (solid lines) between the thermal forcing magnitude and the jet shift.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The jet response to temperature tendencies near the polar surface and the mid-tropospheric mid-latitudes are the most linear as shown by the green line in Figure 5b and the blue line in Figure 5c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' In both of these cases, the CNN-predicted jet shift is most similar to the linear dashed line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' In contrast, temperature tendencies in the tropics and the upper troposphere of the polar region have the largest nonlinear response (yellow line in Figure 5b, pink, and red lines in Figure 5c) as these cases vary greatly from the dashed linear line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' We next explore the nonlinearities learned by the CNN when two thermal forcings are present.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' 12 Nonlinear Response b) 0 400 - Jet Shift (deg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' poleward) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='8 600 - 700 0 800 - F 006 2 c) 10 30 40 20 50 60 70 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='6 80 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='8 Latitude (deg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=') Temperature Tendency Magnitude (K/day)Figure 6: Panel (a) shows the CNN-predicted jet shift from when two thermal forcings vary with magnitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' One at the surface of the pole (x-axis) and the other in the upper troposphere of the tropics (y-axis).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Panel (b) shows the predicted uncertainty for the predictions of panel (a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Panel (c) is similar to panel (a) but the CNN predicts the jet shift from the two thermal forcings independently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Panel (d) is the difference between panel (a) minus panel (c) representing the CNN learned nonlinearity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The thermal forcings are centered on two key regions, the tropical upper troposphere and the polar surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' As discussed previously, warming in the tropical upper troposphere forces the jet to shift poleward (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2008;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Lim and Simmonds, 2009;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Butler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2010) and warming at the polar surface forces the jet to shift equatorward (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Butler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Deser et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Screen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' When they occur simultaneously, they force competing effects that can result in a tug-of-war scenario on the jet stream (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Harvey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' To explore the jet sensitivities to this climate change induced tug-of-war, the temperature tendency inputs are composed of a Gaussian thermal forcing at the polar surface and another in the upper troposphere of the tropics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Both vary independently in magnitude during the analyses (see experiment #25 in Table A1) and Figure 6a shows the predicted jet shift (µ) and 6b shows the predicted uncertainty (σ) for each forcing pattern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' With regards to the tug-of-war, studies use a variety of atmospheric models to show that despite opposite forced jet responses, the jet will likely shift poleward (Yin, 2005;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Harvey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The upper right quadrant of Figure 6a depicts the situation where both thermal forcings are positive (warming).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' In this scenario, the CNN predicts a poleward shift of the jet in agreement with past work, however, the CNN is not equally certain for all predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' As shown in Figure 6b, the CNN is more confident with cooling at the pole and warming in the tropics and less confident with warming in the pole combined with cooling in the tropics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Understanding why these scenarios are more uncertain requires further investigation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Figure 6a shows the CNN-predicted jet response when two thermal forcings are present in the temperature tendency input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' To test whether the CNN has learned a nonlinear impact on the jet from two simultaneous forcings, we task the CNN to predict the jet shift from the two thermal forcings independently (upper tropical troposphere and polar surface) and add the two predicted jet shifts together subsequently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' If the CNN exclusively learned a linear response between two forcings, Figure 6a and Figure 6c would be identical, as predicting a jet shift from combined forcings would be equal to predicting the jet shifts from individual forcing and adding the predictions together.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Instead, Figure 6d shows the difference in predicted jet shifts from these methods and provides evidence of the nonlinearity learned by the CNN where inputs that contain stronger thermal forcings (scenarios in the corners of 6d) have greater learned nonlinearity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' 13 a) Predicted Jet Shift from Combined Forcing b) Uncertainty from Combined Forcing 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='2 0.' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='0 Deg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='0 Deg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Poleward Poleward d) Difference between a) and c) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='2 - 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='5 2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content="1 Fo'0 0 0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='1 2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='5 Deg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='5 Deg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='0 Poleward Poleward Polar Forcing Magnitude (K/day) Polar Forcing Magnitude (K/day)3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='3 Out-of-sample tests Thus far we have compared the CNN-predicted jet shifts to our established baselines, true jet shifts harvested from the internal variability of the control run, and past work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' We next evaluate the ability of the CNN to predict the explicit simulated jet response to an imposed idealized steady thermal forcing outside the training set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The FDT states that the linear response of a nonlinear system to external forcing can be related to the internal variability of the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Under the assumption that FDT holds, our CNN trained on internal variability may also be able to predict a forced response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' We next explore this by comparing the true forced jet shift calculated from additional dry core experiments to the predicted jet shift by the CNN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' We perform 14 additional forced heating experiments with the dry dynamical core (see Methods and Table A1 experiments #1-14).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' These 14 heating experiments are motivated by the tug-of-war on the jet resulting from anthropogenic climate change (Harvey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Stendel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' To mimic the tug-of-war, each experiment contains a thermal forcing in the tropical upper troposphere and at the polar surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The left side of Figure 7 includes the magnitude of each Gaussian shaped thermal forcing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The forced jet response from the dry dynamical core experiments and the CNN-predicted jet response from 14 heating experiments are shown on the right side of Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Comparing the true forced jet shift simulated by the dry core (green dots) and the predicted jet shift by the CNN trained on internal variability (black lines), we see that across all experiments, the CNN accurately captures the sign of the jet shift.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Experiments #1 through #7 exhibit a negative jet shift and #8 through #14 exhibit a positive jet shift.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Furthermore, nearly all of the experiments (excluding #3, #4, and #14) have forced jet shifts that fall well within the uncertainty bounds predicted by the CNN (±2σ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' gray boxes).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Additional discussion of other heating experiments that do not focus on the tug-of-war on the jet can be found in Appendix C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Heating experiments #6, #7, #8, and #9 contain only a thermal forcing at the polar surface (no thermal forcing in the tropical upper troposphere) and are therefore useful for investigating the difference in CNN-predicted uncertainty between polar warming and polar cooling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' In heating experiments #6 and #7, which contain polar warming, the CNN is less certain (larger σ), in contrast to heating experiments #8 and #9, which contains polar cooling, where the CNN is more certain (smaller σ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The CNN’s uncertainty when there is a thermal forcing in the upper troposphere of the tropics is more difficult to discern from Figure 7 because the CNN’s uncertainty is impacted considerably by the thermal forcing at the polar surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' However, heating experiments #3 and #12 include only a thermal forcing in the tropical upper troposphere, one cooling and one warming respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' These heating experiments suggest that the CNN is more certain when the upper tropical troposphere is cooling rather than warming.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' 4 Implications for Sensitivity Analysis Given the CNN’s ability to replicate the sign of the jet stream’s forced response as validated with the additional forced dry dynamical core experiments, we propose that our approach can be deployed as a computationally efficient tool to aid in the design of forced model experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' To demonstrate this, we next revisit a historical study (Butler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' afterward B10) and show how the pre-trained CNN can be used to replicate the study’s results as well as document possible sensitivities not included in the initial work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' In B10, differences in dry core atmospheric circulations due to variations in the location and shape of thermal forcings were identified and documented.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' To test the atmospheric sensitivity, B10 ran multiple experiments with different imposed thermal forcing patterns in the Colorado State University general circulation model (Ringler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' 14 Figure 7: The 14 heating experiments, their resulting jet shift in the dry core, and the jet shift as predicted by the CNN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The left side includes the magnitude of each Gaussian shaped thermal forcing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The right side shows the true forced dry core jet shift (green dots), the predicted CNN jet shift (black line), and the CNN-predicted uncertainty (gray boxes;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' ±2σ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Although B10 did not quantify a shift of the jet stream the same way as we do here, the study showed the zonal-mean zonal wind response and discussed which heating experiments resulted in a stronger wind response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' From this information, we are able to infer the relative magnitude of the jet shift for each experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Here, we focus on four specific heating experiments within B10 that aim to investigate how sensitive the circulation response is to the height and shape of tropical upper tropospheric heating.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Examples of the thermal forcing patterns imposed in B10 are shown in Figure 8a-d and will be referred to as heating experiments #26, #27, #28, and #29 for this discussion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' In the original study, B10 found that the jet shifts poleward in response to all heating experiments, but that the magnitudes of the shifts varied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' B10 shows that heating experiment #26 had the strongest jet response and compressing the forcing vertically (heating experiment #27) or compressing the forcing in the meridional direction (heating experiment #28) weakened the wind response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' In the last experiment (heating experiment #29), B10 showed that when the forcing was compressed 15 Polar Tropical Jet Shift (degrees poleward) Heating Magnitude Magnitude Experiment 4 2 (K/day) (K/day) 2 4 #1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' #2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='1 #11 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='1 #12 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='1 CNN Prediction #13 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='1 CNN Uncertainty Dry Core Output #14 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='1vertically and moved lower in the troposphere, the wind response was even weaker.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Figure 8: Panels (a) - (d) shows example thermal forcings of magnitude 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='5 K day−1 representing the four heating experiments used in Butler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' 2010, Gaussian parameters are found in Table A1 #26-29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The panel outline corresponds to the predicted jet shifts (y-axis) in panel (e) which are shown as a function of the magnitude of the temperate forcing (x-axis).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The vertical gray line at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='5 K day−1 corresponds to the magnitude of the heating experiments used in Butler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Following the same four heating experiments of B10, we recreated the thermal forcing patterns (see experiments #26-29 in Table A1) and input them into the CNN with the initial jet location set to the average jet location of the training data (42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='4°).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' In addition to the magnitude of heating used in B10 (qo = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='5 K day −1), here the jet sensitivity to the magnitude of the thermal forcing is also included since it is trivial to explore once the CNN is trained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Figure 8e shows the predicted jet shift from the four heating experiments with varying magnitudes, and the vertical gray line indicates the 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='5 K day −1 magnitude used in B10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The CNN predicts the same relative relationship between the heating experiments as found in B10, where heating experiment #26 exhibits the strongest jet response and heating experiment #29 exhibits the weakest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Furthermore, by exploring the jet sensitivity to the magnitude of heating, Figure 8e shows new information about jet sensitivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' For example, as the magnitude of the thermal forcing increases, heating experiment #27 (compressed vertically) and heating experiment #28 (compressed meridionally) converge to the same jet shift.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Alternatively, when the magnitude of the thermal forcing decreases, heating experiment #28 and heating experiment #29 (compressed vertically and lower in the troposphere) converge to the same jet shift.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' These two results could be confirmed with a few targeted forced dry core simulations (not done here), though it was the ability provided by the CNN to quickly explore jet shifts in response to thermal forcings that allowed us to discover these possible jet sensitivities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' 16 Temperature Tendencies from Butler2010 300 300 00m 400 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='38 400 400 Pressure (hPa) 500 500 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='25 009 700 700 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='2 800 008 800 300 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='06 b) heating experiment B 900 00 c) heating experiment C d) heating experiment D a) heating experiment A 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='00 (K/day) Latitude (deg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=') Jet Sensitivity 8 6 4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='9 Temperature Tendency Magnitude (K/day)In this chapter, we show a successful example of using the CNN to explore the jet sensitivities inside the dry dynamical core.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The CNN is not perfect in its predictions which may be due to a lack of predictability, non-optimal training of the CNN, a breakdown of the FDT, or a combination of the three.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' However, as demonstrated throughout this paper, the comparisons in the CNN-predicted jet shifts have the same sign and similar magnitudes to the forced jet shifts from the dry core in response to a range of temperature tendencies and once trained, can make predictions quickly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' We wish to emphasize that this method should not replace the need to run designed climate model experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Rather, training CNN on an existing long control run could provide the opportunity to explore a large number of forcing experiments before any forced model runs are simulated and be especially helpful for planning forced experiments in dynamic model simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' 5 Conclusions We explore the jet stream’s response to external forcing by training a CNN on smoothed temper- ature tendencies from a dry dynamical core long control run to predict a shift in the jet stream’s location 30 days later.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The main motivation of this work is to explore the potential for training a CNN on internal variability alone and then using it to examine possible nonlinear responses of the jet to tropospheric thermal forcing that more closely resemble anthropogenic climate change.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Since the CNN is trained entirely on data from a control simulation, it exclusively learns from internal variability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Nevertheless, by comparing the CNN-predicted jet shifts to established base- lines, peer reviewed literature, and additional dry core heating experiments, we show that the CNN can predict the forced jet shift to sustained forcing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The trained CNN is then used to investi- gate jet sensitivities to scenarios that mimic the tug-of-war between the tropics and poles under anthropogenic climate change.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Given the CNN’s ability to predict the jet response to thermal forcings, we propose training a CNN on long control runs that are increasingly becoming more available to explore model sensitivities to various forcings as a tool to aid in early stage climate model experiment design.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Future work could include extending this method to evaluate whether it generalizes to different experimental frameworks, including, but not limited to, evaluating it with three-dimensional predictors, training on coupled climate model simulations, and learning complex non-linear climate responses from forced simulations where FDT does not hold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Acknowledgments CC and EAB are supported, in part, by NSF CAREER AGS-1749261 under the Climate and Large- scale Dynamics program.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The authors thank Marybeth Arcodia for providing valuable support during the writing process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Data availability The code used to prepare the data can be found on github https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='com/connollyc152/ DDC_jet_sensitivity and will be assigned a permanent doi on Zenodo upon publication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Data is available upon request and will be made available on Zenodo and given a doi upon publication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' 17 Appendix A Table of two-dimensional Gaussians parameters Table 1: Parameters for two-dimensional Gaussians for the forced dry core heating experiments and CNN thermal forcings, ”V” indicates varying parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' 18 Ow (degree O。' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (degree Experiment Po (hPa) pw (hPa) qo (K) poleward) poleward) 06 16 1000 250 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='0 #1 0 27 300 125 0.' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='25 #19 10 150 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='0 #20 12 15 850 200 #21 75 15 850 200 #22 45 15 550 200 #23 12 15 300 200 #24 75 15 300 200 90 16 1000 250 #25 0 27 300 125 v #26 27 300 125 v #27 0 27 300 75 0 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='5 125 #28 300 #29 0 27 500 125References Abbot, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' and Tziperman, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' A high-latitude convective cloud feedback and equable climates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Quart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Roy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Meteor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 134(630):165–185.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Athanasiadis, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Wallace, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', and Wettstein, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Patterns of wintertime jet stream variability and their relation to the storm tracks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Atmos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 67(5):1361–1381.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Baker, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Woollings, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', and Mbengue, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Eddy-Driven jet sensitivity to diabatic heating in an idealized GCM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Clim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 30(16):6413–6431.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Barnes, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Barnes, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', and DeMaria, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Sinh-arcsinh-normal distributions to add uncer- tainty to neural network regression tasks: applications to tropical cyclone intensity forecasts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Barnes, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Hartmann, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Frierson, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', and Kidston, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Effect of latitude on the persistence of eddy-driven jets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Geophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 37(11).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Barnes, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' and Polvani, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Response of the midlatitude jets, and of their variability, to increased greenhouse gases in the CMIP5 models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Clim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 26(18):7117–7135.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Bibi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Ullah, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Yushu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Wang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', and Gao, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Role of westerly jet in torrential rainfall during monsoon over northern pakistan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Life Support Biosph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 7(2):e2019EA001022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Blackport, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' and Screen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Insignificant effect of arctic amplification on the amplitude of midlatitude atmospheric waves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Sci Adv, 6(8):eaay2880.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Blunden, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' and Arndt, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' State of the climate in 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Bull.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Am.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Meteorol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 93(7):S1–S282.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Boggs, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' and Rogers, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (1990).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Orthogonal distance regression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Contemporary Mathematics, 112:183–194.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Butler, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Thompson, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', and Heikes, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The Steady-State atmospheric circu- lation response to climate change–like thermal forcings in a simple general circulation model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Clim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 23(13):3474–3496.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Chen, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Lu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', and Frierson, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Phase speed spectra and the latitude of surface westerlies: Interannual variability and global warming trend.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Clim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 21(22):5942–5959.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Chen, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Zhang, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', and Lu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Sensitivity of the latitude of the westerly jet stream to climate forcing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Geophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 47(4):345.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Cohen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Screen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Furtado, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Barlow, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Whittleston, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Coumou, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Francis, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Dethloff, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Entekhabi, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Overland, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', and Jones, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Recent arctic amplification and extreme mid-latitude weather.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Geosci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 7(9):627–637.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Cooper, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' and Haynes, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Climate sensitivity via a nonparametric Fluctuation– Dissipation theorem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Atmos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 68(5):937–953.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Coumou, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' and Rahmstorf, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' A decade of weather extremes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Clim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Chang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 2(7):491– 496.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Dai, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Luo, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Song, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', and Liu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Arctic amplification is caused by sea-ice loss under increasing CO2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 10(1):121.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' 19 Deser, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Tomas, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Alexander, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', and Lawrence, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The seasonal atmospheric response to projected arctic sea ice loss in the late Twenty-First century.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Clim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 23(2):333–351.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Druckenmiller, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Moon, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Thoman, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Ballinger, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Berner, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Bernhard, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Bhatt, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Bjerke, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', and Box (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The arctic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Bull.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Am.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Meteorol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 102(8):S263–S316.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Dunn-Sigouin, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Li, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', and Kushner, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Limited influence of localized tropical sea- surface temperatures on moisture transport into the arctic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Geophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 48(8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Fuchs, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Sherwood, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', and Hernandez, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' An exploration of multivariate fluctuation dissipation operators and their response to sea surface temperature perturbations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Atmos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 72(1):472–486.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Fukushima, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (1980).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Neocognitron: a self organizing neural network model for a mechanism of pattern recognition unaffected by shift in position.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Biol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Cybern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 36(4):193–202.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Garfinkel, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Waugh, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', and Gerber, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The effect of tropospheric jet latitude on coupling between the stratospheric polar vortex and the troposphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Clim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 26(6):2077–2095.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Gerber, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Voronin, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', and Polvani, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Testing the annular mode autocorrelation time scale in simple atmospheric general circulation models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Mon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Weather Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 136(4):1523– 1536.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Gneiting, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Balabdaoui, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', and Raftery, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Probabilistic forecasts, calibration and sharpness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Stat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Series B Stat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Methodol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 69(2):243–268.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Gordon, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' and Barnes, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Incorporating uncertainty into a regression neural network enables identification of decadal state-dependent predictability in CESM2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Geophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 49(15).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Graversen, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' and Langen, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' On the role of the atmospheric energy transport in 2 × CO2–Induced polar amplification in CESM1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Clim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 32(13):3941–3956.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Grise, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' and Polvani, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Is climate sensitivity related to dynamical sensitivity?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Geophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 121(10):5159–5176.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Gritsun, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' and Branstator, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Climate response using a Three-Dimensional operator based on the Fluctuation–Dissipation theorem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Atmos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 64(7):2558–2575.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Harvey, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Shaffrey, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', and Woollings, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Deconstructing the climate change response of the northern hemisphere wintertime storm tracks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Clim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Dyn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 45(9):2847–2860.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Hassanzadeh, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' and Kuang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2016a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The linear response function of an idealized atmosphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' part i: Construction using green’s functions and applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Atmos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 73(9):3423–3439.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Hassanzadeh, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' and Kuang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2016b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The linear response function of an idealized atmosphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' part II: Implications for the practical use of the Fluctuation–Dissipation theorem and the role of operator’s nonnormality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Atmos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 73(9):3441–3452.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Hassanzadeh, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Kuang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', and Farrell, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Responses of midlatitude blocks and wave amplitude to changes in the meridional temperature gradient in an idealized dry GCM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Geophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 41(14):5223–5232.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' 20 Held, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (1993).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Large-Scale dynamics and global warming.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Bull.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Am.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Meteorol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 74(2):228– 242.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Held, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' and Suarez, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (1994).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' A proposal for the intercomparison of the dynamical cores of atmospheric general circulation models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Bull.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Am.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Meteorol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 75(10):1825–1830.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Hunter, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Matplotlib: A 2d graphics environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Computing in Science & Engineering, 9(3):90–95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Hwang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='-T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' and Frierson, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Increasing atmospheric poleward energy transport with global warming.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Geophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 37(24).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Ingrosso, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' and Goldt, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Data-driven emergence of convolutional structure in neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Natl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Acad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 119(40):e2201854119.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Kattsov, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Ryabinin, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Overland, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Serreze, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Visbeck, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Walsh, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Meier, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', and Zhang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Arctic sea-ice change: a grand challenge of climate science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Glaciol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 56(200):1115–1121.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Khodkar, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' and Hassanzadeh, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Data-driven reduced modelling of turbulent Rayleigh– B´enard convection using DMD-enhanced fluctuation–dissipation theorem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Fluid Mech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 852:R3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Kidston, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' and Gerber, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Intermodel variability of the poleward shift of the austral jet stream in the CMIP3 integrations linked to biases in 20th century climatology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' GEOPHYSICAL RESEARCH LETTERS, 37(9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Kim, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Kang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Merlis, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', and Shin, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Atmospheric circulation sensitivity to changes in the vertical structure of polar warming.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Geophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 48(19).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Kingma, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' and Ba, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Adam: A method for stochastic optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Kornhuber, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Coumou, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Vogel, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Lesk, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Donges, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Lehmann, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', and Horton, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Amplified rossby waves enhance risk of concurrent heatwaves in major breadbasket regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Clim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Chang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 10(1):48–53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Kraichnan, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (1959).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Classical Flucationation-Relaxation theorem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Institute of Mathematical Sciences, 113(5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Krawczyk, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Learning from imbalanced data: open challenges and future directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Progress in Artificial Intelligence, 5(4):221–232.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Lauritzen, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Nair, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Herrington, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Callaghan, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Goldhaber, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Dennis, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Bacmeister, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Eaton, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Zarzycki, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Taylor, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Ullrich, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Dubos, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Gettelman, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Neale, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Dobbins, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Reed, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Hannay, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Medeiros, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Benedict, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', and Tribbia, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' NCAR release of CAM-SE in CESM2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='0: A reformulation of the spectral element dynamical core in dry-mass vertical coordinates with comprehensive treatment of condensates and energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Earth Syst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 10(7):1537–1570.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' LeCun, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Bengio, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', and Hinton, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Deep learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Nature, 521(7553):436–444.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Lee, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' A theory for polar amplification from a general circulation perspective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Asia-Pacific Journal of Atmospheric Sciences, 50(1):31–43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' 21 Leith, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (1975).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Climate response and fluctuation dissipation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Atmos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 32(10):2022–2026.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Lim, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='-P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' and Simmonds, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Effect of tropospheric temperature change on the zonal mean circulation and SH winter extratropical cyclones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Clim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Dyn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 33(1):19–32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Lutsko, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Held, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', and Zurita-Gotor, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Applying the Fluctuation–Dissipation theorem to a Two-Layer model of quasigeostrophic turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Atmos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 72(8):3161–3177.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Ma, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', He, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', He, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', and Ma, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Imbalanced Learning : Foundations, Algorithms, and Applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' John Wiley & Sons, Incorporated, Somerset, UNITED STATES.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' MacDonald, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (1992).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Persistence in climate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The MITRE Coporation, JSR–91–340:22102–3481.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Madonna, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Li, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Grams, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', and Woollings, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The link between eddy-driven jet variability and weather regimes in the north Atlantic-European sector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Quart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Roy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Meteor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 143(708):2960–2972.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Mahlstein, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Martius, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Chevalier, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', and Ginsbourger, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Changes in the odds of extreme events in the atlantic basin depending on the position of the extratropical jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Geophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 39(22).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Majda, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Abramov, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', and Grote, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Information Theory and Stochastics for Multiscale Nonlinear Systems, volume 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' American Mathematical Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Manabe, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Hahn, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', and Leith Holloway, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (1974).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The seasonal variation of the tropical circulation as simulated by a global model of the atmosphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Atmos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 31(1):43–83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Manabe, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' and Stouffer, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (1980).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Sensitivity of a global climate model to an increase of CO2concentration in the atmosphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Geophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 85(C10):5529.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Marconi, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Puglisi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Rondoni, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', and Vulpiani, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Fluctuation–dissipation: Response theory in statistical physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 461(4):111–195.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Mattingly, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', McLeod, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Knox, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Shepherd, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', and Mote, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' A climatological assessment of greenland blocking conditions associated with the track of hurricane sandy and historical north atlantic hurricanes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Climatol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 35(5):746–760.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Mbengue, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' and Schneider, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Storm track shifts under climate change: What can be learned from Large-Scale dry dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Clim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 26(24):9923–9930.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' McGraw, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' and Barnes, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Seasonal sensitivity of the Eddy-Driven jet to tropo- spheric heating in an idealized AGCM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Clim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 29(14):5223–5240.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Meehl, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Covey, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Delworth, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Latif, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', McAvaney, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Mitchell, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Stouffer, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', and Taylor, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' THE WCRP CMIP3 multimodel dataset: A new era in climate change research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Bull.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Am.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Meteorol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 88(9):1383–1394.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Nakamura, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Sampe, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Tanimoto, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', and Shimpo, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Observed associations among storm tracks, jet streams and midlatitude oceanic fronts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Earth’s Climate: The Ocean– Atmosphere Interaction, Geophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Monogr, 147:329–345.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Nipen, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' and Stull, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Calibrating probabilistic forecasts from an NWP ensemble.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Tellus Ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' A Dyn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Meteorol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Oceanogr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 63(5):858–875.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' 22 Nix, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' and Weigend, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (1994).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Estimating the mean and variance of the target proba- bility distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' In Proceedings of 1994 IEEE International Conference on Neural Networks (ICNN’94), volume 1, pages 55–60 vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Nix, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' and Weigend, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (1995).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Learning local error bars for nonlinear regression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Advances in Neural Information Processing Systems, 7((NIPS’94)):489–496.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Phipps, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The CSIRO Mk3L climate system model v1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' 4 121 pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' CRC Tech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Pithan, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' and Mauritsen, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Arctic amplification dominated by temperature feedbacks in contemporary climate models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Geosci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 7(3):181–184.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Polvani, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Tropospheric response to stratospheric perturbations in a relatively simple general circulation model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Geophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 29(7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Prechelt, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Early stopping — but when?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' In Montavon, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Orr, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', and M¨uller, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='-R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', editors, Neural Networks: Tricks of the Trade: Second Edition, pages 53–67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Springer Berlin Heidelberg, Berlin, Heidelberg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Ringler, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Heikes, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', and Randall, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Modeling the atmospheric general circulation using a spherical geodesic grid: A new class of dynamical cores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Mon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Weather Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 128(7):2471–2490.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' R¨othlisberger, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Pfahl, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', and Martius, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Regional-scale jet waviness modulates the occurrence of midlatitude weather extremes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Geophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 43(20):10,989–10,997.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Rousi, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Kornhuber, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Beobide-Arsuaga, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Luo, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', and Coumou, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Accelerated west- ern european heatwave trends linked to more-persistent double jets over eurasia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 13(1):3851.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Rousi, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Selten, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Rahmstorf, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', and Coumou, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Changes in north atlantic atmospheric circulation in a warmer climate favor winter flooding and summer drought over europe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Clim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 34(6):2277–2295.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Schubert, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Wang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', and Suarez, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Warm season subseasonal variability and climate extremes in the northern hemisphere: The role of stationary rossby waves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Clim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 24(18):4773– 4792.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Screen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Simmonds, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Deser, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', and Tomas, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' The atmospheric response to three decades of observed arctic sea ice loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Clim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 26(4):1230–1248.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Shaw, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Baldwin, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Barnes, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Caballero, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Garfinkel, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Hwang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='-T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Li, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', O’Gorman, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Rivi`ere, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Simpson, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', and Voigt, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Storm track processes and the opposing influences of climate change.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Geosci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 9:656–664.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Sherwood and Nidhi Nishant, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Atmospheric changes through 2012 as shown by iteratively homogenized radiosonde temperature and wind data (IUKv2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Environ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 10(5):054007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Stendel, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Francis, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', White, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Williams, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', and Woollings, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Chapter 15 - the jet stream and climate change.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' In Letcher, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', editor, Climate Change (Third Edition), pages 327–357.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Elsevier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Swart, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' and Fyfe, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Observed and simulated changes in the southern hemisphere surface westerly wind-stress.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Geophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 39(16).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' 23 Tjernstr¨om, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Sedlar, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', and Shupe, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' How well do regional climate models reproduce radiation and clouds in the arctic?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' an evaluation of ARCMIP simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Meteorol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Climatol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 47(9):2405–2422.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Vihma, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Effects of arctic sea ice decline on weather and climate: A review.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Surv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Geophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 35(5):1175–1214.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Virtanen, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Gommers, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Oliphant, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Haberland, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Reddy, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Cournapeau, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Burovski, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Peterson, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Weckesser, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Bright, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', van der Walt, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Brett, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Wilson, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Millman, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Mayorov, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Nelson, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Jones, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Kern, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Larson, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Carey, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Polat, ˙I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Feng, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Moore, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', VanderPlas, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Laxalde, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Perktold, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Cimrman, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Henriksen, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Quintero, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Harris, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Archibald, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Ribeiro, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Pedregosa, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', van Mulbregt, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', and SciPy 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='0 Contributors (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' SciPy 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content='0: Fundamental Algorithms for Scientific Computing in Python.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Nature Methods, 17:261–272.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Woollings, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Hannachi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', and Hoskins, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Variability of the north atlantic eddy-driven jet stream.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Quart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Roy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Meteor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 136(649):856–868.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Yann, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Leon, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', Yoshia, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', and Haffner, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (1998).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Gradient-Based learning applied to document recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Proceedings of the IEEE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Yin, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' A consistent poleward shift of the storm tracks in simulations of 21st century climate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Geophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=', 32(18).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Zeiler, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' and Fergus, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Visualizing and understanding convolutional networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' In European conference on computer vision, pages 818–833.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydAyT4oBgHgl3EQfnvjm/content/2301.00496v1.pdf'} +page_content=' Springer.' metadata={'source': 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